On 6/26/2026 11:08 AM, dbush wrote:
On 6/26/2026 10:24 AM, olcott wrote:
On 6/26/2026 8:57 AM, dbush wrote:
On 6/26/2026 9:45 AM, olcott wrote:
On 6/26/2026 8:20 AM, dbush wrote:
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms. That doesn't >>>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS Gödel >>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody that >>>>>>>>>>>>>>>>>>>> PTS somehow causes
Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>>>> you certainly don't
understand Gödel's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly >>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not a 'verified >>>>>>>>>>>>>>>>>> fact' when you haven't even adequately explained what >>>>>>>>>>>>>>>>>> it is that you mean.
All of knowledge expressed in language is structured as >>>>>>>>>>>>>>>>> a tree of semantic relations specified syntactically >>>>>>>>>>>>>>>>> between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a >>>>>>>>>>>> loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not
obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is
equal to its successor" has no meaning in Robinson Arithmetic.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof from within a
stipulated atomic base of its own axioms like the one
that you provided.
Then you agree that the above natural language sentence that is
semantically required to be either true or false has no meaning?
Your sentence would be what it always has been
a stipulated true sentence axiom.
False, as that statement is not one of the axioms of Robinson
arithmetic, but it is a statement in its language, and one that has
*only* an infinite connection to the axioms of that system.
By your logic, "no number is equal to its successor" has no meaning in
Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
On 6/26/2026 1:22 PM, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
On 6/26/2026 10:24 AM, olcott wrote:
On 6/26/2026 8:57 AM, dbush wrote:
On 6/26/2026 9:45 AM, olcott wrote:
On 6/26/2026 8:20 AM, dbush wrote:
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms. That doesn't >>>>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS Gödel >>>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody that >>>>>>>>>>>>>>>>>>>>> PTS somehow causes
Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>>>>> you certainly don't
understand Gödel's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly >>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not a 'verified >>>>>>>>>>>>>>>>>>> fact' when you haven't even adequately explained what >>>>>>>>>>>>>>>>>>> it is that you mean.
All of knowledge expressed in language is structured >>>>>>>>>>>>>>>>>> as a tree of semantic relations specified >>>>>>>>>>>>>>>>>> syntactically between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting stuck in >>>>>>>>>>>>> a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not >>>>>>>>> obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is
equal to its successor" has no meaning in Robinson Arithmetic.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof from within a
stipulated atomic base of its own axioms like the one
that you provided.
Then you agree that the above natural language sentence that is
semantically required to be either true or false has no meaning?
Your sentence would be what it always has been
a stipulated true sentence axiom.
False, as that statement is not one of the axioms of Robinson
arithmetic, but it is a statement in its language, and one that has
*only* an infinite connection to the axioms of that system.
By your logic, "no number is equal to its successor" has no meaning
in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
So you agree that Robinson arithmetic is incomplete.
On 6/26/2026 12:25 PM, dbush wrote:
On 6/26/2026 1:22 PM, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
On 6/26/2026 10:24 AM, olcott wrote:
On 6/26/2026 8:57 AM, dbush wrote:
On 6/26/2026 9:45 AM, olcott wrote:
On 6/26/2026 8:20 AM, dbush wrote:
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms. That doesn't >>>>>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS Gödel >>>>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody >>>>>>>>>>>>>>>>>>>>>> that PTS somehow causes
Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, >>>>>>>>>>>>>>>>>>>>>> and you certainly don't
understand Gödel's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not a >>>>>>>>>>>>>>>>>>>> 'verified fact' when you haven't even adequately >>>>>>>>>>>>>>>>>>>> explained what it is that you mean.
All of knowledge expressed in language is structured >>>>>>>>>>>>>>>>>>> as a tree of semantic relations specified >>>>>>>>>>>>>>>>>>> syntactically between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would >>>>>>>>>>>>>>>> one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting stuck in >>>>>>>>>>>>>> a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent >>>>>>>>>>>> loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>> PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability >>>>>>>>>>> or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not >>>>>>>>>> obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is >>>>>>>> equal to its successor" has no meaning in Robinson Arithmetic. >>>>>>>>
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof from within a
stipulated atomic base of its own axioms like the one
that you provided.
Then you agree that the above natural language sentence that is
semantically required to be either true or false has no meaning?
Your sentence would be what it always has been
a stipulated true sentence axiom.
False, as that statement is not one of the axioms of Robinson
arithmetic, but it is a statement in its language, and one that has
*only* an infinite connection to the axioms of that system.
By your logic, "no number is equal to its successor" has no meaning
in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
So you agree that Robinson arithmetic is incomplete.
It is as complete as it was designed to be.
On 6/26/2026 1:39 PM, olcott wrote:
On 6/26/2026 12:25 PM, dbush wrote:
On 6/26/2026 1:22 PM, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
On 6/26/2026 10:24 AM, olcott wrote:
On 6/26/2026 8:57 AM, dbush wrote:
On 6/26/2026 9:45 AM, olcott wrote:
On 6/26/2026 8:20 AM, dbush wrote:
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote:
All of knowledge expressed in language is structured >>>>>>>>>>>>>>>>>>>> as a tree of semantic relations specified >>>>>>>>>>>>>>>>>>>> syntactically between finite strings.On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms. That doesn't >>>>>>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS Gödel >>>>>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody >>>>>>>>>>>>>>>>>>>>>>> that PTS somehow causes
Gödel's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, >>>>>>>>>>>>>>>>>>>>>>> and you certainly don't
understand Gödel's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one which >>>>>>>>>>>>>>>>>>>>> you have never explicitly defined, so the fault >>>>>>>>>>>>>>>>>>>>> here certainly doesn't lie with Alan. It's >>>>>>>>>>>>>>>>>>>>> certainly not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>> even adequately explained what it is that you mean. >>>>>>>>>>>>>>>>>>>
What makes you believe semantic relations that can be >>>>>>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that >>>>>>>>>>>>>>>>>>> is exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would >>>>>>>>>>>>>>>>> one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting stuck >>>>>>>>>>>>>>> in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent >>>>>>>>>>>>> loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>> PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability >>>>>>>>>>>> or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not >>>>>>>>>>> obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is >>>>>>>>> equal to its successor" has no meaning in Robinson Arithmetic. >>>>>>>>>
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof from within a
stipulated atomic base of its own axioms like the one
that you provided.
Then you agree that the above natural language sentence that is >>>>>>> semantically required to be either true or false has no meaning? >>>>>>>
Your sentence would be what it always has been
a stipulated true sentence axiom.
False, as that statement is not one of the axioms of Robinson
arithmetic, but it is a statement in its language, and one that has >>>>> *only* an infinite connection to the axioms of that system.
By your logic, "no number is equal to its successor" has no meaning >>>>> in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
So you agree that Robinson arithmetic is incomplete.
It is as complete as it was designed to be.
There is no "designed to be". There are sentences in the language of Robinson arithmetic that are true but not provable,
therefore making the--
system incomplete, as you have just agreed, meaning that you agree that incompleteness exists.
On 6/26/2026 12:42 PM, dbush wrote:
On 6/26/2026 1:39 PM, olcott wrote:
On 6/26/2026 12:25 PM, dbush wrote:
On 6/26/2026 1:22 PM, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
On 6/26/2026 10:24 AM, olcott wrote:
On 6/26/2026 8:57 AM, dbush wrote:
On 6/26/2026 9:45 AM, olcott wrote:
On 6/26/2026 8:20 AM, dbush wrote:
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]What makes you believe semantic relations that can >>>>>>>>>>>>>>>>>>>> be structured as
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms. That >>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>> understanding them.
The above is the key reason why under PTS Gödel >>>>>>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody >>>>>>>>>>>>>>>>>>>>>>>> that PTS somehow causes
Gödel's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have
some credibility.
If they are mere gibberish words to you then >>>>>>>>>>>>>>>>>>>>>>>>> you will not understand.
You don't understand Proof-theoritic Semantics, >>>>>>>>>>>>>>>>>>>>>>>> and you certainly don't
understand Gödel's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one which >>>>>>>>>>>>>>>>>>>>>> you have never explicitly defined, so the fault >>>>>>>>>>>>>>>>>>>>>> here certainly doesn't lie with Alan. It's >>>>>>>>>>>>>>>>>>>>>> certainly not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is that you mean. >>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge that >>>>>>>>>>>>>>>>>>>> is exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would >>>>>>>>>>>>>>>>>> one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting stuck >>>>>>>>>>>>>>>> in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent >>>>>>>>>>>>>> loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>
compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>> PTS just coherently connects the semantic meanings
expressed in language together into one coherent body >>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>> or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not >>>>>>>>>>>> obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is >>>>>>>>>> equal to its successor" has no meaning in Robinson Arithmetic. >>>>>>>>>>
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof from within a
stipulated atomic base of its own axioms like the one
that you provided.
Then you agree that the above natural language sentence that is >>>>>>>> semantically required to be either true or false has no meaning? >>>>>>>>
Your sentence would be what it always has been
a stipulated true sentence axiom.
False, as that statement is not one of the axioms of Robinson
arithmetic, but it is a statement in its language, and one that
has *only* an infinite connection to the axioms of that system.
By your logic, "no number is equal to its successor" has no
meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
So you agree that Robinson arithmetic is incomplete.
It is as complete as it was designed to be.
There is no "designed to be". There are sentences in the language of
Robinson arithmetic that are true but not provable,
To make is simpler to understand.
In proof theoretic semantics:
unprovable in Q means out-of-scope of Q.
therefore making the system incomplete, as you have just agreed,
meaning that you agree that incompleteness exists.
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no meaning in
Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no meaning
in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning.
André
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no meaning
in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning.
André
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no meaning >>>>> in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning.
André
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable. Then to put
things in words you can understand:
Godel proved that any axiomatic system of arithmetic contains out-of-
scope statements.
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no
meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning.
André
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable. Then to put
things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable in PA.
In both cases the semantics in not represented in PA.
Godel proved that any axiomatic system of arithmetic contains out-of-
scope statements.
Sure, PA also has no idea that driving means operating a motor vehicle.
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no
meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning.
André
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable. Then to put
things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable in PA.
In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
"No number is equal to its successor" is a sentence in RA, and it is
true but unprovable in RA (or as your would call it, "out-of-scope").
--
Godel proved that any axiomatic system of arithmetic contains out-of-
scope statements.
Sure, PA also has no idea that driving means operating a motor vehicle.
Not applicable.
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no
meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning.
André
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable. Then to put
things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable in PA.
In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
"No number is equal to its successor" is a sentence in RA, and it is
true but unprovable in RA (or as your would call it, "out-of-scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
Godel proved that any axiomatic system of arithmetic contains out-
of- scope statements.
Sure, PA also has no idea that driving means operating a motor vehicle.
Not applicable.
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning.
André
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable. Then to put >>>>> things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable in PA.
In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False. The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False. G is simply a sentence like ~∃x x>10 v x<5 but much more complex.
"No number is equal to its successor" is a sentence in RA, and it is
true but unprovable in RA (or as your would call it, "out-of-scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language of
Q. More formally, it is this:
~∃x x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms you would understand, the above is "out-of-scope" of Q).
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning.
André
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable. Then to put >>>>>> things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable in PA.
In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False. The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False. G is simply a sentence like ~∃x x>10 v x<5 but much more complex. >>
"No number is equal to its successor" is a sentence in RA, and it is
true but unprovable in RA (or as your would call it, "out-of-scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language of
Q. More formally, it is this:
~∃x x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms
you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
On 6/26/2026 6:01 PM, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning.
André
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable. Then to >>>>>>> put things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable in PA. >>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False. The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False. G is simply a sentence like ~∃x x>10 v x<5 but much more
complex.
"No number is equal to its successor" is a sentence in RA, and it
is true but unprovable in RA (or as your would call it, "out-of-
scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language
of Q. More formally, it is this:
~∃x x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms
you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
In your own words, what does it mean for a statement to be "semantically grounded" in a formal system?
On 6/26/2026 5:08 PM, dbush wrote:
On 6/26/2026 6:01 PM, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning.
André
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable. Then to >>>>>>>> put things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable in PA. >>>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False. The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False. G is simply a sentence like ~∃x x>10 v x<5 but much more
complex.
"No number is equal to its successor" is a sentence in RA, and it >>>>>> is true but unprovable in RA (or as your would call it, "out-of-
scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language
of Q. More formally, it is this:
~∃x x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms
you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
In your own words, what does it mean for a statement to be
"semantically grounded" in a formal system?
I always do back-chained inference because the typical
math way of doing forward chained inference may take
an infeasibly long time. A finite set of back-chained
inference steps from x to the axioms of Q.
I appreciate that you stopped playing head games.
On 6/26/2026 6:58 PM, olcott wrote:
On 6/26/2026 5:08 PM, dbush wrote:
On 6/26/2026 6:01 PM, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning.
André
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope. >>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable. Then to >>>>>>>>> put things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable in PA. >>>>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False. The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False. G is simply a sentence like ~∃x x>10 v x<5 but much more >>>>> complex.
"No number is equal to its successor" is a sentence in RA, and it >>>>>>> is true but unprovable in RA (or as your would call it, "out-of- >>>>>>> scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language >>>>> of Q. More formally, it is this:
~∃x x=S(x)
And this sentence is not provable from the axioms of Q (or, in
terms you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
In your own words, what does it mean for a statement to be
"semantically grounded" in a formal system?
I always do back-chained inference because the typical
math way of doing forward chained inference may take
an infeasibly long time. A finite set of back-chained
inference steps from x to the axioms of Q.
Back or forward chained doesn't matter, it's essentially the same steps
in a different direction. But in any case, you're saying "semantically grounded" is just another synonym for unprovable.
So to again put things in a way you'll understand, Godel proved that any axiom system of arithmetic contains statements that are not semantically grounded.
That also means that, using your terminology, it has been proven that
the statement ~∃x x=S(x), i.e. "No number is equal to its successor", is not semantically grounded in Q.
On 6/26/2026 6:18 PM, dbush wrote:
On 6/26/2026 6:58 PM, olcott wrote:
On 6/26/2026 5:08 PM, dbush wrote:
On 6/26/2026 6:01 PM, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has >>>>>>>>>>>>>> no meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning.
André
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope. >>>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable. Then to >>>>>>>>>> put things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable in PA. >>>>>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False. The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False. G is simply a sentence like ~∃x x>10 v x<5 but much more >>>>>> complex.
"No number is equal to its successor" is a sentence in RA, and >>>>>>>> it is true but unprovable in RA (or as your would call it, "out- >>>>>>>> of- scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the
language of Q. More formally, it is this:
~∃x x=S(x)
And this sentence is not provable from the axioms of Q (or, in
terms you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
In your own words, what does it mean for a statement to be
"semantically grounded" in a formal system?
I always do back-chained inference because the typical
math way of doing forward chained inference may take
an infeasibly long time. A finite set of back-chained
inference steps from x to the axioms of Q.
Back or forward chained doesn't matter, it's essentially the same
steps in a different direction. But in any case, you're saying
"semantically grounded" is just another synonym for unprovable.
So to again put things in a way you'll understand, Godel proved that
any axiom system of arithmetic contains statements that are not
semantically grounded.
Not quite. G is not semantically grounded
in PA
yet G is semantically grounded
in metamathematics.
When an expression in PA only derives semantic
meaning in PA when grounded in PA
then G has no
meaning in PA.
That also means that, using your terminology, it has been proven that
the statement ~∃x x=S(x), i.e. "No number is equal to its successor",
is not semantically grounded in Q.
Thus is meaningless in Q and out-of-scope in Q.
On 6/26/2026 8:05 PM, olcott wrote:
On 6/26/2026 6:18 PM, dbush wrote:
On 6/26/2026 6:58 PM, olcott wrote:
On 6/26/2026 5:08 PM, dbush wrote:
On 6/26/2026 6:01 PM, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has >>>>>>>>>>>>>>> no meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson >>>>>>>>>>>>>> Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning.
André
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated >>>>>>>>>>>> with alternative views. So I will simply say out-of-scope. >>>>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable. Then >>>>>>>>>>> to put things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable in PA. >>>>>>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False. The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False. G is simply a sentence like ~∃x x>10 v x<5 but much more >>>>>>> complex.
"No number is equal to its successor" is a sentence in RA, and >>>>>>>>> it is true but unprovable in RA (or as your would call it,
"out- of- scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the
language of Q. More formally, it is this:
~∃x x=S(x)
And this sentence is not provable from the axioms of Q (or, in
terms you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
In your own words, what does it mean for a statement to be
"semantically grounded" in a formal system?
I always do back-chained inference because the typical
math way of doing forward chained inference may take
an infeasibly long time. A finite set of back-chained
inference steps from x to the axioms of Q.
Back or forward chained doesn't matter, it's essentially the same
steps in a different direction. But in any case, you're saying
"semantically grounded" is just another synonym for unprovable.
So to again put things in a way you'll understand, Godel proved that
any axiom system of arithmetic contains statements that are not
semantically grounded.
Not quite. G is not semantically grounded
i.e. unprovable
in PA
yet G is semantically grounded
i.e. provable
in metamathematics.
Which is exactly what Godel proved.
When an expression in PA only derives semantic
meaning in PA when grounded in PA then G has no
meaning in PA.
i.e. if a statement is unprovable in PA then it's unprovable in PA.
In other words, a meaningless tautology.
That also means that, using your terminology, it has been proven that
the statement ~∃x x=S(x), i.e. "No number is equal to its successor", >>> is not semantically grounded in Q.
Thus is meaningless in Q and out-of-scope in Q.
Which means the semantically valid statement in Q
On 6/26/2026 7:23 PM, dbush wrote:
On 6/26/2026 8:05 PM, olcott wrote:
On 6/26/2026 6:18 PM, dbush wrote:
On 6/26/2026 6:58 PM, olcott wrote:
On 6/26/2026 5:08 PM, dbush wrote:
On 6/26/2026 6:01 PM, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has >>>>>>>>>>>>>>>> no meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson >>>>>>>>>>>>>>> Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning.
André
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated >>>>>>>>>>>>> with alternative views. So I will simply say out-of-scope. >>>>>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable. Then >>>>>>>>>>>> to put things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable in PA. >>>>>>>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False. The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False. G is simply a sentence like ~∃x x>10 v x<5 but much more >>>>>>>> complex.
"No number is equal to its successor" is a sentence in RA, and >>>>>>>>>> it is true but unprovable in RA (or as your would call it, >>>>>>>>>> "out- of- scope").
If its semantics is not expressible in Q (What RA is called) >>>>>>>>> then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the
language of Q. More formally, it is this:
~∃x x=S(x)
And this sentence is not provable from the axioms of Q (or, in >>>>>>>> terms you would understand, the above is "out-of-scope" of Q). >>>>>>>>
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
In your own words, what does it mean for a statement to be
"semantically grounded" in a formal system?
I always do back-chained inference because the typical
math way of doing forward chained inference may take
an infeasibly long time. A finite set of back-chained
inference steps from x to the axioms of Q.
Back or forward chained doesn't matter, it's essentially the same
steps in a different direction. But in any case, you're saying
"semantically grounded" is just another synonym for unprovable.
So to again put things in a way you'll understand, Godel proved that
any axiom system of arithmetic contains statements that are not
semantically grounded.
Not quite. G is not semantically grounded
i.e. unprovable
in PA
yet G is semantically grounded
i.e. provable
in metamathematics.
Which is exactly what Godel proved.
When an expression in PA only derives semantic
meaning in PA when grounded in PA then G has no
meaning in PA.
i.e. if a statement is unprovable in PA then it's unprovable in PA.
In other words, a meaningless tautology.
That also means that, using your terminology, it has been proven
that the statement ~∃x x=S(x), i.e. "No number is equal to its
successor", is not semantically grounded in Q.
Thus is meaningless in Q and out-of-scope in Q.
Which means the semantically valid statement in Q
does not include ~∃x x=S(x)
On 6/26/2026 8:48 PM, olcott wrote:
On 6/26/2026 7:23 PM, dbush wrote:
On 6/26/2026 8:05 PM, olcott wrote:
On 6/26/2026 6:18 PM, dbush wrote:
On 6/26/2026 6:58 PM, olcott wrote:
On 6/26/2026 5:08 PM, dbush wrote:
On 6/26/2026 6:01 PM, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" >>>>>>>>>>>>>>>>> has no meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement >>>>>>>>>>>>>>>> is true for the standard natural numbers, Robinson >>>>>>>>>>>>>>>> Arithmetic is too weak to prove it universally >>>>>>>>>>>>>>>> (∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning.
André
out-of-scope for Q is more accurate as jargon free. >>>>>>>>>>>>>>
PTS does hold the view that meaning is only derived >>>>>>>>>>>>>> through inference steps. This simple sentence seems >>>>>>>>>>>>>> impossibly too difficult for anyone fully indoctrinated >>>>>>>>>>>>>> with alternative views. So I will simply say out-of-scope. >>>>>>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable. Then >>>>>>>>>>>>> to put things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable in >>>>>>>>>>>> PA.
In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False. The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False. G is simply a sentence like ~∃x x>10 v x<5 but much >>>>>>>>> more complex.
"No number is equal to its successor" is a sentence in RA, >>>>>>>>>>> and it is true but unprovable in RA (or as your would call >>>>>>>>>>> it, "out- of- scope").
If its semantics is not expressible in Q (What RA is called) >>>>>>>>>> then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the
language of Q. More formally, it is this:
~∃x x=S(x)
And this sentence is not provable from the axioms of Q (or, in >>>>>>>>> terms you would understand, the above is "out-of-scope" of Q). >>>>>>>>>
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
In your own words, what does it mean for a statement to be
"semantically grounded" in a formal system?
I always do back-chained inference because the typical
math way of doing forward chained inference may take
an infeasibly long time. A finite set of back-chained
inference steps from x to the axioms of Q.
Back or forward chained doesn't matter, it's essentially the same
steps in a different direction. But in any case, you're saying
"semantically grounded" is just another synonym for unprovable.
So to again put things in a way you'll understand, Godel proved
that any axiom system of arithmetic contains statements that are
not semantically grounded.
Not quite. G is not semantically grounded
i.e. unprovable
in PA
yet G is semantically grounded
i.e. provable
in metamathematics.
Which is exactly what Godel proved.
Your lack of response indicates that you agree with Godel, but used different words to do so.
When an expression in PA only derives semantic
meaning in PA when grounded in PA then G has no
meaning in PA.
i.e. if a statement is unprovable in PA then it's unprovable in PA.
In other words, a meaningless tautology.
That also means that, using your terminology, it has been proven
that the statement ~∃x x=S(x), i.e. "No number is equal to its
successor", is not semantically grounded in Q.
Thus is meaningless in Q and out-of-scope in Q.
Which means the semantically valid statement in Q
does not include ~∃x x=S(x)
False, as it means "no number is equal to its successor", and the
concept of a successor and equality have semantic meaning in Q, as does
the concept of "all", "none", and "exists".
That makes the statement semantically valid, so any alternate system
that concludes otherwise is necessarily faulty.
On 6/26/2026 8:11 PM, dbush wrote:
On 6/26/2026 8:48 PM, olcott wrote:
On 6/26/2026 7:23 PM, dbush wrote:
On 6/26/2026 8:05 PM, olcott wrote:
On 6/26/2026 6:18 PM, dbush wrote:
On 6/26/2026 6:58 PM, olcott wrote:
On 6/26/2026 5:08 PM, dbush wrote:
On 6/26/2026 6:01 PM, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:Not applicable, as that is not a sentence in PA.
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" >>>>>>>>>>>>>>>>>> has no meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q), >>>>>>>>>>>>>>>>> the statement "no number is equal to its
successor" is not provable.While this statement >>>>>>>>>>>>>>>>> is true for the standard natural numbers, Robinson >>>>>>>>>>>>>>>>> Arithmetic is too weak to prove it universally >>>>>>>>>>>>>>>>> (∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning. >>>>>>>>>>>>>>>>
André
out-of-scope for Q is more accurate as jargon free. >>>>>>>>>>>>>>>
PTS does hold the view that meaning is only derived >>>>>>>>>>>>>>> through inference steps. This simple sentence seems >>>>>>>>>>>>>>> impossibly too difficult for anyone fully indoctrinated >>>>>>>>>>>>>>> with alternative views. So I will simply say out-of-scope. >>>>>>>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable. >>>>>>>>>>>>>> Then to put things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable >>>>>>>>>>>>> in PA.
In both cases the semantics in not represented in PA. >>>>>>>>>>>>
It is expressed in PA
False. The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and >>>>>>>>>>> the semantics of G are neither expressible in PA.
False. G is simply a sentence like ~∃x x>10 v x<5 but much >>>>>>>>>> more complex.
"No number is equal to its successor" is a sentence in RA, >>>>>>>>>>>> and it is true but unprovable in RA (or as your would call >>>>>>>>>>>> it, "out- of- scope").
If its semantics is not expressible in Q (What RA is called) >>>>>>>>>>> then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the >>>>>>>>>> language of Q. More formally, it is this:
~∃x x=S(x)
And this sentence is not provable from the axioms of Q (or, in >>>>>>>>>> terms you would understand, the above is "out-of-scope" of Q). >>>>>>>>>>
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
In your own words, what does it mean for a statement to be
"semantically grounded" in a formal system?
I always do back-chained inference because the typical
math way of doing forward chained inference may take
an infeasibly long time. A finite set of back-chained
inference steps from x to the axioms of Q.
Back or forward chained doesn't matter, it's essentially the same >>>>>> steps in a different direction. But in any case, you're saying
"semantically grounded" is just another synonym for unprovable.
So to again put things in a way you'll understand, Godel proved
that any axiom system of arithmetic contains statements that are
not semantically grounded.
Not quite. G is not semantically grounded
i.e. unprovable
in PA
yet G is semantically grounded
i.e. provable
in metamathematics.
Which is exactly what Godel proved.
Your lack of response indicates that you agree with Godel, but used
different words to do so.
When an expression in PA only derives semantic
meaning in PA when grounded in PA then G has no
meaning in PA.
i.e. if a statement is unprovable in PA then it's unprovable in PA.
In other words, a meaningless tautology.
That also means that, using your terminology, it has been proven
that the statement ~∃x x=S(x), i.e. "No number is equal to its
successor", is not semantically grounded in Q.
Thus is meaningless in Q and out-of-scope in Q.
Which means the semantically valid statement in Q
does not include ~∃x x=S(x)
False, as it means "no number is equal to its successor", and the
concept of a successor and equality have semantic meaning in Q, as
does the concept of "all", "none", and "exists".
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is
ungrounded in the PTS atomic base of Q.
On 6/26/2026 9:39 PM, olcott wrote:
On 6/26/2026 8:11 PM, dbush wrote:
On 6/26/2026 8:48 PM, olcott wrote:
On 6/26/2026 7:23 PM, dbush wrote:
On 6/26/2026 8:05 PM, olcott wrote:
On 6/26/2026 6:18 PM, dbush wrote:
On 6/26/2026 6:58 PM, olcott wrote:
On 6/26/2026 5:08 PM, dbush wrote:
On 6/26/2026 6:01 PM, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:Not applicable, as that is not a sentence in PA.
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" >>>>>>>>>>>>>>>>>>> has no meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q), >>>>>>>>>>>>>>>>>> the statement "no number is equal to its
successor" is not provable.While this statement >>>>>>>>>>>>>>>>>> is true for the standard natural numbers, Robinson >>>>>>>>>>>>>>>>>> Arithmetic is too weak to prove it universally >>>>>>>>>>>>>>>>>> (∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning. >>>>>>>>>>>>>>>>>
André
out-of-scope for Q is more accurate as jargon free. >>>>>>>>>>>>>>>>
PTS does hold the view that meaning is only derived >>>>>>>>>>>>>>>> through inference steps. This simple sentence seems >>>>>>>>>>>>>>>> impossibly too difficult for anyone fully indoctrinated >>>>>>>>>>>>>>>> with alternative views. So I will simply say out-of-scope. >>>>>>>>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable. >>>>>>>>>>>>>>> Then to put things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable >>>>>>>>>>>>>> in PA.
In both cases the semantics in not represented in PA. >>>>>>>>>>>>>
It is expressed in PA
False. The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and >>>>>>>>>>>> the semantics of G are neither expressible in PA.
False. G is simply a sentence like ~∃x x>10 v x<5 but much >>>>>>>>>>> more complex.
"No number is equal to its successor" is a sentence in RA, >>>>>>>>>>>>> and it is true but unprovable in RA (or as your would call >>>>>>>>>>>>> it, "out- of- scope").
If its semantics is not expressible in Q (What RA is called) >>>>>>>>>>>> then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the >>>>>>>>>>> language of Q. More formally, it is this:
~∃x x=S(x)
And this sentence is not provable from the axioms of Q (or, >>>>>>>>>>> in terms you would understand, the above is "out-of-scope" of >>>>>>>>>>> Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
In your own words, what does it mean for a statement to be
"semantically grounded" in a formal system?
I always do back-chained inference because the typical
math way of doing forward chained inference may take
an infeasibly long time. A finite set of back-chained
inference steps from x to the axioms of Q.
Back or forward chained doesn't matter, it's essentially the same >>>>>>> steps in a different direction. But in any case, you're saying >>>>>>> "semantically grounded" is just another synonym for unprovable.
So to again put things in a way you'll understand, Godel proved >>>>>>> that any axiom system of arithmetic contains statements that are >>>>>>> not semantically grounded.
Not quite. G is not semantically grounded
i.e. unprovable
in PA
yet G is semantically grounded
i.e. provable
in metamathematics.
Which is exactly what Godel proved.
Your lack of response indicates that you agree with Godel, but used
different words to do so.
When an expression in PA only derives semantic
meaning in PA when grounded in PA then G has no
meaning in PA.
i.e. if a statement is unprovable in PA then it's unprovable in PA.
In other words, a meaningless tautology.
That also means that, using your terminology, it has been proven >>>>>>> that the statement ~∃x x=S(x), i.e. "No number is equal to its >>>>>>> successor", is not semantically grounded in Q.
Thus is meaningless in Q and out-of-scope in Q.
Which means the semantically valid statement in Q
does not include ~∃x x=S(x)
False, as it means "no number is equal to its successor", and the
concept of a successor and equality have semantic meaning in Q, as
does the concept of "all", "none", and "exists".
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is
ungrounded in the PTS atomic base of Q.
In other words, ~∃x x=S(x) is unprovable in Q, as is commonly known.
So once again, you agree with everyone else, but are using different
words to say so.
On 6/26/2026 1:17 AM, Mikko wrote:
On 25/06/2026 16:43, olcott wrote:
On 6/25/2026 2:09 AM, Mikko wrote:
On 24/06/2026 23:19, olcott wrote:
On 6/24/2026 3:23 AM, Mikko wrote:
On 23/06/2026 17:29, olcott wrote:
On 6/23/2026 12:39 AM, Mikko wrote:
On 22/06/2026 16:13, olcott wrote:
On 6/22/2026 2:13 AM, Mikko wrote:
On 22/06/2026 02:51, olcott wrote:
On 6/21/2026 4:57 AM, Mikko wrote:
On 20/06/2026 23:03, olcott wrote:
On 6/20/2026 2:17 PM, dbush wrote:That only means that your DD is not a strictly confoming C >>>>>>>>>>>> program.
On 6/20/2026 3:02 PM, olcott wrote:
On 6/20/2026 12:40 PM, André G. Isaak wrote:
On 2026-06-19 20:40, olcott wrote:
On 6/19/2026 3:28 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>> [ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> https://www.youtube.com/@rossfinlayson >>>>>>>>>>>>>>>>>>>>>> Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof- >>>>>>>>>>>>>>>>>>>>>> theoretic- semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>>>>Whereas you are stuck to your own incoherent views >>>>>>>>>>>>>>>>>>>> and reject
alternative views out-of-hand without review. >>>>>>>>>>>>>>>>>>
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>>>>>> look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>>> semantics/
I've spent a couple of hours reading that web page. >>>>>>>>>>>>>>>>>> It is abstract in
the extreme. One thing is utterly clear: its level of >>>>>>>>>>>>>>>>>> abstraction is
well beyond the comprehension capabilities of Peter >>>>>>>>>>>>>>>>>> Olcott, who can't
even understand proof by contradiction.
What superficially looks like contradiction
"This sentence is not true"
Once again, you're responding to people's posts with >>>>>>>>>>>>>>>> irrelevancy.
The Liar's Paradox has absolutely nothing to do with >>>>>>>>>>>>>>>> proof by contradiction. The LP isn't a contradiction; >>>>>>>>>>>>>>>> it's a paradox. The two are different things. A >>>>>>>>>>>>>>>> contradiction is a statement which is necessarily false. >>>>>>>>>>>>>>>> A paradox is a statement to which no truth value can be >>>>>>>>>>>>>>>> consistently assigned.
André
Then I have never spoken of anything where proof by >>>>>>>>>>>>>>> contradiction applies,
False, as that is exactly the method uses by the halting >>>>>>>>>>>>>> problem proof, Godel's proof, and Tarski's proof, each of >>>>>>>>>>>>>> which you've been attempting (and failing) to refute for >>>>>>>>>>>>>> years.
Proof Theoretic Semantics halt prover HHH correctly determines >>>>>>>>>>>>> that its input DD is ungrounded in its atomic base according >>>>>>>>>>>>> to the operational semantics of the C programming language. >>>>>>>>>>>>
The exact operational semantics of C conclusively
prove that the input DD to HHH is ungrounded in
these operational semantics because this input
specifies non-terminating recursive simulation
to HHH.
