On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote:
On 4/3/2026 2:13 AM, Mikko wrote:
On 02/04/2026 23:58, olcott wrote:
To be able to properly ground this in existing foundational
peer reviewed papers will take some time.
Do you think 100 years would be enough, or at least some finite >>>>>>>> time?
I have to carefully study at least a dozen papers
that may average 15 pages each. The basic notion
of a "well founded justification tree" essentially
means the Proof Theoretic notion of reduction to
a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
The above Prolog determines that LP does not
have a "well founded justification tree".
If you want to illustrate with examples you should have two examples: >>>>>> one with a negative result (as above) and one with a positive one. >>>>>> So the above example should be paired with one that has someting
else in place of not(provable(F, G)) so that the result will not be >>>>>> false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the discussion should >>>> be restricted to Prolog specific things, in this case to the Prolog
example above and the contrasting Prolog example not yet shown.
In order to elaborate the details of my system
I require some way to formalize natural language.
Montague Grammar, Rudolf Carnap Meaning Postulates,
the CycL language of the Cyc project and Prolog
are the options that I have been considering.
The notion of how a well-founded justification tree
eliminates undecidability is a key element of my system.
Prolog shows this best.
It is not Prolog computable to determine whether a sentence of Peano
arithmetic has a well-founded justification tree in Peano arithmetic.
A formal language similar to Prolog that can represent
all of the semantics of PA can be developed so that
it detects and rejects expressions that lack well-founded
justification trees.
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:A formal language similar to Prolog that can represent
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote:
On 4/3/2026 2:13 AM, Mikko wrote:
On 02/04/2026 23:58, olcott wrote:
To be able to properly ground this in existing foundational >>>>>>>>>>>>> peer reviewed papers will take some time.
Do you think 100 years would be enough, or at least some >>>>>>>>>>>> finite time?
I have to carefully study at least a dozen papers
that may average 15 pages each. The basic notion
of a "well founded justification tree" essentially
means the Proof Theoretic notion of reduction to
a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
The above Prolog determines that LP does not
have a "well founded justification tree".
If you want to illustrate with examples you should have two >>>>>>>>>> examples:
one with a negative result (as above) and one with a positive >>>>>>>>>> one.
So the above example should be paired with one that has someting >>>>>>>>>> else in place of not(provable(F, G)) so that the result will >>>>>>>>>> not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the discussion >>>>>>>> should
be restricted to Prolog specific things, in this case to the Prolog >>>>>>>> example above and the contrasting Prolog example not yet shown. >>>>>>>>
In order to elaborate the details of my system
I require some way to formalize natural language.
Montague Grammar, Rudolf Carnap Meaning Postulates,
the CycL language of the Cyc project and Prolog
are the options that I have been considering.
The notion of how a well-founded justification tree
eliminates undecidability is a key element of my system.
Prolog shows this best.
It is not Prolog computable to determine whether a sentence of Peano >>>>>> arithmetic has a well-founded justification tree in Peano arithmetic. >>>>>
all of the semantics of PA can be developed so that
it detects and rejects expressions that lack well-founded
justification trees.
A language does not detect. For detection you need an algorithm.
unify_with_occurs_check(LP, not(true(LP))).
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well-founded
justification tree is a question about one thing so it needs an
algrotim that takes only one input but uunify_with_occurs_check
takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018
If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue.
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote:
On 4/3/2026 2:13 AM, Mikko wrote:
On 02/04/2026 23:58, olcott wrote:
To be able to properly ground this in existing foundational >>>>>>>>>>>>>> peer reviewed papers will take some time.
Do you think 100 years would be enough, or at least some >>>>>>>>>>>>> finite time?
I have to carefully study at least a dozen papers
that may average 15 pages each. The basic notion
of a "well founded justification tree" essentially
means the Proof Theoretic notion of reduction to
a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
The above Prolog determines that LP does not
have a "well founded justification tree".
If you want to illustrate with examples you should have two >>>>>>>>>>> examples:
one with a negative result (as above) and one with a positive >>>>>>>>>>> one.
So the above example should be paired with one that has someting >>>>>>>>>>> else in place of not(provable(F, G)) so that the result will >>>>>>>>>>> not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the discussion >>>>>>>>> should
be restricted to Prolog specific things, in this case to the >>>>>>>>> Prolog
example above and the contrasting Prolog example not yet shown. >>>>>>>>>
In order to elaborate the details of my system
I require some way to formalize natural language.
Montague Grammar, Rudolf Carnap Meaning Postulates,
the CycL language of the Cyc project and Prolog
are the options that I have been considering.
The notion of how a well-founded justification tree
eliminates undecidability is a key element of my system.
Prolog shows this best.
It is not Prolog computable to determine whether a sentence of Peano >>>>>>> arithmetic has a well-founded justification tree in Peano
arithmetic.
A formal language similar to Prolog that can represent
all of the semantics of PA can be developed so that
it detects and rejects expressions that lack well-founded
justification trees.
A language does not detect. For detection you need an algorithm.
unify_with_occurs_check(LP, not(true(LP))).
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well-founded
justification tree is a question about one thing so it needs an
algrotim that takes only one input but uunify_with_occurs_check
takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018
If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue.
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote:
On 4/3/2026 2:13 AM, Mikko wrote:
On 02/04/2026 23:58, olcott wrote:
To be able to properly ground this in existing foundational >>>>>>>>>>>>>>> peer reviewed papers will take some time.
Do you think 100 years would be enough, or at least some >>>>>>>>>>>>>> finite time?
I have to carefully study at least a dozen papers
that may average 15 pages each. The basic notion
of a "well founded justification tree" essentially
means the Proof Theoretic notion of reduction to
a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
The above Prolog determines that LP does not
have a "well founded justification tree".
If you want to illustrate with examples you should have two >>>>>>>>>>>> examples:
one with a negative result (as above) and one with a
positive one.
So the above example should be paired with one that has >>>>>>>>>>>> someting
else in place of not(provable(F, G)) so that the result will >>>>>>>>>>>> not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the
discussion should
be restricted to Prolog specific things, in this case to the >>>>>>>>>> Prolog
example above and the contrasting Prolog example not yet shown. >>>>>>>>>>
In order to elaborate the details of my system
I require some way to formalize natural language.
Montague Grammar, Rudolf Carnap Meaning Postulates,
the CycL language of the Cyc project and Prolog
are the options that I have been considering.
The notion of how a well-founded justification tree
eliminates undecidability is a key element of my system.
Prolog shows this best.
It is not Prolog computable to determine whether a sentence of >>>>>>>> Peano
arithmetic has a well-founded justification tree in Peano
arithmetic.
A formal language similar to Prolog that can represent
all of the semantics of PA can be developed so that
it detects and rejects expressions that lack well-founded
justification trees.
A language does not detect. For detection you need an algorithm.
unify_with_occurs_check(LP, not(true(LP))).
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well-founded
justification tree is a question about one thing so it needs an
algrotim that takes only one input but uunify_with_occurs_check
takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018 >>> If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue.
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine whether
∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L.
You can't use nify_with_occurs_check/2 to deremine whether True(X, L).