Because DD is not strictly conforming the exact operational >>>>>>>>>> semantics
do not fully specify the behaviour of DD. In order to prove >>>>>>>>>> that DD
halts you also need additional operational spemantics provided >>>>>>>>>> by the
C implementation you have used. When DD iss executed in that >>>>>>>>>> environment
it halts, which is sufficient to prove that in that
environment DD
halts. In some other environment its execution might be
aborted or it
could be rejected by the compiler.
Proof Theoretic Semantics provides the correct way
to handle pathological self-reference (PSR).
This would be dead obvious if you were not totally
clueless about Prolog.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Nice to see that you don't disagree.
Not nice to see that everyone continues to
totally ignore my best validation of proof
theoretic semantics.
Unfortunately that is unavoidable as long as your best presentation >>>>>> of the validation and of your version of proof theoretic semantics >>>>>> are not good enough.
Is is dead obvious and completely clear example
of the final resolution of the Liar Paradox using
generic proof theoretic semantics implemented in
Prolog.
Except that it is not final -- others will continue presenting
different views about it -- and not even a resolution.
If others did not reject mine out-of-hand
without review they could understand that
it is final.
Even those who think your resolution is the best there can be should
understand that there are others who don't shate that opinion.
There are many people that are certain that the Earth is flat.
On 6/26/2026 1:23 AM, Mikko wrote:
On 25/06/2026 16:47, olcott wrote:
On 6/25/2026 2:14 AM, Mikko wrote:
On 24/06/2026 23:23, olcott wrote:(a) Extracting atomic facts, would be the hardest part,
On 6/24/2026 4:45 AM, Mikko wrote:
On 23/06/2026 17:40, olcott wrote:
On 6/23/2026 12:49 AM, Mikko wrote:
On 22/06/2026 18:16, olcott wrote:
On 6/22/2026 2:46 AM, Mikko wrote:
On 22/06/2026 03:44, olcott wrote:
On 6/21/2026 7:32 PM, phoenix wrote:It is fairly simple to build a system of essentially infallible >>>>>>>>>> reasoning that never errs even when it doesn't have all the >>>>>>>>>> relevant information. The real problem is to construct a system >>>>>>>>>> that tells something interesting instead of just different >>>>>>>>>> presentations of the same already known facts.
olcott wrote:It is not that they never admit defeat.
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit defeat? >>>>>>>>>>>
olcott wrote:
On 6/21/2026 3:18 PM, André G. Isaak wrote:Lastly, and why should we care? Please answer this and >>>>>>>>>>>>>> other questions presented.
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> https://www.youtube.com/@rossfinlayson >>>>>>>>>>>>>>>>>>>>>>> Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof- >>>>>>>>>>>>>>>>>>>>>>> theoretic- semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>>>Whereas you are stuck to your own incoherent views >>>>>>>>>>>>>>>>>>>>> and reject
alternative views out-of-hand without review. >>>>>>>>>>>>>>>>>
Calling my views (anchored in proof theoretic >>>>>>>>>>>>>>>>>>>> semantics)
incoherent merely proves that you are too damned >>>>>>>>>>>>>>>>>>>> lazy to
look into proof theoretic semantics.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>>>> semantics/
I've spent a couple of hours reading that web page. >>>>>>>>>>>>>>>>>>> It is abstract in
the extreme. One thing is utterly clear: its level >>>>>>>>>>>>>>>>>>> of abstraction is
well beyond the comprehension capabilities of Peter >>>>>>>>>>>>>>>>>>> Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that >>>>>>>>>>>>>>>>>>> I can't be bothered
to read it any further. If it actually says anything >>>>>>>>>>>>>>>>>>> at all, that
something is heavily disguised. From it's >>>>>>>>>>>>>>>>>>> "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically >>>>>>>>>>>>>>>>>>> exclusively been
| occupied with logical constants. Logical constants >>>>>>>>>>>>>>>>>>> play a central role
| in reasoning and inference, but are definitely not >>>>>>>>>>>>>>>>>>> the exclusive, and
| perhaps not even the most typical sort of entities >>>>>>>>>>>>>>>>>>> that can be defined
| inferentially. A framework is needed that deals >>>>>>>>>>>>>>>>>>> with inferential
| definitions in a wider sense and covers both >>>>>>>>>>>>>>>>>>> logical and extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is >>>>>>>>>>>>>>>>>> currently and in the
near future not useful as making it useful requires >>>>>>>>>>>>>>>>>> much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be >>>>>>>>>>>>>>>>> useful for? What it
ought to be able to do that standard logic fails at? >>>>>>>>>>>>>>>>> Maybe André could
elucidate. He seems to have a better grasp of it than >>>>>>>>>>>>>>>>> anybody else here.
I doubt my understanding of PTS is any better than >>>>>>>>>>>>>>>> yours. I basically only know what is presented in the >>>>>>>>>>>>>>>> Stanford Encyclopedia article (which you correctly point >>>>>>>>>>>>>>>> out is not exactly aimed at beginners) and the Wikipedia >>>>>>>>>>>>>>>> article. What I am quite certain of, however, is that >>>>>>>>>>>>>>>> Olcott lacks any understanding of what PTS actually says >>>>>>>>>>>>>>>> as he's made a variety of fairly absurd claims regarding >>>>>>>>>>>>>>>> it (for example, that PTS claims that unproven >>>>>>>>>>>>>>>> propositions are 'meaningless' or that the goal of PTS >>>>>>>>>>>>>>>> is to completely overthrow standard truth- theoretic >>>>>>>>>>>>>>>> semantics).
André
Proof-theoretic semantics is an alternative to >>>>>>>>>>>>>>> truth-condition semantics. It is based on the >>>>>>>>>>>>>>> fundamental assumption that the central notion >>>>>>>>>>>>>>> in terms of which meanings are assigned to certain >>>>>>>>>>>>>>> expressions of our language, in particular to >>>>>>>>>>>>>>> logical constants, is that of proof rather than >>>>>>>>>>>>>>> truth. In this sense proof-theoretic semantics >>>>>>>>>>>>>>> is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>> semantics/
In other words it answers the question:
What happens when truth conditional semantics is >>>>>>>>>>>>>>> utterly abandoned and is totally replaced by proof >>>>>>>>>>>>>>> theoretic semantics?
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time. >>>>>>>>>>>>>
We can make these lies look foolish at every language >>>>>>>>>>>>> level from below average kindergarten to profoundly
brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more
than 100-fold more valuable.
It is that that have a system of essentially infallible >>>>>>>>>>> reasoning
that never errs as long as it has all the relevant information. >>>>>>>>>>
It will have the exhaustively complete list of
every atomic fact of general knowledge of the
actual world.
That is impossible. By the time you have all facts of general >>>>>>>> knowledge
in your system the general knowledge has grown to inlude more >>>>>>>> facts.
It can be reasonably approximated pretty quickly.
We start with all of the textbooks.
That is a lot of reading, though those for the same topic area tend >>>>>> to say the same, and the old ones add very little to the new ones, >>>>>> mainly some now obsolete technology.
It would not be too much reading for LLMs.
It could start with all of the latest textbooks
for all of the fields. Some of these latest
textbooks may be hundreds of years old for
fields that have become obsolete.
Perhaps that apprach should be tried. The problem involves extracting
atomic facts, detecting repeated facts, and encoding facts for the
inference system.
yet not too hard.
(b) Detecting repeated facts, string comparison.
(c) Encoding facts, CycL
https://en.wikipedia.org/wiki/CycL
I still have the original user's manuals
as PDFs and hard copies.
--The encoding must be normalized as much as possible in order to reduce
repetition to a string comparison. That is not a trivial problem if one
wants a total or nearly total prevention of repetition.
On 6/26/2026 1:34 AM, Mikko wrote:
On 25/06/2026 16:58, olcott wrote:
On 6/25/2026 2:18 AM, Mikko wrote:
On 24/06/2026 23:25, olcott wrote:
On 6/24/2026 4:52 AM, Mikko wrote:
On 23/06/2026 17:47, olcott wrote:
On 6/23/2026 12:55 AM, Mikko wrote:
On 22/06/2026 15:09, olcott wrote:
On 6/22/2026 1:41 AM, Mikko wrote:
On 22/06/2026 02:58, olcott wrote:
On 6/21/2026 5:17 AM, Mikko wrote:
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:Whereas you are stuck to your own incoherent views and >>>>>>>>>>>>>>>> reject
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>>
alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>> look into proof theoretic semantics.
At different times you have expressed different opinions, >>>>>>>>>>>>>> which
sometimes have been incompatible. But you have never clearly >>>>>>>>>>>>>> retracted your earlier opitions that conflict with your >>>>>>>>>>>>>> present
ones.
All of the ideas that I have ever had about these things >>>>>>>>>>>>> are now under the Proof Theoretic Semantics category. >>>>>>>>>>>>> These ideas have evolved over time, yet their essence >>>>>>>>>>>>> has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a >>>>>>>>>>>> publishable
(or nearly publishable) article about them.
I have 50 pre prints articles. Because not one single> human >>>>>>>>>>> being on the face of the Earth could understand
me I could not publish.
As far as I have seen, all interesting content in those articles >>>>>>>>>> that have any is or depends on claims that should be proven but >>>>>>>>>> aren't.
They are proven in Proof Theoretic Semantics
An aricle is not publishable unless it either contains the proof or >>>>>>>> has a pointer to an olready published proof.
Only now after 28 years am I acquiring the lingua Franca
terms-of-the-art of proof theoretic semantics such that
I can anchor my ideas in the foundational work of the
most respected authors in the field.
My issue with you guys is that you only spend 1%
of your concentration understanding me and the other
99% trying to artificially contrive some baseless
rebuttal.
THat "baseless" is false but otherwise, what is wrong is more
important than what is right. Of one ignores what is right one
mai fail to achieve what one could, but if one believs what is
wrong one may achieve a disaseter.
Proof-theoretic semantics is an alternative to truth-condition
semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
So far no one has even acknowledged that PTS is an alternative
to truth-conditional semantics. Several people have seemed
to same that no alternative can possibly exist.
You have not shown that there is any need for any alternative
semantics.
With dangerous lies that can destroy Democracy
and kill the planet with climate change having
an ultimate arbiter of truth would be useful.
Those who are able and willing to destroy democracy are able to provice
an ultimate arbiter of truth and usually do so. But they don't need any
proof theoretic semantics.
An ultimate arbiter of truth blows their whole game away.
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>>>>You can find any number of terms. That doesn't mean >>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 >>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody that PTS >>>>>>>>>>>>>> somehow causes
Gödel's theorem not to hold, then cite an academic expert >>>>>>>>>>>>>> who'll have
some credibility.
If they are mere gibberish words to you then you will not >>>>>>>>>>>>>>> understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>>>>> certainly don't
understand Gödel's Theorem, neither the theorem itself nor >>>>>>>>>>>>>> any proof of
it.
in the atomic base of PA. That you do not understand >>>>>>>>>>>>> what: "grounded in the atomic base" means is less
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used >>>>>>>>>>>> only by you, and it is one which you have never explicitly >>>>>>>>>>>> defined, so the fault here certainly doesn't lie with Alan. >>>>>>>>>>>> It's certainly not a 'verified fact' when you haven't even >>>>>>>>>>>> adequately explained what it is that you mean.
All of knowledge expressed in language is structured as a >>>>>>>>>>> tree of semantic relations specified syntactically between >>>>>>>>>>> finite strings.
What makes you believe semantic relations that can be
structured as
a tree are sufficient to contain all knowledge that is
exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to >>>>>>>> put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
This is the same sort of thing as finding the definedThat does not follow. Words have meanings even without definitions.
meaning of a word. If you cannot find its recursively
defined meaning then it never gains any meaning.
On 6/26/2026 10:24 AM, olcott wrote:
On 6/26/2026 8:57 AM, dbush wrote:
On 6/26/2026 9:45 AM, olcott wrote:
On 6/26/2026 8:20 AM, dbush wrote:
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms. That doesn't >>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 >>>>>>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody that >>>>>>>>>>>>>>>>>>> PTS somehow causes
Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>>> you certainly don't
understand Gödel's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly doesn't >>>>>>>>>>>>>>>>> lie with Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>> when you haven't even adequately explained what it is >>>>>>>>>>>>>>>>> that you mean.
All of knowledge expressed in language is structured as >>>>>>>>>>>>>>>> a tree of semantic relations specified syntactically >>>>>>>>>>>>>>>> between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a >>>>>>>>>>> loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious >>>>>>> how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is equal >>>>> to its successor" has no meaning in Robinson Arithmetic.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof from within a
stipulated atomic base of its own axioms like the one
that you provided.
Then you agree that the above natural language sentence that is
semantically required to be either true or false has no meaning?
Your sentence would be what it always has been
a stipulated true sentence axiom.
False, as that statement is not one of the axioms of Robinson
arithmetic, but it is a statement in its language, and one that has
*only* an infinite connection to the axioms of that system.
By your logic, "no number is equal to its successor" has no meaning in Robinson arithmetic.--
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning.
André
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable. Then to put >>>>>> things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable in PA.
In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False. The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False. G is simply a sentence like ~∃x x>10 v x<5 but much more complex. >>
"No number is equal to its successor" is a sentence in RA, and it is
true but unprovable in RA (or as your would call it, "out-of-scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language of
Q. More formally, it is this:
~∃x x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms
you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
On 6/26/2026 1:45 AM, Mikko wrote:If anyone and everyone that claims that someone is dishonest
On 25/06/2026 19:16, olcott wrote:
On 6/25/2026 2:29 AM, Mikko wrote:
On 25/06/2026 00:33, olcott wrote:
On 6/24/2026 5:13 AM, Mikko wrote:
On 23/06/2026 21:20, olcott wrote:
On 6/23/2026 12:32 PM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>> On 6/22/2026 1:42 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> On 6/22/2026 10:48 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>
G is true.
I put it to you you're lying again. No reputable >>>>>>>>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things. If Dag >>>>>>>>>>>>>>>>>>>> Prawitz
really
did
"agree" (with whom?) that Gödel's sentence G is not >>>>>>>>>>>>>>>>>>>> true in
Peano
Arithmetic, then produce a citation for this. >>>>>>>>>>>>>>>>
He never gets to Gödel. He essentially says unprovable >>>>>>>>>>>>>>>>>>> means untrue all the time for everything within his >>>>>>>>>>>>>>>>>>> own Theory of Grounds of strict Proof Theoretic >>>>>>>>>>>>>>>>>>> Semantics.
You won't understand it, but that _is_ essentially >>>>>>>>>>>>>>>>>> Gödel's
Incompleteness
Theorem. It is a statement that any sufficiently >>>>>>>>>>>>>>>>>> powerful
system can
express true things it can't prove. So Dag Prawitz, >>>>>>>>>>>>>>>>>> had he been
saying
the things you falsely attributed to him, would >>>>>>>>>>>>>>>>>> certainly have
"got" to
Gödel, and would have understood full well what he was >>>>>>>>>>>>>>>>>> saying.
You did not pay close enough attention to my exact words. >>>>>>>>>>>>>>>>I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>
Yeah, I'm pretty sure that "Dag Prawitz says what Dag >>>>>>>>>>>>>> Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz >>>>>>>>>>>>>> doesn't
say",
then looking a bit into his tremendous volume of works, >>>>>>>>>>>>>> he talks about "natural deduction" then specifically an >>>>>>>>>>>>>> "inverse
principle" so I think these are key aspects of fundamental >>>>>>>>>>>>>> logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself, >>>>>>>>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to >>>>>>>>>>>>>> generate
new ad-
missible rules within a certain syntactic context. Some >>>>>>>>>>>>>> fifteen years
later, the idea was taken up by Dag Prawitz to devise a >>>>>>>>>>>>>> strategy of
normalization for natural deduction calculi (this being an >>>>>>>>>>>>>> analogue of
Gentzen’s cut-elimination theorem for sequent calculi). >>>>>>>>>>>>>> Later,
Prawitz
used the inversion principle again, attributing it with a >>>>>>>>>>>>>> semantic
role.
Still working in natural deduction calculi, he formulated >>>>>>>>>>>>>> a general
type
of schematic Introduction rules to be matched—thanks to >>>>>>>>>>>>>> the idea
supporting the inversion principle — by a corresponding >>>>>>>>>>>>>> general
schematic Elimination rule. This was an attempt to provide a >>>>>>>>>>>>>> solution to
the problem suggested by the often quoted note of Gentzen. >>>>>>>>>>>>>> According to
Gentzen “it should be possible to display the elimination >>>>>>>>>>>>>> rules as
unique functions of the corresponding introduction rules >>>>>>>>>>>>>> on the
basis of
certain requirements.” Many people have since worked on >>>>>>>>>>>>>> this topic,
which can be appropriately seen as the birthplace of what >>>>>>>>>>>>>> are now
referred to as “general elimination rules”, recently studied >>>>>>>>>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace >>>>>>>>>>>>>> the main
threads of this chapter of proof-theoretical
investigation, using
Lorenzen’s original framework as a general guide" >>>>>>>>>>>>>>
Hm, "general elimination rules", seem derivable from De >>>>>>>>>>>>>> Morgan's
laws,
and that being the usual account of naive deductive >>>>>>>>>>>>>> analysis, then
since
"natural deduction", which here is held as part of the theory >>>>>>>>>>>>>> since it's naturally logical, then has for Gentzen that >>>>>>>>>>>>>> besides
Kripke
afterward there's also Sheffer and Chwistek before, and >>>>>>>>>>>>>> instead of
Montague for semantics there's Herbrand for semantics, so, >>>>>>>>>>>>>> what to do
about "inversion principle" is here that the thea-theory >>>>>>>>>>>>>> has that
it's
what subsumes "non-contradiction principle", here hoping >>>>>>>>>>>>>> that the
interpretation aligns and thusly that "principle of >>>>>>>>>>>>>> inversion"
wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334 >>>>>>>>>>>>>>
https://www.strandbooks.com/natural-deduction-a-proof- >>>>>>>>>>>>>> theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the >>>>>>>>>>>>>> foundation of
most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a >>>>>>>>>>>>>> principle of
thorough reason as subsuming principles of non-
contradiction and what
suffices, so, I'll be curious then about what to make of >>>>>>>>>>>>>> Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as >>>>>>>>>>>>>> old as the
oldest account of Western philosophy like Heraclitus with >>>>>>>>>>>>>> dual
monism.
In fact by definition it's about the most basic aspect of >>>>>>>>>>>>>> contemplation
and deliberation in abstraction of looking at both sides >>>>>>>>>>>>>> of issues
and
resolving inductive impasses with analytical bridges after >>>>>>>>>>>>>> complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as >>>>>>>>>>>>>> one of the
characteristic features of Gentzen's intuitionistic natural >>>>>>>>>>>>>> deduction.
In the literature on proof-theoretic semantics, this >>>>>>>>>>>>>> principle is
often
coupled with another that is called the recovery
principle. By
adopting
the Computational Ludics framework, we reformulate these >>>>>>>>>>>>>> principles
into
one and the same condition, which we call the harmony >>>>>>>>>>>>>> condition. We
show
that this reformulation allows us to reveal two intuitive >>>>>>>>>>>>>> ideas
standing
behind these principles: the idea of "containment" present >>>>>>>>>>>>>> in the
inversion principle, and the idea that the recovery >>>>>>>>>>>>>> principle is the
"converse" of the inversion principle. We also formulate >>>>>>>>>>>>>> two other
conditions in the Computational Ludics framework, and we >>>>>>>>>>>>>> show that
each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and >>>>>>>>>>>>>> knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical >>>>>>>>>>>>>> connectives,
proof-theoretic semantics rests on the idea that we know the >>>>>>>>>>>>>> meaning of
a compound sentence when we know what counts as a >>>>>>>>>>>>>> canonical proof of
it.
And if proofs are formalised within the framework of natural >>>>>>>>>>>>>> deduction,
then a canonical proof of a sentence A is nothing but a >>>>>>>>>>>>>> closed
derivation ending with an introduction rule of the main >>>>>>>>>>>>>> connective
of A."
The "canonical proofs" are not unique, in any system >>>>>>>>>>>>>> strong enough
to make for infinitary reasoning and super-classical results >>>>>>>>>>>>>> requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6 >>>>>>>>>>>>> That is the most important gist of his whole work.
He later goes on to develop and further elaborate his >>>>>>>>>>>>> Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches >>>>>>>>>>>>> Thomas Piecha & Peter Schroeder-Heister do this same sort of >>>>>>>>>>>>> thing two different ways.
Furthermore I say there are "canonical proofs" of inductive >>>>>>>>>>>> sorts that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical >>>>>>>>>>> proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make >>>>>>>>>>>> repairs
of what otherwise is flawed, or for hard constructivist realist >>>>>>>>>>>> structuralist model theorists: not-theories (examples of >>>>>>>>>>>> wrong).
Induction and counter-induction contradict each other, it's >>>>>>>>>> simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
So you are going to imply that I am incorrect
about Prolog when you yourself remain clueless about Prolog?
That would be dishonest.
No, pointing out that you are worng about Prolog when you are wrong >>>>>> about Prolog is never dishohest.
That is correct Prolog and that is the
result of the correct run of correct Prolog.
Irrelevant. Nobody claimed there be Prolog errors in your queries.
Implying that I am wrong about Prolog without
pointing out any actual mistake is also DISHONEST.
How did Ross FInlayson imply that you were wrong about Prolog?
If an error is claimed then it must be specifically
pointed out otherwise the clam of error is dishonest.
Yet you claim that Ross Finlayson be dishonest without pointing
out what is dishonest in his words.
If anyone and everyone that claims that they found an
error and never points out what the error is and why
it is an error then they are merely a baseless denigrator.
On 6/26/2026 9:39 PM, olcott wrote:
On 6/26/2026 8:11 PM, dbush wrote:
On 6/26/2026 8:48 PM, olcott wrote:
On 6/26/2026 7:23 PM, dbush wrote:
On 6/26/2026 8:05 PM, olcott wrote:
On 6/26/2026 6:18 PM, dbush wrote:
On 6/26/2026 6:58 PM, olcott wrote:
On 6/26/2026 5:08 PM, dbush wrote:
On 6/26/2026 6:01 PM, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:Not applicable, as that is not a sentence in PA.
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" >>>>>>>>>>>>>>>>>>> has no meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q), >>>>>>>>>>>>>>>>>> the statement "no number is equal to its
successor" is not provable.While this statement >>>>>>>>>>>>>>>>>> is true for the standard natural numbers, Robinson >>>>>>>>>>>>>>>>>> Arithmetic is too weak to prove it universally >>>>>>>>>>>>>>>>>> (∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning. >>>>>>>>>>>>>>>>>
André
out-of-scope for Q is more accurate as jargon free. >>>>>>>>>>>>>>>>
PTS does hold the view that meaning is only derived >>>>>>>>>>>>>>>> through inference steps. This simple sentence seems >>>>>>>>>>>>>>>> impossibly too difficult for anyone fully indoctrinated >>>>>>>>>>>>>>>> with alternative views. So I will simply say out-of-scope. >>>>>>>>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable. >>>>>>>>>>>>>>> Then to put things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable >>>>>>>>>>>>>> in PA.
In both cases the semantics in not represented in PA. >>>>>>>>>>>>>
It is expressed in PA
False. The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and >>>>>>>>>>>> the semantics of G are neither expressible in PA.
False. G is simply a sentence like ~∃x x>10 v x<5 but much >>>>>>>>>>> more complex.
"No number is equal to its successor" is a sentence in RA, >>>>>>>>>>>>> and it is true but unprovable in RA (or as your would call >>>>>>>>>>>>> it, "out- of- scope").
If its semantics is not expressible in Q (What RA is called) >>>>>>>>>>>> then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the >>>>>>>>>>> language of Q. More formally, it is this:
~∃x x=S(x)
And this sentence is not provable from the axioms of Q (or, >>>>>>>>>>> in terms you would understand, the above is "out-of-scope" of >>>>>>>>>>> Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
In your own words, what does it mean for a statement to be
"semantically grounded" in a formal system?
I always do back-chained inference because the typical
math way of doing forward chained inference may take
an infeasibly long time. A finite set of back-chained
inference steps from x to the axioms of Q.
Back or forward chained doesn't matter, it's essentially the same >>>>>>> steps in a different direction. But in any case, you're saying >>>>>>> "semantically grounded" is just another synonym for unprovable.
So to again put things in a way you'll understand, Godel proved >>>>>>> that any axiom system of arithmetic contains statements that are >>>>>>> not semantically grounded.
Not quite. G is not semantically grounded
i.e. unprovable
in PA
yet G is semantically grounded
i.e. provable
in metamathematics.
Which is exactly what Godel proved.
Your lack of response indicates that you agree with Godel, but used
different words to do so.
When an expression in PA only derives semantic
meaning in PA when grounded in PA then G has no
meaning in PA.
i.e. if a statement is unprovable in PA then it's unprovable in PA.
In other words, a meaningless tautology.
That also means that, using your terminology, it has been proven >>>>>>> that the statement ~∃x x=S(x), i.e. "No number is equal to its >>>>>>> successor", is not semantically grounded in Q.
Thus is meaningless in Q and out-of-scope in Q.
Which means the semantically valid statement in Q
does not include ~∃x x=S(x)
False, as it means "no number is equal to its successor", and the
concept of a successor and equality have semantic meaning in Q, as
does the concept of "all", "none", and "exists".
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is
ungrounded in the PTS atomic base of Q.
In other words, ~∃x x=S(x) is unprovable in Q, as is commonly known.
So once again, you agree with everyone else, but are using different
words to say so.
On 26/06/2026 16:15, olcott wrote:
On 6/26/2026 1:45 AM, Mikko wrote:If anyone and everyone that claims that someone is dishonest
On 25/06/2026 19:16, olcott wrote:
On 6/25/2026 2:29 AM, Mikko wrote:
On 25/06/2026 00:33, olcott wrote:
On 6/24/2026 5:13 AM, Mikko wrote:
On 23/06/2026 21:20, olcott wrote:
On 6/23/2026 12:32 PM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>> On 6/22/2026 1:42 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>> On 6/22/2026 10:48 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>
G is true.
I put it to you you're lying again. No reputable >>>>>>>>>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things. If Dag >>>>>>>>>>>>>>>>>>>>> Prawitz
really
did
"agree" (with whom?) that Gödel's sentence G is not >>>>>>>>>>>>>>>>>>>>> true in
Peano
Arithmetic, then produce a citation for this. >>>>>>>>>>>>>>>>>
He never gets to Gödel. He essentially says unprovable >>>>>>>>>>>>>>>>>>>> means untrue all the time for everything within his >>>>>>>>>>>>>>>>>>>> own Theory of Grounds of strict Proof Theoretic >>>>>>>>>>>>>>>>>>>> Semantics.
You won't understand it, but that _is_ essentially >>>>>>>>>>>>>>>>>>> Gödel's
Incompleteness
Theorem. It is a statement that any sufficiently >>>>>>>>>>>>>>>>>>> powerful
system can
express true things it can't prove. So Dag Prawitz, >>>>>>>>>>>>>>>>>>> had he been
saying
the things you falsely attributed to him, would >>>>>>>>>>>>>>>>>>> certainly have
"got" to
Gödel, and would have understood full well what he >>>>>>>>>>>>>>>>>>> was saying.
You did not pay close enough attention to my exact words. >>>>>>>>>>>>>>>>>I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>>
Yeah, I'm pretty sure that "Dag Prawitz says what Dag >>>>>>>>>>>>>>> Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz >>>>>>>>>>>>>>> doesn't
say",
then looking a bit into his tremendous volume of works, >>>>>>>>>>>>>>> he talks about "natural deduction" then specifically an >>>>>>>>>>>>>>> "inverse
principle" so I think these are key aspects of
fundamental logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself, >>>>>>>>>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to >>>>>>>>>>>>>>> generate
new ad-
missible rules within a certain syntactic context. Some >>>>>>>>>>>>>>> fifteen years
later, the idea was taken up by Dag Prawitz to devise a >>>>>>>>>>>>>>> strategy of
normalization for natural deduction calculi (this being an >>>>>>>>>>>>>>> analogue of
Gentzen’s cut-elimination theorem for sequent calculi). >>>>>>>>>>>>>>> Later,
Prawitz
used the inversion principle again, attributing it with a >>>>>>>>>>>>>>> semantic
role.
Still working in natural deduction calculi, he formulated >>>>>>>>>>>>>>> a general
type
of schematic Introduction rules to be matched—thanks to >>>>>>>>>>>>>>> the idea
supporting the inversion principle — by a corresponding >>>>>>>>>>>>>>> general
schematic Elimination rule. This was an attempt to provide a >>>>>>>>>>>>>>> solution to
the problem suggested by the often quoted note of Gentzen. >>>>>>>>>>>>>>> According to
Gentzen “it should be possible to display the elimination >>>>>>>>>>>>>>> rules as
unique functions of the corresponding introduction rules >>>>>>>>>>>>>>> on the
basis of
certain requirements.” Many people have since worked on >>>>>>>>>>>>>>> this topic,
which can be appropriately seen as the birthplace of what >>>>>>>>>>>>>>> are now
referred to as “general elimination rules”, recently studied
thoroughly
by Sara Negri and Jan von Plato. In this paper, we >>>>>>>>>>>>>>> retrace the main
threads of this chapter of proof-theoretical
investigation, using
Lorenzen’s original framework as a general guide" >>>>>>>>>>>>>>>
Hm, "general elimination rules", seem derivable from De >>>>>>>>>>>>>>> Morgan's
laws,
and that being the usual account of naive deductive >>>>>>>>>>>>>>> analysis, then
since
"natural deduction", which here is held as part of the >>>>>>>>>>>>>>> theory
since it's naturally logical, then has for Gentzen that >>>>>>>>>>>>>>> besides
Kripke
afterward there's also Sheffer and Chwistek before, and >>>>>>>>>>>>>>> instead of
Montague for semantics there's Herbrand for semantics, >>>>>>>>>>>>>>> so, what to do
about "inversion principle" is here that the thea-theory >>>>>>>>>>>>>>> has that
it's
what subsumes "non-contradiction principle", here hoping >>>>>>>>>>>>>>> that the
interpretation aligns and thusly that "principle of >>>>>>>>>>>>>>> inversion"
wouldn't
need dis-ambiguation from "inversion principle". >>>>>>>>>>>>>>>
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334 >>>>>>>>>>>>>>>
https://www.strandbooks.com/natural-deduction-a-proof- >>>>>>>>>>>>>>> theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the >>>>>>>>>>>>>>> foundation of
most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a >>>>>>>>>>>>>>> principle of
thorough reason as subsuming principles of non-
contradiction and what
suffices, so, I'll be curious then about what to make of >>>>>>>>>>>>>>> Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as >>>>>>>>>>>>>>> old as the
oldest account of Western philosophy like Heraclitus with >>>>>>>>>>>>>>> dual
monism.
In fact by definition it's about the most basic aspect of >>>>>>>>>>>>>>> contemplation
and deliberation in abstraction of looking at both sides >>>>>>>>>>>>>>> of issues
and
resolving inductive impasses with analytical bridges after >>>>>>>>>>>>>>> complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as >>>>>>>>>>>>>>> one of the
characteristic features of Gentzen's intuitionistic natural >>>>>>>>>>>>>>> deduction.
In the literature on proof-theoretic semantics, this >>>>>>>>>>>>>>> principle is
often
coupled with another that is called the recovery >>>>>>>>>>>>>>> principle. By
adopting
the Computational Ludics framework, we reformulate these >>>>>>>>>>>>>>> principles
into
one and the same condition, which we call the harmony >>>>>>>>>>>>>>> condition. We
show
that this reformulation allows us to reveal two intuitive >>>>>>>>>>>>>>> ideas
standing
behind these principles: the idea of "containment" >>>>>>>>>>>>>>> present in the
inversion principle, and the idea that the recovery >>>>>>>>>>>>>>> principle is the
"converse" of the inversion principle. We also formulate >>>>>>>>>>>>>>> two other
conditions in the Computational Ludics framework, and we >>>>>>>>>>>>>>> show that
each
of them is equivalent to the harmony condition." >>>>>>>>>>>>>>>
The "ludicus" is Latin and for accounts of wisdom and >>>>>>>>>>>>>>> knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical >>>>>>>>>>>>>>> connectives,
proof-theoretic semantics rests on the idea that we know the >>>>>>>>>>>>>>> meaning of
a compound sentence when we know what counts as a >>>>>>>>>>>>>>> canonical proof of
it.
And if proofs are formalised within the framework of natural >>>>>>>>>>>>>>> deduction,
then a canonical proof of a sentence A is nothing but a >>>>>>>>>>>>>>> closed
derivation ending with an introduction rule of the main >>>>>>>>>>>>>>> connective
of A."
The "canonical proofs" are not unique, in any system >>>>>>>>>>>>>>> strong enough
to make for infinitary reasoning and super-classical results >>>>>>>>>>>>>>> requiring
analytical bridges about infinity and continuity. >>>>>>>>>>>>>>>
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6 >>>>>>>>>>>>>> That is the most important gist of his whole work. >>>>>>>>>>>>>>
He later goes on to develop and further elaborate his >>>>>>>>>>>>>> Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches >>>>>>>>>>>>>> Thomas Piecha & Peter Schroeder-Heister do this same sort of >>>>>>>>>>>>>> thing two different ways.
Furthermore I say there are "canonical proofs" of inductive >>>>>>>>>>>>> sorts that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by
"canonical proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make >>>>>>>>>>>>> repairs
of what otherwise is flawed, or for hard constructivist >>>>>>>>>>>>> realist
structuralist model theorists: not-theories (examples of >>>>>>>>>>>>> wrong).
Induction and counter-induction contradict each other, it's >>>>>>>>>>> simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
So you are going to imply that I am incorrect
about Prolog when you yourself remain clueless about Prolog?
That would be dishonest.
No, pointing out that you are worng about Prolog when you are wrong >>>>>>> about Prolog is never dishohest.
That is correct Prolog and that is the
result of the correct run of correct Prolog.
Irrelevant. Nobody claimed there be Prolog errors in your queries.
Implying that I am wrong about Prolog without
pointing out any actual mistake is also DISHONEST.
How did Ross FInlayson imply that you were wrong about Prolog?
If an error is claimed then it must be specifically
pointed out otherwise the clam of error is dishonest.
Yet you claim that Ross Finlayson be dishonest without pointing
out what is dishonest in his words.
If anyone and everyone that claims that they found an
error and never points out what the error is and why
it is an error then they are merely a baseless denigrator.
never points out what the dishonesty is is and why it is
dishones then they are merely a baseless denigrator.
On 06/23/2026 10:32 AM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 1:42 PM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote:
On 6/22/2026 10:48 AM, Alan Mackenzie wrote:
G is true.
I put it to you you're lying again. No reputable
mathematician
would
risk his reputation by saying false things. If Dag Prawitz >>>>>>>>>>>>>> really
did
"agree" (with whom?) that Gödel's sentence G is not true in >>>>>>>>>>>>>> Peano
Arithmetic, then produce a citation for this.
I was right, you didn't understand it.He never gets to Gödel. He essentially says unprovable >>>>>>>>>>>>> means untrue all the time for everything within hisYou won't understand it, but that _is_ essentially Gödel's >>>>>>>>>>>> Incompleteness
own Theory of Grounds of strict Proof Theoretic Semantics. >>>>>>>>>>
Theorem. It is a statement that any sufficiently powerful >>>>>>>>>>>> system can
express true things it can't prove. So Dag Prawitz, had he >>>>>>>>>>>> been
saying
the things you falsely attributed to him, would certainly have >>>>>>>>>>>> "got" to
Gödel, and would have understood full well what he was saying. >>>>>>>>>>
You did not pay close enough attention to my exact words. >>>>>>>>>>
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Dag Prawitz says: Unprovable ALWAYS means untrue
Yeah, I'm pretty sure that "Dag Prawitz says what Dag Prawitz
says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz doesn't >>>>>>>> say",
then looking a bit into his tremendous volume of works,
he talks about "natural deduction" then specifically an "inverse >>>>>>>> principle" so I think these are key aspects of fundamental logic. >>>>>>>>
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself, >>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to generate >>>>>>>> new ad-
missible rules within a certain syntactic context. Some fifteen >>>>>>>> years
later, the idea was taken up by Dag Prawitz to devise a strategy of >>>>>>>> normalization for natural deduction calculi (this being an
analogue of
Gentzen’s cut-elimination theorem for sequent calculi). Later, >>>>>>>> Prawitz
used the inversion principle again, attributing it with a semantic >>>>>>>> role.
Still working in natural deduction calculi, he formulated a general >>>>>>>> type
of schematic Introduction rules to be matched—thanks to the idea >>>>>>>> supporting the inversion principle — by a corresponding general >>>>>>>> schematic Elimination rule. This was an attempt to provide a
solution to
the problem suggested by the often quoted note of Gentzen.
According to
Gentzen “it should be possible to display the elimination rules as >>>>>>>> unique functions of the corresponding introduction rules on the >>>>>>>> basis of
certain requirements.” Many people have since worked on this topic, >>>>>>>> which can be appropriately seen as the birthplace of what are now >>>>>>>> referred to as “general elimination rules”, recently studied >>>>>>>> thoroughly
by Sara Negri and Jan von Plato. In this paper, we retrace the main >>>>>>>> threads of this chapter of proof-theoretical investigation, using >>>>>>>> Lorenzen’s original framework as a general guide"
Hm, "general elimination rules", seem derivable from De Morgan's >>>>>>>> laws,
and that being the usual account of naive deductive analysis, then >>>>>>>> since
"natural deduction", which here is held as part of the theory
since it's naturally logical, then has for Gentzen that besides >>>>>>>> Kripke
afterward there's also Sheffer and Chwistek before, and instead of >>>>>>>> Montague for semantics there's Herbrand for semantics, so, what >>>>>>>> to do
about "inversion principle" is here that the thea-theory has that >>>>>>>> it's
what subsumes "non-contradiction principle", here hoping that the >>>>>>>> interpretation aligns and thusly that "principle of inversion" >>>>>>>> wouldn't
need dis-ambiguation from "inversion principle".
https://www.tandfonline.com/doi/abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof-theoretical- >>>>>>>> study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the foundation of >>>>>>>> most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a
principle of
thorough reason as subsuming principles of non-contradiction and >>>>>>>> what
suffices, so, I'll be curious then about what to make of Prawitz' >>>>>>>> "inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as old as the >>>>>>>> oldest account of Western philosophy like Heraclitus with dual >>>>>>>> monism.
In fact by definition it's about the most basic aspect of
contemplation
and deliberation in abstraction of looking at both sides of issues >>>>>>>> and
resolving inductive impasses with analytical bridges after
complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as one of the >>>>>>>> characteristic features of Gentzen's intuitionistic natural
deduction.
In the literature on proof-theoretic semantics, this principle is >>>>>>>> often
coupled with another that is called the recovery principle. By >>>>>>>> adopting
the Computational Ludics framework, we reformulate these principles >>>>>>>> into
one and the same condition, which we call the harmony condition. We >>>>>>>> show
that this reformulation allows us to reveal two intuitive ideas >>>>>>>> standing
behind these principles: the idea of "containment" present in the >>>>>>>> inversion principle, and the idea that the recovery principle is >>>>>>>> the
"converse" of the inversion principle. We also formulate two other >>>>>>>> conditions in the Computational Ludics framework, and we show that >>>>>>>> each
of them is equivalent to the harmony condition."
The "ludicus" is Latin and for accounts of wisdom and knowledge. >>>>>>>>
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical connectives, >>>>>>>> proof-theoretic semantics rests on the idea that we know the
meaning of
a compound sentence when we know what counts as a canonical
proof of
it.
And if proofs are formalised within the framework of natural
deduction,
then a canonical proof of a sentence A is nothing but a closed >>>>>>>> derivation ending with an introduction rule of the main connective >>>>>>>> of A."
The "canonical proofs" are not unique, in any system strong enough >>>>>>>> to make for infinitary reasoning and super-classical results
requiring
analytical bridges about infinity and continuity.
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6
That is the most important gist of his whole work.
He later goes on to develop and further elaborate his
Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches
Thomas Piecha & Peter Schroeder-Heister do this same sort of
thing two different ways.
Furthermore I say there are "canonical proofs" of inductive sorts
that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by "canonical proofs". >>>>> Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make repairs >>>>>> of what otherwise is flawed, or for hard constructivist realist
structuralist model theorists: not-theories (examples of wrong).
Induction and counter-induction contradict each other, it's simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
P.S. there's no reason at all to "get back to you".
... Except countering the waste-ful spammy trolling.
Finding cycles in derivations of arguments is exactly
what makes for detection of circularities then as to
whether they're the virtuous or vicious sorts of circles,
it's the act of being diligent itself, you brainless, memoryless bot.
On 26/06/2026 16:02, olcott wrote:
On 6/26/2026 1:23 AM, Mikko wrote:
On 25/06/2026 16:47, olcott wrote:
On 6/25/2026 2:14 AM, Mikko wrote:
On 24/06/2026 23:23, olcott wrote:(a) Extracting atomic facts, would be the hardest part,
On 6/24/2026 4:45 AM, Mikko wrote:
On 23/06/2026 17:40, olcott wrote:
On 6/23/2026 12:49 AM, Mikko wrote:
On 22/06/2026 18:16, olcott wrote:
On 6/22/2026 2:46 AM, Mikko wrote:
On 22/06/2026 03:44, olcott wrote:
On 6/21/2026 7:32 PM, phoenix wrote:It is fairly simple to build a system of essentially infallible >>>>>>>>>>> reasoning that never errs even when it doesn't have all the >>>>>>>>>>> relevant information. The real problem is to construct a system >>>>>>>>>>> that tells something interesting instead of just different >>>>>>>>>>> presentations of the same already known facts.
olcott wrote:
On 6/21/2026 5:36 PM, phoenix wrote:What good does it do to program the LLMs to never admit >>>>>>>>>>>>> defeat?
olcott wrote:
On 6/21/2026 3:18 PM, André G. Isaak wrote:Lastly, and why should we care? Please answer this and >>>>>>>>>>>>>>> other questions presented.
On 2026-06-20 04:26, Alan Mackenzie wrote:
Mikko <mikko.levanto@iki.fi> wrote:
On 19/06/2026 23:28, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>> On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/17/2026 4:14 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> https://www.youtube.com/@rossfinlayson >>>>>>>>>>>>>>>>>>>>>>>> Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof- >>>>>>>>>>>>>>>>>>>>>>>> theoretic- semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>>>>Whereas you are stuck to your own incoherent views >>>>>>>>>>>>>>>>>>>>>> and reject
alternative views out-of-hand without review. >>>>>>>>>>>>>>>>>>
Calling my views (anchored in proof theoretic >>>>>>>>>>>>>>>>>>>>> semantics)
incoherent merely proves that you are too damned >>>>>>>>>>>>>>>>>>>>> lazy to
look into proof theoretic semantics. >>>>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>>>>> semantics/
I've spent a couple of hours reading that web page. >>>>>>>>>>>>>>>>>>>> It is abstract in
the extreme. One thing is utterly clear: its level >>>>>>>>>>>>>>>>>>>> of abstraction is
well beyond the comprehension capabilities of Peter >>>>>>>>>>>>>>>>>>>> Olcott, who can't
even understand proof by contradiction.
That page's level of abstraction is high enough that >>>>>>>>>>>>>>>>>>>> I can't be bothered
to read it any further. If it actually says >>>>>>>>>>>>>>>>>>>> anything at all, that
something is heavily disguised. From it's >>>>>>>>>>>>>>>>>>>> "Conclusion and Outlook"
section at the end:
| Standard proof-theoretic semantics has practically >>>>>>>>>>>>>>>>>>>> exclusively been
| occupied with logical constants. Logical constants >>>>>>>>>>>>>>>>>>>> play a central role
| in reasoning and inference, but are definitely not >>>>>>>>>>>>>>>>>>>> the exclusive, and
| perhaps not even the most typical sort of entities >>>>>>>>>>>>>>>>>>>> that can be defined
| inferentially. A framework is needed that deals >>>>>>>>>>>>>>>>>>>> with inferential
| definitions in a wider sense and covers both >>>>>>>>>>>>>>>>>>>> logical and extra- logical
| inferential definitions alike.
Does this have any meaning?
Yes. It means that proof-theoretic semantics is >>>>>>>>>>>>>>>>>>> currently and in the
near future not useful as making it useful requires >>>>>>>>>>>>>>>>>>> much time and
effort if it is possible at all.
Do its proponents have any idea what PTS ought to be >>>>>>>>>>>>>>>>>> useful for? What it
ought to be able to do that standard logic fails at? >>>>>>>>>>>>>>>>>> Maybe André could
elucidate. He seems to have a better grasp of it than >>>>>>>>>>>>>>>>>> anybody else here.
I doubt my understanding of PTS is any better than >>>>>>>>>>>>>>>>> yours. I basically only know what is presented in the >>>>>>>>>>>>>>>>> Stanford Encyclopedia article (which you correctly >>>>>>>>>>>>>>>>> point out is not exactly aimed at beginners) and the >>>>>>>>>>>>>>>>> Wikipedia article. What I am quite certain of, however, >>>>>>>>>>>>>>>>> is that Olcott lacks any understanding of what PTS >>>>>>>>>>>>>>>>> actually says as he's made a variety of fairly absurd >>>>>>>>>>>>>>>>> claims regarding it (for example, that PTS claims that >>>>>>>>>>>>>>>>> unproven propositions are 'meaningless' or that the >>>>>>>>>>>>>>>>> goal of PTS is to completely overthrow standard truth- >>>>>>>>>>>>>>>>> theoretic semantics).
André
Proof-theoretic semantics is an alternative to >>>>>>>>>>>>>>>> truth-condition semantics. It is based on the >>>>>>>>>>>>>>>> fundamental assumption that the central notion >>>>>>>>>>>>>>>> in terms of which meanings are assigned to certain >>>>>>>>>>>>>>>> expressions of our language, in particular to >>>>>>>>>>>>>>>> logical constants, is that of proof rather than >>>>>>>>>>>>>>>> truth. In this sense proof-theoretic semantics >>>>>>>>>>>>>>>> is semantics in terms of proof.
https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>> semantics/
In other words it answers the question:
What happens when truth conditional semantics is >>>>>>>>>>>>>>>> utterly abandoned and is totally replaced by proof >>>>>>>>>>>>>>>> theoretic semantics?
This is the key element to creating the algorithm
that divides truth was well-crafted lies in real time. >>>>>>>>>>>>>>
We can make these lies look foolish at every language >>>>>>>>>>>>>> level from below average kindergarten to profoundly >>>>>>>>>>>>>> brilliant genius with a PhD in everything and we
can do this before the liar finishes saying their
sentence.
It also make the trillion dollar LLM industry more >>>>>>>>>>>>>> than 100-fold more valuable.
It is not that they never admit defeat.
It is that that have a system of essentially infallible >>>>>>>>>>>> reasoning
that never errs as long as it has all the relevant information. >>>>>>>>>>>
It will have the exhaustively complete list of
every atomic fact of general knowledge of the
actual world.
That is impossible. By the time you have all facts of general >>>>>>>>> knowledge
in your system the general knowledge has grown to inlude more >>>>>>>>> facts.
It can be reasonably approximated pretty quickly.
We start with all of the textbooks.
That is a lot of reading, though those for the same topic area tend >>>>>>> to say the same, and the old ones add very little to the new ones, >>>>>>> mainly some now obsolete technology.
It would not be too much reading for LLMs.
It could start with all of the latest textbooks
for all of the fields. Some of these latest
textbooks may be hundreds of years old for
fields that have become obsolete.
Perhaps that apprach should be tried. The problem involves extracting >>>>> atomic facts, detecting repeated facts, and encoding facts for the
inference system.
yet not too hard.
(b) Detecting repeated facts, string comparison.
(c) Encoding facts, CycL
https://en.wikipedia.org/wiki/CycL
I still have the original user's manuals
as PDFs and hard copies.
Do they say anything about normalization?
--The encoding must be normalized as much as possible in order to reduce
repetition to a string comparison. That is not a trivial problem if one
wants a total or nearly total prevention of repetition.
On 26/06/2026 16:05, olcott wrote:
On 6/26/2026 1:34 AM, Mikko wrote:
On 25/06/2026 16:58, olcott wrote:
On 6/25/2026 2:18 AM, Mikko wrote:
On 24/06/2026 23:25, olcott wrote:
On 6/24/2026 4:52 AM, Mikko wrote:
On 23/06/2026 17:47, olcott wrote:
On 6/23/2026 12:55 AM, Mikko wrote:
On 22/06/2026 15:09, olcott wrote:
On 6/22/2026 1:41 AM, Mikko wrote:
On 22/06/2026 02:58, olcott wrote:
On 6/21/2026 5:17 AM, Mikko wrote:
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:
On 6/17/2026 4:14 PM, olcott wrote:Whereas you are stuck to your own incoherent views and >>>>>>>>>>>>>>>>> reject
https://www.youtube.com/@rossfinlayson
Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>>>
alternative views out-of-hand without review
Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>>> look into proof theoretic semantics.
At different times you have expressed different opinions, >>>>>>>>>>>>>>> which
sometimes have been incompatible. But you have never clearly >>>>>>>>>>>>>>> retracted your earlier opitions that conflict with your >>>>>>>>>>>>>>> present
ones.
All of the ideas that I have ever had about these things >>>>>>>>>>>>>> are now under the Proof Theoretic Semantics category. >>>>>>>>>>>>>> These ideas have evolved over time, yet their essence >>>>>>>>>>>>>> has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a >>>>>>>>>>>>> publishable
(or nearly publishable) article about them.
I have 50 pre prints articles. Because not one single> human >>>>>>>>>>>> being on the face of the Earth could understand
me I could not publish.
As far as I have seen, all interesting content in those articles >>>>>>>>>>> that have any is or depends on claims that should be proven but >>>>>>>>>>> aren't.
They are proven in Proof Theoretic Semantics
An aricle is not publishable unless it either contains the
proof or
has a pointer to an olready published proof.
Only now after 28 years am I acquiring the lingua Franca
terms-of-the-art of proof theoretic semantics such that
I can anchor my ideas in the foundational work of the
most respected authors in the field.
My issue with you guys is that you only spend 1%
of your concentration understanding me and the other
99% trying to artificially contrive some baseless
rebuttal.
THat "baseless" is false but otherwise, what is wrong is more
important than what is right. Of one ignores what is right one
mai fail to achieve what one could, but if one believs what is
wrong one may achieve a disaseter.
Proof-theoretic semantics is an alternative to truth-condition
semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
So far no one has even acknowledged that PTS is an alternative
to truth-conditional semantics. Several people have seemed
to same that no alternative can possibly exist.
You have not shown that there is any need for any alternative
semantics.
With dangerous lies that can destroy Democracy
and kill the planet with climate change having
an ultimate arbiter of truth would be useful.
Those who are able and willing to destroy democracy are able to provice
an ultimate arbiter of truth and usually do so. But they don't need any
proof theoretic semantics.
An ultimate arbiter of truth blows their whole game away.
THe point of the ultimate arbiter of truth is that the errors in the determinations of any alternative arbiter can be detected and similar
errors in future can be avoided with suitable admistrative or other
actions if regarded necessary.
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>> what: "grounded in the atomic base" means is less
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote:
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>>>>>You can find any number of terms. That doesn't mean >>>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 >>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody that PTS >>>>>>>>>>>>>>> somehow causes
Gödel's theorem not to hold, then cite an academic expert >>>>>>>>>>>>>>> who'll have
some credibility.
If they are mere gibberish words to you then you will >>>>>>>>>>>>>>>> not understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>>>>>> certainly don't
understand Gödel's Theorem, neither the theorem itself >>>>>>>>>>>>>>> nor any proof of
it.
than no rebuttal at all.
"grounded in the atomic base of PA" is an expression used >>>>>>>>>>>>> only by you, and it is one which you have never explicitly >>>>>>>>>>>>> defined, so the fault here certainly doesn't lie with Alan. >>>>>>>>>>>>> It's certainly not a 'verified fact' when you haven't even >>>>>>>>>>>>> adequately explained what it is that you mean.
All of knowledge expressed in language is structured as a >>>>>>>>>>>> tree of semantic relations specified syntactically between >>>>>>>>>>>> finite strings.
What makes you believe semantic relations that can be
structured as
a tree are sufficient to contain all knowledge that is
exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to >>>>>>>>> put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop >>>>>>> when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before
looking for a proof.
This is the same sort of thing as finding the defined
meaning of a word. If you cannot find its recursively
defined meaning then it never gains any meaning.
That does not follow. Words have meanings even without definitions.
You can't present the first definition unless you already have
meaningful words.
Typically the presentation of a formal theory begins with the
introduction of undefined symbols. But the symbols are not
fully meaningless. They get some amount of meaning from being
introduces as symbols of a particular syntactic category and
more from being used in the postulates of the theory.
On 26/06/2026 19:08, dbush wrote:
On 6/26/2026 10:24 AM, olcott wrote:
On 6/26/2026 8:57 AM, dbush wrote:
On 6/26/2026 9:45 AM, olcott wrote:
On 6/26/2026 8:20 AM, dbush wrote:
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms. That doesn't >>>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS Gödel >>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody that >>>>>>>>>>>>>>>>>>>> PTS somehow causes
Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>>>> you certainly don't
understand Gödel's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly >>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not a 'verified >>>>>>>>>>>>>>>>>> fact' when you haven't even adequately explained what >>>>>>>>>>>>>>>>>> it is that you mean.
All of knowledge expressed in language is structured as >>>>>>>>>>>>>>>>> a tree of semantic relations specified syntactically >>>>>>>>>>>>>>>>> between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a >>>>>>>>>>>> loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not
obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is
equal to its successor" has no meaning in Robinson Arithmetic.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof from within a
stipulated atomic base of its own axioms like the one
that you provided.
Then you agree that the above natural language sentence that is
semantically required to be either true or false has no meaning?
Your sentence would be what it always has been
a stipulated true sentence axiom.
False, as that statement is not one of the axioms of Robinson
arithmetic, but it is a statement in its language, and one that has
*only* an infinite connection to the axioms of that system.
What infinite connection? The statement is false in natural numbers,
which is one model of Robinson Arithmetic but not the only one.
In another model there may be a number that is its successor. There
may even be more than one such number.
By your logic, "no number is equal to its successor" has no meaning in
Robinson arithmetic.
On 27/06/2026 01:01, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning.
André
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable. Then to >>>>>>> put things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable in PA. >>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False. The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False. G is simply a sentence like ~∃x x>10 v x<5 but much more
complex.
"No number is equal to its successor" is a sentence in RA, and it
is true but unprovable in RA (or as your would call it, "out-of-
scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language
of Q. More formally, it is this:
~∃x x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms
you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
Nevertheless a sentence like ~∃x x=S(x) is in the language of Q and
that way in the theory.
On 26/06/2026 16:15, olcott wrote:
On 6/26/2026 1:45 AM, Mikko wrote:
On 25/06/2026 19:16, olcott wrote:
On 6/25/2026 2:29 AM, Mikko wrote:
On 25/06/2026 00:33, olcott wrote:
On 6/24/2026 5:13 AM, Mikko wrote:
On 23/06/2026 21:20, olcott wrote:
On 6/23/2026 12:32 PM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote:
[ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>> On 6/22/2026 1:42 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>> On 6/22/2026 10:48 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>
G is true.
I put it to you you're lying again. No reputable >>>>>>>>>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things. If Dag >>>>>>>>>>>>>>>>>>>>> Prawitz
really
did
"agree" (with whom?) that Gödel's sentence G is not >>>>>>>>>>>>>>>>>>>>> true in
Peano
Arithmetic, then produce a citation for this. >>>>>>>>>>>>>>>>>
He never gets to Gödel. He essentially says unprovable >>>>>>>>>>>>>>>>>>>> means untrue all the time for everything within his >>>>>>>>>>>>>>>>>>>> own Theory of Grounds of strict Proof Theoretic >>>>>>>>>>>>>>>>>>>> Semantics.
You won't understand it, but that _is_ essentially >>>>>>>>>>>>>>>>>>> Gödel's
Incompleteness
Theorem. It is a statement that any sufficiently >>>>>>>>>>>>>>>>>>> powerful
system can
express true things it can't prove. So Dag Prawitz, >>>>>>>>>>>>>>>>>>> had he been
saying
the things you falsely attributed to him, would >>>>>>>>>>>>>>>>>>> certainly have
"got" to
Gödel, and would have understood full well what he >>>>>>>>>>>>>>>>>>> was saying.
You did not pay close enough attention to my exact words. >>>>>>>>>>>>>>>>>I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>>
Yeah, I'm pretty sure that "Dag Prawitz says what Dag >>>>>>>>>>>>>>> Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag Prawitz >>>>>>>>>>>>>>> doesn't
say",
then looking a bit into his tremendous volume of works, >>>>>>>>>>>>>>> he talks about "natural deduction" then specifically an >>>>>>>>>>>>>>> "inverse
principle" so I think these are key aspects of
fundamental logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself, >>>>>>>>>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to >>>>>>>>>>>>>>> generate
new ad-
missible rules within a certain syntactic context. Some >>>>>>>>>>>>>>> fifteen years
later, the idea was taken up by Dag Prawitz to devise a >>>>>>>>>>>>>>> strategy of
normalization for natural deduction calculi (this being an >>>>>>>>>>>>>>> analogue of
Gentzen’s cut-elimination theorem for sequent calculi). >>>>>>>>>>>>>>> Later,
Prawitz
used the inversion principle again, attributing it with a >>>>>>>>>>>>>>> semantic
role.
Still working in natural deduction calculi, he formulated >>>>>>>>>>>>>>> a general
type
of schematic Introduction rules to be matched—thanks to >>>>>>>>>>>>>>> the idea
supporting the inversion principle — by a corresponding >>>>>>>>>>>>>>> general
schematic Elimination rule. This was an attempt to provide a >>>>>>>>>>>>>>> solution to
the problem suggested by the often quoted note of Gentzen. >>>>>>>>>>>>>>> According to
Gentzen “it should be possible to display the elimination >>>>>>>>>>>>>>> rules as
unique functions of the corresponding introduction rules >>>>>>>>>>>>>>> on the
basis of
certain requirements.” Many people have since worked on >>>>>>>>>>>>>>> this topic,
which can be appropriately seen as the birthplace of what >>>>>>>>>>>>>>> are now
referred to as “general elimination rules”, recently studied
thoroughly
by Sara Negri and Jan von Plato. In this paper, we >>>>>>>>>>>>>>> retrace the main
threads of this chapter of proof-theoretical
investigation, using
Lorenzen’s original framework as a general guide" >>>>>>>>>>>>>>>
Hm, "general elimination rules", seem derivable from De >>>>>>>>>>>>>>> Morgan's
laws,
and that being the usual account of naive deductive >>>>>>>>>>>>>>> analysis, then
since
"natural deduction", which here is held as part of the >>>>>>>>>>>>>>> theory
since it's naturally logical, then has for Gentzen that >>>>>>>>>>>>>>> besides
Kripke
afterward there's also Sheffer and Chwistek before, and >>>>>>>>>>>>>>> instead of
Montague for semantics there's Herbrand for semantics, >>>>>>>>>>>>>>> so, what to do
about "inversion principle" is here that the thea-theory >>>>>>>>>>>>>>> has that
it's
what subsumes "non-contradiction principle", here hoping >>>>>>>>>>>>>>> that the
interpretation aligns and thusly that "principle of >>>>>>>>>>>>>>> inversion"
wouldn't
need dis-ambiguation from "inversion principle". >>>>>>>>>>>>>>>
https://www.tandfonline.com/doi/
abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof- >>>>>>>>>>>>>>> theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the >>>>>>>>>>>>>>> foundation of
most
modern accounts of proof-theoretic semantics."
I already have a principle of inversion and furthermore a >>>>>>>>>>>>>>> principle of
thorough reason as subsuming principles of non- >>>>>>>>>>>>>>> contradiction and what
suffices, so, I'll be curious then about what to make of >>>>>>>>>>>>>>> Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as >>>>>>>>>>>>>>> old as the
oldest account of Western philosophy like Heraclitus with >>>>>>>>>>>>>>> dual
monism.
In fact by definition it's about the most basic aspect of >>>>>>>>>>>>>>> contemplation
and deliberation in abstraction of looking at both sides >>>>>>>>>>>>>>> of issues
and
resolving inductive impasses with analytical bridges after >>>>>>>>>>>>>>> complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as >>>>>>>>>>>>>>> one of the
characteristic features of Gentzen's intuitionistic natural >>>>>>>>>>>>>>> deduction.
In the literature on proof-theoretic semantics, this >>>>>>>>>>>>>>> principle is
often
coupled with another that is called the recovery >>>>>>>>>>>>>>> principle. By
adopting
the Computational Ludics framework, we reformulate these >>>>>>>>>>>>>>> principles
into
one and the same condition, which we call the harmony >>>>>>>>>>>>>>> condition. We
show
that this reformulation allows us to reveal two intuitive >>>>>>>>>>>>>>> ideas
standing
behind these principles: the idea of "containment" >>>>>>>>>>>>>>> present in the
inversion principle, and the idea that the recovery >>>>>>>>>>>>>>> principle is the
"converse" of the inversion principle. We also formulate >>>>>>>>>>>>>>> two other
conditions in the Computational Ludics framework, and we >>>>>>>>>>>>>>> show that
each
of them is equivalent to the harmony condition." >>>>>>>>>>>>>>>
The "ludicus" is Latin and for accounts of wisdom and >>>>>>>>>>>>>>> knowledge.
"In particular, by taking inspiration from the
Brouwer-Heyting-Kolmogorov explanation of logical >>>>>>>>>>>>>>> connectives,
proof-theoretic semantics rests on the idea that we know the >>>>>>>>>>>>>>> meaning of
a compound sentence when we know what counts as a >>>>>>>>>>>>>>> canonical proof of
it.
And if proofs are formalised within the framework of natural >>>>>>>>>>>>>>> deduction,
then a canonical proof of a sentence A is nothing but a >>>>>>>>>>>>>>> closed
derivation ending with an introduction rule of the main >>>>>>>>>>>>>>> connective
of A."
The "canonical proofs" are not unique, in any system >>>>>>>>>>>>>>> strong enough
to make for infinitary reasoning and super-classical results >>>>>>>>>>>>>>> requiring
analytical bridges about infinity and continuity. >>>>>>>>>>>>>>>
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6 >>>>>>>>>>>>>> That is the most important gist of his whole work. >>>>>>>>>>>>>>
He later goes on to develop and further elaborate his >>>>>>>>>>>>>> Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches >>>>>>>>>>>>>> Thomas Piecha & Peter Schroeder-Heister do this same sort of >>>>>>>>>>>>>> thing two different ways.
Furthermore I say there are "canonical proofs" of inductive >>>>>>>>>>>>> sorts that
make contradictions and thusly destroy each other.
Clearly you have no idea what Dag Prawitz means by
"canonical proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make >>>>>>>>>>>>> repairs
of what otherwise is flawed, or for hard constructivist >>>>>>>>>>>>> realist
structuralist model theorists: not-theories (examples of >>>>>>>>>>>>> wrong).
Induction and counter-induction contradict each other, it's >>>>>>>>>>> simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
So you are going to imply that I am incorrect
about Prolog when you yourself remain clueless about Prolog?
That would be dishonest.
No, pointing out that you are worng about Prolog when you are wrong >>>>>>> about Prolog is never dishohest.
That is correct Prolog and that is the
result of the correct run of correct Prolog.
Irrelevant. Nobody claimed there be Prolog errors in your queries.
Implying that I am wrong about Prolog without
pointing out any actual mistake is also DISHONEST.
How did Ross FInlayson imply that you were wrong about Prolog?
If an error is claimed then it must be specifically
pointed out otherwise the clam of error is dishonest.
Yet you claim that Ross Finlayson be dishonest without pointing
out what is dishonest in his words.
If anyone and everyone that claims that they found an
error and never points out what the error is and why
it is an error then they are merely a baseless denigrator.
If anyone and everyone that claims that someone is dishonest
never points out what the dishonesty is is and why it is
dishones then they are merely a baseless denigrator.
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:All of knowledge expressed in language is structured as a >>>>>>>>>>>>> tree of semantic relations specified syntactically between >>>>>>>>>>>>> finite strings.
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>>>>>>You can find any number of terms. That doesn't mean >>>>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 >>>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody that PTS >>>>>>>>>>>>>>>> somehow causes
Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you will >>>>>>>>>>>>>>>>> not understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>>>>>>> certainly don't
understand Gödel's Theorem, neither the theorem itself >>>>>>>>>>>>>>>> nor any proof of
it.
"grounded in the atomic base of PA" is an expression used >>>>>>>>>>>>>> only by you, and it is one which you have never explicitly >>>>>>>>>>>>>> defined, so the fault here certainly doesn't lie with >>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' when you >>>>>>>>>>>>>> haven't even adequately explained what it is that you mean. >>>>>>>>>>>>
What makes you believe semantic relations that can be >>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to >>>>>>>>>> put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop >>>>>>>> when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before
looking for a proof.
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q
then ~∃x x=S(x) is
ungrounded in the PTS atomic base of Q.
This does not mean undecidable or incomplete
it means that ~∃x x=S(x) is out-of-scope for Q.
This is the same sort of thing as finding the defined
meaning of a word. If you cannot find its recursively
defined meaning then it never gains any meaning.
That does not follow. Words have meanings even without definitions.
You can't present the first definition unless you already have
meaningful words.
A particular new word can only be defined in terms
of other existing words that already have definitions.
PTS works in a similar way. If ~∃x x=S(x)
cannot connect
to its meanings in Q the it remains undefined in Q.
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>>>>>>>You can find any number of terms. That doesn't mean >>>>>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 >>>>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody that PTS >>>>>>>>>>>>>>>>> somehow causes
Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you will >>>>>>>>>>>>>>>>>> not understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>>>>>>>> certainly don't
understand Gödel's Theorem, neither the theorem itself >>>>>>>>>>>>>>>>> nor any proof of
it.
"grounded in the atomic base of PA" is an expression used >>>>>>>>>>>>>>> only by you, and it is one which you have never >>>>>>>>>>>>>>> explicitly defined, so the fault here certainly doesn't >>>>>>>>>>>>>>> lie with Alan. It's certainly not a 'verified fact' when >>>>>>>>>>>>>>> you haven't even adequately explained what it is that you >>>>>>>>>>>>>>> mean.
All of knowledge expressed in language is structured as a >>>>>>>>>>>>>> tree of semantic relations specified syntactically between >>>>>>>>>>>>>> finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to >>>>>>>>>>> put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop >>>>>>>>> when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious >>>>> how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before
looking for a proof.