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote:
On 4/3/2026 2:13 AM, Mikko wrote:
On 02/04/2026 23:58, olcott wrote:
To be able to properly ground this in existing foundational >>>>>>>>>>>>>>>> peer reviewed papers will take some time.
Do you think 100 years would be enough, or at least some >>>>>>>>>>>>>>> finite time?
I have to carefully study at least a dozen papers
that may average 15 pages each. The basic notion
of a "well founded justification tree" essentially >>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to
a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
The above Prolog determines that LP does not
have a "well founded justification tree".
If you want to illustrate with examples you should have two >>>>>>>>>>>>> examples:
one with a negative result (as above) and one with a >>>>>>>>>>>>> positive one.
So the above example should be paired with one that has >>>>>>>>>>>>> someting
else in place of not(provable(F, G)) so that the result >>>>>>>>>>>>> will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the
discussion should
be restricted to Prolog specific things, in this case to the >>>>>>>>>>> Prolog
example above and the contrasting Prolog example not yet shown. >>>>>>>>>>>
In order to elaborate the details of my system
I require some way to formalize natural language.
Montague Grammar, Rudolf Carnap Meaning Postulates,
the CycL language of the Cyc project and Prolog
are the options that I have been considering.
The notion of how a well-founded justification tree
eliminates undecidability is a key element of my system.
Prolog shows this best.
It is not Prolog computable to determine whether a sentence of >>>>>>>>> Peano
arithmetic has a well-founded justification tree in Peano
arithmetic.
A formal language similar to Prolog that can represent
all of the semantics of PA can be developed so that
it detects and rejects expressions that lack well-founded
justification trees.
A language does not detect. For detection you need an algorithm.
unify_with_occurs_check(LP, not(true(LP))).
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well-founded
justification tree is a question about one thing so it needs an
algrotim that takes only one input but uunify_with_occurs_check
takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018 >>>> If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue.
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine whether
∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L.
You can't use nify_with_occurs_check/2 to deremine whether True(X, L).
If there is a finite back-chained inference path from X
to Γ then X is true.
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:unify_with_occurs_check(LP, not(true(LP))).
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote:
On 4/3/2026 2:13 AM, Mikko wrote:
On 02/04/2026 23:58, olcott wrote:
To be able to properly ground this in existing >>>>>>>>>>>>>>>>> foundational
peer reviewed papers will take some time.
Do you think 100 years would be enough, or at least some >>>>>>>>>>>>>>>> finite time?
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
The above Prolog determines that LP does not
have a "well founded justification tree".
If you want to illustrate with examples you should have >>>>>>>>>>>>>> two examples:
one with a negative result (as above) and one with a >>>>>>>>>>>>>> positive one.
So the above example should be paired with one that has >>>>>>>>>>>>>> someting
else in place of not(provable(F, G)) so that the result >>>>>>>>>>>>>> will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the
discussion should
be restricted to Prolog specific things, in this case to the >>>>>>>>>>>> Prolog
example above and the contrasting Prolog example not yet shown. >>>>>>>>>>>>
In order to elaborate the details of my system
I require some way to formalize natural language.
Montague Grammar, Rudolf Carnap Meaning Postulates,
the CycL language of the Cyc project and Prolog
are the options that I have been considering.
The notion of how a well-founded justification tree
eliminates undecidability is a key element of my system. >>>>>>>>>>> Prolog shows this best.
It is not Prolog computable to determine whether a sentence of >>>>>>>>>> Peano
arithmetic has a well-founded justification tree in Peano >>>>>>>>>> arithmetic.
A formal language similar to Prolog that can represent
all of the semantics of PA can be developed so that
it detects and rejects expressions that lack well-founded
justification trees.
A language does not detect. For detection you need an algorithm. >>>>>>>
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well-founded
justification tree is a question about one thing so it needs an
algrotim that takes only one input but uunify_with_occurs_check
takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018 >>>>> If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue.
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine whether
∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L.
You can't use nify_with_occurs_check/2 to deremine whether True(X, L).
If there is a finite back-chained inference path from X
to Γ then X is true.
That does not help if you don't know whether there is a finite
back-chained inference path from X to Γ.
Besides it that path is insufficient. You must also know that
the inferences are actually truth-preserving and that everything
in Γ is true.
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:unify_with_occurs_check(LP, not(true(LP))).
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote:
On 4/3/2026 2:13 AM, Mikko wrote:
On 02/04/2026 23:58, olcott wrote:
To be able to properly ground this in existing >>>>>>>>>>>>>>>>>> foundational
peer reviewed papers will take some time.
Do you think 100 years would be enough, or at least >>>>>>>>>>>>>>>>> some finite time?
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
The above Prolog determines that LP does not
have a "well founded justification tree".
If you want to illustrate with examples you should have >>>>>>>>>>>>>>> two examples:
one with a negative result (as above) and one with a >>>>>>>>>>>>>>> positive one.
So the above example should be paired with one that has >>>>>>>>>>>>>>> someting
else in place of not(provable(F, G)) so that the result >>>>>>>>>>>>>>> will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the >>>>>>>>>>>>> discussion should
be restricted to Prolog specific things, in this case to >>>>>>>>>>>>> the Prolog
example above and the contrasting Prolog example not yet >>>>>>>>>>>>> shown.
In order to elaborate the details of my system
I require some way to formalize natural language.
Montague Grammar, Rudolf Carnap Meaning Postulates,
the CycL language of the Cyc project and Prolog
are the options that I have been considering.
The notion of how a well-founded justification tree
eliminates undecidability is a key element of my system. >>>>>>>>>>>> Prolog shows this best.
It is not Prolog computable to determine whether a sentence >>>>>>>>>>> of Peano
arithmetic has a well-founded justification tree in Peano >>>>>>>>>>> arithmetic.
A formal language similar to Prolog that can represent
all of the semantics of PA can be developed so that
it detects and rejects expressions that lack well-founded
justification trees.
A language does not detect. For detection you need an algorithm. >>>>>>>>
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well-founded >>>>>>> justification tree is a question about one thing so it needs an
algrotim that takes only one input but uunify_with_occurs_check
takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018 >>>>>> If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue.
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine whether
∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L.
You can't use nify_with_occurs_check/2 to deremine whether True(X, L).
If there is a finite back-chained inference path from X
to Γ then X is true.
That does not help if you don't know whether there is a finite
back-chained inference path from X to Γ.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
Besides it that path is insufficient. You must also know that
the inferences are actually truth-preserving and that everything
in Γ is true.
Back-chained inference that reaches the subset of BaseFacts
by semantic entailment specified syntactically proves that
it is true.
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:unify_with_occurs_check(LP, not(true(LP))).
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote:
On 4/3/2026 2:13 AM, Mikko wrote:
On 02/04/2026 23:58, olcott wrote:
To be able to properly ground this in existing >>>>>>>>>>>>>>>>>> foundational
peer reviewed papers will take some time.
Do you think 100 years would be enough, or at least >>>>>>>>>>>>>>>>> some finite time?
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
The above Prolog determines that LP does not
have a "well founded justification tree".
If you want to illustrate with examples you should have >>>>>>>>>>>>>>> two examples:
one with a negative result (as above) and one with a >>>>>>>>>>>>>>> positive one.
So the above example should be paired with one that has >>>>>>>>>>>>>>> someting
else in place of not(provable(F, G)) so that the result >>>>>>>>>>>>>>> will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the >>>>>>>>>>>>> discussion should
be restricted to Prolog specific things, in this case to >>>>>>>>>>>>> the Prolog
example above and the contrasting Prolog example not yet >>>>>>>>>>>>> shown.
In order to elaborate the details of my system
I require some way to formalize natural language.
Montague Grammar, Rudolf Carnap Meaning Postulates,
the CycL language of the Cyc project and Prolog
are the options that I have been considering.
The notion of how a well-founded justification tree
eliminates undecidability is a key element of my system. >>>>>>>>>>>> Prolog shows this best.
It is not Prolog computable to determine whether a sentence >>>>>>>>>>> of Peano
arithmetic has a well-founded justification tree in Peano >>>>>>>>>>> arithmetic.
A formal language similar to Prolog that can represent
all of the semantics of PA can be developed so that
it detects and rejects expressions that lack well-founded
justification trees.
A language does not detect. For detection you need an algorithm. >>>>>>>>
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well-founded >>>>>>> justification tree is a question about one thing so it needs an
algrotim that takes only one input but uunify_with_occurs_check
takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018 >>>>>> If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue.
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine whether
∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L.
You can't use nify_with_occurs_check/2 to deremine whether True(X, L).
If there is a finite back-chained inference path from X
to Γ then X is true.
That does not help if you don't know whether there is a finite
back-chained inference path from X to Γ.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
Besides it that path is insufficient. You must also know that
the inferences are actually truth-preserving and that everything
in Γ is true.
Back-chained inference that reaches the subset of BaseFacts
by semantic entailment specified syntactically proves that
it is true.
On 04/10/2026 04:18 AM, olcott wrote:
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:If there is a finite back-chained inference path from X
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:unify_with_occurs_check(LP, not(true(LP))).
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote:
On 4/3/2026 2:13 AM, Mikko wrote:
On 02/04/2026 23:58, olcott wrote:
To be able to properly ground this in existing >>>>>>>>>>>>>>>>>>> foundationalDo you think 100 years would be enough, or at least >>>>>>>>>>>>>>>>>> some finite time?
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>> have a "well founded justification tree".
If you want to illustrate with examples you should have >>>>>>>>>>>>>>>> two examples:
one with a negative result (as above) and one with a >>>>>>>>>>>>>>>> positive one.
So the above example should be paired with one that has >>>>>>>>>>>>>>>> someting
else in place of not(provable(F, G)) so that the result >>>>>>>>>>>>>>>> will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the >>>>>>>>>>>>>> discussion should
be restricted to Prolog specific things, in this case to >>>>>>>>>>>>>> the Prolog
example above and the contrasting Prolog example not yet >>>>>>>>>>>>>> shown.
In order to elaborate the details of my system
I require some way to formalize natural language.
Montague Grammar, Rudolf Carnap Meaning Postulates,
the CycL language of the Cyc project and Prolog
are the options that I have been considering.
The notion of how a well-founded justification tree
eliminates undecidability is a key element of my system. >>>>>>>>>>>>> Prolog shows this best.
It is not Prolog computable to determine whether a sentence >>>>>>>>>>>> of Peano
arithmetic has a well-founded justification tree in Peano >>>>>>>>>>>> arithmetic.
A formal language similar to Prolog that can represent
all of the semantics of PA can be developed so that
it detects and rejects expressions that lack well-founded >>>>>>>>>>> justification trees.
A language does not detect. For detection you need an algorithm. >>>>>>>>>
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well-founded >>>>>>>> justification tree is a question about one thing so it needs an >>>>>>>> algrotim that takes only one input but uunify_with_occurs_check >>>>>>>> takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018
If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue.
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine whether
∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L.
You can't use nify_with_occurs_check/2 to deremine whether True(X, L). >>>>
to Γ then X is true.
That does not help if you don't know whether there is a finite
back-chained inference path from X to Γ.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
Besides it that path is insufficient. You must also know that
the inferences are actually truth-preserving and that everything
in Γ is true.
Back-chained inference that reaches the subset of BaseFacts
by semantic entailment specified syntactically proves that
it is true.
Why don't you provide all your references then that
we can put them in a fishbowl and critique them.
On 4/10/2026 8:04 AM, Ross Finlayson wrote:
On 04/10/2026 04:18 AM, olcott wrote:
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:unify_with_occurs_check(LP, not(true(LP))).
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote:
On 4/3/2026 2:13 AM, Mikko wrote:
On 02/04/2026 23:58, olcott wrote:
To be able to properly ground this in existing >>>>>>>>>>>>>>>>>>>> foundationalDo you think 100 years would be enough, or at least >>>>>>>>>>>>>>>>>>> some finite time?
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>> false.
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>> have a "well founded justification tree".
If you want to illustrate with examples you should have >>>>>>>>>>>>>>>>> two examples:
one with a negative result (as above) and one with a >>>>>>>>>>>>>>>>> positive one.
So the above example should be paired with one that has >>>>>>>>>>>>>>>>> someting
else in place of not(provable(F, G)) so that the result >>>>>>>>>>>>>>>>> will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the >>>>>>>>>>>>>>> discussion should
be restricted to Prolog specific things, in this case to >>>>>>>>>>>>>>> the Prolog
example above and the contrasting Prolog example not yet >>>>>>>>>>>>>>> shown.
In order to elaborate the details of my system
I require some way to formalize natural language.
Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog
are the options that I have been considering.
The notion of how a well-founded justification tree >>>>>>>>>>>>>> eliminates undecidability is a key element of my system. >>>>>>>>>>>>>> Prolog shows this best.
It is not Prolog computable to determine whether a sentence >>>>>>>>>>>>> of Peano
arithmetic has a well-founded justification tree in Peano >>>>>>>>>>>>> arithmetic.
A formal language similar to Prolog that can represent >>>>>>>>>>>> all of the semantics of PA can be developed so that
it detects and rejects expressions that lack well-founded >>>>>>>>>>>> justification trees.
A language does not detect. For detection you need an algorithm. >>>>>>>>>>
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well-founded >>>>>>>>> justification tree is a question about one thing so it needs an >>>>>>>>> algrotim that takes only one input but uunify_with_occurs_check >>>>>>>>> takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018
If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue.
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine whether
∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L.
You can't use nify_with_occurs_check/2 to deremine whether True(X, >>>>>> L).
If there is a finite back-chained inference path from X
to Γ then X is true.
That does not help if you don't know whether there is a finite
back-chained inference path from X to Γ.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
Besides it that path is insufficient. You must also know that
the inferences are actually truth-preserving and that everything
in Γ is true.
Back-chained inference that reaches the subset of BaseFacts
by semantic entailment specified syntactically proves that
it is true.
Why don't you provide all your references then that
we can put them in a fishbowl and critique them.
This is my most concrete basis. I have the whole paper
yet cannot violate copyright. https://link.springer.com/article/10.1007/s11245-011-9107-6
My ideas that you referenced above are my own unique
augmentations to the above cited work.