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms. That doesn't mean >>>>>>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 >>>>>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody that >>>>>>>>>>>>>>>>>> PTS somehow causes
Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you will >>>>>>>>>>>>>>>>>>> not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>> you certainly don't
understand Gödel's Theorem, neither the theorem itself >>>>>>>>>>>>>>>>>> nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly doesn't >>>>>>>>>>>>>>>> lie with Alan. It's certainly not a 'verified fact' when >>>>>>>>>>>>>>>> you haven't even adequately explained what it is that >>>>>>>>>>>>>>>> you mean.
All of knowledge expressed in language is structured as a >>>>>>>>>>>>>>> tree of semantic relations specified syntactically >>>>>>>>>>>>>>> between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop >>>>>>>>>> when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious >>>>>> how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before
looking for a proof.
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q.
On 6/27/2026 2:27 PM, olcott wrote:
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms. That doesn't >>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 >>>>>>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody that >>>>>>>>>>>>>>>>>>> PTS somehow causes
Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>>> you certainly don't
understand Gödel's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly doesn't >>>>>>>>>>>>>>>>> lie with Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>> when you haven't even adequately explained what it is >>>>>>>>>>>>>>>>> that you mean.
All of knowledge expressed in language is structured as >>>>>>>>>>>>>>>> a tree of semantic relations specified syntactically >>>>>>>>>>>>>>>> between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a >>>>>>>>>>> loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious >>>>>>> how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before
looking for a proof.
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known.
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms. That doesn't >>>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS Gödel >>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody that >>>>>>>>>>>>>>>>>>>> PTS somehow causes
Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>>>> you certainly don't
understand Gödel's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly >>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not a 'verified >>>>>>>>>>>>>>>>>> fact' when you haven't even adequately explained what >>>>>>>>>>>>>>>>>> it is that you mean.
All of knowledge expressed in language is structured as >>>>>>>>>>>>>>>>> a tree of semantic relations specified syntactically >>>>>>>>>>>>>>>>> between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a >>>>>>>>>>>> loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not
obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before
looking for a proof.
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known.
is semantic nonsense in Q?
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms. That doesn't >>>>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS Gödel >>>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody that >>>>>>>>>>>>>>>>>>>>> PTS somehow causes
Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>>>>> you certainly don't
understand Gödel's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly >>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not a 'verified >>>>>>>>>>>>>>>>>>> fact' when you haven't even adequately explained what >>>>>>>>>>>>>>>>>>> it is that you mean.
All of knowledge expressed in language is structured >>>>>>>>>>>>>>>>>> as a tree of semantic relations specified >>>>>>>>>>>>>>>>>> syntactically between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting stuck in >>>>>>>>>>>>> a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not >>>>>>>>> obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before >>>>>>> looking for a proof.
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known.
Which has the semantic meaning "no number is equal to its successor" as
per the definition of Q.
is semantic nonsense in Q?
False, see above.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms. That doesn't >>>>>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS Gödel >>>>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody >>>>>>>>>>>>>>>>>>>>>> that PTS somehow causes
Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, >>>>>>>>>>>>>>>>>>>>>> and you certainly don't
understand Gödel's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not a >>>>>>>>>>>>>>>>>>>> 'verified fact' when you haven't even adequately >>>>>>>>>>>>>>>>>>>> explained what it is that you mean.
All of knowledge expressed in language is structured >>>>>>>>>>>>>>>>>>> as a tree of semantic relations specified >>>>>>>>>>>>>>>>>>> syntactically between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would >>>>>>>>>>>>>>>> one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting stuck in >>>>>>>>>>>>>> a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent >>>>>>>>>>>> loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>> PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability >>>>>>>>>>> or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not >>>>>>>>>> obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before >>>>>>>> looking for a proof.
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known.
Which has the semantic meaning "no number is equal to its successor"
as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
It is more accurate to say it this way
than to say that it is semantically incoherent in Q.
It is great that you brought this up: ~∃x x=S(x).
We can have much clearer communication about that
then we can about Gödel's 1931 Incompleteness.
is semantic nonsense in Q?
False, see above.
On 6/27/2026 3:01 PM, olcott wrote:
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote:
All of knowledge expressed in language is structured >>>>>>>>>>>>>>>>>>>> as a tree of semantic relations specified >>>>>>>>>>>>>>>>>>>> syntactically between finite strings.On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms. That doesn't >>>>>>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS Gödel >>>>>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody >>>>>>>>>>>>>>>>>>>>>>> that PTS somehow causes
Gödel's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, >>>>>>>>>>>>>>>>>>>>>>> and you certainly don't
understand Gödel's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one which >>>>>>>>>>>>>>>>>>>>> you have never explicitly defined, so the fault >>>>>>>>>>>>>>>>>>>>> here certainly doesn't lie with Alan. It's >>>>>>>>>>>>>>>>>>>>> certainly not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>> even adequately explained what it is that you mean. >>>>>>>>>>>>>>>>>>>
What makes you believe semantic relations that can be >>>>>>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that >>>>>>>>>>>>>>>>>>> is exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would >>>>>>>>>>>>>>>>> one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting stuck >>>>>>>>>>>>>>> in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent >>>>>>>>>>>>> loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>> PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability >>>>>>>>>>>> or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not >>>>>>>>>>> obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before >>>>>>>>> looking for a proof.
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known.
Which has the semantic meaning "no number is equal to its successor"
as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]What makes you believe semantic relations that can >>>>>>>>>>>>>>>>>>>> be structured as
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms. That >>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>> understanding them.
The above is the key reason why under PTS Gödel >>>>>>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody >>>>>>>>>>>>>>>>>>>>>>>> that PTS somehow causes
Gödel's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have
some credibility.
If they are mere gibberish words to you then >>>>>>>>>>>>>>>>>>>>>>>>> you will not understand.
You don't understand Proof-theoritic Semantics, >>>>>>>>>>>>>>>>>>>>>>>> and you certainly don't
understand Gödel's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one which >>>>>>>>>>>>>>>>>>>>>> you have never explicitly defined, so the fault >>>>>>>>>>>>>>>>>>>>>> here certainly doesn't lie with Alan. It's >>>>>>>>>>>>>>>>>>>>>> certainly not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is that you mean. >>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge that >>>>>>>>>>>>>>>>>>>> is exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would >>>>>>>>>>>>>>>>>> one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting stuck >>>>>>>>>>>>>>>> in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent >>>>>>>>>>>>>> loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>
compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>> PTS just coherently connects the semantic meanings
expressed in language together into one coherent body >>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>> or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not >>>>>>>>>>>> obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before >>>>>>>>>> looking for a proof.
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known.
Which has the semantic meaning "no number is equal to its successor"
as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms. That doesn't mean >>>>>>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 >>>>>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody that >>>>>>>>>>>>>>>>>> PTS somehow causes
Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you will >>>>>>>>>>>>>>>>>>> not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>> you certainly don't
understand Gödel's Theorem, neither the theorem itself >>>>>>>>>>>>>>>>>> nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly doesn't >>>>>>>>>>>>>>>> lie with Alan. It's certainly not a 'verified fact' when >>>>>>>>>>>>>>>> you haven't even adequately explained what it is that >>>>>>>>>>>>>>>> you mean.
All of knowledge expressed in language is structured as a >>>>>>>>>>>>>>> tree of semantic relations specified syntactically >>>>>>>>>>>>>>> between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop >>>>>>>>>> when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious >>>>>> how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before
looking for a proof.
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q.
PTS also says FINITE sequence.
I cannot use the convoluted way that PTS says it in
all of their different author-by-author terms-of-the-art
and still be understood.
The above version is very close to the way that one
PTS author would say it and does convey the same
gist of meanings that other PTS authors accept.
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]What makes you believe semantic relations that can >>>>>>>>>>>>>>>>>>>>> be structured as
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>> understand
In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms. That >>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them.
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>> Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no respect for >>>>>>>>>>>>>>>>>>>>>>>>> or understanding of the
truth. If you really want to persuade anybody >>>>>>>>>>>>>>>>>>>>>>>>> that PTS somehow causes
Gödel's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have
some credibility.
If they are mere gibberish words to you then >>>>>>>>>>>>>>>>>>>>>>>>>> you will not understand.
You don't understand Proof-theoritic Semantics, >>>>>>>>>>>>>>>>>>>>>>>>> and you certainly don't
understand Gödel's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one which >>>>>>>>>>>>>>>>>>>>>>> you have never explicitly defined, so the fault >>>>>>>>>>>>>>>>>>>>>>> here certainly doesn't lie with Alan. It's >>>>>>>>>>>>>>>>>>>>>>> certainly not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is that you mean. >>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge that >>>>>>>>>>>>>>>>>>>>> is exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would >>>>>>>>>>>>>>>>>>> one try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting stuck >>>>>>>>>>>>>>>>> in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent >>>>>>>>>>>>>>> loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>
compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>>> or mathematical incompleteness.
Looking for a proof does not need any semantics so it is >>>>>>>>>>>>> not obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before >>>>>>>>>>> looking for a proof.
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known.
Which has the semantic meaning "no number is equal to its
successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
On 2026-06-27 12:27, olcott wrote:
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms. That doesn't >>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 >>>>>>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody that >>>>>>>>>>>>>>>>>>> PTS somehow causes
Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>>> you certainly don't
understand Gödel's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly doesn't >>>>>>>>>>>>>>>>> lie with Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>> when you haven't even adequately explained what it is >>>>>>>>>>>>>>>>> that you mean.
All of knowledge expressed in language is structured as >>>>>>>>>>>>>>>> a tree of semantic relations specified syntactically >>>>>>>>>>>>>>>> between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a >>>>>>>>>>> loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious >>>>>>> how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before
looking for a proof.
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q.
PTS also says FINITE sequence.
I cannot use the convoluted way that PTS says it in
all of their different author-by-author terms-of-the-art
and still be understood.
If PTS is so convoluted, why should we take your word for it that you
are actually interpreting it correctly?
The above version is very close to the way that one
PTS author would say it and does convey the same
gist of meanings that other PTS authors accept.
very close to doesn't mean the same as. Why don't you actually quote the author in question so we can see for ourselves exactly how close to it
your formulation is?
André
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>>>> or mathematical incompleteness.
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>> would one try to
On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
What makes you believe semantic relations that can >>>>>>>>>>>>>>>>>>>>>> be structured asAll of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>> understand
In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday.
You can find any number of terms. That >>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them.
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no respect for >>>>>>>>>>>>>>>>>>>>>>>>>> or understanding of the
truth. If you really want to persuade anybody >>>>>>>>>>>>>>>>>>>>>>>>>> that PTS somehow causes
Gödel's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you then >>>>>>>>>>>>>>>>>>>>>>>>>>> you will not understand.
You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>> it.
what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one which >>>>>>>>>>>>>>>>>>>>>>>> you have never explicitly defined, so the fault >>>>>>>>>>>>>>>>>>>>>>>> here certainly doesn't lie with Alan. It's >>>>>>>>>>>>>>>>>>>>>>>> certainly not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>> prevent loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>
Looking for a proof does not need any semantics so it is >>>>>>>>>>>>>> not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>
It should be obvious that finding a proof does not happen >>>>>>>>>>>> before
looking for a proof.
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known.
Which has the semantic meaning "no number is equal to its
successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>>>>> or mathematical incompleteness.
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>> would one try to
What makes you believe semantic relations that >>>>>>>>>>>>>>>>>>>>>>> can be structured asIt is a verified fact that Gödel's G is >>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday.
You can find any number of terms. That >>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them.
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no respect for >>>>>>>>>>>>>>>>>>>>>>>>>>> or understanding of the
truth. If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you then >>>>>>>>>>>>>>>>>>>>>>>>>>>> you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so the >>>>>>>>>>>>>>>>>>>>>>>>> fault here certainly doesn't lie with Alan. >>>>>>>>>>>>>>>>>>>>>>>>> It's certainly not a 'verified fact' when you >>>>>>>>>>>>>>>>>>>>>>>>> haven't even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>> that you mean.
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>> prevent loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>
Looking for a proof does not need any semantics so it is >>>>>>>>>>>>>>> not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>
It should be obvious that finding a proof does not happen >>>>>>>>>>>>> before
looking for a proof.
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>
Which has the semantic meaning "no number is equal to its
successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q "no number
is equal to its successor" is not semantically valid, it must be
discarded as useless.
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>>>>>> or mathematical incompleteness.
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>>> would one try toWhat makes you believe semantic relations that >>>>>>>>>>>>>>>>>>>>>>>> can be structured asIt is a verified fact that Gödel's G is >>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday.
You can find any number of terms. That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them.
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no respect >>>>>>>>>>>>>>>>>>>>>>>>>>>> for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means is >>>>>>>>>>>>>>>>>>>>>>>>>>> less
than no rebuttal at all.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so >>>>>>>>>>>>>>>>>>>>>>>>>> the fault here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean.
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>> prevent loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>
Looking for a proof does not need any semantics so it is >>>>>>>>>>>>>>>> not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>
It should be obvious that finding a proof does not happen >>>>>>>>>>>>>> before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>
Which has the semantic meaning "no number is equal to its
successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q "no number
is equal to its successor" is not semantically valid, it must be
discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~∃x x=S(x) is untrue
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>>>>>>> or mathematical incompleteness.
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>>> completes.They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>>>> would one try toWhat makes you believe semantic relations that >>>>>>>>>>>>>>>>>>>>>>>>> can be structured as"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so >>>>>>>>>>>>>>>>>>>>>>>>>>> the fault here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean.In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday.It is a verified fact that Gödel's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
You can find any number of terms. That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no respect >>>>>>>>>>>>>>>>>>>>>>>>>>>>> for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means is >>>>>>>>>>>>>>>>>>>>>>>>>>>> less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>> prevent loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>
Looking for a proof does not need any semantics so it >>>>>>>>>>>>>>>>> is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not happen >>>>>>>>>>>>>>> before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>
Which has the semantic meaning "no number is equal to its
successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q "no
number is equal to its successor" is not semantically valid, it must
be discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~∃x x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but with
different words.
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>> undecidability
On 6/24/2026 5:00 AM, Mikko wrote:If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>> prevent loops.
On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>>>> completes.They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>>>>> would one try toWhat makes you believe semantic relations that >>>>>>>>>>>>>>>>>>>>>>>>>> can be structured asAll of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so >>>>>>>>>>>>>>>>>>>>>>>>>>>> the fault here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
You can find any number of terms. That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no respect >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means >>>>>>>>>>>>>>>>>>>>>>>>>>>>> is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>
or mathematical incompleteness.
Looking for a proof does not need any semantics so it >>>>>>>>>>>>>>>>>> is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q "no
number is equal to its successor" is not semantically valid, it must
be discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~∃x x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but with
different words.
So everyone says that ~∃x x=S(x)
is simply untrue
in Q and does nor derive either undecidability or
incompleteness?
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>> Essentially
On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>>> prevent loops.
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>>>>> completes.They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>>>>>> would one try toWhat makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>> some language?All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so >>>>>>>>>>>>>>>>>>>>>>>>>>>>> the fault here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
You can find any number of terms. That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no respect >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it >>>>>>>>>>>>>>>>>>> is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is >>>>>>> unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q "no
number is equal to its successor" is not semantically valid, it
must be discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~∃x x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but with
different words.
So everyone says that ~∃x x=S(x)
which has the semantic meaning "no number is equal to its successor" as
per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is incomplete because
"no number is equal to its successor" is unprovable in Q.
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>> Essentially
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>>>> prevent loops.It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>>>>>> completes.They use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>> why would one try toAll of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>> strings."grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> so the fault here certainly doesn't lie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with Alan. It's certainly not a 'verified >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fact' when you haven't even adequately >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explained what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:It is a verified fact that Gödel's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so >>>>>>>>>>>>>>>>>>>> it is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is >>>>>>>> unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q "no
number is equal to its successor" is not semantically valid, it
must be discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~∃x x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but with
different words.
So everyone says that ~∃x x=S(x)
which has the semantic meaning "no number is equal to its successor"
as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is incomplete
because "no number is equal to its successor" is unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost caught up
to Wittgenstein (1937) on this point. They are
very much farther along on related points.
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>> EssentiallyIf you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>>>>> prevent loops.It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and >>>>>>>>>>>>>>>>>>>>>>>>>> neverThey use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>>> why would one try to"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a 'verified fact' when you haven't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> adequately explained what it is that you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean.In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:It is a verified fact that Gödel's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> strings.
What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so >>>>>>>>>>>>>>>>>>>>> it is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>> in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is >>>>>>>>> unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q "no >>>>>>> number is equal to its successor" is not semantically valid, it >>>>>>> must be discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~∃x x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but with
different words.
So everyone says that ~∃x x=S(x)
which has the semantic meaning "no number is equal to its successor"
as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is incomplete
because "no number is equal to its successor" is unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an infinite sequence of inference steps between it and the axioms of the system?
Similarly, what term would you use to describe a sentence whose inverse
has an infinite sequence of inference steps between it and the axioms of
the system?
Proof Theoretic Semantics has almost caught up
to Wittgenstein (1937) on this point. They are
very much farther along on related points.
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>> EssentiallyIf you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>>>>> prevent loops.It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and >>>>>>>>>>>>>>>>>>>>>>>>>> neverThey use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>>> why would one try to"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a 'verified fact' when you haven't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> adequately explained what it is that you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean.In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:It is a verified fact that Gödel's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> strings.
What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so >>>>>>>>>>>>>>>>>>>>> it is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>> in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is >>>>>>>>> unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q "no >>>>>>> number is equal to its successor" is not semantically valid, it >>>>>>> must be discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~∃x x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but with
different words.
So everyone says that ~∃x x=S(x)
which has the semantic meaning "no number is equal to its successor"
as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is incomplete
because "no number is equal to its successor" is unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an infinite sequence of inference steps between it and the axioms of the system?
Similarly, what term would you use to describe a sentence whose inverse
has an infinite sequence of inference steps between it and the axioms of
the system?
Proof Theoretic Semantics has almost caught up
to Wittgenstein (1937) on this point. They are
very much farther along on related points.
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>> EssentiallyIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and >>>>>>>>>>>>>>>>>>>>>>>>>>> neverThey use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>>>> why would one try to"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean.[ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically between >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finite strings.
What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent >>>>>>>>>>>>>>>>>>>>>>> body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so >>>>>>>>>>>>>>>>>>>>>> it is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is >>>>>>>>>> unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>>
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q "no >>>>>>>> number is equal to its successor" is not semantically valid, it >>>>>>>> must be discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~∃x x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but with
different words.
So everyone says that ~∃x x=S(x)
which has the semantic meaning "no number is equal to its successor"
as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is incomplete
because "no number is equal to its successor" is unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an infinite
sequence of inference steps between it and the axioms of the system?
untrue and unfalse.
Similarly, what term would you use to describe a sentence whose
inverse has an infinite sequence of inference steps between it and the
axioms of the system?
I don't know what you mean by inverse.
If you mean negation you should have said negation.
Proof Theoretic Semantics has almost caught up
to Wittgenstein (1937) on this point. They are
very much farther along on related points.
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>>> happen before
In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>Looking for a proof does not need any semantics >>>>>>>>>>>>>>>>>>>>>>> so it is not obviousIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and >>>>>>>>>>>>>>>>>>>>>>>>>>>> neverThey use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>>>>> why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?All of knowledge expressed in language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>[ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the >>>>>>>>>>>>>>>>>>>>>>>>> proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent >>>>>>>>>>>>>>>>>>>>>>>> body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) >>>>>>>>>>> is unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>>>
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q "no >>>>>>>>> number is equal to its successor" is not semantically valid, it >>>>>>>>> must be discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~∃x x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but with >>>>>>> different words.
So everyone says that ~∃x x=S(x)
which has the semantic meaning "no number is equal to its
successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is incomplete
because "no number is equal to its successor" is unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an
infinite sequence of inference steps between it and the axioms of the
system?
untrue and unfalse.
What about the more general case, i.e. a term for a statement that has
*any* sequence of inference steps, either finite or infinite, between it
and the axioms of the system? And what would the negation of such a statement be called?
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:i.e., ~∃x x=S(x) is unprovable is Q, as is commonly >>>>>>>>>>>>>>>>>> known.
On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>>>> happen beforeLooking for a proof does not need any semantics >>>>>>>>>>>>>>>>>>>>>>>> so it is not obviousIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for concepts. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:All of knowledge expressed in language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>[ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
the proof gets stuck in an infinite loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>> and never
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the >>>>>>>>>>>>>>>>>>>>>>>>>> proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>
how switching to another semantics could improve >>>>>>>>>>>>>>>>>>>>>>>> it.
In proof theoretic semantics an expression only >>>>>>>>>>>>>>>>>>>>>>> gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>> its successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) >>>>>>>>>>>> is unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>>>>
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q >>>>>>>>>> "no number is equal to its successor" is not semantically >>>>>>>>>> valid, it must be discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~∃x x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but with >>>>>>>> different words.
So everyone says that ~∃x x=S(x)
which has the semantic meaning "no number is equal to its
successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is incomplete
because "no number is equal to its successor" is unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an
infinite sequence of inference steps between it and the axioms of
the system?
untrue and unfalse.
What about the more general case, i.e. a term for a statement that has
*any* sequence of inference steps, either finite or infinite, between
it and the axioms of the system? And what would the negation of such
a statement be called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
On 6/27/2026 5:24 PM, olcott wrote:
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:i.e., ~∃x x=S(x) is unprovable is Q, as is commonly >>>>>>>>>>>>>>>>>>> known.
On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
It should be obvious that finding a proof does >>>>>>>>>>>>>>>>>>>>>>> not happen beforeLooking for a proof does not need any semantics >>>>>>>>>>>>>>>>>>>>>>>>> so it is not obviousIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for concepts. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>All of knowledge expressed in language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
"grounded in the atomic base of PA" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is an expression used only by you, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and it is one which you have never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explicitly defined, so the fault here >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly doesn't lie with Alan. It's >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly not a 'verified fact' when >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> do not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof- >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoritic Semantics, and you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
the proof gets stuck in an infinite loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and never
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the >>>>>>>>>>>>>>>>>>>>>>>>>>> proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic >>>>>>>>>>>>>>>>>>>>>>>>>> meanings
expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>
how switching to another semantics could >>>>>>>>>>>>>>>>>>>>>>>>> improve it.
In proof theoretic semantics an expression only >>>>>>>>>>>>>>>>>>>>>>>> gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>>> its successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) >>>>>>>>>>>>> is unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>>>>>
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q >>>>>>>>>>> "no number is equal to its successor" is not semantically >>>>>>>>>>> valid, it must be discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~∃x x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but >>>>>>>>> with different words.
So everyone says that ~∃x x=S(x)
which has the semantic meaning "no number is equal to its
successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is incomplete >>>>>>> because "no number is equal to its successor" is unprovable in Q. >>>>>>>
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an
infinite sequence of inference steps between it and the axioms of
the system?
untrue and unfalse.
What about the more general case, i.e. a term for a statement that
has *any* sequence of inference steps, either finite or infinite,
between it and the axioms of the system? And what would the negation
of such a statement be called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
That's not the definition I asked for.
What term would you use for a statement that has *any* sequence of
inference steps, either finite or infinite, between it and the axioms of
the system?
What term would you use for the negation of the above statement?
On 6/27/2026 4:50 PM, dbush wrote:
On 6/27/2026 5:24 PM, olcott wrote:
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:And because PTS claims the semantically valid sentence in Q >>>>>>>>>>>> "no number is equal to its successor" is not semantically >>>>>>>>>>>> valid, it must be discarded as useless.
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:i.e., ~∃x x=S(x) is unprovable is Q, as is commonly >>>>>>>>>>>>>>>>>>>> known.
On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
It should be obvious that finding a proof does >>>>>>>>>>>>>>>>>>>>>>>> not happen beforeLooking for a proof does not need any >>>>>>>>>>>>>>>>>>>>>>>>>> semantics so it is not obvious >>>>>>>>>>>>>>>>>>>>>>>>>> how switching to another semantics could >>>>>>>>>>>>>>>>>>>>>>>>>> improve it.If you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for concepts. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>All of knowledge expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language is structured as a tree of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic relations specified >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
"grounded in the atomic base of PA" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is an expression used only by you, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and it is one which you have never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explicitly defined, so the fault >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fact' when you haven't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> adequately explained what it is that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> do not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You can find any number of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> terms. That doesn't mean you're >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof- >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoritic Semantics, and you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> neither the theorem itself nor any >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
the proof gets stuck in an infinite loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and never
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the >>>>>>>>>>>>>>>>>>>>>>>>>>>> proof.
Truth Conditional Semantics (TCS) <is> >>>>>>>>>>>>>>>>>>>>>>>>>>> incoherent
compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic >>>>>>>>>>>>>>>>>>>>>>>>>>> meanings
expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>>
In proof theoretic semantics an expression only >>>>>>>>>>>>>>>>>>>>>>>>> gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x >>>>>>>>>>>>>>>>>>>>> x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>>>> its successor" as per the definition of Q. >>>>>>>>>>>>>>>>>>
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known. >>>>>>>>>>>>>>>>
False, as by definition, Q is incomplete because ~∃x >>>>>>>>>>>>>> x=S(x) is unprovable / out-of-scope / not semantically >>>>>>>>>>>>>> grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!! >>>>>>>>>>>>
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~∃x x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but >>>>>>>>>> with different words.
So everyone says that ~∃x x=S(x)
which has the semantic meaning "no number is equal to its
successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is incomplete >>>>>>>> because "no number is equal to its successor" is unprovable in Q. >>>>>>>>
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an
infinite sequence of inference steps between it and the axioms of >>>>>> the system?
untrue and unfalse.
What about the more general case, i.e. a term for a statement that
has *any* sequence of inference steps, either finite or infinite,
between it and the axioms of the system? And what would the
negation of such a statement be called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
That's not the definition I asked for.
What term would you use for a statement that has *any* sequence of
inference steps, either finite or infinite, between it and the axioms
of the system?
"true on the basis of meaning expressed in language"
reliably computable for the entire body of GENERAL knowledge.
Is the limit of the topic of all my posts.
Infinite inference steps are off topic.
What term would you use for the negation of the above statement?
Does not have any proof finite or infinite?
That would be untrue and possibly nonsense.
On 6/27/2026 6:11 PM, olcott wrote:
On 6/27/2026 4:50 PM, dbush wrote:
On 6/27/2026 5:24 PM, olcott wrote:
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:And because PTS claims the semantically valid sentence in Q >>>>>>>>>>>>> "no number is equal to its successor" is not semantically >>>>>>>>>>>>> valid, it must be discarded as useless.
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of >>>>>>>>>>>>>>>> incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:Which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>>>>> its successor" as per the definition of Q. >>>>>>>>>>>>>>>>>>>
On 6/27/2026 2:27 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:01 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Is it commonly known that ~∃x x=S(x) >>>>>>>>>>>>>>>>>>>
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly >>>>>>>>>>>>>>>>>>>>> known.There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>>>It should be obvious that finding a proof does >>>>>>>>>>>>>>>>>>>>>>>>> not happen beforeLooking for a proof does not need any >>>>>>>>>>>>>>>>>>>>>>>>>>> semantics so it is not obvious >>>>>>>>>>>>>>>>>>>>>>>>>>> how switching to another semantics could >>>>>>>>>>>>>>>>>>>>>>>>>>> improve it.If you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops. >>>>>>>>>>>>>>>>>>>>>>>>>>>>> In most cases that also prevents finding >>>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for concepts. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>All of knowledge expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language is structured as a tree of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic relations specified >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>"grounded in the atomic base of PA" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is an expression used only by you, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and it is one which you have never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explicitly defined, so the fault >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoretic atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You can find any number of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> terms. That doesn't mean you're >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> do not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If they are mere gibberish words >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to you then you will not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You don't understand Proof- >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoritic Semantics, and you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> neither the theorem itself nor >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
the proof gets stuck in an infinite loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and never
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Truth Conditional Semantics (TCS) <is> >>>>>>>>>>>>>>>>>>>>>>>>>>>> incoherent
compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>> meanings
expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>>>
In proof theoretic semantics an expression >>>>>>>>>>>>>>>>>>>>>>>>>> only gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q >>>>>>>>>>>>>>>>>>>>>>>> from
~∃x x=S(x) to the axioms of Q >>>>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x >>>>>>>>>>>>>>>>>>>>>> x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>>
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known. >>>>>>>>>>>>>>>>>
False, as by definition, Q is incomplete because ~∃x >>>>>>>>>>>>>>> x=S(x) is unprovable / out-of-scope / not semantically >>>>>>>>>>>>>>> grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!! >>>>>>>>>>>>>
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~∃x x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but >>>>>>>>>>> with different words.
So everyone says that ~∃x x=S(x)
which has the semantic meaning "no number is equal to its
successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is incomplete >>>>>>>>> because "no number is equal to its successor" is unprovable in Q. >>>>>>>>>
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an
infinite sequence of inference steps between it and the axioms of >>>>>>> the system?
untrue and unfalse.
What about the more general case, i.e. a term for a statement that
has *any* sequence of inference steps, either finite or infinite,
between it and the axioms of the system? And what would the
negation of such a statement be called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
That's not the definition I asked for.
What term would you use for a statement that has *any* sequence of
inference steps, either finite or infinite, between it and the axioms
of the system?
"true on the basis of meaning expressed in language"
reliably computable for the entire body of GENERAL knowledge.
Is the limit of the topic of all my posts.
Infinite inference steps are off topic.
Why are you so reluctant to provide a simple term?
It seems you're attempting to engage in Newspeak.
https://en.wikipedia.org/wiki/Newspeak
What term would you use for the negation of the above statement?
Does not have any proof finite or infinite?
That would be untrue and possibly nonsense.
On 6/27/2026 5:15 PM, dbush wrote:
On 6/27/2026 6:11 PM, olcott wrote:
On 6/27/2026 4:50 PM, dbush wrote:
On 6/27/2026 5:24 PM, olcott wrote:
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:And because PTS claims the semantically valid sentence in >>>>>>>>>>>>>> Q "no number is equal to its successor" is not
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of >>>>>>>>>>>>>>>>> incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:Which has the semantic meaning "no number is equal >>>>>>>>>>>>>>>>>>>> to its successor" as per the definition of Q. >>>>>>>>>>>>>>>>>>>>
On 6/27/2026 2:27 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:01 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You can find any number of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> terms. That doesn't mean >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS Gödel 1931 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I don't believe you. You have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> no respect for or understanding >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then cite an academic expert >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If they are mere gibberish >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words to you then you will not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You don't understand Proof- >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoritic Semantics, and you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> neither the theorem itself nor >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is a verified fact that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you do not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Is it commonly known that ~∃x x=S(x) >>>>>>>>>>>>>>>>>>>>
i.e., ~∃x x=S(x) is unprovable is Q, as is >>>>>>>>>>>>>>>>>>>>>> commonly known.There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>>>>It should be obvious that finding a proof does >>>>>>>>>>>>>>>>>>>>>>>>>> not happen beforeLooking for a proof does not need any >>>>>>>>>>>>>>>>>>>>>>>>>>>> semantics so it is not obvious >>>>>>>>>>>>>>>>>>>>>>>>>>>> how switching to another semantics could >>>>>>>>>>>>>>>>>>>>>>>>>>>> improve it.If you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In most cases that also prevents finding >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> concepts. But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>"grounded in the atomic base of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PA" is an expression used only by >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you, and it is one which you have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> never explicitly defined, so the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fault here certainly doesn't lie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with Alan. It's certainly not a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>All of knowledge expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language is structured as a tree of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic relations specified >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
the proof gets stuck in an infinite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop and never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> prevent getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Truth Conditional Semantics (TCS) <is> >>>>>>>>>>>>>>>>>>>>>>>>>>>>> incoherent
compared to Proof Theoretic Semantics >>>>>>>>>>>>>>>>>>>>>>>>>>>>> (PTS). Essentially
PTS just coherently connects the semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>> meanings
expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
In proof theoretic semantics an expression >>>>>>>>>>>>>>>>>>>>>>>>>>> only gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q >>>>>>>>>>>>>>>>>>>>>>>>> from
~∃x x=S(x) to the axioms of Q >>>>>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x >>>>>>>>>>>>>>>>>>>>>>> x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>>>
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known. >>>>>>>>>>>>>>>>>>
False, as by definition, Q is incomplete because ~∃x >>>>>>>>>>>>>>>> x=S(x) is unprovable / out-of-scope / not semantically >>>>>>>>>>>>>>>> grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!! >>>>>>>>>>>>>>
semantically valid, it must be discarded as useless. >>>>>>>>>>>>>>
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
i.e. proven
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~∃x x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but >>>>>>>>>>>> with different words.
So everyone says that ~∃x x=S(x)
which has the semantic meaning "no number is equal to its >>>>>>>>>> successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is
incomplete because "no number is equal to its successor" is >>>>>>>>>> unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an >>>>>>>> infinite sequence of inference steps between it and the axioms >>>>>>>> of the system?
untrue and unfalse.
What about the more general case, i.e. a term for a statement that >>>>>> has *any* sequence of inference steps, either finite or infinite, >>>>>> between it and the axioms of the system? And what would the
negation of such a statement be called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
That's not the definition I asked for.
What term would you use for a statement that has *any* sequence of
inference steps, either finite or infinite, between it and the
axioms of the system?
"true on the basis of meaning expressed in language"
reliably computable for the entire body of GENERAL knowledge.
Is the limit of the topic of all my posts.
Infinite inference steps are off topic.
Why are you so reluctant to provide a simple term?
OFF-TOPIC <is> THE TERM.
It seems you're attempting to engage in Newspeak.
https://en.wikipedia.org/wiki/Newspeak
What term would you use for the negation of the above statement?
Does not have any proof finite or infinite?
That would be untrue and possibly nonsense.
On 6/27/2026 6:18 PM, olcott wrote:
On 6/27/2026 5:15 PM, dbush wrote:
On 6/27/2026 6:11 PM, olcott wrote:
On 6/27/2026 4:50 PM, dbush wrote:
On 6/27/2026 5:24 PM, olcott wrote:
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:i.e. proven
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:And because PTS claims the semantically valid sentence in >>>>>>>>>>>>>>> Q "no number is equal to its successor" is not
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of >>>>>>>>>>>>>>>>>> incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:29 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:27 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:01 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You can find any number of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> terms. That doesn't mean >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The above is the key reason >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> why under PTS Gödel 1931 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I don't believe you. You have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> no respect for or understanding >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then cite an academic expert >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If they are mere gibberish >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words to you then you will not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You don't understand Proof- >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoritic Semantics, and you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> neither the theorem itself nor >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is a verified fact that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you do not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal >>>>>>>>>>>>>>>>>>>>> to its successor" as per the definition of Q. >>>>>>>>>>>>>>>>>>>>>Is it commonly known that ~∃x x=S(x) >>>>>>>>>>>>>>>>>>>>>i.e., ~∃x x=S(x) is unprovable is Q, as is >>>>>>>>>>>>>>>>>>>>>>> commonly known.There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>>>>>It should be obvious that finding a proof >>>>>>>>>>>>>>>>>>>>>>>>>>> does not happen beforeLooking for a proof does not need any >>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantics so it is not obvious >>>>>>>>>>>>>>>>>>>>>>>>>>>>> how switching to another semantics could >>>>>>>>>>>>>>>>>>>>>>>>>>>>> improve it.If you mean not looking elsewhere that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> may indeed prevent loops. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In most cases that also prevents finding >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> concepts. But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> all knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>"grounded in the atomic base of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PA" is an expression used only by >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you, and it is one which you have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> never explicitly defined, so the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fault here certainly doesn't lie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with Alan. It's certainly not a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>All of knowledge expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language is structured as a tree >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of semantic relations specified >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
the proof gets stuck in an infinite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop and never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> prevent getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Truth Conditional Semantics (TCS) <is> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> incoherent
compared to Proof Theoretic Semantics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (PTS). Essentially >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS just coherently connects the semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meanings
expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In proof theoretic semantics an expression >>>>>>>>>>>>>>>>>>>>>>>>>>>> only gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in >>>>>>>>>>>>>>>>>>>>>>>>>> Q from
~∃x x=S(x) to the axioms of Q >>>>>>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x >>>>>>>>>>>>>>>>>>>>>>>> x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>>>>
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known. >>>>>>>>>>>>>>>>>>>
False, as by definition, Q is incomplete because ~∃x >>>>>>>>>>>>>>>>> x=S(x) is unprovable / out-of-scope / not semantically >>>>>>>>>>>>>>>>> grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!! >>>>>>>>>>>>>>>
semantically valid, it must be discarded as useless. >>>>>>>>>>>>>>>
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's >>>>>>>>>>>>>> system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there. >>>>>>>>>>>>>> For the most part they stop at semantically grounded >>>>>>>>>>>>>
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~∃x x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever
heard of Wittgenstein.
So again, you're saying the same thing as everyone else but >>>>>>>>>>>>> with different words.
So everyone says that ~∃x x=S(x)
which has the semantic meaning "no number is equal to its >>>>>>>>>>> successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is
incomplete because "no number is equal to its successor" is >>>>>>>>>>> unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an >>>>>>>>> infinite sequence of inference steps between it and the axioms >>>>>>>>> of the system?
untrue and unfalse.
What about the more general case, i.e. a term for a statement
that has *any* sequence of inference steps, either finite or
infinite, between it and the axioms of the system? And what
would the negation of such a statement be called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
That's not the definition I asked for.
What term would you use for a statement that has *any* sequence of
inference steps, either finite or infinite, between it and the
axioms of the system?
"true on the basis of meaning expressed in language"
reliably computable for the entire body of GENERAL knowledge.
Is the limit of the topic of all my posts.
Infinite inference steps are off topic.
Why are you so reluctant to provide a simple term?
OFF-TOPIC <is> THE TERM.
So we've established that "off-topic" means "a statement that has *any* sequence of inference steps, either finite or infinite, between it and
the axioms of the system".
On 6/27/2026 5:21 PM, dbush wrote:
On 6/27/2026 6:18 PM, olcott wrote:
On 6/27/2026 5:15 PM, dbush wrote:
On 6/27/2026 6:11 PM, olcott wrote:
On 6/27/2026 4:50 PM, dbush wrote:
On 6/27/2026 5:24 PM, olcott wrote:
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:i.e. proven
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:And because PTS claims the semantically valid sentence >>>>>>>>>>>>>>>> in Q "no number is equal to its successor" is not >>>>>>>>>>>>>>>> semantically valid, it must be discarded as useless. >>>>>>>>>>>>>>>>
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of >>>>>>>>>>>>>>>>>>> incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:29 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:27 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:01 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You can find any number of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> terms. That doesn't mean >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The above is the key reason >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> why under PTS Gödel 1931 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I don't believe you. You have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> no respect for or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then cite an academic expert >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If they are mere gibberish >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words to you then you will >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You don't understand Proof- >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoritic Semantics, and you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> neither the theorem itself nor >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is a verified fact that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you do not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounded in the atomic base of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PA" is an expression used only >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> by you, and it is one which you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have never explicitly defined, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explained what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal >>>>>>>>>>>>>>>>>>>>>> to its successor" as per the definition of Q. >>>>>>>>>>>>>>>>>>>>>>Is it commonly known that ~∃x x=S(x) >>>>>>>>>>>>>>>>>>>>>>i.e., ~∃x x=S(x) is unprovable is Q, as is >>>>>>>>>>>>>>>>>>>>>>>> commonly known.There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>>>>>>It should be obvious that finding a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>> does not happen before >>>>>>>>>>>>>>>>>>>>>>>>>>>> looking for a proof.Looking for a proof does not need any >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantics so it is not obvious >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> how switching to another semantics could >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> improve it.If you mean not looking elsewhere that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> may indeed prevent loops. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In most cases that also prevents finding >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>How can any ordering of knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> prevent getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop and never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> completes. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>They use a tree structure for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> concepts. But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>All of knowledge expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language is structured as a tree >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of semantic relations specified >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> syntactically between finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> all knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Truth Conditional Semantics (TCS) <is> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> incoherent
compared to Proof Theoretic Semantics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (PTS). Essentially >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS just coherently connects the semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> meanings
expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> without undecidability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In proof theoretic semantics an expression >>>>>>>>>>>>>>>>>>>>>>>>>>>>> only gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no sequence of inference steps in >>>>>>>>>>>>>>>>>>>>>>>>>>> Q from
~∃x x=S(x) to the axioms of Q >>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then >>>>>>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>>>>>
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known. >>>>>>>>>>>>>>>>>>>>
False, as by definition, Q is incomplete because ~∃x >>>>>>>>>>>>>>>>>> x=S(x) is unprovable / out-of-scope / not semantically >>>>>>>>>>>>>>>>>> grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!! >>>>>>>>>>>>>>>>
No you are just not bothering to pay 100% totally >>>>>>>>>>>>>>> complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's >>>>>>>>>>>>>>> system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there. >>>>>>>>>>>>>>> For the most part they stop at semantically grounded >>>>>>>>>>>>>>
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS
notion ~∃x x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever >>>>>>>>>>>>>>> heard of Wittgenstein.
So again, you're saying the same thing as everyone else >>>>>>>>>>>>>> but with different words.
So everyone says that ~∃x x=S(x)
which has the semantic meaning "no number is equal to its >>>>>>>>>>>> successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is
incomplete because "no number is equal to its successor" is >>>>>>>>>>>> unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an >>>>>>>>>> infinite sequence of inference steps between it and the axioms >>>>>>>>>> of the system?
untrue and unfalse.
What about the more general case, i.e. a term for a statement >>>>>>>> that has *any* sequence of inference steps, either finite or
infinite, between it and the axioms of the system? And what >>>>>>>> would the negation of such a statement be called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
That's not the definition I asked for.
What term would you use for a statement that has *any* sequence of >>>>>> inference steps, either finite or infinite, between it and the
axioms of the system?
"true on the basis of meaning expressed in language"
reliably computable for the entire body of GENERAL knowledge.
Is the limit of the topic of all my posts.
Infinite inference steps are off topic.
Why are you so reluctant to provide a simple term?
OFF-TOPIC <is> THE TERM.
So we've established that "off-topic" means "a statement that has
*any* sequence of inference steps, either finite or infinite, between
it and the axioms of the system".
The ones that have infinite steps out outside the
body of knowledge and off topic for that reason.
On 6/27/2026 3:05 AM, Mikko wrote:
On 27/06/2026 01:01, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning.
André
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable. Then to >>>>>>>> put things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable in PA. >>>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False. The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False. G is simply a sentence like ~∃x x>10 v x<5 but much more
complex.
"No number is equal to its successor" is a sentence in RA, and it
is true but unprovable in RA (or as your would call it, "out-of-
scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language
of Q. More formally, it is this:
~∃x x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms
you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
Nevertheless a sentence like ~∃x x=S(x) is in the language of Q and
that way in the theory.
Colorless green ideas sleep furiously
was composed by Noam Chomsky in his 1957 book
Syntactic Structures as an example of a sentence
that is grammatically well-formed, but semantically
nonsensical.
Proving that syntax is not enough.
On 6/27/2026 6:29 PM, olcott wrote:
On 6/27/2026 5:21 PM, dbush wrote:
On 6/27/2026 6:18 PM, olcott wrote:
On 6/27/2026 5:15 PM, dbush wrote:
On 6/27/2026 6:11 PM, olcott wrote:
On 6/27/2026 4:50 PM, dbush wrote:
On 6/27/2026 5:24 PM, olcott wrote:
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:i.e. proven
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:And because PTS claims the semantically valid sentence >>>>>>>>>>>>>>>>> in Q "no number is equal to its successor" is not >>>>>>>>>>>>>>>>> semantically valid, it must be discarded as useless. >>>>>>>>>>>>>>>>>
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:39 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:38 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:29 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:27 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:01 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You can find any number of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> terms. That doesn't mean >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The above is the key reason >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> why under PTS Gödel 1931 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I don't believe you. You >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have no respect for or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then cite an academic expert >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If they are mere gibberish >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words to you then you will >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You don't understand Proof- >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoritic Semantics, and you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> neither the theorem itself >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is a verified fact that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you do not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounded in the atomic base of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PA" is an expression used only >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> by you, and it is one which you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have never explicitly defined, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> All of knowledge expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language is structured as a tree >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of semantic relations specified >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> syntactically between finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Yet never gets to undecidable or in any sense of >>>>>>>>>>>>>>>>>>>> incomplete.
Which has the semantic meaning "no number is >>>>>>>>>>>>>>>>>>>>>>> equal to its successor" as per the definition of Q. >>>>>>>>>>>>>>>>>>>>>>>Is it commonly known that ~∃x x=S(x) >>>>>>>>>>>>>>>>>>>>>>>i.e., ~∃x x=S(x) is unprovable is Q, as is >>>>>>>>>>>>>>>>>>>>>>>>> commonly known.There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>>>>>>>It should be obvious that finding a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>> does not happen before >>>>>>>>>>>>>>>>>>>>>>>>>>>>> looking for a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>Looking for a proof does not need any >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantics so it is not obvious >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> how switching to another semantics could >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> improve it.Truth Conditional Semantics (TCS) <is> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> incoherentIf you mean not looking elsewhere that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> may indeed prevent loops. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In most cases that also prevents >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finding the proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>How can any ordering of knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> prevent getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop and never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> completes. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>They use a tree structure for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> concepts. But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> all knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The CycL language and the Cyc >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
compared to Proof Theoretic Semantics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (PTS). Essentially >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS just coherently connects the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic meanings >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> without undecidability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In proof theoretic semantics an expression >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no sequence of inference steps >>>>>>>>>>>>>>>>>>>>>>>>>>>> in Q from
~∃x x=S(x) to the axioms of Q >>>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then >>>>>>>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>>>>>>
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known. >>>>>>>>>>>>>>>>>>>>>
False, as by definition, Q is incomplete because ~∃x >>>>>>>>>>>>>>>>>>> x=S(x) is unprovable / out-of-scope / not >>>>>>>>>>>>>>>>>>> semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!! >>>>>>>>>>>>>>>>>
No you are just not bothering to pay 100% totally >>>>>>>>>>>>>>>> complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said: >>>>>>>>>>>>>>>> proved in Russell's system; and 'false in Russell's >>>>>>>>>>>>>>>> system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there. >>>>>>>>>>>>>>>> For the most part they stop at semantically grounded >>>>>>>>>>>>>>>
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS >>>>>>>>>>>>>>>> notion ~∃x x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever >>>>>>>>>>>>>>>> heard of Wittgenstein.
So again, you're saying the same thing as everyone else >>>>>>>>>>>>>>> but with different words.
So everyone says that ~∃x x=S(x)
which has the semantic meaning "no number is equal to its >>>>>>>>>>>>> successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or
incompleteness?
It does derive incompleteness, as by definition Q is >>>>>>>>>>>>> incomplete because "no number is equal to its successor" is >>>>>>>>>>>>> unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has an >>>>>>>>>>> infinite sequence of inference steps between it and the >>>>>>>>>>> axioms of the system?
untrue and unfalse.
What about the more general case, i.e. a term for a statement >>>>>>>>> that has *any* sequence of inference steps, either finite or >>>>>>>>> infinite, between it and the axioms of the system? And what >>>>>>>>> would the negation of such a statement be called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
That's not the definition I asked for.
What term would you use for a statement that has *any* sequence >>>>>>> of inference steps, either finite or infinite, between it and the >>>>>>> axioms of the system?
"true on the basis of meaning expressed in language"
reliably computable for the entire body of GENERAL knowledge.
Is the limit of the topic of all my posts.
Infinite inference steps are off topic.
Why are you so reluctant to provide a simple term?
OFF-TOPIC <is> THE TERM.
So we've established that "off-topic" means "a statement that has
*any* sequence of inference steps, either finite or infinite, between
it and the axioms of the system".
The ones that have infinite steps out outside the
body of knowledge and off topic for that reason.
So you're claiming the sentence "no number is equal to its successor" in
Q is "off topic".
Rejected, as it is a semantically valid sentence in the language of Q.
On 06/27/2026 08:47 AM, polcott wrote:
On 6/27/2026 3:05 AM, Mikko wrote:
On 27/06/2026 01:01, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning.
André
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope. >>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable. Then to >>>>>>>>> put things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable in PA. >>>>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False. The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False. G is simply a sentence like ~∃x x>10 v x<5 but much more
complex.
"No number is equal to its successor" is a sentence in RA, and it >>>>>>> is true but unprovable in RA (or as your would call it, "out-of- >>>>>>> scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language
of Q. More formally, it is this:
~∃x x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms >>>>> you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
Nevertheless a sentence like ~∃x x=S(x) is in the language of Q and
that way in the theory.
Colorless green ideas sleep furiously
was composed by Noam Chomsky in his 1957 book
Syntactic Structures as an example of a sentence
that is grammatically well-formed, but semantically
nonsensical.
Proving that syntax is not enough.
"Colorless green" is actually two colors
since there's a dual-tristimulus colorspace
the chromatic and the prismatic,
a fact of the science of the theory of light and color,
of which you are ignorant, then making for a reasonable
reading of the usual apocryphal comment.
Then, ideas can sleep however they want.
On 6/27/2026 5:33 PM, dbush wrote:
On 6/27/2026 6:29 PM, olcott wrote:
On 6/27/2026 5:21 PM, dbush wrote:
On 6/27/2026 6:18 PM, olcott wrote:
On 6/27/2026 5:15 PM, dbush wrote:
On 6/27/2026 6:11 PM, olcott wrote:
On 6/27/2026 4:50 PM, dbush wrote:
On 6/27/2026 5:24 PM, olcott wrote:
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:i.e. proven
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:And because PTS claims the semantically valid sentence >>>>>>>>>>>>>>>>>> in Q "no number is equal to its successor" is not >>>>>>>>>>>>>>>>>> semantically valid, it must be discarded as useless. >>>>>>>>>>>>>>>>>>
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:39 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:38 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:29 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:27 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:01 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You can find any number of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> terms. That doesn't mean >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The above is the key reason >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> why under PTS Gödel 1931 >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I don't believe you. You >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have no respect for or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to persuade anybody that PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then cite an academic expert >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If they are mere gibberish >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words to you then you will >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You don't understand Proof- >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoritic Semantics, and you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> neither the theorem itself >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is a verified fact that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That you do not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounded in the atomic base >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of PA" is an expression used >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explicitly defined, so the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fault here certainly doesn't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> haven't even adequately >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explained what it is that you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> All of knowledge expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language is structured as a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> all knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Yet never gets to undecidable or in any sense of >>>>>>>>>>>>>>>>>>>>> incomplete.
Which has the semantic meaning "no number is >>>>>>>>>>>>>>>>>>>>>>>> equal to its successor" as per the definition of Q. >>>>>>>>>>>>>>>>>>>>>>>>Is it commonly known that ~∃x x=S(x) >>>>>>>>>>>>>>>>>>>>>>>>i.e., ~∃x x=S(x) is unprovable is Q, as is >>>>>>>>>>>>>>>>>>>>>>>>>> commonly known.There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>>>>>>>>It should be obvious that finding a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> does not happen before >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> looking for a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Looking for a proof does not need any >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantics so it is not obvious >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> how switching to another semantics could >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> improve it.Truth Conditional Semantics (TCS) <is> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> incoherentIf you mean not looking elsewhere that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> may indeed prevent loops. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In most cases that also prevents >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finding the proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>How can any ordering of knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> prevent getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> loop and never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> completes. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The CycL language and the Cyc >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>They use a tree structure for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> concepts. But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
compared to Proof Theoretic Semantics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (PTS). Essentially >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS just coherently connects the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic meanings >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> coherent body >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of general knowledge. It does this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> without undecidability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In proof theoretic semantics an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression only gains >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no sequence of inference steps >>>>>>>>>>>>>>>>>>>>>>>>>>>>> in Q from
~∃x x=S(x) to the axioms of Q >>>>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference >>>>>>>>>>>>>>>>>>>>>>>>>>> steps
in Q from ~∃x x=S(x) to the axioms of Q then >>>>>>>>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>>>>>>>
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known. >>>>>>>>>>>>>>>>>>>>>>
False, as by definition, Q is incomplete because ~∃x >>>>>>>>>>>>>>>>>>>> x=S(x) is unprovable / out-of-scope / not >>>>>>>>>>>>>>>>>>>> semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!! >>>>>>>>>>>>>>>>>>
No you are just not bothering to pay 100% totally >>>>>>>>>>>>>>>>> complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said: >>>>>>>>>>>>>>>>> proved in Russell's system; and 'false in Russell's >>>>>>>>>>>>>>>>> system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there. >>>>>>>>>>>>>>>>> For the most part they stop at semantically grounded >>>>>>>>>>>>>>>>
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS >>>>>>>>>>>>>>>>> notion ~∃x x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever >>>>>>>>>>>>>>>>> heard of Wittgenstein.
So again, you're saying the same thing as everyone else >>>>>>>>>>>>>>>> but with different words.
So everyone says that ~∃x x=S(x)
which has the semantic meaning "no number is equal to its >>>>>>>>>>>>>> successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or >>>>>>>>>>>>>>> incompleteness?
It does derive incompleteness, as by definition Q is >>>>>>>>>>>>>> incomplete because "no number is equal to its successor" >>>>>>>>>>>>>> is unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has >>>>>>>>>>>> an infinite sequence of inference steps between it and the >>>>>>>>>>>> axioms of the system?
untrue and unfalse.
What about the more general case, i.e. a term for a statement >>>>>>>>>> that has *any* sequence of inference steps, either finite or >>>>>>>>>> infinite, between it and the axioms of the system? And what >>>>>>>>>> would the negation of such a statement be called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
That's not the definition I asked for.
What term would you use for a statement that has *any* sequence >>>>>>>> of inference steps, either finite or infinite, between it and >>>>>>>> the axioms of the system?
"true on the basis of meaning expressed in language"
reliably computable for the entire body of GENERAL knowledge.
Is the limit of the topic of all my posts.
Infinite inference steps are off topic.
Why are you so reluctant to provide a simple term?
OFF-TOPIC <is> THE TERM.
So we've established that "off-topic" means "a statement that has
*any* sequence of inference steps, either finite or infinite,
between it and the axioms of the system".
The ones that have infinite steps out outside the
body of knowledge and off topic for that reason.
So you're claiming the sentence "no number is equal to its successor"
in Q is "off topic".
Rejected, as it is a semantically valid sentence in the language of Q.
If there is no finite sequence of inference steps
between x and the axioms of Q then PTS stipulates
that x is not semantically valid in Q.
On 6/27/2026 6:44 PM, olcott wrote:
On 6/27/2026 5:33 PM, dbush wrote:
On 6/27/2026 6:29 PM, olcott wrote:
On 6/27/2026 5:21 PM, dbush wrote:
On 6/27/2026 6:18 PM, olcott wrote:
On 6/27/2026 5:15 PM, dbush wrote:
On 6/27/2026 6:11 PM, olcott wrote:
On 6/27/2026 4:50 PM, dbush wrote:
On 6/27/2026 5:24 PM, olcott wrote:
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:i.e. proven
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:And because PTS claims the semantically valid >>>>>>>>>>>>>>>>>>> sentence in Q "no number is equal to its successor" >>>>>>>>>>>>>>>>>>> is not semantically valid, it must be discarded as >>>>>>>>>>>>>>>>>>> useless.
On 6/27/2026 3:16 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:04 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 3:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:39 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:38 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:29 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:27 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:01 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You can find any number >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of terms. That doesn't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The above is the key >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> reason why under PTS Gödel >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I don't believe you. You >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have no respect for or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to persuade anybody that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> hold, then cite an academic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If they are mere gibberish >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> words to you then you will >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You don't understand Proof- >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoritic Semantics, and >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> neither the theorem itself >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is a verified fact that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That you do not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounded in the atomic base >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of PA" is an expression used >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explicitly defined, so the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fault here certainly doesn't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you haven't even adequately >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explained what it is that you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> All of knowledge expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language is structured as a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> contain all knowledge that is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The CycL language and the Cyc >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Yet never gets to undecidable or in any sense of >>>>>>>>>>>>>>>>>>>>>> incomplete.Which has the semantic meaning "no number is >>>>>>>>>>>>>>>>>>>>>>>>> equal to its successor" as per the definition >>>>>>>>>>>>>>>>>>>>>>>>> of Q.Is it commonly known that ~∃x x=S(x) >>>>>>>>>>>>>>>>>>>>>>>>>i.e., ~∃x x=S(x) is unprovable is Q, as is >>>>>>>>>>>>>>>>>>>>>>>>>>> commonly known.There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>It should be obvious that finding a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> does not happen before >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> looking for a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>In proof theoretic semantics an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression only gains >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Looking for a proof does not need any >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantics so it is not obvious >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> how switching to another semantics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> could improve it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Truth Conditional Semantics (TCS) <is> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> incoherent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (PTS). Essentially >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS just coherently connects the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic meanings >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> one coherent body >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of general knowledge. It does this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> without undecidability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>If you mean not looking elsewhere >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that may indeed prevent loops. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In most cases that also prevents >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finding the proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>How can any ordering of knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> prevent getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>They use a tree structure for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> concepts. But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> infinite loop and never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> completes. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no sequence of inference steps >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in Q from
~∃x x=S(x) to the axioms of Q >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference >>>>>>>>>>>>>>>>>>>>>>>>>>>> steps
in Q from ~∃x x=S(x) to the axioms of Q then >>>>>>>>>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>>>>>>>>
Since there are no steps in Q that affirm ~∃x >>>>>>>>>>>>>>>>>>>>>>>> x=S(x)
in Q it is an open question in Q and not a >>>>>>>>>>>>>>>>>>>>>>>> confirmed
statement in Q.
In other words, unproven as is commonly known. >>>>>>>>>>>>>>>>>>>>>>>
False, as by definition, Q is incomplete because >>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) is unprovable / out-of-scope / not >>>>>>>>>>>>>>>>>>>>> semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!! >>>>>>>>>>>>>>>>>>>
No you are just not bothering to pay 100% totally >>>>>>>>>>>>>>>>>> complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said: >>>>>>>>>>>>>>>>>> proved in Russell's system; and 'false in Russell's >>>>>>>>>>>>>>>>>> system' means: the opposite has been proved >>>>>>>>>>>>>>>>>> in Russell's system
Proof Theoretic Semantics has almost gotten there. >>>>>>>>>>>>>>>>>> For the most part they stop at semantically grounded >>>>>>>>>>>>>>>>>
and never quite get all the way to True.
For Wittgenstein's slight extension of the PTS >>>>>>>>>>>>>>>>>> notion ~∃x x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever >>>>>>>>>>>>>>>>>> heard of Wittgenstein.
So again, you're saying the same thing as everyone else >>>>>>>>>>>>>>>>> but with different words.
So everyone says that ~∃x x=S(x)
which has the semantic meaning "no number is equal to its >>>>>>>>>>>>>>> successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or >>>>>>>>>>>>>>>> incompleteness?
It does derive incompleteness, as by definition Q is >>>>>>>>>>>>>>> incomplete because "no number is equal to its successor" >>>>>>>>>>>>>>> is unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's >>>>>>>>>>>>>> system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has >>>>>>>>>>>>> an infinite sequence of inference steps between it and the >>>>>>>>>>>>> axioms of the system?
untrue and unfalse.
What about the more general case, i.e. a term for a statement >>>>>>>>>>> that has *any* sequence of inference steps, either finite or >>>>>>>>>>> infinite, between it and the axioms of the system? And what >>>>>>>>>>> would the negation of such a statement be called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
That's not the definition I asked for.
What term would you use for a statement that has *any* sequence >>>>>>>>> of inference steps, either finite or infinite, between it and >>>>>>>>> the axioms of the system?
"true on the basis of meaning expressed in language"
reliably computable for the entire body of GENERAL knowledge.
Is the limit of the topic of all my posts.
Infinite inference steps are off topic.
Why are you so reluctant to provide a simple term?
OFF-TOPIC <is> THE TERM.
So we've established that "off-topic" means "a statement that has
*any* sequence of inference steps, either finite or infinite,
between it and the axioms of the system".
The ones that have infinite steps out outside the
body of knowledge and off topic for that reason.
So you're claiming the sentence "no number is equal to its successor"
in Q is "off topic".
Rejected, as it is a semantically valid sentence in the language of Q.
If there is no finite sequence of inference steps
between x and the axioms of Q then PTS stipulates
that x is not semantically valid in Q.
And since x = "no number is equal to its successor" is semantically
valid as per the definition of Q, PTS must be discarded as useless.
On 6/27/2026 5:53 PM, dbush wrote:
On 6/27/2026 6:44 PM, olcott wrote:
On 6/27/2026 5:33 PM, dbush wrote:
On 6/27/2026 6:29 PM, olcott wrote:
On 6/27/2026 5:21 PM, dbush wrote:
On 6/27/2026 6:18 PM, olcott wrote:
On 6/27/2026 5:15 PM, dbush wrote:
On 6/27/2026 6:11 PM, olcott wrote:
On 6/27/2026 4:50 PM, dbush wrote:
On 6/27/2026 5:24 PM, olcott wrote:
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:i.e. proven
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:And because PTS claims the semantically valid >>>>>>>>>>>>>>>>>>>> sentence in Q "no number is equal to its successor" >>>>>>>>>>>>>>>>>>>> is not semantically valid, it must be discarded as >>>>>>>>>>>>>>>>>>>> useless.
On 6/27/2026 3:16 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:04 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 3:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:39 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:38 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:29 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:27 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:01 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You can find any number >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of terms. That doesn't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The above is the key >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I don't believe you. You >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have no respect for or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> to persuade anybody that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If they are mere >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You don't understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Proof- theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is a verified fact that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That you do not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounded in the atomic base >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of PA" is an expression used >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explicitly defined, so the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fault here certainly doesn't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> lie with Alan. It's >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly not a 'verified >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fact' when you haven't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> adequately explained what it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> All of knowledge expressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> language is structured as a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What makes you believe >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic relations that can be >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> contain all knowledge that is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The CycL language and the Cyc >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> They use a tree structure for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> concepts. But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Yet never gets to undecidable or in any sense of >>>>>>>>>>>>>>>>>>>>>>> incomplete.Which has the semantic meaning "no number is >>>>>>>>>>>>>>>>>>>>>>>>>> equal to its successor" as per the definition >>>>>>>>>>>>>>>>>>>>>>>>>> of Q.Is it commonly known that ~∃x x=S(x) >>>>>>>>>>>>>>>>>>>>>>>>>>i.e., ~∃x x=S(x) is unprovable is Q, as is >>>>>>>>>>>>>>>>>>>>>>>>>>>> commonly known.There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It should be obvious that finding a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proof does not happen before >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> looking for a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>In proof theoretic semantics an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression only gains >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Looking for a proof does not need any >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantics so it is not obvious >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> how switching to another semantics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> could improve it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Truth Conditional Semantics (TCS) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (PTS). Essentially >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS just coherently connects the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic meanings >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> one coherent body >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of general knowledge. It does this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> without undecidability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>If you mean not looking elsewhere >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that may indeed prevent loops. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In most cases that also prevents >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finding the proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> infinite loop and never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> completes. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>How can any ordering of knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> prevent getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no sequence of inference >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> steps in Q from
~∃x x=S(x) to the axioms of Q >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference >>>>>>>>>>>>>>>>>>>>>>>>>>>>> steps
in Q from ~∃x x=S(x) to the axioms of Q >>>>>>>>>>>>>>>>>>>>>>>>>>>>> then ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
Since there are no steps in Q that affirm ~∃x >>>>>>>>>>>>>>>>>>>>>>>>> x=S(x)
in Q it is an open question in Q and not a >>>>>>>>>>>>>>>>>>>>>>>>> confirmed
statement in Q.
In other words, unproven as is commonly known. >>>>>>>>>>>>>>>>>>>>>>>>
False, as by definition, Q is incomplete because >>>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) is unprovable / out-of-scope / not >>>>>>>>>>>>>>>>>>>>>> semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!! >>>>>>>>>>>>>>>>>>>>
No you are just not bothering to pay 100% totally >>>>>>>>>>>>>>>>>>> complete attention to every single word. >>>>>>>>>>>>>>>>>>>
Wittgenstein
'True in Russell's system' means, as was said: >>>>>>>>>>>>>>>>>>> proved in Russell's system; and 'false in Russell's >>>>>>>>>>>>>>>>>>> system' means: the opposite has been proved >>>>>>>>>>>>>>>>>>> in Russell's system
Proof Theoretic Semantics has almost gotten there. >>>>>>>>>>>>>>>>>>> For the most part they stop at semantically grounded >>>>>>>>>>>>>>>>>>
and never quite get all the way to True. >>>>>>>>>>>>>>>>>>>
For Wittgenstein's slight extension of the PTS >>>>>>>>>>>>>>>>>>> notion ~∃x x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever >>>>>>>>>>>>>>>>>>> heard of Wittgenstein.
So again, you're saying the same thing as everyone >>>>>>>>>>>>>>>>>> else but with different words.
So everyone says that ~∃x x=S(x)
which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>> its successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or >>>>>>>>>>>>>>>>> incompleteness?
It does derive incompleteness, as by definition Q is >>>>>>>>>>>>>>>> incomplete because "no number is equal to its successor" >>>>>>>>>>>>>>>> is unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's >>>>>>>>>>>>>>> system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that has >>>>>>>>>>>>>> an infinite sequence of inference steps between it and the >>>>>>>>>>>>>> axioms of the system?
untrue and unfalse.
What about the more general case, i.e. a term for a
statement that has *any* sequence of inference steps, either >>>>>>>>>>>> finite or infinite, between it and the axioms of the
system? And what would the negation of such a statement be >>>>>>>>>>>> called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
That's not the definition I asked for.
What term would you use for a statement that has *any*
sequence of inference steps, either finite or infinite,
between it and the axioms of the system?
"true on the basis of meaning expressed in language"
reliably computable for the entire body of GENERAL knowledge. >>>>>>>>> Is the limit of the topic of all my posts.
Infinite inference steps are off topic.
Why are you so reluctant to provide a simple term?
OFF-TOPIC <is> THE TERM.
So we've established that "off-topic" means "a statement that has >>>>>> *any* sequence of inference steps, either finite or infinite,
between it and the axioms of the system".
The ones that have infinite steps out outside the
body of knowledge and off topic for that reason.
So you're claiming the sentence "no number is equal to its
successor" in Q is "off topic".
Rejected, as it is a semantically valid sentence in the language of Q.
If there is no finite sequence of inference steps
between x and the axioms of Q then PTS stipulates
that x is not semantically valid in Q.
And since x = "no number is equal to its successor" is semantically
valid as per the definition of Q, PTS must be discarded as useless.