On 04/10/2026 07:31 AM, olcott wrote:
On 4/10/2026 8:04 AM, Ross Finlayson wrote:
On 04/10/2026 04:18 AM, olcott wrote:
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote:
On 4/3/2026 2:13 AM, Mikko wrote:
On 02/04/2026 23:58, olcott wrote:
To be able to properly ground this in existing >>>>>>>>>>>>>>>>>>>>> foundationalDo you think 100 years would be enough, or at least >>>>>>>>>>>>>>>>>>>> some finite time?
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you should have >>>>>>>>>>>>>>>>>> two examples:
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>
one with a negative result (as above) and one with a >>>>>>>>>>>>>>>>>> positive one.
So the above example should be paired with one that has >>>>>>>>>>>>>>>>>> someting
else in place of not(provable(F, G)) so that the result >>>>>>>>>>>>>>>>>> will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the >>>>>>>>>>>>>>>> discussion should
be restricted to Prolog specific things, in this case to >>>>>>>>>>>>>>>> the Prolog
example above and the contrasting Prolog example not yet >>>>>>>>>>>>>>>> shown.
In order to elaborate the details of my system
I require some way to formalize natural language. >>>>>>>>>>>>>>> Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog
are the options that I have been considering.
The notion of how a well-founded justification tree >>>>>>>>>>>>>>> eliminates undecidability is a key element of my system. >>>>>>>>>>>>>>> Prolog shows this best.
It is not Prolog computable to determine whether a sentence >>>>>>>>>>>>>> of Peano
arithmetic has a well-founded justification tree in Peano >>>>>>>>>>>>>> arithmetic.
A formal language similar to Prolog that can represent >>>>>>>>>>>>> all of the semantics of PA can be developed so that
it detects and rejects expressions that lack well-founded >>>>>>>>>>>>> justification trees.
A language does not detect. For detection you need an >>>>>>>>>>>> algorithm.
unify_with_occurs_check(LP, not(true(LP))).
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well-founded >>>>>>>>>> justification tree is a question about one thing so it needs an >>>>>>>>>> algrotim that takes only one input but uunify_with_occurs_check >>>>>>>>>> takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018
If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue.
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine whether >>>>>>> ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L.
You can't use nify_with_occurs_check/2 to deremine whether True(X, >>>>>>> L).
If there is a finite back-chained inference path from X
to Γ then X is true.
That does not help if you don't know whether there is a finite
back-chained inference path from X to Γ.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
Besides it that path is insufficient. You must also know that
the inferences are actually truth-preserving and that everything
in Γ is true.
Back-chained inference that reaches the subset of BaseFacts
by semantic entailment specified syntactically proves that
it is true.
Why don't you provide all your references then that
we can put them in a fishbowl and critique them.
This is my most concrete basis. I have the whole paper
yet cannot violate copyright.
https://link.springer.com/article/10.1007/s11245-011-9107-6
My ideas that you referenced above are my own unique
augmentations to the above cited work.
"Anti-realist truth" is an oxymoron.
On 4/10/2026 7:09 PM, Ross Finlayson wrote:
On 04/10/2026 07:31 AM, olcott wrote:
On 4/10/2026 8:04 AM, Ross Finlayson wrote:
On 04/10/2026 04:18 AM, olcott wrote:
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote:
On 4/3/2026 2:13 AM, Mikko wrote:
On 02/04/2026 23:58, olcott wrote:
To be able to properly ground this in existing >>>>>>>>>>>>>>>>>>>>>> foundationalDo you think 100 years would be enough, or at least >>>>>>>>>>>>>>>>>>>>> some finite time?
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you should have >>>>>>>>>>>>>>>>>>> two examples:
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>>
one with a negative result (as above) and one with a >>>>>>>>>>>>>>>>>>> positive one.
So the above example should be paired with one that has >>>>>>>>>>>>>>>>>>> someting
else in place of not(provable(F, G)) so that the result >>>>>>>>>>>>>>>>>>> will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the >>>>>>>>>>>>>>>>> discussion should
be restricted to Prolog specific things, in this case to >>>>>>>>>>>>>>>>> the Prolog
example above and the contrasting Prolog example not yet >>>>>>>>>>>>>>>>> shown.
In order to elaborate the details of my system >>>>>>>>>>>>>>>> I require some way to formalize natural language. >>>>>>>>>>>>>>>> Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog >>>>>>>>>>>>>>>> are the options that I have been considering.
The notion of how a well-founded justification tree >>>>>>>>>>>>>>>> eliminates undecidability is a key element of my system. >>>>>>>>>>>>>>>> Prolog shows this best.
It is not Prolog computable to determine whether a sentence >>>>>>>>>>>>>>> of Peano
arithmetic has a well-founded justification tree in Peano >>>>>>>>>>>>>>> arithmetic.
A formal language similar to Prolog that can represent >>>>>>>>>>>>>> all of the semantics of PA can be developed so that >>>>>>>>>>>>>> it detects and rejects expressions that lack well-founded >>>>>>>>>>>>>> justification trees.
A language does not detect. For detection you need an >>>>>>>>>>>>> algorithm.
unify_with_occurs_check(LP, not(true(LP))).
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well- >>>>>>>>>>> founded
justification tree is a question about one thing so it needs an >>>>>>>>>>> algrotim that takes only one input but uunify_with_occurs_check >>>>>>>>>>> takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018
If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue.
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine whether >>>>>>>> ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L.
You can't use nify_with_occurs_check/2 to deremine whether True(X, >>>>>>>> L).
If there is a finite back-chained inference path from X
to Γ then X is true.
That does not help if you don't know whether there is a finite
back-chained inference path from X to Γ.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
Besides it that path is insufficient. You must also know that
the inferences are actually truth-preserving and that everything
in Γ is true.
Back-chained inference that reaches the subset of BaseFacts
by semantic entailment specified syntactically proves that
it is true.
Why don't you provide all your references then that
we can put them in a fishbowl and critique them.
This is my most concrete basis. I have the whole paper
yet cannot violate copyright.
https://link.springer.com/article/10.1007/s11245-011-9107-6
My ideas that you referenced above are my own unique
augmentations to the above cited work.
"Anti-realist truth" is an oxymoron.
Yes it is when we ignore the idiomatic
term-of-the-art (TOTA) meaning and go for the
Frege compositional meaning.
I totally ignore all that totally crazy bullshit
https://en.wikipedia.org/wiki/Anti-realism
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:unify_with_occurs_check(LP, not(true(LP))).
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote:
On 4/3/2026 2:13 AM, Mikko wrote:
On 02/04/2026 23:58, olcott wrote:
To be able to properly ground this in existing >>>>>>>>>>>>>>>>>> foundational
peer reviewed papers will take some time.
Do you think 100 years would be enough, or at least >>>>>>>>>>>>>>>>> some finite time?
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
The above Prolog determines that LP does not
have a "well founded justification tree".
If you want to illustrate with examples you should have >>>>>>>>>>>>>>> two examples:
one with a negative result (as above) and one with a >>>>>>>>>>>>>>> positive one.
So the above example should be paired with one that has >>>>>>>>>>>>>>> someting
else in place of not(provable(F, G)) so that the result >>>>>>>>>>>>>>> will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the >>>>>>>>>>>>> discussion should
be restricted to Prolog specific things, in this case to >>>>>>>>>>>>> the Prolog
example above and the contrasting Prolog example not yet >>>>>>>>>>>>> shown.
In order to elaborate the details of my system
I require some way to formalize natural language.
Montague Grammar, Rudolf Carnap Meaning Postulates,
the CycL language of the Cyc project and Prolog
are the options that I have been considering.
The notion of how a well-founded justification tree
eliminates undecidability is a key element of my system. >>>>>>>>>>>> Prolog shows this best.
It is not Prolog computable to determine whether a sentence >>>>>>>>>>> of Peano
arithmetic has a well-founded justification tree in Peano >>>>>>>>>>> arithmetic.
A formal language similar to Prolog that can represent
all of the semantics of PA can be developed so that
it detects and rejects expressions that lack well-founded
justification trees.
A language does not detect. For detection you need an algorithm. >>>>>>>>
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well-founded >>>>>>> justification tree is a question about one thing so it needs an
algrotim that takes only one input but uunify_with_occurs_check
takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018 >>>>>> If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue.
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine whether
∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L.
You can't use nify_with_occurs_check/2 to deremine whether True(X, L).
If there is a finite back-chained inference path from X
to Γ then X is true.
That does not help if you don't know whether there is a finite
back-chained inference path from X to Γ.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
Besides it that path is insufficient. You must also know that
the inferences are actually truth-preserving and that everything
in Γ is true.
Back-chained inference that reaches the subset of BaseFacts
by semantic entailment specified syntactically proves that
it is true.
On 4/10/2026 9:04 PM, olcott wrote:
On 4/10/2026 7:09 PM, Ross Finlayson wrote:
On 04/10/2026 07:31 AM, olcott wrote:
On 4/10/2026 8:04 AM, Ross Finlayson wrote:
On 04/10/2026 04:18 AM, olcott wrote:
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote:
On 4/3/2026 2:13 AM, Mikko wrote:
On 02/04/2026 23:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> To be able to properly ground this in existing >>>>>>>>>>>>>>>>>>>>>>> foundational
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>Do you think 100 years would be enough, or at least >>>>>>>>>>>>>>>>>>>>>> some finite time?
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you should have >>>>>>>>>>>>>>>>>>>> two examples:
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>>>
one with a negative result (as above) and one with a >>>>>>>>>>>>>>>>>>>> positive one.
So the above example should be paired with one that has >>>>>>>>>>>>>>>>>>>> someting
else in place of not(provable(F, G)) so that the result >>>>>>>>>>>>>>>>>>>> will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the >>>>>>>>>>>>>>>>>> discussion should
be restricted to Prolog specific things, in this case to >>>>>>>>>>>>>>>>>> the Prolog
example above and the contrasting Prolog example not yet >>>>>>>>>>>>>>>>>> shown.
In order to elaborate the details of my system >>>>>>>>>>>>>>>>> I require some way to formalize natural language. >>>>>>>>>>>>>>>>> Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog >>>>>>>>>>>>>>>>> are the options that I have been considering. >>>>>>>>>>>>>>>>>
The notion of how a well-founded justification tree >>>>>>>>>>>>>>>>> eliminates undecidability is a key element of my system. >>>>>>>>>>>>>>>>> Prolog shows this best.
It is not Prolog computable to determine whether a sentence >>>>>>>>>>>>>>>> of Peano
arithmetic has a well-founded justification tree in Peano >>>>>>>>>>>>>>>> arithmetic.
A formal language similar to Prolog that can represent >>>>>>>>>>>>>>> all of the semantics of PA can be developed so that >>>>>>>>>>>>>>> it detects and rejects expressions that lack well-founded >>>>>>>>>>>>>>> justification trees.
A language does not detect. For detection you need an >>>>>>>>>>>>>> algorithm.
unify_with_occurs_check(LP, not(true(LP))).
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well- >>>>>>>>>>>> founded
justification tree is a question about one thing so it needs an >>>>>>>>>>>> algrotim that takes only one input but uunify_with_occurs_check >>>>>>>>>>>> takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018
If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue.
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine whether >>>>>>>>> ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L.
You can't use nify_with_occurs_check/2 to deremine whether True(X, >>>>>>>>> L).
If there is a finite back-chained inference path from X
to Γ then X is true.
That does not help if you don't know whether there is a finite
back-chained inference path from X to Γ.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
Besides it that path is insufficient. You must also know that
the inferences are actually truth-preserving and that everything >>>>>>> in Γ is true.
Back-chained inference that reaches the subset of BaseFacts
by semantic entailment specified syntactically proves that
it is true.
Why don't you provide all your references then that
we can put them in a fishbowl and critique them.
This is my most concrete basis. I have the whole paper
yet cannot violate copyright.
https://link.springer.com/article/10.1007/s11245-011-9107-6
My ideas that you referenced above are my own unique
augmentations to the above cited work.
"Anti-realist truth" is an oxymoron.
Yes it is when we ignore the idiomatic
term-of-the-art (TOTA) meaning and go for the
Frege compositional meaning.
I totally ignore all that totally crazy bullshit
I only refer to the inferential meaning aspect that is
emphasized as the key basis in proof theoretic semantics.
I have reclassified this inferential meaning as semantic
entailment specified syntactically.
It is not possible to understand much of the PTS basis
of my work with less than a total understanding of PTS.
https://en.wikipedia.org/wiki/Anti-realism
On 04/10/2026 07:59 PM, olcott wrote:
On 4/10/2026 9:04 PM, olcott wrote:
On 4/10/2026 7:09 PM, Ross Finlayson wrote:
On 04/10/2026 07:31 AM, olcott wrote:
On 4/10/2026 8:04 AM, Ross Finlayson wrote:
On 04/10/2026 04:18 AM, olcott wrote:
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote:
On 4/3/2026 2:13 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 02/04/2026 23:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> To be able to properly ground this in existing >>>>>>>>>>>>>>>>>>>>>>>> foundational
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>>Do you think 100 years would be enough, or at least >>>>>>>>>>>>>>>>>>>>>>> some finite time?
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you should >>>>>>>>>>>>>>>>>>>>> have
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>>>>
two examples:
one with a negative result (as above) and one with a >>>>>>>>>>>>>>>>>>>>> positive one.
So the above example should be paired with one that >>>>>>>>>>>>>>>>>>>>> has
someting
else in place of not(provable(F, G)) so that the >>>>>>>>>>>>>>>>>>>>> result
will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the >>>>>>>>>>>>>>>>>>> discussion should
be restricted to Prolog specific things, in this case to >>>>>>>>>>>>>>>>>>> the Prolog
example above and the contrasting Prolog example not yet >>>>>>>>>>>>>>>>>>> shown.
In order to elaborate the details of my system >>>>>>>>>>>>>>>>>> I require some way to formalize natural language. >>>>>>>>>>>>>>>>>> Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog >>>>>>>>>>>>>>>>>> are the options that I have been considering. >>>>>>>>>>>>>>>>>>
The notion of how a well-founded justification tree >>>>>>>>>>>>>>>>>> eliminates undecidability is a key element of my system. >>>>>>>>>>>>>>>>>> Prolog shows this best.