So you also have no idea what Stipulative definition is.
A stipulative definition is a type of definition in which
a new or currently existing term is given a new specific meaning
https://en.wikipedia.org/wiki/Stipulative_definition
On 6/27/2026 7:27 PM, olcott wrote:
On 6/27/2026 5:53 PM, dbush wrote:
On 6/27/2026 6:44 PM, olcott wrote:
On 6/27/2026 5:33 PM, dbush wrote:
On 6/27/2026 6:29 PM, olcott wrote:If there is no finite sequence of inference steps
On 6/27/2026 5:21 PM, dbush wrote:
On 6/27/2026 6:18 PM, olcott wrote:
On 6/27/2026 5:15 PM, dbush wrote:
On 6/27/2026 6:11 PM, olcott wrote:
On 6/27/2026 4:50 PM, dbush wrote:
On 6/27/2026 5:24 PM, olcott wrote:
On 6/27/2026 3:59 PM, dbush wrote:
On 6/27/2026 4:52 PM, olcott wrote:
On 6/27/2026 3:30 PM, dbush wrote:
On 6/27/2026 4:27 PM, olcott wrote:
On 6/27/2026 3:22 PM, dbush wrote:
On 6/27/2026 4:17 PM, olcott wrote:
On 6/27/2026 3:11 PM, dbush wrote:
On 6/27/2026 4:04 PM, olcott wrote:
On 6/27/2026 2:54 PM, dbush wrote:i.e. proven
On 6/27/2026 3:40 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:23 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 3:16 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:04 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 3:01 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:39 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:38 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:29 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:27 PM, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 1:01 PM, dbush wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You can find any number >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of terms. That doesn't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The above is the key >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I don't believe you. You >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> have no respect for or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> want to persuade anybody >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> If they are mere >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You don't understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Proof- theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is a verified fact that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That you do not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounded in the atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you, and it is one which >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> 'verified fact' when you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> haven't even adequately >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explained what it is that >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> All of knowledge expressed >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in language is structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What makes you believe >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic relations that can >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> contain all knowledge that is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The CycL language and the Cyc >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> They use a tree structure for >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> concepts. But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It must at least be a directed >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> infinite loop and never >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> completes. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
And because PTS claims the semantically valid >>>>>>>>>>>>>>>>>>>>> sentence in Q "no number is equal to its successor" >>>>>>>>>>>>>>>>>>>>> is not semantically valid, it must be discarded as >>>>>>>>>>>>>>>>>>>>> useless.Yet never gets to undecidable or in any sense of >>>>>>>>>>>>>>>>>>>>>>>> incomplete.Which has the semantic meaning "no number is >>>>>>>>>>>>>>>>>>>>>>>>>>> equal to its successor" as per the definition >>>>>>>>>>>>>>>>>>>>>>>>>>> of Q.Is it commonly known that ~∃x x=S(x) >>>>>>>>>>>>>>>>>>>>>>>>>>>i.e., ~∃x x=S(x) is unprovable is Q, as is >>>>>>>>>>>>>>>>>>>>>>>>>>>>> commonly known.There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It should be obvious that finding a >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> proof does not happen before >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> looking for a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>In proof theoretic semantics an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression only gains >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Looking for a proof does not need any >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantics so it is not obvious >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> how switching to another semantics >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> could improve it. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Truth Conditional Semantics (TCS) >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics (PTS). Essentially >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS just coherently connects the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> semantic meanings >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> one coherent body >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> of general knowledge. It does this >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> without undecidability >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>If you mean not looking elsewhere >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that may indeed prevent loops. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In most cases that also prevents >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finding the proof. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>How can any ordering of knowledge >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> prevent getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>By looking upward in a type >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no sequence of inference >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> steps in Q from >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> inference steps
in Q from ~∃x x=S(x) to the axioms of Q >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Since there are no steps in Q that affirm ~∃x >>>>>>>>>>>>>>>>>>>>>>>>>> x=S(x)
in Q it is an open question in Q and not a >>>>>>>>>>>>>>>>>>>>>>>>>> confirmed
statement in Q.
In other words, unproven as is commonly known. >>>>>>>>>>>>>>>>>>>>>>>>>
False, as by definition, Q is incomplete because >>>>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) is unprovable / out-of-scope / not >>>>>>>>>>>>>>>>>>>>>>> semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!! >>>>>>>>>>>>>>>>>>>>>
No you are just not bothering to pay 100% totally >>>>>>>>>>>>>>>>>>>> complete attention to every single word. >>>>>>>>>>>>>>>>>>>>
Wittgenstein
'True in Russell's system' means, as was said: >>>>>>>>>>>>>>>>>>>> proved in Russell's system; and 'false in Russell's >>>>>>>>>>>>>>>>>>>> system' means: the opposite has been proved >>>>>>>>>>>>>>>>>>>> in Russell's system
Proof Theoretic Semantics has almost gotten there. >>>>>>>>>>>>>>>>>>>> For the most part they stop at semantically grounded >>>>>>>>>>>>>>>>>>>
and never quite get all the way to True. >>>>>>>>>>>>>>>>>>>>
For Wittgenstein's slight extension of the PTS >>>>>>>>>>>>>>>>>>>> notion ~∃x x=S(x) is untrue
i.e. unproven
in Q and true in PA.
I have been saying it that way long before I ever >>>>>>>>>>>>>>>>>>>> heard of Wittgenstein.
So again, you're saying the same thing as everyone >>>>>>>>>>>>>>>>>>> else but with different words.
So everyone says that ~∃x x=S(x)
which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>>> its successor" as per the definition of Q
is simply untrue
i.e. unprovable
in Q and does nor derive either undecidability or >>>>>>>>>>>>>>>>>> incompleteness?
It does derive incompleteness, as by definition Q is >>>>>>>>>>>>>>>>> incomplete because "no number is equal to its >>>>>>>>>>>>>>>>> successor" is unprovable in Q.
Wittgenstein (1937)
'True in Russell's system' means, as was said: >>>>>>>>>>>>>>>> proved in Russell's system; and 'false in Russell's >>>>>>>>>>>>>>>> system' means: the opposite has been proved
in Russell's system
So what term would you use to describe a sentence that >>>>>>>>>>>>>>> has an infinite sequence of inference steps between it >>>>>>>>>>>>>>> and the axioms of the system?
untrue and unfalse.
What about the more general case, i.e. a term for a >>>>>>>>>>>>> statement that has *any* sequence of inference steps, >>>>>>>>>>>>> either finite or infinite, between it and the axioms of the >>>>>>>>>>>>> system? And what would the negation of such a statement be >>>>>>>>>>>>> called?
The truth value of the Goldbach conjecture
may have an infinite number of steps thus
would be unknowable and not a member of the
body of knowledge that can be expressed in
language. Negation has no effect on expressions
that are neither true no false.
Every finite string including gibberish has the
truth value of: {True, False, Neither}.
Finite strings are a superset of expressions
of language.
That's not the definition I asked for.
What term would you use for a statement that has *any*
sequence of inference steps, either finite or infinite, >>>>>>>>>>> between it and the axioms of the system?
"true on the basis of meaning expressed in language"
reliably computable for the entire body of GENERAL knowledge. >>>>>>>>>> Is the limit of the topic of all my posts.
Infinite inference steps are off topic.
Why are you so reluctant to provide a simple term?
OFF-TOPIC <is> THE TERM.
So we've established that "off-topic" means "a statement that has >>>>>>> *any* sequence of inference steps, either finite or infinite,
between it and the axioms of the system".
The ones that have infinite steps out outside the
body of knowledge and off topic for that reason.
So you're claiming the sentence "no number is equal to its
successor" in Q is "off topic".
Rejected, as it is a semantically valid sentence in the language of Q. >>>>
between x and the axioms of Q then PTS stipulates
that x is not semantically valid in Q.
And since x = "no number is equal to its successor" is semantically
valid as per the definition of Q, PTS must be discarded as useless.
So you also have no idea what Stipulative definition is.
A stipulative definition is a type of definition in which
a new or currently existing term is given a new specific meaning
https://en.wikipedia.org/wiki/Stipulative_definition
Not allowed, as "semantically valid" is already defined, and "no number
is equal to its successor" meets that definition.
On 6/27/2026 6:33 PM, dbush wrote:
On 6/27/2026 7:27 PM, olcott wrote:
On 6/27/2026 5:53 PM, dbush wrote:
On 6/27/2026 6:44 PM, olcott wrote:
On 6/27/2026 5:33 PM, dbush wrote:
So you're claiming the sentence "no number is equal to its
successor" in Q is "off topic".
Rejected, as it is a semantically valid sentence in the language
of Q.
If there is no finite sequence of inference steps
between x and the axioms of Q then PTS stipulates
that x is not semantically valid in Q.
And since x = "no number is equal to its successor" is semantically
valid as per the definition of Q, PTS must be discarded as useless.
So you also have no idea what Stipulative definition is.
A stipulative definition is a type of definition in which
a new or currently existing term is given a new specific meaning
https://en.wikipedia.org/wiki/Stipulative_definition
Not allowed, as "semantically valid" is already defined, and "no
number is equal to its successor" meets that definition.
Proof Theoretic Semantics (PTS) supersedes and overrules this.
On 6/27/2026 7:59 PM, olcott wrote:
On 6/27/2026 6:33 PM, dbush wrote:
On 6/27/2026 7:27 PM, olcott wrote:
On 6/27/2026 5:53 PM, dbush wrote:
On 6/27/2026 6:44 PM, olcott wrote:
On 6/27/2026 5:33 PM, dbush wrote:
So you're claiming the sentence "no number is equal to its
successor" in Q is "off topic".
Rejected, as it is a semantically valid sentence in the language >>>>>>> of Q.
If there is no finite sequence of inference steps
between x and the axioms of Q then PTS stipulates
that x is not semantically valid in Q.
And since x = "no number is equal to its successor" is semantically >>>>> valid as per the definition of Q, PTS must be discarded as useless.
So you also have no idea what Stipulative definition is.
A stipulative definition is a type of definition in which
a new or currently existing term is given a new specific meaning
https://en.wikipedia.org/wiki/Stipulative_definition
Not allowed, as "semantically valid" is already defined, and "no
number is equal to its successor" meets that definition.
Proof Theoretic Semantics (PTS) supersedes and overrules this.
Then PTS is discarded as useless because it rejects "no number is equal
to its successor".
On 6/27/2026 5:37 PM, Ross Finlayson wrote:
On 06/27/2026 08:47 AM, polcott wrote:
On 6/27/2026 3:05 AM, Mikko wrote:
On 27/06/2026 01:01, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning.
André
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope. >>>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable. Then to >>>>>>>>>> put things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable in PA. >>>>>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False. The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False. G is simply a sentence like ~∃x x>10 v x<5 but much more >>>>>> complex.
"No number is equal to its successor" is a sentence in RA, and it >>>>>>>> is true but unprovable in RA (or as your would call it, "out-of- >>>>>>>> scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language >>>>>> of Q. More formally, it is this:
~∃x x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms >>>>>> you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
Nevertheless a sentence like ~∃x x=S(x) is in the language of Q and
that way in the theory.
Colorless green ideas sleep furiously
was composed by Noam Chomsky in his 1957 book
Syntactic Structures as an example of a sentence
that is grammatically well-formed, but semantically
nonsensical.
Proving that syntax is not enough.
"Colorless green" is actually two colors
since there's a dual-tristimulus colorspace
the chromatic and the prismatic,
a fact of the science of the theory of light and color,
of which you are ignorant, then making for a reasonable
reading of the usual apocryphal comment.
Then, ideas can sleep however they want.
The point is that syntactically correct expressions
can be semantically incoherent. Math always makes
sure to ignore this. The gibberish cannot be proven
counts as undecidability in math.
On 06/27/2026 03:47 PM, olcott wrote:
On 6/27/2026 5:37 PM, Ross Finlayson wrote:
On 06/27/2026 08:47 AM, polcott wrote:
On 6/27/2026 3:05 AM, Mikko wrote:
On 27/06/2026 01:01, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson >>>>>>>>>>>>>> Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning.
André
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated >>>>>>>>>>>> with alternative views. So I will simply say out-of-scope. >>>>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable. Then to >>>>>>>>>>> put things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable in PA. >>>>>>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False. The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False. G is simply a sentence like ~∃x x>10 v x<5 but much more >>>>>>> complex.
"No number is equal to its successor" is a sentence in RA, and it >>>>>>>>> is true but unprovable in RA (or as your would call it, "out-of- >>>>>>>>> scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language >>>>>>> of Q. More formally, it is this:
~∃x x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms >>>>>>> you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
Nevertheless a sentence like ~∃x x=S(x) is in the language of Q and >>>>> that way in the theory.
Colorless green ideas sleep furiously
was composed by Noam Chomsky in his 1957 book
Syntactic Structures as an example of a sentence
that is grammatically well-formed, but semantically
nonsensical.
Proving that syntax is not enough.
"Colorless green" is actually two colors
since there's a dual-tristimulus colorspace
the chromatic and the prismatic,
a fact of the science of the theory of light and color,
of which you are ignorant, then making for a reasonable
reading of the usual apocryphal comment.
Then, ideas can sleep however they want.
The point is that syntactically correct expressions
can be semantically incoherent. Math always makes
sure to ignore this. The gibberish cannot be proven
counts as undecidability in math.
That's yanking one's own chain, and doesn't work on others.
The "grammar" hierarchy of Chomsky is of a very limited and simple model
of computation and a very direct connection to "regular expressions",
with regards to formal methods, finite automata,
linear, right linear, and regular expressions, and of accounts
of the various amounts of look-ahead or memory in scanners what
result productions, that then in any account of source models
involves linking and dictionaries of symbols, that essentially
it's not saying much and isn't much of "grammar".
Notions for example of the "railroad diagram" simply equip what
are models of languages like "SQL" that are complicated in Chomsky
to be simple in alternatives/optionals/loops with regards to the
declarations of "grammars".
Any sort of usual useful "grammar" involves a "multi-pass parser",
with regards to parsing, for example for natural language, which
usually has a direct account of nouns and verbs, when really the
infinitives are always interrupted by instantiating a verb tense,
and nouns are particulars and simple.
Then, for natural language, all readers of natural human language
using something alike "Tesniere grammars" as of "dependency grammars"
that all learned in school with regards to diagramming any well-formed sentence.
Aristotle is not a fool - and Aristotle won't be made a fool.
That that that that that that that, ....
The problem is not that "colorless green ideas sleep furiously"
is given a _context_ where it's not simply mimsy as the borogoves,
then that besides, all utterances are in a large overall context.
So now you don't know grammar, either.
On 6/27/2026 2:27 AM, Mikko wrote:
On 26/06/2026 16:05, olcott wrote:
On 6/26/2026 1:34 AM, Mikko wrote:
On 25/06/2026 16:58, olcott wrote:
On 6/25/2026 2:18 AM, Mikko wrote:
On 24/06/2026 23:25, olcott wrote:
On 6/24/2026 4:52 AM, Mikko wrote:
On 23/06/2026 17:47, olcott wrote:
On 6/23/2026 12:55 AM, Mikko wrote:
On 22/06/2026 15:09, olcott wrote:
On 6/22/2026 1:41 AM, Mikko wrote:
On 22/06/2026 02:58, olcott wrote:
On 6/21/2026 5:17 AM, Mikko wrote:
On 20/06/2026 17:41, olcott wrote:
On 6/20/2026 2:50 AM, Mikko wrote:
On 19/06/2026 15:46, olcott wrote:
On 6/19/2026 2:23 AM, Mikko wrote:
On 18/06/2026 22:35, olcott wrote:Calling my views (anchored in proof theoretic semantics) >>>>>>>>>>>>>>>>> incoherent merely proves that you are too damned lazy to >>>>>>>>>>>>>>>>> look into proof theoretic semantics.
On 6/17/2026 4:14 PM, olcott wrote:Whereas you are stuck to your own incoherent views and >>>>>>>>>>>>>>>>>> reject
https://www.youtube.com/@rossfinlayson >>>>>>>>>>>>>>>>>>>> Making sure to leave out
Proof-theoretic semantics
(an alternative to truth-condition semantics) >>>>>>>>>>>>>>>>>>>> https://plato.stanford.edu/entries/proof-theoretic- >>>>>>>>>>>>>>>>>>>> semantics/
Some people only memorize conventional views and >>>>>>>>>>>>>>>>>>> reject alternative views out-of-hand without review. >>>>>>>>>>>>>>>>>>
alternative views out-of-hand without review >>>>>>>>>>>>>>>>>
At different times you have expressed different >>>>>>>>>>>>>>>> opinions, which
sometimes have been incompatible. But you have never >>>>>>>>>>>>>>>> clearly
retracted your earlier opitions that conflict with your >>>>>>>>>>>>>>>> present
ones.
All of the ideas that I have ever had about these things >>>>>>>>>>>>>>> are now under the Proof Theoretic Semantics category. >>>>>>>>>>>>>>> These ideas have evolved over time, yet their essence >>>>>>>>>>>>>>> has remained utterly unchanged since 1997.
That's nearly thirty years, and you still havn't written a >>>>>>>>>>>>>> publishable
(or nearly publishable) article about them.
I have 50 pre prints articles. Because not one single> >>>>>>>>>>>>> human being on the face of the Earth could understand >>>>>>>>>>>>> me I could not publish.
As far as I have seen, all interesting content in those >>>>>>>>>>>> articles
that have any is or depends on claims that should be proven but >>>>>>>>>>>> aren't.
They are proven in Proof Theoretic Semantics
An aricle is not publishable unless it either contains the >>>>>>>>>> proof or
has a pointer to an olready published proof.
Only now after 28 years am I acquiring the lingua Franca
terms-of-the-art of proof theoretic semantics such that
I can anchor my ideas in the foundational work of the
most respected authors in the field.
My issue with you guys is that you only spend 1%
of your concentration understanding me and the other
99% trying to artificially contrive some baseless
rebuttal.
THat "baseless" is false but otherwise, what is wrong is more
important than what is right. Of one ignores what is right one >>>>>>>> mai fail to achieve what one could, but if one believs what is >>>>>>>> wrong one may achieve a disaseter.
Proof-theoretic semantics is an alternative to truth-condition
semantics.
https://plato.stanford.edu/entries/proof-theoretic-semantics/
So far no one has even acknowledged that PTS is an alternative
to truth-conditional semantics. Several people have seemed
to same that no alternative can possibly exist.
You have not shown that there is any need for any alternative
semantics.
With dangerous lies that can destroy Democracy
and kill the planet with climate change having
an ultimate arbiter of truth would be useful.
Those who are able and willing to destroy democracy are able to provice >>>> an ultimate arbiter of truth and usually do so. But they don't need any >>>> proof theoretic semantics.
An ultimate arbiter of truth blows their whole game away.
THe point of the ultimate arbiter of truth is that the errors in the
determinations of any alternative arbiter can be detected and similar
errors in future can be avoided with suitable admistrative or other
actions if regarded necessary.
When all of the relevant facts are known then
counter-factual lies are easy to detect.
On 6/27/2026 3:05 AM, Mikko wrote:
On 27/06/2026 01:01, olcott wrote:
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning.
André
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope.
So "out-of-scope" is merely a synonym for unprovable. Then to >>>>>>>> put things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable in PA. >>>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False. The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False. G is simply a sentence like ~∃x x>10 v x<5 but much more
complex.
"No number is equal to its successor" is a sentence in RA, and it >>>>>> is true but unprovable in RA (or as your would call it, "out-of-
scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language
of Q. More formally, it is this:
~∃x x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms
you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
Nevertheless a sentence like ~∃x x=S(x) is in the language of Q and
that way in the theory.
Colorless green ideas sleep furiously
was composed by Noam Chomsky in his 1957 book
Syntactic Structures as an example of a sentence
that is grammatically well-formed, but semantically
nonsensical.
Proving that syntax is not enough.
On 06/27/2026 08:47 AM, polcott wrote:
On 6/27/2026 3:05 AM, Mikko wrote:
On 27/06/2026 01:01, olcott wrote:Colorless green ideas sleep furiously
On 6/26/2026 2:55 PM, dbush wrote:
On 6/26/2026 3:38 PM, olcott wrote:
On 6/26/2026 2:17 PM, dbush wrote:
On 6/26/2026 3:07 PM, olcott wrote:
On 6/26/2026 1:51 PM, dbush wrote:
On 6/26/2026 2:48 PM, olcott wrote:
On 6/26/2026 1:14 PM, André G. Isaak wrote:
On 2026-06-26 11:22, olcott wrote:
On 6/26/2026 11:08 AM, dbush wrote:
By your logic, "no number is equal to its successor" has no >>>>>>>>>>>>> meaning in Robinson arithmetic.
In Robinson Arithmetic (often denoted as Q),
the statement "no number is equal to its
successor" is not provable.While this statement
is true for the standard natural numbers, Robinson
Arithmetic is too weak to prove it universally
(∀ x, S(x) ≠ x).
It's not provable but it certainly has meaning.
André
out-of-scope for Q is more accurate as jargon free.
PTS does hold the view that meaning is only derived
through inference steps. This simple sentence seems
impossibly too difficult for anyone fully indoctrinated
with alternative views. So I will simply say out-of-scope. >>>>>>>>>>
So "out-of-scope" is merely a synonym for unprovable. Then to >>>>>>>>> put things in words you can understand:
"I am driving to Walmart to buy a carton of
Breyer's natural vanilla ice cream." is also unprovable in PA. >>>>>>>> In both cases the semantics in not represented in PA.
Not applicable, as that is not a sentence in PA.
It is expressed in PA
False. The above is not a sentence of PA.
to the same degree that G is expressed
in PA has a huge natural number. The semantics of it and
the semantics of G are neither expressible in PA.
False. G is simply a sentence like ~∃x x>10 v x<5 but much more
complex.
"No number is equal to its successor" is a sentence in RA, and it >>>>>>> is true but unprovable in RA (or as your would call it, "out-of- >>>>>>> scope").
If its semantics is not expressible in Q (What RA is called)
then it is not actually expressible in Q.
"No number is equal to its successor" is a sentence in the language
of Q. More formally, it is this:
~∃x x=S(x)
And this sentence is not provable from the axioms of Q (or, in terms >>>>> you would understand, the above is "out-of-scope" of Q).
OK I checked the details so I need to make my
language more precise.
Within proof theoretic semantics any expression
that cannot be proven in Q is not semantically
grounded in Q.
Nevertheless a sentence like ~∃x x=S(x) is in the language of Q and
that way in the theory.
was composed by Noam Chomsky in his 1957 book
Syntactic Structures as an example of a sentence
that is grammatically well-formed, but semantically
nonsensical.
Proving that syntax is not enough.
"Colorless green" is actually two colors
since there's a dual-tristimulus colorspace
the chromatic and the prismatic,
a fact of the science of the theory of light and color,
of which you are ignorant, then making for a reasonable
reading of the usual apocryphal comment.
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote:
On 2026-06-21 14:42, olcott wrote:All of knowledge expressed in language is structured as a >>>>>>>>>>>>> tree of semantic relations specified syntactically between >>>>>>>>>>>>> finite strings.
On 6/21/2026 3:04 PM, Alan Mackenzie wrote:
[ Followup-To: set ]It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" yesterday. >>>>>>>>>>>>>>>>You can find any number of terms. That doesn't mean >>>>>>>>>>>>>>>>>> you're capable of
understanding them.
The above is the key reason why under PTS Gödel 1931 >>>>>>>>>>>>>>>>> incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody that PTS >>>>>>>>>>>>>>>> somehow causes
Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you will >>>>>>>>>>>>>>>>> not understand.
You don't understand Proof-theoritic Semantics, and you >>>>>>>>>>>>>>>> certainly don't
understand Gödel's Theorem, neither the theorem itself >>>>>>>>>>>>>>>> nor any proof of
it.
"grounded in the atomic base of PA" is an expression used >>>>>>>>>>>>>> only by you, and it is one which you have never explicitly >>>>>>>>>>>>>> defined, so the fault here certainly doesn't lie with >>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' when you >>>>>>>>>>>>>> haven't even adequately explained what it is that you mean. >>>>>>>>>>>>
What makes you believe semantic relations that can be >>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one try to >>>>>>>>>> put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a loop >>>>>>>> when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops.
In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before
looking for a proof.
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) is
ungrounded in the PTS atomic base of Q.
This does not mean undecidable or incomplete
it means that ~∃x x=S(x) is out-of-scope for Q.
This is the same sort of thing as finding the defined
meaning of a word. If you cannot find its recursively
defined meaning then it never gains any meaning.
That does not follow. Words have meanings even without definitions.
You can't present the first definition unless you already have
meaningful words.
A particular new word can only be defined in terms
of other existing words that already have definitions.
PTS works in a similar way. If ~∃x x=S(x) cannot connect
to its meanings in Q the it remains undefined in Q.
Typically the presentation of a formal theory begins with the
introduction of undefined symbols. But the symbols are not
fully meaningless. They get some amount of meaning from being
introduces as symbols of a particular syntactic category and
more from being used in the postulates of the theory.
The body of knowledge expressed in language starts
with an atomic basis of expressions of language that
are stipulated to be true.
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x) is
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms. That doesn't >>>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS Gödel >>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody that >>>>>>>>>>>>>>>>>>>> PTS somehow causes
Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>>>> you certainly don't
understand Gödel's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly >>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not a 'verified >>>>>>>>>>>>>>>>>> fact' when you haven't even adequately explained what >>>>>>>>>>>>>>>>>> it is that you mean.
All of knowledge expressed in language is structured as >>>>>>>>>>>>>>>>> a tree of semantic relations specified syntactically >>>>>>>>>>>>>>>>> between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never
completes.
How can any ordering of knowledge prevent getting stuck in a >>>>>>>>>>>> loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not
obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
It should be obvious that finding a proof does not happen before
looking for a proof.
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known.
semantic nonsense in Q? All of logic took
a psychotic break from reality when they
took semantics out of logic and put it in
a separate model.
On 6/27/2026 2:48 AM, Mikko wrote:
On 26/06/2026 19:08, dbush wrote:
On 6/26/2026 10:24 AM, olcott wrote:
On 6/26/2026 8:57 AM, dbush wrote:
On 6/26/2026 9:45 AM, olcott wrote:
On 6/26/2026 8:20 AM, dbush wrote:
On 6/26/2026 9:10 AM, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:
On 22/06/2026 02:02, olcott wrote:
On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote:
On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not understand >>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>> I just found the term:
"grounding in a proof theoretic atomic base" >>>>>>>>>>>>>>>>>>>>>>>> yesterday.
You can find any number of terms. That doesn't >>>>>>>>>>>>>>>>>>>>>>> mean you're capable of
understanding them.
The above is the key reason why under PTS Gödel >>>>>>>>>>>>>>>>>>>>>> 1931 incompleteness
fails.
I don't believe you. You have no respect for or >>>>>>>>>>>>>>>>>>>>> understanding of the
truth. If you really want to persuade anybody that >>>>>>>>>>>>>>>>>>>>> PTS somehow causes
Gödel's theorem not to hold, then cite an academic >>>>>>>>>>>>>>>>>>>>> expert who'll have
some credibility.
If they are mere gibberish words to you then you >>>>>>>>>>>>>>>>>>>>>> will not understand.
You don't understand Proof-theoritic Semantics, and >>>>>>>>>>>>>>>>>>>>> you certainly don't
understand Gödel's Theorem, neither the theorem >>>>>>>>>>>>>>>>>>>>> itself nor any proof of
it.
"grounded in the atomic base of PA" is an expression >>>>>>>>>>>>>>>>>>> used only by you, and it is one which you have never >>>>>>>>>>>>>>>>>>> explicitly defined, so the fault here certainly >>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not a 'verified >>>>>>>>>>>>>>>>>>> fact' when you haven't even adequately explained what >>>>>>>>>>>>>>>>>>> it is that you mean.
All of knowledge expressed in language is structured >>>>>>>>>>>>>>>>>> as a tree of semantic relations specified >>>>>>>>>>>>>>>>>> syntactically between finite strings.
What makes you believe semantic relations that can be >>>>>>>>>>>>>>>>> structured as
a tree are sufficient to contain all knowledge that is >>>>>>>>>>>>>>>>> exressed in
some language?
The CycL language and the Cyc Project.
They use a tree structure for concepts. But why would one >>>>>>>>>>>>>>> try to
put knowledge in a tree structure?
It must at least be a directed acyclic graph or
the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting stuck in >>>>>>>>>>>>> a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed prevent loops. >>>>>>>>>>> In most cases that also prevents finding the proof.
Truth Conditional Semantics (TCS) <is> incoherent
compared to Proof Theoretic Semantics (PTS). Essentially
PTS just coherently connects the semantic meanings
expressed in language together into one coherent body
of general knowledge. It does this without undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it is not >>>>>>>>> obvious
how switching to another semantics could improve it.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof.
In other words, you're saying that the sentence "no number is
equal to its successor" has no meaning in Robinson Arithmetic.
In proof theoretic semantics an expression only gains
semantic meaning by finding a proof from within a
stipulated atomic base of its own axioms like the one
that you provided.
Then you agree that the above natural language sentence that is
semantically required to be either true or false has no meaning?
Your sentence would be what it always has been
a stipulated true sentence axiom.
False, as that statement is not one of the axioms of Robinson
arithmetic, but it is a statement in its language, and one that has
*only* an infinite connection to the axioms of that system.
What infinite connection? The statement is false in natural numbers,
which is one model of Robinson Arithmetic but not the only one.
In another model there may be a number that is its successor. There
may even be more than one such number.
It cannot be proved in Q and can be proved in PA.
Thus its semantic meaning is out-of-scope in Q.
--By your logic, "no number is equal to its successor" has no meaning
in Robinson arithmetic.
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>>>> or mathematical incompleteness.
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote:They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>> would one try to
On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
What makes you believe semantic relations that can >>>>>>>>>>>>>>>>>>>>>> be structured asAll of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>> understand
In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday.
You can find any number of terms. That >>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them.
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no respect for >>>>>>>>>>>>>>>>>>>>>>>>>> or understanding of the
truth. If you really want to persuade anybody >>>>>>>>>>>>>>>>>>>>>>>>>> that PTS somehow causes
Gödel's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you then >>>>>>>>>>>>>>>>>>>>>>>>>>> you will not understand.
You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>> it.
what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one which >>>>>>>>>>>>>>>>>>>>>>>> you have never explicitly defined, so the fault >>>>>>>>>>>>>>>>>>>>>>>> here certainly doesn't lie with Alan. It's >>>>>>>>>>>>>>>>>>>>>>>> certainly not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>> prevent loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>
Looking for a proof does not need any semantics so it is >>>>>>>>>>>>>> not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>
It should be obvious that finding a proof does not happen >>>>>>>>>>>> before
looking for a proof.
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known.
Which has the semantic meaning "no number is equal to its
successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
On 6/27/2026 2:54 PM, dbush wrote:
On 6/27/2026 3:40 PM, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>>>>>> or mathematical incompleteness.
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>>> would one try toWhat makes you believe semantic relations that >>>>>>>>>>>>>>>>>>>>>>>> can be structured asIt is a verified fact that Gödel's G is >>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday.
You can find any number of terms. That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them.
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no respect >>>>>>>>>>>>>>>>>>>>>>>>>>>> for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means is >>>>>>>>>>>>>>>>>>>>>>>>>>> less
than no rebuttal at all.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so >>>>>>>>>>>>>>>>>>>>>>>>>> the fault here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean.
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>> prevent loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>
Looking for a proof does not need any semantics so it is >>>>>>>>>>>>>>>> not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>
It should be obvious that finding a proof does not happen >>>>>>>>>>>>>> before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>
Which has the semantic meaning "no number is equal to its
successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
And because PTS claims the semantically valid sentence in Q "no number
is equal to its successor" is not semantically valid, it must be
discarded as useless.
No you are just not bothering to pay 100% totally
complete attention to every single word.
Wittgenstein
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics has almost gotten there.
For the most part they stop at semantically grounded
and never quite get all the way to True.
On 6/27/2026 3:13 AM, Mikko wrote:
On 26/06/2026 16:15, olcott wrote:
On 6/26/2026 1:45 AM, Mikko wrote:
On 25/06/2026 19:16, olcott wrote:
On 6/25/2026 2:29 AM, Mikko wrote:
On 25/06/2026 00:33, olcott wrote:
On 6/24/2026 5:13 AM, Mikko wrote:
On 23/06/2026 21:20, olcott wrote:
On 6/23/2026 12:32 PM, Ross Finlayson wrote:
On 06/23/2026 09:54 AM, olcott wrote:
On 6/23/2026 10:51 AM, Ross Finlayson wrote:
On 06/23/2026 07:22 AM, olcott wrote:
On 6/22/2026 11:31 PM, Ross Finlayson wrote:
On 06/22/2026 09:14 PM, olcott wrote:
On 6/22/2026 11:00 PM, Ross Finlayson wrote:
On 06/22/2026 01:06 PM, olcott wrote:
On 6/22/2026 2:50 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>> [ Followup-To: set ]
In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>> On 6/22/2026 1:42 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>> In comp.theory olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>> On 6/22/2026 10:48 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>
G is true.
I put it to you you're lying again. No reputable >>>>>>>>>>>>>>>>>>>>>> mathematician
would
risk his reputation by saying false things. If >>>>>>>>>>>>>>>>>>>>>> Dag Prawitz
really
did
"agree" (with whom?) that Gödel's sentence G is >>>>>>>>>>>>>>>>>>>>>> not true in
Peano
Arithmetic, then produce a citation for this. >>>>>>>>>>>>>>>>>>
He never gets to Gödel. He essentially says unprovable >>>>>>>>>>>>>>>>>>>>> means untrue all the time for everything within his >>>>>>>>>>>>>>>>>>>>> own Theory of Grounds of strict Proof Theoretic >>>>>>>>>>>>>>>>>>>>> Semantics.
You won't understand it, but that _is_ essentially >>>>>>>>>>>>>>>>>>>> Gödel's
Incompleteness
Theorem. It is a statement that any sufficiently >>>>>>>>>>>>>>>>>>>> powerful
system can
express true things it can't prove. So Dag Prawitz, >>>>>>>>>>>>>>>>>>>> had he been
saying
the things you falsely attributed to him, would >>>>>>>>>>>>>>>>>>>> certainly have
"got" to
Gödel, and would have understood full well what he >>>>>>>>>>>>>>>>>>>> was saying.
You did not pay close enough attention to my exact >>>>>>>>>>>>>>>>>>> words.
I was right, you didn't understand it.
Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>>> Dag Prawitz says: Unprovable ALWAYS means untrue >>>>>>>>>>>>>>>>>
Yeah, I'm pretty sure that "Dag Prawitz says what Dag >>>>>>>>>>>>>>>> Prawitz says",
and furthermore "Dag Prawitz doesn't say what Dag >>>>>>>>>>>>>>>> Prawitz doesn't
say",
then looking a bit into his tremendous volume of works, >>>>>>>>>>>>>>>> he talks about "natural deduction" then specifically an >>>>>>>>>>>>>>>> "inverse
principle" so I think these are key aspects of >>>>>>>>>>>>>>>> fundamental logic.
https://www.researchgate.net/
publication/233365263_On_Inversion_Principles
"On Inversion Principles
Enrico Moriconi∗Laura Tesconi†
May 8, 2007
Abstract
The idea of an “inversion principle”, and the name itself, >>>>>>>>>>>>>>>> originated in
the work of Paul Lorenzen in the 1950s, as a method to >>>>>>>>>>>>>>>> generate
new ad-
missible rules within a certain syntactic context. Some >>>>>>>>>>>>>>>> fifteen years
later, the idea was taken up by Dag Prawitz to devise a >>>>>>>>>>>>>>>> strategy of
normalization for natural deduction calculi (this being an >>>>>>>>>>>>>>>> analogue of
Gentzen’s cut-elimination theorem for sequent calculi). >>>>>>>>>>>>>>>> Later,
Prawitz
used the inversion principle again, attributing it with >>>>>>>>>>>>>>>> a semantic
role.
Still working in natural deduction calculi, he >>>>>>>>>>>>>>>> formulated a general
type
of schematic Introduction rules to be matched—thanks to >>>>>>>>>>>>>>>> the idea
supporting the inversion principle — by a corresponding >>>>>>>>>>>>>>>> general
schematic Elimination rule. This was an attempt to >>>>>>>>>>>>>>>> provide a
solution to
the problem suggested by the often quoted note of Gentzen. >>>>>>>>>>>>>>>> According to
Gentzen “it should be possible to display the >>>>>>>>>>>>>>>> elimination rules as
unique functions of the corresponding introduction rules >>>>>>>>>>>>>>>> on the
basis of
certain requirements.” Many people have since worked on >>>>>>>>>>>>>>>> this topic,
which can be appropriately seen as the birthplace of >>>>>>>>>>>>>>>> what are now
referred to as “general elimination rules”, recently >>>>>>>>>>>>>>>> studied
thoroughly
by Sara Negri and Jan von Plato. In this paper, we >>>>>>>>>>>>>>>> retrace the main
threads of this chapter of proof-theoretical
investigation, using
Lorenzen’s original framework as a general guide" >>>>>>>>>>>>>>>>
Hm, "general elimination rules", seem derivable from De >>>>>>>>>>>>>>>> Morgan's
laws,
and that being the usual account of naive deductive >>>>>>>>>>>>>>>> analysis, then
since
"natural deduction", which here is held as part of the >>>>>>>>>>>>>>>> theory
since it's naturally logical, then has for Gentzen that >>>>>>>>>>>>>>>> besides
Kripke
afterward there's also Sheffer and Chwistek before, and >>>>>>>>>>>>>>>> instead of
Montague for semantics there's Herbrand for semantics, >>>>>>>>>>>>>>>> so, what to do
about "inversion principle" is here that the thea-theory >>>>>>>>>>>>>>>> has that
it's
what subsumes "non-contradiction principle", here hoping >>>>>>>>>>>>>>>> that the
interpretation aligns and thusly that "principle of >>>>>>>>>>>>>>>> inversion"
wouldn't
need dis-ambiguation from "inversion principle". >>>>>>>>>>>>>>>>
https://www.tandfonline.com/doi/
abs/10.1080/01445340701830334
https://www.strandbooks.com/natural-deduction-a-proof- >>>>>>>>>>>>>>>> theoretical-
study-9780486446554.html
"... [Prawitz'] inversion principle constitutes the >>>>>>>>>>>>>>>> foundation of
most
modern accounts of proof-theoretic semantics." >>>>>>>>>>>>>>>>
I already have a principle of inversion and furthermore a >>>>>>>>>>>>>>>> principle of
thorough reason as subsuming principles of non- >>>>>>>>>>>>>>>> contradiction and what
suffices, so, I'll be curious then about what to make of >>>>>>>>>>>>>>>> Prawitz'
"inversion principle" since Lorenzen.
Of course the concept of an "inversion principle" is as >>>>>>>>>>>>>>>> old as the
oldest account of Western philosophy like Heraclitus >>>>>>>>>>>>>>>> with dual
monism.
In fact by definition it's about the most basic aspect of >>>>>>>>>>>>>>>> contemplation
and deliberation in abstraction of looking at both sides >>>>>>>>>>>>>>>> of issues
and
resolving inductive impasses with analytical bridges after >>>>>>>>>>>>>>>> complementary
duals.
https://arxiv.org/abs/2112.14967
"Prawitz formulated the so-called inversion principle as >>>>>>>>>>>>>>>> one of the
characteristic features of Gentzen's intuitionistic natural >>>>>>>>>>>>>>>> deduction.
In the literature on proof-theoretic semantics, this >>>>>>>>>>>>>>>> principle is
often
coupled with another that is called the recovery >>>>>>>>>>>>>>>> principle. By
adopting
the Computational Ludics framework, we reformulate these >>>>>>>>>>>>>>>> principles
into
one and the same condition, which we call the harmony >>>>>>>>>>>>>>>> condition. We
show
that this reformulation allows us to reveal two >>>>>>>>>>>>>>>> intuitive ideas
standing
behind these principles: the idea of "containment" >>>>>>>>>>>>>>>> present in the
inversion principle, and the idea that the recovery >>>>>>>>>>>>>>>> principle is the
"converse" of the inversion principle. We also formulate >>>>>>>>>>>>>>>> two other
conditions in the Computational Ludics framework, and we >>>>>>>>>>>>>>>> show that
each
of them is equivalent to the harmony condition." >>>>>>>>>>>>>>>>
The "ludicus" is Latin and for accounts of wisdom and >>>>>>>>>>>>>>>> knowledge.
"In particular, by taking inspiration from the >>>>>>>>>>>>>>>> Brouwer-Heyting-Kolmogorov explanation of logical >>>>>>>>>>>>>>>> connectives,
proof-theoretic semantics rests on the idea that we know >>>>>>>>>>>>>>>> the
meaning of
a compound sentence when we know what counts as a >>>>>>>>>>>>>>>> canonical proof of
it.
And if proofs are formalised within the framework of >>>>>>>>>>>>>>>> natural
deduction,
then a canonical proof of a sentence A is nothing but a >>>>>>>>>>>>>>>> closed
derivation ending with an introduction rule of the main >>>>>>>>>>>>>>>> connective
of A."
The "canonical proofs" are not unique, in any system >>>>>>>>>>>>>>>> strong enough
to make for infinitary reasoning and super-classical >>>>>>>>>>>>>>>> results
requiring
analytical bridges about infinity and continuity. >>>>>>>>>>>>>>>>
It is the role that "canonical proofs" play in
Truth as an Epistemic Notion
https://link.springer.com/article/10.1007/s11245-011-9107-6 >>>>>>>>>>>>>>> That is the most important gist of his whole work. >>>>>>>>>>>>>>>
He later goes on to develop and further elaborate his >>>>>>>>>>>>>>> Theory of Grounds.
Atomic Systems in Proof-Theoretic Semantics: Two Approaches >>>>>>>>>>>>>>> Thomas Piecha & Peter Schroeder-Heister do this same sort of >>>>>>>>>>>>>>> thing two different ways.
Furthermore I say there are "canonical proofs" of >>>>>>>>>>>>>> inductive sorts that
make contradictions and thusly destroy each other. >>>>>>>>>>>>>>
Clearly you have no idea what Dag Prawitz means by
"canonical proofs".
Go find out and then get back to me.
This is where "the thorough" and "analytical bridges" make >>>>>>>>>>>>>> repairs
of what otherwise is flawed, or for hard constructivist >>>>>>>>>>>>>> realist
structuralist model theorists: not-theories (examples of >>>>>>>>>>>>>> wrong).
Induction and counter-induction contradict each other, it's >>>>>>>>>>>> simple,
it's the grounds for most things called "paradox".
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
After you totally understand how and why the proof
theoretic semantics of that is correct and resolves
the Liar Paradox get back to me.
The essential principle involved that I derived
in my own Minimal Type Theory before I knew that
Prolog could do the same thing is that:
When the directed graph of the evaluation
sequence of an expression contains a cycle
then the input is determined to be incoherent
on the basis that its proof would never terminate.
Proof Theoretic Semantics does this exact same thing.
Don't get back to me until you attain the required
prerequisites. I am sure that you already know
all about cycles in directed graphs.
Declaring oneself ignorant thus wise
doesn't make much of a case
except being ignorant.
300 mile per hour wheelchair: can't take stairs.
Except down, ....
So you are going to imply that I am incorrect
about Prolog when you yourself remain clueless about Prolog? >>>>>>>>> That would be dishonest.
No, pointing out that you are worng about Prolog when you are wrong >>>>>>>> about Prolog is never dishohest.
That is correct Prolog and that is the
result of the correct run of correct Prolog.
Irrelevant. Nobody claimed there be Prolog errors in your queries. >>>>>>
Implying that I am wrong about Prolog without
pointing out any actual mistake is also DISHONEST.
How did Ross FInlayson imply that you were wrong about Prolog?
If an error is claimed then it must be specifically
pointed out otherwise the clam of error is dishonest.
Yet you claim that Ross Finlayson be dishonest without pointing
out what is dishonest in his words.
If anyone and everyone that claims that they found an
error and never points out what the error is and why
it is an error then they are merely a baseless denigrator.
If anyone and everyone that claims that someone is dishonest
never points out what the dishonesty is is and why it is
dishones then they are merely a baseless denigrator.
Hopefully
news.eternal-september.org
will be back up.
The dishonesty is claiming an error without pointing it out.
The dishonesty is also relying on rhetoric and ad hominem
instead of reasoning and evidence, Trump's favorite ploy.
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>>>>> or mathematical incompleteness.
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote:
On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>> would one try to
What makes you believe semantic relations that >>>>>>>>>>>>>>>>>>>>>>> can be structured asIt is a verified fact that Gödel's G is >>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday.
You can find any number of terms. That >>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them.
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no respect for >>>>>>>>>>>>>>>>>>>>>>>>>>> or understanding of the
truth. If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you then >>>>>>>>>>>>>>>>>>>>>>>>>>>> you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means is less >>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so the >>>>>>>>>>>>>>>>>>>>>>>>> fault here certainly doesn't lie with Alan. >>>>>>>>>>>>>>>>>>>>>>>>> It's certainly not a 'verified fact' when you >>>>>>>>>>>>>>>>>>>>>>>>> haven't even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>> that you mean.
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>> prevent loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>
Looking for a proof does not need any semantics so it is >>>>>>>>>>>>>>> not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>
It should be obvious that finding a proof does not happen >>>>>>>>>>>>> before
looking for a proof.
If there is no sequence of inference steps in Q from
~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>
Which has the semantic meaning "no number is equal to its
successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are sentences of Q but neither is a rheorem or Q does not depend on
any semantics.
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>>>>>> or mathematical incompleteness.
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote:
On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ]
They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>>> would one try toWhat makes you believe semantic relations that >>>>>>>>>>>>>>>>>>>>>>>> can be structured asIt is a verified fact that Gödel's G is >>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday.
You can find any number of terms. That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them.
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no respect >>>>>>>>>>>>>>>>>>>>>>>>>>>> for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means is >>>>>>>>>>>>>>>>>>>>>>>>>>> less
than no rebuttal at all.
"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so >>>>>>>>>>>>>>>>>>>>>>>>>> the fault here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean.
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure?
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>> completes.
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>> prevent loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>
Looking for a proof does not need any semantics so it is >>>>>>>>>>>>>>>> not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>
It should be obvious that finding a proof does not happen >>>>>>>>>>>>>> before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>
Which has the semantic meaning "no number is equal to its
successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are
sentences of Q but neither is a rheorem or Q does not depend on
any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
On 29/06/2026 06:12, olcott wrote:
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>> of general knowledge. It does this without undecidability >>>>>>>>>>>>>>>>>> or mathematical incompleteness.
On 6/24/2026 5:00 AM, Mikko wrote:
On 23/06/2026 17:48, olcott wrote:
On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>>> completes.They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>>>> would one try toWhat makes you believe semantic relations that >>>>>>>>>>>>>>>>>>>>>>>>> can be structured as"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so >>>>>>>>>>>>>>>>>>>>>>>>>>> the fault here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean.In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday.It is a verified fact that Gödel's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
You can find any number of terms. That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no respect >>>>>>>>>>>>>>>>>>>>>>>>>>>>> for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means is >>>>>>>>>>>>>>>>>>>>>>>>>>>> less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy.
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>> prevent loops.
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>
Looking for a proof does not need any semantics so it >>>>>>>>>>>>>>>>> is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not happen >>>>>>>>>>>>>>> before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>
Which has the semantic meaning "no number is equal to its
successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are
sentences of Q but neither is a rheorem or Q does not depend on
any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies
because the determination of their truth does not need any knowledge
beyond a method to determine whether a string is a tautology in the
relevant language.
When the word "knowledge" is used it usually means knowing about the
real world something that cannot be determined without observation.
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>> undecidability
On 6/24/2026 5:00 AM, Mikko wrote:If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>> prevent loops.
On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>>>> completes.They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>>>>> would one try toWhat makes you believe semantic relations that >>>>>>>>>>>>>>>>>>>>>>>>>> can be structured asAll of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so >>>>>>>>>>>>>>>>>>>>>>>>>>>> the fault here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
You can find any number of terms. That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no respect >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means >>>>>>>>>>>>>>>>>>>>>>>>>>>>> is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>
or mathematical incompleteness.
Looking for a proof does not need any semantics so it >>>>>>>>>>>>>>>>>> is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are
sentences of Q but neither is a rheorem or Q does not depend on
any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies
You are not paying close enough attention. I did not say logical
tautology. I said semantic tautology. That cats are defined to
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency. Thus,
“All humans are mammals” is held to assert with
regard to anything whatsoever that either it is
not a human or it is a mammal.
https://www.britannica.com/topic/tautology
https://en.wikipedia.org/wiki/Tautology_(logic)
because the determination of their truth does not need any knowledge
beyond a method to determine whether a string is a tautology in the
relevant language.
When the word "knowledge" is used it usually means knowing about the
real world something that cannot be determined without observation.
One can know that "cats are animals" when this is
stipulated as an axiom.
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). Essentially >>>>>>>>>>>>>>>>>>> PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>> undecidability
On 6/24/2026 5:00 AM, Mikko wrote:If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>> prevent loops.
On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>>>> completes.They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>>>>> would one try toWhat makes you believe semantic relations that >>>>>>>>>>>>>>>>>>>>>>>>>> can be structured asAll of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so >>>>>>>>>>>>>>>>>>>>>>>>>>>> the fault here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
You can find any number of terms. That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under PTS >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no respect >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility.
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means >>>>>>>>>>>>>>>>>>>>>>>>>>>>> is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
a tree are sufficient to contain all knowledge >>>>>>>>>>>>>>>>>>>>>>>>>> that is exressed in
some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>
or mathematical incompleteness.
Looking for a proof does not need any semantics so it >>>>>>>>>>>>>>>>>> is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is
unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are
sentences of Q but neither is a rheorem or Q does not depend on
any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies
You are not paying close enough attention. I did not say logical
tautology. I said semantic tautology. That cats are defined to
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>> Essentially
On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>>> prevent loops.
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>>>>> completes.They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>>>>>> would one try toWhat makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>> some language?All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so >>>>>>>>>>>>>>>>>>>>>>>>>>>>> the fault here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
You can find any number of terms. That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no respect >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it >>>>>>>>>>>>>>>>>>> is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is >>>>>>> unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are >>>>> sentences of Q but neither is a rheorem or Q does not depend on
any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies
You are not paying close enough attention. I did not say logical
tautology. I said semantic tautology. That cats are defined to
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency. Thus,
“All humans are mammals” is held to assert with
regard to anything whatsoever that either it is
not a human or it is a mammal.
https://www.britannica.com/topic/tautology
https://en.wikipedia.org/wiki/Tautology_(logic)
because the determination of their truth does not need any knowledge
beyond a method to determine whether a string is a tautology in the
relevant language.
When the word "knowledge" is used it usually means knowing about the
real world something that cannot be determined without observation.
One can know that "cats are animals" when this is
stipulated as an axiom.
That axiom only realtes the words "cat" and "animal". It does not tell anything about the real world.
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete.
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote:Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>> Essentially
On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>>> prevent loops.
It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>>>>> completes.They use a tree structure for concepts. But why >>>>>>>>>>>>>>>>>>>>>>>>> would one try toWhat makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>> some language?All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, so >>>>>>>>>>>>>>>>>>>>>>>>>>>>> the fault here certainly doesn't lie with >>>>>>>>>>>>>>>>>>>>>>>>>>>>> Alan. It's certainly not a 'verified fact' >>>>>>>>>>>>>>>>>>>>>>>>>>>>> when you haven't even adequately explained >>>>>>>>>>>>>>>>>>>>>>>>>>>>> what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic atomic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
You can find any number of terms. That >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no respect >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>
How can any ordering of knowledge prevent getting >>>>>>>>>>>>>>>>>>>>>>> stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so it >>>>>>>>>>>>>>>>>>> is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps
in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is >>>>>>> unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are >>>>> sentences of Q but neither is a rheorem or Q does not depend on
any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies
You are not paying close enough attention. I did not say logical
tautology. I said semantic tautology. That cats are defined to
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
So, if you want to know more about my theory, which is an account
of reason, and for Foundations, then I'd suggest first making for
yourself a "universal education", then finding resolutions to the
"paradoxes" of mathematical logic,
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" the
"great atlas of mathematical independence", then for "higher
mathematics", and quite about "continuity" and "infinity",
then there's also "the physics" after "the logic" and "the mathematics".
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an account
of reason, and for Foundations, then I'd suggest first making for
yourself a "universal education", then finding resolutions to the
"paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G ↔ ¬Prov_PA(⌜G⌝)
Directed Graph of evaluation sequence
00 ↔ 01 02
01 G
02 ¬ 03
03 Prov_PA 04
04 Gödel_Number_of 01 // cycle indicates no well-founded justification
tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
Curry–Howard correspondence
In programming language theory and proof theory,
the Curry–Howard correspondence is a direct relationship
between computer programs and mathematical proofs. https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" the
"great atlas of mathematical independence", then for "higher
mathematics", and quite about "continuity" and "infinity",
then there's also "the physics" after "the logic" and "the mathematics".
On 06/30/2026 07:53 AM, olcott wrote:
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an account
of reason, and for Foundations, then I'd suggest first making for
yourself a "universal education", then finding resolutions to the
"paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G ↔ ¬Prov_PA(⌜G⌝)
Directed Graph of evaluation sequence
00 ↔ 01 02
01 G
02 ¬ 03
03 Prov_PA 04
04 Gödel_Number_of 01 // cycle indicates no well-founded justification
tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
Curry–Howard correspondence
In programming language theory and proof theory,
the Curry–Howard correspondence is a direct relationship
between computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" the
"great atlas of mathematical independence", then for "higher
mathematics", and quite about "continuity" and "infinity",
then there's also "the physics" after "the logic" and "the mathematics". >>>
"Curry's poor substitute" at least rejects material implication.
Matters of meaning or the epistemological is a field called "semiotics". Semantics after syntax is properly logical, that's all.
Cycle-detection is a usual routine involving memory and time, the
resources.
The Liar Paradox is just a template of what would be a fallacy:
two wrongs don't make a right.
unify_with_occurs_check(and(false(LP), true(LP)))
Two wrongs don't make a right.
Russell's retro-thesis is hypocrisy veiled as authority.
Where's the GUID for "dictionary", or "vocabulary", and what's in it.
"Cat" is a word.
On 06/30/2026 10:36 AM, Ross Finlayson wrote:
On 06/30/2026 07:53 AM, olcott wrote:
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an account
of reason, and for Foundations, then I'd suggest first making for
yourself a "universal education", then finding resolutions to the
"paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G ↔ ¬Prov_PA(⌜G⌝)
Directed Graph of evaluation sequence
00 ↔ 01 02
01 G
02 ¬ 03
03 Prov_PA 04
04 Gödel_Number_of 01 // cycle indicates no well-founded justification >>> tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
Curry–Howard correspondence
In programming language theory and proof theory,
the Curry–Howard correspondence is a direct relationship
between computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" the
"great atlas of mathematical independence", then for "higher
mathematics", and quite about "continuity" and "infinity",
then there's also "the physics" after "the logic" and "the
mathematics".
"Curry's poor substitute" at least rejects material implication.
Matters of meaning or the epistemological is a field called "semiotics".
Semantics after syntax is properly logical, that's all.
Cycle-detection is a usual routine involving memory and time, the
resources.
The Liar Paradox is just a template of what would be a fallacy:
two wrongs don't make a right.
unify_with_occurs_check(and(false(LP), true(LP)))
Two wrongs don't make a right.
Russell's retro-thesis is hypocrisy veiled as authority.
Where's the GUID for "dictionary", or "vocabulary", and what's in it.
"Cat" is a word.
It's fair to say "the Liar Paradox is false",
then that the negation translates through the copula "is"
to result "this sentence is true", a meaningless, empty tautology
(except as quoted a meaningless, empty, tautology).
It doesn't work on other "paradoxes", though.
Finlayson's paradox: there are none.
On 6/30/2026 2:48 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>> Essentially
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>>>> prevent loops.It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>>>>>> completes.They use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>> why would one try toAll of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>> strings."grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> so the fault here certainly doesn't lie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with Alan. It's certainly not a 'verified >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fact' when you haven't even adequately >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explained what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:It is a verified fact that Gödel's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so >>>>>>>>>>>>>>>>>>>> it is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is >>>>>>>> unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are >>>>>> sentences of Q but neither is a rheorem or Q does not depend on
any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies
You are not paying close enough attention. I did not say logical
tautology. I said semantic tautology. That cats are defined to
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency. Thus,
“All humans are mammals” is held to assert with
regard to anything whatsoever that either it is
not a human or it is a mammal.
https://www.britannica.com/topic/tautology
https://en.wikipedia.org/wiki/Tautology_(logic)
because the determination of their truth does not need any knowledge
beyond a method to determine whether a string is a tautology in the
relevant language.
When the word "knowledge" is used it usually means knowing about the
real world something that cannot be determined without observation.
One can know that "cats are animals" when this is
stipulated as an axiom.
That axiom only realtes the words "cat" and "animal". It does not tell
anything about the real world.
It tells us exactly one thing about the real world.
On 6/30/2026 3:43 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote:
On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>> Essentially
If you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>>>> prevent loops.It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and never >>>>>>>>>>>>>>>>>>>>>>>>> completes.They use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>> why would one try toAll of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>> strings."grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is one >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> which you have never explicitly defined, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> so the fault here certainly doesn't lie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> with Alan. It's certainly not a 'verified >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fact' when you haven't even adequately >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> explained what it is that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:It is a verified fact that Gödel's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand
what: "grounded in the atomic base" means >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so >>>>>>>>>>>>>>>>>>>> it is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x)
in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is >>>>>>>> unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are >>>>>> sentences of Q but neither is a rheorem or Q does not depend on
any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies
You are not paying close enough attention. I did not say logical
tautology. I said semantic tautology. That cats are defined to
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
When a complete set of general "atomic facts" of the
actual world is encoded as axioms along with all of
the semantic entailment relations between these facts
then every element of general knowledge that can be
expressed in language is known by this system.
On 6/30/2026 9:47 PM, Ross Finlayson wrote:
On 06/30/2026 10:36 AM, Ross Finlayson wrote:
On 06/30/2026 07:53 AM, olcott wrote:
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an account
of reason, and for Foundations, then I'd suggest first making for
yourself a "universal education", then finding resolutions to the
"paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G ↔ ¬Prov_PA(⌜G⌝)
Directed Graph of evaluation sequence
00 ↔ 01 02
01 G
02 ¬ 03
03 Prov_PA 04
04 Gödel_Number_of 01 // cycle indicates no well-founded justification >>>> tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
Curry–Howard correspondence
In programming language theory and proof theory,
the Curry–Howard correspondence is a direct relationship
between computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" the
"great atlas of mathematical independence", then for "higher
mathematics", and quite about "continuity" and "infinity",
then there's also "the physics" after "the logic" and "the
mathematics".
"Curry's poor substitute" at least rejects material implication.
Matters of meaning or the epistemological is a field called "semiotics". >>> Semantics after syntax is properly logical, that's all.
Cycle-detection is a usual routine involving memory and time, the
resources.
The Liar Paradox is just a template of what would be a fallacy:
two wrongs don't make a right.
unify_with_occurs_check(and(false(LP), true(LP)))
Two wrongs don't make a right.
Russell's retro-thesis is hypocrisy veiled as authority.
Where's the GUID for "dictionary", or "vocabulary", and what's in it.
"Cat" is a word.
It's fair to say "the Liar Paradox is false",
then that the negation translates through the copula "is"
to result "this sentence is true", a meaningless, empty tautology
(except as quoted a meaningless, empty, tautology).
It doesn't work on other "paradoxes", though.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics almost gets there
through an enormously more convoluted process.
They almost always utterly avoid any nuance of
true. Instead they focus on meaning.
Finlayson's paradox: there are none.
On 06/30/2026 08:01 PM, olcott wrote:
On 6/30/2026 9:47 PM, Ross Finlayson wrote:
On 06/30/2026 10:36 AM, Ross Finlayson wrote:
On 06/30/2026 07:53 AM, olcott wrote:
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an account
of reason, and for Foundations, then I'd suggest first making for
yourself a "universal education", then finding resolutions to the
"paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G ↔ ¬Prov_PA(⌜G⌝)
Directed Graph of evaluation sequence
00 ↔ 01 02
01 G
02 ¬ 03
03 Prov_PA 04
04 Gödel_Number_of 01 // cycle indicates no well-founded
justification
tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
Curry–Howard correspondence
In programming language theory and proof theory,
the Curry–Howard correspondence is a direct relationship
between computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" the >>>>>> "great atlas of mathematical independence", then for "higher
mathematics", and quite about "continuity" and "infinity",
then there's also "the physics" after "the logic" and "the
mathematics".
"Curry's poor substitute" at least rejects material implication.
Matters of meaning or the epistemological is a field called
"semiotics".
Semantics after syntax is properly logical, that's all.
Cycle-detection is a usual routine involving memory and time, the
resources.
The Liar Paradox is just a template of what would be a fallacy:
two wrongs don't make a right.
unify_with_occurs_check(and(false(LP), true(LP)))
Two wrongs don't make a right.
Russell's retro-thesis is hypocrisy veiled as authority.
Where's the GUID for "dictionary", or "vocabulary", and what's in it.
"Cat" is a word.
It's fair to say "the Liar Paradox is false",
then that the negation translates through the copula "is"
to result "this sentence is true", a meaningless, empty tautology
(except as quoted a meaningless, empty, tautology).
It doesn't work on other "paradoxes", though.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics almost gets there
through an enormously more convoluted process.
They almost always utterly avoid any nuance of
true. Instead they focus on meaning.
Finlayson's paradox: there are none.
That quote of Wittgenstein's just a weak echo of Leibnitz' "principle of sufficient reason" about what an inference is. The Tractatus
Logicophilosophicus starts alright then Wittgenstein wimps out while
being all hot-headed about it later. Russell's favorite philosophers, Plotinus after Philo, are early weak nominalist fictionalists, and
having material implication in their vacuous implicits and so on,
Chrysippus could throw them from the boat since neither are they Pythagoreans.
A much simpler process arrives at a "principle of _thorough_ reason",
where not only are affirmatory and negatory inferences found,
also in the diligence any their contradictions.
Russell's retro-thesis simply can't make the extra-ordinary go away.
It's considered a quasi-modal variety of the weaker sort of the
logicist positivism, which has a stronger variety after a strong
mathematical platonism which invigorates it as "must be science".
Old schlock wrapped as new, ....
On 30/06/2026 16:43, olcott wrote:
On 6/30/2026 2:48 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>> EssentiallyIf you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>>>>> prevent loops.It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and >>>>>>>>>>>>>>>>>>>>>>>>>> neverThey use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>>> why would one try to"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a 'verified fact' when you haven't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> adequately explained what it is that you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean.In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:It is a verified fact that Gödel's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> strings.
What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so >>>>>>>>>>>>>>>>>>>>> it is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>> in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is >>>>>>>>> unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are >>>>>>> sentences of Q but neither is a rheorem or Q does not depend on
any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies
You are not paying close enough attention. I did not say logical
tautology. I said semantic tautology. That cats are defined to
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
tautology, in logic, a statement so framed that
it cannot be denied without inconsistency. Thus,
“All humans are mammals” is held to assert with
regard to anything whatsoever that either it is
not a human or it is a mammal.
https://www.britannica.com/topic/tautology
https://en.wikipedia.org/wiki/Tautology_(logic)
because the determination of their truth does not need any knowledge >>>>> beyond a method to determine whether a string is a tautology in the
relevant language.
When the word "knowledge" is used it usually means knowing about the >>>>> real world something that cannot be determined without observation.
One can know that "cats are animals" when this is
stipulated as an axiom.
That axiom only realtes the words "cat" and "animal". It does not tell
anything about the real world.
It tells us exactly one thing about the real world.
Only to those who already know that there are things called "cat"
in the real world and know what kind of things the words "cat" and
"animal" refer to but don't already know that every thing that the
word "cat" refers to is a thing that the word "animal" refers to.
On 30/06/2026 17:22, olcott wrote:
On 6/30/2026 3:43 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>> EssentiallyIf you mean not looking elsewhere that may indeed >>>>>>>>>>>>>>>>>>>>>>> prevent loops.It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and >>>>>>>>>>>>>>>>>>>>>>>>>> neverThey use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>>> why would one try to"grounded in the atomic base of PA" is an >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> expression used only by you, and it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly not >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a 'verified fact' when you haven't even >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> adequately explained what it is that you >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> mean.In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:It is a verified fact that Gödel's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less
than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> specified syntactically between finite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> strings.
What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent body >>>>>>>>>>>>>>>>>>>>>> of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so >>>>>>>>>>>>>>>>>>>>> it is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>> in Q it is an open question in Q and not a confirmed
statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is >>>>>>>>> unprovable / out-of-scope / not semantically grounded in Q.
Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are >>>>>>> sentences of Q but neither is a rheorem or Q does not depend on
any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies
You are not paying close enough attention. I did not say logical
tautology. I said semantic tautology. That cats are defined to
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
When a complete set of general "atomic facts" of the
actual world is encoded as axioms along with all of
the semantic entailment relations between these facts
then every element of general knowledge that can be
expressed in language is known by this system.
In order to achieve that the atomic facts must be non-tautologies.
Tautologies need not be included. They can be concluded from nothing.
The only semantic entailments that need be encoded are definitions. Everything else is covered by requiring that an inference from A nnd
B to X is accepted as valid only if ¬A ∨ ¬B ∨ X is a tautology.
Nothing else is semantically entailed.
On 7/1/2026 7:13 AM, Ross Finlayson wrote:
On 06/30/2026 08:01 PM, olcott wrote:
On 6/30/2026 9:47 PM, Ross Finlayson wrote:
On 06/30/2026 10:36 AM, Ross Finlayson wrote:
On 06/30/2026 07:53 AM, olcott wrote:
On 6/30/2026 8:23 AM, Ross Finlayson wrote:
So, if you want to know more about my theory, which is an account >>>>>>> of reason, and for Foundations, then I'd suggest first making for >>>>>>> yourself a "universal education", then finding resolutions to the >>>>>>> "paradoxes" of mathematical logic,
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
Olcott's Minimal Type Theory
G ↔ ¬Prov_PA(⌜G⌝)
Directed Graph of evaluation sequence
00 ↔ 01 02
01 G
02 ¬ 03
03 Prov_PA 04
04 Gödel_Number_of 01 // cycle indicates no well-founded
justification
tree exists.
ZFC already handled Russell's Paradox converting set
theory into Naive set theory.
It is important to keep computation in the loop
because computation exposes the hidden assumptions
that math makes.