It is not Prolog computable to determine whether a >>>>>>>>>>>>>>>>> sentence
of Peano
arithmetic has a well-founded justification tree in Peano >>>>>>>>>>>>>>>>> arithmetic.
A formal language similar to Prolog that can represent >>>>>>>>>>>>>>>> all of the semantics of PA can be developed so that >>>>>>>>>>>>>>>> it detects and rejects expressions that lack well-founded >>>>>>>>>>>>>>>> justification trees.
A language does not detect. For detection you need an >>>>>>>>>>>>>>> algorithm.
unify_with_occurs_check(LP, not(true(LP))).
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well- >>>>>>>>>>>>> founded
justification tree is a question about one thing so it >>>>>>>>>>>>> needs an
algrotim that takes only one input but
uunify_with_occurs_check
takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott
2018
If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue.
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine whether >>>>>>>>>> ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L.
You can't use nify_with_occurs_check/2 to deremine whether >>>>>>>>>> True(X,
L).
If there is a finite back-chained inference path from X
to Γ then X is true.
That does not help if you don't know whether there is a finite >>>>>>>> back-chained inference path from X to Γ.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
Besides it that path is insufficient. You must also know that
the inferences are actually truth-preserving and that everything >>>>>>>> in Γ is true.
Back-chained inference that reaches the subset of BaseFacts
by semantic entailment specified syntactically proves that
it is true.
Why don't you provide all your references then that
we can put them in a fishbowl and critique them.
This is my most concrete basis. I have the whole paper
yet cannot violate copyright.
https://link.springer.com/article/10.1007/s11245-011-9107-6
My ideas that you referenced above are my own unique
augmentations to the above cited work.
"Anti-realist truth" is an oxymoron.
Yes it is when we ignore the idiomatic
term-of-the-art (TOTA) meaning and go for the
Frege compositional meaning.
I totally ignore all that totally crazy bullshit
I only refer to the inferential meaning aspect that is
emphasized as the key basis in proof theoretic semantics.
I have reclassified this inferential meaning as semantic
entailment specified syntactically.
It is not possible to understand much of the PTS basis
of my work with less than a total understanding of PTS.
https://en.wikipedia.org/wiki/Anti-realism
"Realism" is simple enough that there exists an objective truth,
regardless of what we _see_, and irrespective of what we _say_,
then with regards to what we imagine to see or articulate to say,
to see or say, and to see and say.
So, "realism" the account is that there is "truth", and at least
one objective truth.
Then, a stronger universalism is that there's a totality,
a universal realism, then with regards to that being
about the "inter-objectivity", of a universe of truth,
then the "inter-subjectivity" is what's all involved in
all the accounts of different things people see and say.
So, the human condition, is usually given to be both an
individual account, yet also among others. Yet, we can
all attain to truth in logic, for example, or truth in
mathematics, for example, and find the relevant structures
so present everywhere, then besides that science makes for
so their existence, that they must exist also in theory,
at least one, then, only one.
The "analytic philosophy" with regards to the "idealistic
philosophy", about both the idealistic and the analytical
traditions, doesn't say much except that it doesn't say much.
That said, it has strong opinions about what also others
can't say much, while being entirely dependent on what
is say-able, the inter-relayable, the inter-subjective.
Then, both camps of the analytical and idealistic are
always trying to say that the great figures of philosophy
like Plato and Aristotle and DesCartes and Leibnitz and
Kant and Hegel say what they're saying, then, one rather
imagines it's quite the bit of both, and, not so much
the either.
Then, a "strong mathematical platonism" and a "stronger
logicist positivism" can be a greater account together
while though it involves resolving all the paradoxes of
the logic and mathematics: not ignoring them, and similarly
it's so for science and all the data: not ignoring them.
Then, what you have there appears to be a "synthetic
syncretism", since restriction of comprehension is just
another intentional ignorance about a perspective of
"the well-founded", instead of a mono-heno-theory",
which is all expansion of comprehension.
So, a mono-heno-theory can be the theory of "truth in truth itself",
since "weaker logicist positivism" is "contradiction in
contradiction itself", then since talking about truth,
is subject its own terms and its own deconstructive account.
The article again reflects on "the authorities", or for
example Plato and Aristotle and DesCartes and Leibnitz
and Kant and Hegel, each of which has a rather rational
account of truth in nature, and the synthetic the techno-analytic.
... None of which can eventually ignore any truth or all the data.
Anyways, modern accounts of quasi-modal logic basically have
given something that appears agreeable, then that direct
contradictions can be given in the framework and it's broken.
On 4/11/2026 3:09 AM, Ross Finlayson wrote:
On 04/10/2026 07:59 PM, olcott wrote:
On 4/10/2026 9:04 PM, olcott wrote:
On 4/10/2026 7:09 PM, Ross Finlayson wrote:
On 04/10/2026 07:31 AM, olcott wrote:
On 4/10/2026 8:04 AM, Ross Finlayson wrote:
On 04/10/2026 04:18 AM, olcott wrote:
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 4/3/2026 2:13 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 02/04/2026 23:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> To be able to properly ground this in existing >>>>>>>>>>>>>>>>>>>>>>>>> foundational
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>>>Do you think 100 years would be enough, or at least >>>>>>>>>>>>>>>>>>>>>>>> some finite time?
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you should >>>>>>>>>>>>>>>>>>>>>> have
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>>>>>
two examples:
one with a negative result (as above) and one with a >>>>>>>>>>>>>>>>>>>>>> positive one.
So the above example should be paired with one >>>>>>>>>>>>>>>>>>>>>> that has
someting
else in place of not(provable(F, G)) so that the >>>>>>>>>>>>>>>>>>>>>> result
will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the >>>>>>>>>>>>>>>>>>>> discussion should
be restricted to Prolog specific things, in this >>>>>>>>>>>>>>>>>>>> case to
the Prolog
example above and the contrasting Prolog example not >>>>>>>>>>>>>>>>>>>> yet
shown.
In order to elaborate the details of my system >>>>>>>>>>>>>>>>>>> I require some way to formalize natural language. >>>>>>>>>>>>>>>>>>> Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog >>>>>>>>>>>>>>>>>>> are the options that I have been considering. >>>>>>>>>>>>>>>>>>>
The notion of how a well-founded justification tree >>>>>>>>>>>>>>>>>>> eliminates undecidability is a key element of my system. >>>>>>>>>>>>>>>>>>> Prolog shows this best.
It is not Prolog computable to determine whether a >>>>>>>>>>>>>>>>>> sentence
of Peano
arithmetic has a well-founded justification tree in Peano >>>>>>>>>>>>>>>>>> arithmetic.
A formal language similar to Prolog that can represent >>>>>>>>>>>>>>>>> all of the semantics of PA can be developed so that >>>>>>>>>>>>>>>>> it detects and rejects expressions that lack well-founded >>>>>>>>>>>>>>>>> justification trees.
A language does not detect. For detection you need an >>>>>>>>>>>>>>>> algorithm.
unify_with_occurs_check(LP, not(true(LP))).