Curry–Howard correspondence
In programming language theory and proof theory,
the Curry–Howard correspondence is a direct relationship
between computer programs and mathematical proofs.
https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
then revealing the "super-classical"
results of classical mathematics, then for the "extra-ordinary" the >>>>>>> "great atlas of mathematical independence", then for "higher
mathematics", and quite about "continuity" and "infinity",
then there's also "the physics" after "the logic" and "the
mathematics".
"Curry's poor substitute" at least rejects material implication.
Matters of meaning or the epistemological is a field called
"semiotics".
Semantics after syntax is properly logical, that's all.
Cycle-detection is a usual routine involving memory and time, the
resources.
The Liar Paradox is just a template of what would be a fallacy:
two wrongs don't make a right.
unify_with_occurs_check(and(false(LP), true(LP)))
Two wrongs don't make a right.
Russell's retro-thesis is hypocrisy veiled as authority.
Where's the GUID for "dictionary", or "vocabulary", and what's in it. >>>>> "Cat" is a word.
It's fair to say "the Liar Paradox is false",
then that the negation translates through the copula "is"
to result "this sentence is true", a meaningless, empty tautology
(except as quoted a meaningless, empty, tautology).
It doesn't work on other "paradoxes", though.
Wittgenstein (1937)
'True in Russell's system' means, as was said:
proved in Russell's system; and 'false in Russell's
system' means: the opposite has been proved
in Russell's system
Proof Theoretic Semantics almost gets there
through an enormously more convoluted process.
They almost always utterly avoid any nuance of
true. Instead they focus on meaning.
Finlayson's paradox: there are none.
That quote of Wittgenstein's just a weak echo of Leibnitz' "principle of
sufficient reason" about what an inference is. The Tractatus
Correct reasoning is not correctly evaluated on the
basis of who came up with the ideas. These ideas either
has a sound basis or not.
It just the same thing that I have been saying fir years.
True on the basis of meaning expressed in language must
have a direct semantic connection to those things in the
directly in the formal system of this language that make it
true.
(a) Cats are animals
(b) Animals are living things
(c) ∴ Cats are living things
No jumping outside of the language to a separate model.
Logicophilosophicus starts alright then Wittgenstein wimps out while
being all hot-headed about it later. Russell's favorite philosophers,
Plotinus after Philo, are early weak nominalist fictionalists, and
having material implication in their vacuous implicits and so on,
Chrysippus could throw them from the boat since neither are they
Pythagoreans.
A much simpler process arrives at a "principle of _thorough_ reason",
where not only are affirmatory and negatory inferences found,
also in the diligence any their contradictions.
That is what I just showed.
Russell's retro-thesis simply can't make the extra-ordinary go away.
It's considered a quasi-modal variety of the weaker sort of the
logicist positivism, which has a stronger variety after a strong
mathematical platonism which invigorates it as "must be science".
Old schlock wrapped as new, ....
The only way to obtain a correct foundation of these
things is to reverse-engineer them from first principles.
If one does not do that then the extraneous baggage
of the differing human perspectives prevent a fully
coherent view.
On 7/1/2026 2:13 AM, Mikko wrote:
On 30/06/2026 17:22, olcott wrote:
On 6/30/2026 3:43 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote:
On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>> EssentiallyIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and >>>>>>>>>>>>>>>>>>>>>>>>>>> neverThey use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>>>> why would one try to"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean.[ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ungrounded
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why under >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to persuade >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then cite >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
All of knowledge expressed in language is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically between >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> finite strings.
What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>
put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof?
By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the proof. >>>>>>>>>>>>>>>>>>>>>>>
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent >>>>>>>>>>>>>>>>>>>>>>> body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness.
Looking for a proof does not need any semantics so >>>>>>>>>>>>>>>>>>>>>> it is not obvious
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>>>
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>> happen before
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) is >>>>>>>>>> unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are >>>>>>>> sentences of Q but neither is a rheorem or Q does not depend on >>>>>>>> any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies
You are not paying close enough attention. I did not say logical
tautology. I said semantic tautology. That cats are defined to
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
When a complete set of general "atomic facts" of the
actual world is encoded as axioms along with all of
the semantic entailment relations between these facts
then every element of general knowledge that can be
expressed in language is known by this system.
In order to achieve that the atomic facts must be non-tautologies.
That "cats" <are> "animals" is a semantic tautology.
"atomic facts" that correspond to things in the worldOne usually says "assumption" instead of "stipulation". The latter
only have stipulation as their basis in truth within
the formal system.
On 01/07/2026 18:13, olcott wrote:
On 7/1/2026 2:13 AM, Mikko wrote:
On 30/06/2026 17:22, olcott wrote:
On 6/30/2026 3:43 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:You are not paying close enough attention. I did not say logical
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:
On 6/27/2026 11:43 AM, polcott wrote:
On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote:
On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>>> happen before
In proof theoretic semantics an expression only gains >>>>>>>>>>>>>>>>>>>>>> semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>Looking for a proof does not need any semantics >>>>>>>>>>>>>>>>>>>>>>> so it is not obviousIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic graph or >>>>>>>>>>>>>>>>>>>>>>>>>>>> the proof gets stuck in an infinite loop and >>>>>>>>>>>>>>>>>>>>>>>>>>>> neverThey use a tree structure for concepts. But >>>>>>>>>>>>>>>>>>>>>>>>>>>>> why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic relations >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?All of knowledge expressed in language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>[ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails.
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop
when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the >>>>>>>>>>>>>>>>>>>>>>>>> proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into one coherent >>>>>>>>>>>>>>>>>>>>>>>> body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>
how switching to another semantics could improve it. >>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q.
i.e., ~∃x x=S(x) is unprovable is Q, as is commonly known. >>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to its >>>>>>>>>>>>>>> successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) >>>>>>>>>>> is unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>>
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are >>>>>>>>> sentences of Q but neither is a rheorem or Q does not depend on >>>>>>>>> any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies >>>>>>
tautology. I said semantic tautology. That cats are defined to
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
When a complete set of general "atomic facts" of the
actual world is encoded as axioms along with all of
the semantic entailment relations between these facts
then every element of general knowledge that can be
expressed in language is known by this system.
In order to achieve that the atomic facts must be non-tautologies.
That "cats" <are> "animals" is a semantic tautology.
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
or it can be a consequence of the
definitions of "cat" and "animal" and terms used in these definitions
that tells nothing about the real world, or it can be a statement
about the real world that cannot be inferred from definitions alne.
"atomic facts" that correspond to things in the world
only have stipulation as their basis in truth within
the formal system.
One usually says "assumption" instead of "stipulation". The latter
usually means a rfusal to proceed before the stipulation is accepted
or an alternative agreed.
On 7/2/2026 1:44 AM, Mikko wrote:
On 01/07/2026 18:13, olcott wrote:
On 7/1/2026 2:13 AM, Mikko wrote:
On 30/06/2026 17:22, olcott wrote:
On 6/30/2026 3:43 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:You are not paying close enough attention. I did not say logical >>>>>>> tautology. I said semantic tautology. That cats are defined to
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:i.e., ~∃x x=S(x) is unprovable is Q, as is commonly >>>>>>>>>>>>>>>>>> known.
On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>>>> happen beforeLooking for a proof does not need any semantics >>>>>>>>>>>>>>>>>>>>>>>> so it is not obviousIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for concepts. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:All of knowledge expressed in language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>[ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
the proof gets stuck in an infinite loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>> and never
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the >>>>>>>>>>>>>>>>>>>>>>>>>> proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>
how switching to another semantics could improve >>>>>>>>>>>>>>>>>>>>>>>> it.
In proof theoretic semantics an expression only >>>>>>>>>>>>>>>>>>>>>>> gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>> its successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) >>>>>>>>>>>> is unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>>>
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are >>>>>>>>>> sentences of Q but neither is a rheorem or Q does not depend on >>>>>>>>>> any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies >>>>>>>
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
When a complete set of general "atomic facts" of the
actual world is encoded as axioms along with all of
the semantic entailment relations between these facts
then every element of general knowledge that can be
expressed in language is known by this system.
In order to achieve that the atomic facts must be non-tautologies.
That "cats" <are> "animals" is a semantic tautology.
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
or it can be a consequence of the
definitions of "cat" and "animal" and terms used in these definitions
it tells us exactly one thong about the real world
through the definition of terms.
that tells nothing about the real world, or it can be a statement
about the real world that cannot be inferred from definitions alne.
"atomic facts" that correspond to things in the world
only have stipulation as their basis in truth within
the formal system.
One usually says "assumption" instead of "stipulation". The latter
usually means a rfusal to proceed before the stipulation is accepted
or an alternative agreed.
https://en.wikipedia.org/wiki/Stipulative_definition
Cats are animals, if you disagree then you are necessarily incorrect.
On 07/02/2026 07:45 AM, olcott wrote:
On 7/2/2026 1:44 AM, Mikko wrote:
On 01/07/2026 18:13, olcott wrote:
On 7/1/2026 2:13 AM, Mikko wrote:
On 30/06/2026 17:22, olcott wrote:
On 6/30/2026 3:43 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:You are not paying close enough attention. I did not say logical >>>>>>>> tautology. I said semantic tautology. That cats are defined to >>>>>>>> be animals is a semantic tautology. That cats are defined to be >>>>>>>> cats is a logical tautology. Here is a definition of that fits >>>>>>>> my definition of semantic tautology.
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:i.e., ~∃x x=S(x) is unprovable is Q, as is commonly >>>>>>>>>>>>>>>>>>> known.
On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>>>>> happen beforeLooking for a proof does not need any semantics >>>>>>>>>>>>>>>>>>>>>>>>> so it is not obviousIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for concepts. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>All of knowledge expressed in language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
the proof gets stuck in an infinite loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and never
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the >>>>>>>>>>>>>>>>>>>>>>>>>>> proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic >>>>>>>>>>>>>>>>>>>>>>>>>> meanings
expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>
how switching to another semantics could improve >>>>>>>>>>>>>>>>>>>>>>>>> it.
In proof theoretic semantics an expression only >>>>>>>>>>>>>>>>>>>>>>>> gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>>> its successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) >>>>>>>>>>>>> is unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>>>>
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are
sentences of Q but neither is a rheorem or Q does not depend on >>>>>>>>>>> any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies >>>>>>>>
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
When a complete set of general "atomic facts" of the
actual world is encoded as axioms along with all of
the semantic entailment relations between these facts
then every element of general knowledge that can be
expressed in language is known by this system.
In order to achieve that the atomic facts must be non-tautologies.
That "cats" <are> "animals" is a semantic tautology.
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
or it can be a consequence of the
definitions of "cat" and "animal" and terms used in these definitions
it tells us exactly one thong about the real world
through the definition of terms.
that tells nothing about the real world, or it can be a statement
about the real world that cannot be inferred from definitions alne.
"atomic facts" that correspond to things in the world
only have stipulation as their basis in truth within
the formal system.
One usually says "assumption" instead of "stipulation". The latter
usually means a rfusal to proceed before the stipulation is accepted
or an alternative agreed.
https://en.wikipedia.org/wiki/Stipulative_definition
Cats are animals, if you disagree then you are necessarily incorrect.
Animals are {cats, dogs, wallabies, llamas, aardvarks, crustaceans,
...}, a potentially infinitary expression.
On 7/2/2026 1:44 AM, Mikko wrote:
On 01/07/2026 18:13, olcott wrote:
On 7/1/2026 2:13 AM, Mikko wrote:
On 30/06/2026 17:22, olcott wrote:
On 6/30/2026 3:43 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:You are not paying close enough attention. I did not say logical >>>>>>> tautology. I said semantic tautology. That cats are defined to
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:i.e., ~∃x x=S(x) is unprovable is Q, as is commonly >>>>>>>>>>>>>>>>>> known.
On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>>>> happen beforeLooking for a proof does not need any semantics >>>>>>>>>>>>>>>>>>>>>>>> so it is not obviousIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for concepts. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:All of knowledge expressed in language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>[ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
the proof gets stuck in an infinite loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>> and never
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the >>>>>>>>>>>>>>>>>>>>>>>>>> proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>
how switching to another semantics could improve >>>>>>>>>>>>>>>>>>>>>>>> it.
In proof theoretic semantics an expression only >>>>>>>>>>>>>>>>>>>>>>> gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>> its successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) >>>>>>>>>>>> is unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>>>
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are >>>>>>>>>> sentences of Q but neither is a rheorem or Q does not depend on >>>>>>>>>> any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies >>>>>>>
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
When a complete set of general "atomic facts" of the
actual world is encoded as axioms along with all of
the semantic entailment relations between these facts
then every element of general knowledge that can be
expressed in language is known by this system.
In order to achieve that the atomic facts must be non-tautologies.
That "cats" <are> "animals" is a semantic tautology.
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
On 07/02/2026 07:45 AM, olcott wrote:
On 7/2/2026 1:44 AM, Mikko wrote:
On 01/07/2026 18:13, olcott wrote:
On 7/1/2026 2:13 AM, Mikko wrote:
On 30/06/2026 17:22, olcott wrote:
On 6/30/2026 3:43 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:You are not paying close enough attention. I did not say logical >>>>>>>> tautology. I said semantic tautology. That cats are defined to >>>>>>>> be animals is a semantic tautology. That cats are defined to be >>>>>>>> cats is a logical tautology. Here is a definition of that fits >>>>>>>> my definition of semantic tautology.
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:i.e., ~∃x x=S(x) is unprovable is Q, as is commonly >>>>>>>>>>>>>>>>>>> known.
On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>>>>> happen beforeLooking for a proof does not need any semantics >>>>>>>>>>>>>>>>>>>>>>>>> so it is not obviousIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for concepts. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> [ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>All of knowledge expressed in language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
the proof gets stuck in an infinite loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and never
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the >>>>>>>>>>>>>>>>>>>>>>>>>>> proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic >>>>>>>>>>>>>>>>>>>>>>>>>> meanings
expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>>
how switching to another semantics could improve >>>>>>>>>>>>>>>>>>>>>>>>> it.
In proof theoretic semantics an expression only >>>>>>>>>>>>>>>>>>>>>>>> gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x)
is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>>> its successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) >>>>>>>>>>>>> is unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>>>>
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are
sentences of Q but neither is a rheorem or Q does not depend on >>>>>>>>>>> any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies >>>>>>>>
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
When a complete set of general "atomic facts" of the
actual world is encoded as axioms along with all of
the semantic entailment relations between these facts
then every element of general knowledge that can be
expressed in language is known by this system.
In order to achieve that the atomic facts must be non-tautologies.
That "cats" <are> "animals" is a semantic tautology.
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
or it can be a consequence of the
definitions of "cat" and "animal" and terms used in these definitions
it tells us exactly one thong about the real world
through the definition of terms.
that tells nothing about the real world, or it can be a statement
about the real world that cannot be inferred from definitions alne.
"atomic facts" that correspond to things in the world
only have stipulation as their basis in truth within
the formal system.
One usually says "assumption" instead of "stipulation". The latter
usually means a rfusal to proceed before the stipulation is accepted
or an alternative agreed.
https://en.wikipedia.org/wiki/Stipulative_definition
Cats are animals, if you disagree then you are necessarily incorrect.
Animals are {cats, dogs, wallabies, llamas, aardvarks, crustaceans,
...}, a potentially infinitary expression.
On 7/2/2026 1:44 AM, Mikko wrote:
On 01/07/2026 18:13, olcott wrote:
On 7/1/2026 2:13 AM, Mikko wrote:
On 30/06/2026 17:22, olcott wrote:
On 6/30/2026 3:43 AM, Mikko wrote:
On 29/06/2026 16:38, olcott wrote:
On 6/29/2026 1:23 AM, Mikko wrote:
On 29/06/2026 06:12, olcott wrote:You are not paying close enough attention. I did not say logical >>>>>>> tautology. I said semantic tautology. That cats are defined to
On 6/28/2026 4:31 AM, Mikko wrote:
On 27/06/2026 22:40, olcott wrote:
On 6/27/2026 2:23 PM, dbush wrote:
On 6/27/2026 3:16 PM, olcott wrote:Proof theoretic semantics DOES NOT DO IT THAT WAY !!!
On 6/27/2026 2:04 PM, dbush wrote:
On 6/27/2026 3:01 PM, olcott wrote:Yet never gets to undecidable or in any sense of incomplete. >>>>>>>>>>>>>
On 6/27/2026 1:39 PM, dbush wrote:
On 6/27/2026 2:38 PM, olcott wrote:
On 6/27/2026 1:29 PM, dbush wrote:
On 6/27/2026 2:27 PM, olcott wrote:Is it commonly known that ~∃x x=S(x)
On 6/27/2026 1:01 PM, dbush wrote:i.e., ~∃x x=S(x) is unprovable is Q, as is commonly >>>>>>>>>>>>>>>>>> known.
On 6/27/2026 11:43 AM, polcott wrote: >>>>>>>>>>>>>>>>>>>>> On 6/27/2026 2:35 AM, Mikko wrote:
On 26/06/2026 16:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 6/26/2026 1:39 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 25/06/2026 19:14, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 6/25/2026 2:21 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 24/06/2026 23:26, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/24/2026 5:00 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 23/06/2026 17:48, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/23/2026 1:06 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 15:10, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/22/2026 1:49 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 22/06/2026 02:02, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 4:08 PM, André G. Isaak >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:
It should be obvious that finding a proof does not >>>>>>>>>>>>>>>>>>>>>> happen beforeLooking for a proof does not need any semantics >>>>>>>>>>>>>>>>>>>>>>>> so it is not obviousIf you mean not looking elsewhere that may >>>>>>>>>>>>>>>>>>>>>>>>>> indeed prevent loops.By looking upward in a type hierarchy. >>>>>>>>>>>>>>>>>>>>>>>>>>It must at least be a directed acyclic >>>>>>>>>>>>>>>>>>>>>>>>>>>>> graph orThey use a tree structure for concepts. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> But why would one try to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> put knowledge in a tree structure? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>What makes you believe semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations that can be structured as >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> a tree are sufficient to contain all >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> knowledge that is exressed in >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some language?On 2026-06-21 14:42, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 3:04 PM, Alan Mackenzie >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrote:All of knowledge expressed in language >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is structured as a tree of semantic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> relations specified syntactically >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> between finite strings. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
"grounded in the atomic base of PA" is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> an expression used only by you, and it >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is one which you have never explicitly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> defined, so the fault here certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> doesn't lie with Alan. It's certainly >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not a 'verified fact' when you haven't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> even adequately explained what it is >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that you mean. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>[ Followup-To: set ] >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>It is a verified fact that Gödel's G >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is ungrounded >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in the atomic base of PA. That you do >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> not understand >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> what: "grounded in the atomic base" >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> means is less >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> than no rebuttal at all. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 6/21/2026 6:26 AM, Alan >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Mackenzie wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> In comp.theory olcott >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> I just found the term: >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> "grounding in a proof theoretic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> atomic base" yesterday. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
I don't believe you. You have no >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> respect for or understanding of the >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> truth. If you really want to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> persuade anybody that PTS somehow >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> causes >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Gödel's theorem not to hold, then >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cite an academic expert who'll have >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> some credibility. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You can find any number of terms. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That doesn't mean you're capable of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understanding them. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
The above is the key reason why >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> under PTS Gödel 1931 incompleteness >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> fails. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
If they are mere gibberish words to >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> you then you will not understand. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>You don't understand Proof-theoritic >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Semantics, and you certainly don't >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> understand Gödel's Theorem, neither >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the theorem itself nor any proof of >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it.
The CycL language and the Cyc Project. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
the proof gets stuck in an infinite loop >>>>>>>>>>>>>>>>>>>>>>>>>>>>> and never
completes.
How can any ordering of knowledge prevent >>>>>>>>>>>>>>>>>>>>>>>>>>>> getting stuck in a loop >>>>>>>>>>>>>>>>>>>>>>>>>>>> when looking for a proof? >>>>>>>>>>>>>>>>>>>>>>>>>>>
In most cases that also prevents finding the >>>>>>>>>>>>>>>>>>>>>>>>>> proof.
Truth Conditional Semantics (TCS) <is> incoherent >>>>>>>>>>>>>>>>>>>>>>>>> compared to Proof Theoretic Semantics (PTS). >>>>>>>>>>>>>>>>>>>>>>>>> Essentially
PTS just coherently connects the semantic meanings >>>>>>>>>>>>>>>>>>>>>>>>> expressed in language together into one >>>>>>>>>>>>>>>>>>>>>>>>> coherent body
of general knowledge. It does this without >>>>>>>>>>>>>>>>>>>>>>>>> undecidability
or mathematical incompleteness. >>>>>>>>>>>>>>>>>>>>>>>>
how switching to another semantics could improve >>>>>>>>>>>>>>>>>>>>>>>> it.
In proof theoretic semantics an expression only >>>>>>>>>>>>>>>>>>>>>>> gains
semantic meaning by finding a proof. >>>>>>>>>>>>>>>>>>>>>>
looking for a proof.
If there is no sequence of inference steps in Q from >>>>>>>>>>>>>>>>>>>>> ~∃x x=S(x) to the axioms of Q
There are, but that sequence is infinite >>>>>>>>>>>>>>>>>>>>
If there is no FINITE sequence of inference steps >>>>>>>>>>>>>>>>>>> in Q from ~∃x x=S(x) to the axioms of Q then ~∃x x=S(x) >>>>>>>>>>>>>>>>>>> is ungrounded in the PTS atomic base of Q. >>>>>>>>>>>>>>>>>>
Which has the semantic meaning "no number is equal to >>>>>>>>>>>>>>>> its successor" as per the definition of Q.
Since there are no steps in Q that affirm ~∃x x=S(x) >>>>>>>>>>>>>>> in Q it is an open question in Q and not a confirmed >>>>>>>>>>>>>>> statement in Q.
In other words, unproven as is commonly known.
False, as by definition, Q is incomplete because ~∃x x=S(x) >>>>>>>>>>>> is unprovable / out-of-scope / not semantically grounded in Q. >>>>>>>>>>>
Irrelevant. The statement that both ∃x x=S(x) and ~∃x x=S(x) are >>>>>>>>>> sentences of Q but neither is a rheorem or Q does not depend on >>>>>>>>>> any semantics.
The entire body of knowledge expressed in language
can be represented as a semantic tautology in an
acyclic directed graph. That knowledge is a DAG was
my very thought on this subject more than 30 years ago.
This single idea gets rid of all undecidability
within the entire body of knowledge.
No, it cannot. The usual meaning of knoledge excludes tautologies >>>>>>>
be animals is a semantic tautology. That cats are defined to be
cats is a logical tautology. Here is a definition of that fits
my definition of semantic tautology.
What I said applies to logical tautologies, too. That cats are
defined to be animals only tells somthing (but not much) about
the meanings of the words but nothing about the real world.
When a complete set of general "atomic facts" of the
actual world is encoded as axioms along with all of
the semantic entailment relations between these facts
then every element of general knowledge that can be
expressed in language is known by this system.
In order to achieve that the atomic facts must be non-tautologies.
That "cats" <are> "animals" is a semantic tautology.
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
or it can be a consequence of the
definitions of "cat" and "animal" and terms used in these definitions
it tells us exactly one thong about the real world
through the definition of terms.
that tells nothing about the real world, or it can be a statement
about the real world that cannot be inferred from definitions alne.
"atomic facts" that correspond to things in the world
only have stipulation as their basis in truth within
the formal system.
One usually says "assumption" instead of "stipulation". The latter
usually means a rfusal to proceed before the stipulation is accepted
or an alternative agreed.
https://en.wikipedia.org/wiki/Stipulative_definition
Cats are animals, if you disagree then you are necessarily incorrect.
On 02/07/2026 17:45, olcott wrote:
On 7/2/2026 1:44 AM, Mikko wrote:
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
A tautology tells nothing about the real world. Sometimes one can
have a false impression that something is said about the real world
when a tautology is presented. But that impression is a consequence
of insufficient or invalid consideration of logic and semantics.
On 02/07/2026 17:45, olcott wrote:
https://en.wikipedia.org/wiki/Stipulative_definition
Cats are animals, if you disagree then you are necessarily incorrect.
You may use "cats are animals" as a part of the defintion of "cat"
or of the definition of "animal" but not both. However, above you
have done neither, so you haven't excluded the possibility that
"cats are animals" is a statement about the real world.
On 7/3/2026 3:41 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:Stipulative definition of relations between finite
On 7/2/2026 1:44 AM, Mikko wrote:
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
A tautology tells nothing about the real world. Sometimes one can
have a false impression that something is said about the real world
when a tautology is presented. But that impression is a consequence
of insufficient or invalid consideration of logic and semantics.
strings is the only way that these finite strings
acquire semantic meaning.
Try to find some other way that "cats" <are> "animals"
can acquire semantic meaning besides Davidson Semantics.
On 07/03/2026 08:23 AM, olcott wrote:
On 7/3/2026 3:41 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:Stipulative definition of relations between finite
On 7/2/2026 1:44 AM, Mikko wrote:
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
A tautology tells nothing about the real world. Sometimes one can
have a false impression that something is said about the real world
when a tautology is presented. But that impression is a consequence
of insufficient or invalid consideration of logic and semantics.
strings is the only way that these finite strings
acquire semantic meaning.
Try to find some other way that "cats" <are> "animals"
can acquire semantic meaning besides Davidson Semantics.
Yet: man is an animal, yet, man is not an animal.
computer science 101
On 7/3/2026 12:34 PM, Ross Finlayson wrote:
On 07/03/2026 08:23 AM, olcott wrote:
On 7/3/2026 3:41 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:Stipulative definition of relations between finite
On 7/2/2026 1:44 AM, Mikko wrote:
That depends on the semantic system. Often the meaning of the word >>>>>> "cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells >>>>>> nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
A tautology tells nothing about the real world. Sometimes one can
have a false impression that something is said about the real world
when a tautology is presented. But that impression is a consequence
of insufficient or invalid consideration of logic and semantics.
strings is the only way that these finite strings
acquire semantic meaning.
Try to find some other way that "cats" <are> "animals"
can acquire semantic meaning besides Davidson Semantics.
Yet: man is an animal, yet, man is not an animal.
By different definitions of animal that would have
different GUIDs in my system. Most literally man
is an animal and "man is not an animal" is objectively
incorrect. That man has a different set of abilities
than most animals is also being updated. Chimps have
been proven capable of abstract thought.
computer science 101
On 07/03/2026 11:17 AM, olcott wrote:
On 7/3/2026 12:34 PM, Ross Finlayson wrote:
On 07/03/2026 08:23 AM, olcott wrote:
On 7/3/2026 3:41 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:Stipulative definition of relations between finite
On 7/2/2026 1:44 AM, Mikko wrote:
That depends on the semantic system. Often the meaning of the word >>>>>>> "cat" indeed involves that what is called a "cat" is also called >>>>>>> an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells >>>>>>> nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
A tautology tells nothing about the real world. Sometimes one can
have a false impression that something is said about the real world
when a tautology is presented. But that impression is a consequence
of insufficient or invalid consideration of logic and semantics.
strings is the only way that these finite strings
acquire semantic meaning.
Try to find some other way that "cats" <are> "animals"
can acquire semantic meaning besides Davidson Semantics.
Yet: man is an animal, yet, man is not an animal.
By different definitions of animal that would have
different GUIDs in my system. Most literally man
is an animal and "man is not an animal" is objectively
incorrect. That man has a different set of abilities
than most animals is also being updated. Chimps have
been proven capable of abstract thought.
computer science 101
Most thinking beings are feeling beings
and most feeling beings are thinking beings.
Not all, though, ....
On 7/3/2026 3:41 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:Stipulative definition of relations between finite
On 7/2/2026 1:44 AM, Mikko wrote:
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
A tautology tells nothing about the real world. Sometimes one can
have a false impression that something is said about the real world
when a tautology is presented. But that impression is a consequence
of insufficient or invalid consideration of logic and semantics.
strings is the only way that these finite strings
acquire semantic meaning.
Try to find some other way that "cats" <are> "animals"
can acquire semantic meaning besides Davidson Semantics.
On 07/03/2026 11:17 AM, olcott wrote:
On 7/3/2026 12:34 PM, Ross Finlayson wrote:
On 07/03/2026 08:23 AM, olcott wrote:
On 7/3/2026 3:41 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:Stipulative definition of relations between finite
On 7/2/2026 1:44 AM, Mikko wrote:
That depends on the semantic system. Often the meaning of the word >>>>>>> "cat" indeed involves that what is called a "cat" is also called >>>>>>> an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells >>>>>>> nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
A tautology tells nothing about the real world. Sometimes one can
have a false impression that something is said about the real world
when a tautology is presented. But that impression is a consequence
of insufficient or invalid consideration of logic and semantics.
strings is the only way that these finite strings
acquire semantic meaning.
Try to find some other way that "cats" <are> "animals"
can acquire semantic meaning besides Davidson Semantics.
Yet: man is an animal, yet, man is not an animal.
By different definitions of animal that would have
different GUIDs in my system. Most literally man
is an animal and "man is not an animal" is objectively
incorrect. That man has a different set of abilities
than most animals is also being updated. Chimps have
been proven capable of abstract thought.
computer science 101
Most thinking beings are feeling beings
and most feeling beings are thinking beings.
On 7/3/2026 4:39 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:
https://en.wikipedia.org/wiki/Stipulative_definition
Cats are animals, if you disagree then you are necessarily incorrect.
You may use "cats are animals" as a part of the defintion of "cat"
or of the definition of "animal" but not both. However, above you
have done neither, so you haven't excluded the possibility that
"cats are animals" is a statement about the real world.
cats ⊂ animals
animals ⊃ cats
They prove each other, thus only one of them is
an atomic fact. Atomic facts are facts that cannot
be derived from other facts.
In my actual system cats would inherit from animals
in the knowledge ontology / simple type hierarchy.
On 03/07/2026 18:23, olcott wrote:
On 7/3/2026 3:41 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:Stipulative definition of relations between finite
On 7/2/2026 1:44 AM, Mikko wrote:
That depends on the semantic system. Often the meaning of the word
"cat" indeed involves that what is called a "cat" is also called
an "animal" but there are other posiibilities. Conseqently, the
sentence "cats are animals" can be a semantic tautology that tells
nothing about the real world,
It tells us exactly one thing about the real world 1 != 0
A tautology tells nothing about the real world. Sometimes one can
have a false impression that something is said about the real world
when a tautology is presented. But that impression is a consequence
of insufficient or invalid consideration of logic and semantics.
strings is the only way that these finite strings
acquire semantic meaning.
For some kind of formal semantics where the meaning of a fintite
string is another finite string (or perhaps, in some cases, the
same). That way does not get any real world semantics, though
it can extend real world semantics if you already have some.
Try to find some other way that "cats" <are> "animals"
can acquire semantic meaning besides Davidson Semantics.
They come from experiences about uses of those words by other people. Likewise for most of commonly used words and phrases.
On 03/07/2026 19:43, olcott wrote:
On 7/3/2026 4:39 AM, Mikko wrote:
On 02/07/2026 17:45, olcott wrote:
https://en.wikipedia.org/wiki/Stipulative_definition
Cats are animals, if you disagree then you are necessarily incorrect.
You may use "cats are animals" as a part of the defintion of "cat"
or of the definition of "animal" but not both. However, above you
have done neither, so you haven't excluded the possibility that
"cats are animals" is a statement about the real world.
cats ⊂ animals
animals ⊃ cats
They prove each other, thus only one of them is
an atomic fact. Atomic facts are facts that cannot
be derived from other facts.
In my actual system cats would inherit from animals
in the knowledge ontology / simple type hierarchy.
In that case the sentence "cats are animals" does not tell anyting
about the real world.
A complete finite list of "atomic facts" of general
knowledge tells us everything that can be expressed
in language. This finite list also has all of the
kinds of relations between these facts.
----
Copyright 2026 Olcott
[ Followup-To: set ]
In sci.math olcott <polcott333@gmail.com> wrote:
[ .... ]
A complete finite list of "atomic facts" of general
knowledge tells us everything that can be expressed
in language. This finite list also has all of the
kinds of relations between these facts.
Seems doubtful. Falsehoods can also be expressed in language, together
with that vast trove of expressions which are neither true nor false. In fact, when it comes to "everything that can be expressed in language", a
list of "atomic facts" would appear to be unhelpful, just as much as a
list of "atomic falsehoods" would be, whatever that might mean.
--
Copyright 2026 Olcott
On 7/4/2026 9:07 AM, Alan Mackenzie wrote:
In sci.math olcott <polcott333@gmail.com> wrote:
[ .... ]
A complete finite list of "atomic facts" of general
knowledge tells us everything that can be expressed
in language. This finite list also has all of the
kinds of relations between these facts.
Seems doubtful. Falsehoods can also be expressed in language, together with that vast trove of expressions which are neither true nor false. In fact, when it comes to "everything that can be expressed in language", a list of "atomic facts" would appear to be unhelpful, just as much as a
list of "atomic falsehoods" would be, whatever that might mean.
A complete finite list of "atomic facts" of general knowledge
only includes true truth bearers and only facts that cannot
be derived from anything else. This excludes falsehoods and
expressions that are neither true nor false. It is the axiomatic
basis of knowledge of the world.
----
Copyright 2026 Olcott
| Sysop: | DaiTengu |
|---|---|
| Location: | Appleton, WI |
| Users: | 1,126 |
| Nodes: | 10 (0 / 10) |
| Uptime: | 51:58:21 |
| Calls: | 14,414 |
| Calls today: | 2 |
| Files: | 186,401 |
| D/L today: |
11,531 files (3,175M bytes) |
| Messages: | 2,548,956 |
| Posted today: | 1 |