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well- >>>>>>>>>>>>>> founded
justification tree is a question about one thing so it >>>>>>>>>>>>>> needs an
algrotim that takes only one input but
uunify_with_occurs_check
takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott
2018
If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue. >>>>>>>>>>>>>
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine whether >>>>>>>>>>> ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L. >>>>>>>>>>>
You can't use nify_with_occurs_check/2 to deremine whether >>>>>>>>>>> True(X,
L).
If there is a finite back-chained inference path from X
to Γ then X is true.
That does not help if you don't know whether there is a finite >>>>>>>>> back-chained inference path from X to Γ.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
Besides it that path is insufficient. You must also know that >>>>>>>>> the inferences are actually truth-preserving and that everything >>>>>>>>> in Γ is true.
Back-chained inference that reaches the subset of BaseFacts
by semantic entailment specified syntactically proves that
it is true.
Why don't you provide all your references then that
we can put them in a fishbowl and critique them.
This is my most concrete basis. I have the whole paper
yet cannot violate copyright.
https://link.springer.com/article/10.1007/s11245-011-9107-6
My ideas that you referenced above are my own unique
augmentations to the above cited work.
"Anti-realist truth" is an oxymoron.
Yes it is when we ignore the idiomatic
term-of-the-art (TOTA) meaning and go for the
Frege compositional meaning.
I totally ignore all that totally crazy bullshit
I only refer to the inferential meaning aspect that is
emphasized as the key basis in proof theoretic semantics.
I have reclassified this inferential meaning as semantic
entailment specified syntactically.
It is not possible to understand much of the PTS basis
of my work with less than a total understanding of PTS.
https://en.wikipedia.org/wiki/Anti-realism
"Realism" is simple enough that there exists an objective truth,
regardless of what we _see_, and irrespective of what we _say_,
then with regards to what we imagine to see or articulate to say,
to see or say, and to see and say.
So, "realism" the account is that there is "truth", and at least
one objective truth.
Then, a stronger universalism is that there's a totality,
a universal realism, then with regards to that being
about the "inter-objectivity", of a universe of truth,
then the "inter-subjectivity" is what's all involved in
all the accounts of different things people see and say.
So, the human condition, is usually given to be both an
individual account, yet also among others. Yet, we can
all attain to truth in logic, for example, or truth in
mathematics, for example, and find the relevant structures
so present everywhere, then besides that science makes for
so their existence, that they must exist also in theory,
at least one, then, only one.
The "analytic philosophy" with regards to the "idealistic
philosophy", about both the idealistic and the analytical
traditions, doesn't say much except that it doesn't say much.
That said, it has strong opinions about what also others
can't say much, while being entirely dependent on what
is say-able, the inter-relayable, the inter-subjective.
Then, both camps of the analytical and idealistic are
always trying to say that the great figures of philosophy
like Plato and Aristotle and DesCartes and Leibnitz and
Kant and Hegel say what they're saying, then, one rather
imagines it's quite the bit of both, and, not so much
the either.
Then, a "strong mathematical platonism" and a "stronger
logicist positivism" can be a greater account together
while though it involves resolving all the paradoxes of
the logic and mathematics: not ignoring them, and similarly
it's so for science and all the data: not ignoring them.
Then, what you have there appears to be a "synthetic
syncretism", since restriction of comprehension is just
another intentional ignorance about a perspective of
"the well-founded", instead of a mono-heno-theory",
which is all expansion of comprehension.
So, a mono-heno-theory can be the theory of "truth in truth itself",
since "weaker logicist positivism" is "contradiction in
contradiction itself", then since talking about truth,
is subject its own terms and its own deconstructive account.
The article again reflects on "the authorities", or for
example Plato and Aristotle and DesCartes and Leibnitz
and Kant and Hegel, each of which has a rather rational
account of truth in nature, and the synthetic the techno-analytic.
... None of which can eventually ignore any truth or all the data.
Anyways, modern accounts of quasi-modal logic basically have
given something that appears agreeable, then that direct
contradictions can be given in the framework and it's broken.
None of that has anything to do with:
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
On 10/04/2026 14:18, olcott wrote:
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:If there is a finite back-chained inference path from X
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:unify_with_occurs_check(LP, not(true(LP))).
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote:
On 4/3/2026 2:13 AM, Mikko wrote:
On 02/04/2026 23:58, olcott wrote:
To be able to properly ground this in existing >>>>>>>>>>>>>>>>>>> foundationalDo you think 100 years would be enough, or at least >>>>>>>>>>>>>>>>>> some finite time?
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))).
false.
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>> have a "well founded justification tree".
If you want to illustrate with examples you should have >>>>>>>>>>>>>>>> two examples:
one with a negative result (as above) and one with a >>>>>>>>>>>>>>>> positive one.
So the above example should be paired with one that has >>>>>>>>>>>>>>>> someting
else in place of not(provable(F, G)) so that the result >>>>>>>>>>>>>>>> will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the >>>>>>>>>>>>>> discussion should
be restricted to Prolog specific things, in this case to >>>>>>>>>>>>>> the Prolog
example above and the contrasting Prolog example not yet >>>>>>>>>>>>>> shown.
In order to elaborate the details of my system
I require some way to formalize natural language.
Montague Grammar, Rudolf Carnap Meaning Postulates,
the CycL language of the Cyc project and Prolog
are the options that I have been considering.
The notion of how a well-founded justification tree
eliminates undecidability is a key element of my system. >>>>>>>>>>>>> Prolog shows this best.
It is not Prolog computable to determine whether a sentence >>>>>>>>>>>> of Peano
arithmetic has a well-founded justification tree in Peano >>>>>>>>>>>> arithmetic.
A formal language similar to Prolog that can represent
all of the semantics of PA can be developed so that
it detects and rejects expressions that lack well-founded >>>>>>>>>>> justification trees.
A language does not detect. For detection you need an algorithm. >>>>>>>>>
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well-founded >>>>>>>> justification tree is a question about one thing so it needs an >>>>>>>> algrotim that takes only one input but uunify_with_occurs_check >>>>>>>> takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018
If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue.
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine whether
∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L.
You can't use nify_with_occurs_check/2 to deremine whether True(X, L). >>>>
to Γ then X is true.
That does not help if you don't know whether there is a finite
back-chained inference path from X to Γ.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
And if it does neither ?
Besides it that path is insufficient. You must also know that
the inferences are actually truth-preserving and that everything
in Γ is true.
Back-chained inference that reaches the subset of BaseFacts
by semantic entailment specified syntactically proves that
it is true.
Only if all members of the set of Basefacts are true
and all inferences
are truth-preserving. And only if you know or can find one such chain.
There is no method to find one or to determine that there is none.
On 04/11/2026 06:49 AM, olcott wrote:
On 4/11/2026 3:09 AM, Ross Finlayson wrote:
On 04/10/2026 07:59 PM, olcott wrote:
On 4/10/2026 9:04 PM, olcott wrote:
On 4/10/2026 7:09 PM, Ross Finlayson wrote:
On 04/10/2026 07:31 AM, olcott wrote:
On 4/10/2026 8:04 AM, Ross Finlayson wrote:
On 04/10/2026 04:18 AM, olcott wrote:
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 03/04/2026 16:35, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 4/3/2026 2:13 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 02/04/2026 23:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> To be able to properly ground this in existing >>>>>>>>>>>>>>>>>>>>>>>>>> foundationalThat's mainly true. However, in como.lang.prolog the >>>>>>>>>>>>>>>>>>>>> discussion should
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>>>>Do you think 100 years would be enough, or at >>>>>>>>>>>>>>>>>>>>>>>>> least
some finite time?
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you should >>>>>>>>>>>>>>>>>>>>>>> have
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>>>>>>
two examples:
one with a negative result (as above) and one with a >>>>>>>>>>>>>>>>>>>>>>> positive one.
So the above example should be paired with one >>>>>>>>>>>>>>>>>>>>>>> that has
someting
else in place of not(provable(F, G)) so that the >>>>>>>>>>>>>>>>>>>>>>> result
will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING >>>>>>>>>>>>>>>>>>>>>
be restricted to Prolog specific things, in this >>>>>>>>>>>>>>>>>>>>> case to
the Prolog
example above and the contrasting Prolog example not >>>>>>>>>>>>>>>>>>>>> yet
shown.
In order to elaborate the details of my system >>>>>>>>>>>>>>>>>>>> I require some way to formalize natural language. >>>>>>>>>>>>>>>>>>>> Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog >>>>>>>>>>>>>>>>>>>> are the options that I have been considering. >>>>>>>>>>>>>>>>>>>>
The notion of how a well-founded justification tree >>>>>>>>>>>>>>>>>>>> eliminates undecidability is a key element of my >>>>>>>>>>>>>>>>>>>> system.
Prolog shows this best.
It is not Prolog computable to determine whether a >>>>>>>>>>>>>>>>>>> sentence
of Peano
arithmetic has a well-founded justification tree in >>>>>>>>>>>>>>>>>>> Peano
arithmetic.
A formal language similar to Prolog that can represent >>>>>>>>>>>>>>>>>> all of the semantics of PA can be developed so that >>>>>>>>>>>>>>>>>> it detects and rejects expressions that lack well-founded >>>>>>>>>>>>>>>>>> justification trees.
A language does not detect. For detection you need an >>>>>>>>>>>>>>>>> algorithm.
unify_with_occurs_check(LP, not(true(LP))).
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well- >>>>>>>>>>>>>>> founded
justification tree is a question about one thing so it >>>>>>>>>>>>>>> needs an
algrotim that takes only one input but
uunify_with_occurs_check
takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott
2018
If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue. >>>>>>>>>>>>>>
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine >>>>>>>>>>>> whether
∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L. >>>>>>>>>>>>
You can't use nify_with_occurs_check/2 to deremine whether >>>>>>>>>>>> True(X,
L).
If there is a finite back-chained inference path from X
to Γ then X is true.
That does not help if you don't know whether there is a finite >>>>>>>>>> back-chained inference path from X to Γ.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
Besides it that path is insufficient. You must also know that >>>>>>>>>> the inferences are actually truth-preserving and that everything >>>>>>>>>> in Γ is true.
Back-chained inference that reaches the subset of BaseFacts
by semantic entailment specified syntactically proves that
it is true.
Why don't you provide all your references then that
we can put them in a fishbowl and critique them.
This is my most concrete basis. I have the whole paper
yet cannot violate copyright.
https://link.springer.com/article/10.1007/s11245-011-9107-6
My ideas that you referenced above are my own unique
augmentations to the above cited work.
"Anti-realist truth" is an oxymoron.
Yes it is when we ignore the idiomatic
term-of-the-art (TOTA) meaning and go for the
Frege compositional meaning.
I totally ignore all that totally crazy bullshit
I only refer to the inferential meaning aspect that is
emphasized as the key basis in proof theoretic semantics.
I have reclassified this inferential meaning as semantic
entailment specified syntactically.
It is not possible to understand much of the PTS basis
of my work with less than a total understanding of PTS.
https://en.wikipedia.org/wiki/Anti-realism
"Realism" is simple enough that there exists an objective truth,
regardless of what we _see_, and irrespective of what we _say_,
then with regards to what we imagine to see or articulate to say,
to see or say, and to see and say.
So, "realism" the account is that there is "truth", and at least
one objective truth.
Then, a stronger universalism is that there's a totality,
a universal realism, then with regards to that being
about the "inter-objectivity", of a universe of truth,
then the "inter-subjectivity" is what's all involved in
all the accounts of different things people see and say.
So, the human condition, is usually given to be both an
individual account, yet also among others. Yet, we can
all attain to truth in logic, for example, or truth in
mathematics, for example, and find the relevant structures
so present everywhere, then besides that science makes for
so their existence, that they must exist also in theory,
at least one, then, only one.
The "analytic philosophy" with regards to the "idealistic
philosophy", about both the idealistic and the analytical
traditions, doesn't say much except that it doesn't say much.
That said, it has strong opinions about what also others
can't say much, while being entirely dependent on what
is say-able, the inter-relayable, the inter-subjective.
Then, both camps of the analytical and idealistic are
always trying to say that the great figures of philosophy
like Plato and Aristotle and DesCartes and Leibnitz and
Kant and Hegel say what they're saying, then, one rather
imagines it's quite the bit of both, and, not so much
the either.
Then, a "strong mathematical platonism" and a "stronger
logicist positivism" can be a greater account together
while though it involves resolving all the paradoxes of
the logic and mathematics: not ignoring them, and similarly
it's so for science and all the data: not ignoring them.
Then, what you have there appears to be a "synthetic
syncretism", since restriction of comprehension is just
another intentional ignorance about a perspective of
"the well-founded", instead of a mono-heno-theory",
which is all expansion of comprehension.
So, a mono-heno-theory can be the theory of "truth in truth itself",
since "weaker logicist positivism" is "contradiction in
contradiction itself", then since talking about truth,
is subject its own terms and its own deconstructive account.
The article again reflects on "the authorities", or for
example Plato and Aristotle and DesCartes and Leibnitz
and Kant and Hegel, each of which has a rather rational
account of truth in nature, and the synthetic the techno-analytic.
... None of which can eventually ignore any truth or all the data.
Anyways, modern accounts of quasi-modal logic basically have
given something that appears agreeable, then that direct
contradictions can be given in the framework and it's broken.
None of that has anything to do with:
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
It seems you're making "claims", and should simply enough
talk about "claims" instead of "truths", then though it's
usual enough to say that "well Tarski says that suffices
for true", yet scientists may say "not falsified".
Then, about the body of knowledge and the body of fact,
those are also two different things.
So, neither "claims" nor "knowledge" are infallible,
unless the theory is "constant, consistent, complete,
and concrete", which few are (or, only one is).
Otherwise that's just spouting the line that quasi-modal
logic given a body of presumed facts can presume other
facts, which is not a modal temporal relevance logic
(since adding any presumed or alleged fact basically
breaks any other depending on which order it's read,
instead of maintaing modal temporal relevance, the
constancy). I.e., quasi-modal logic has no real claim
to monotonicity, nor entailment, only naive induction,
and non-contradiction. Anything that requires deductive
inference for completions or resolution of contradictions
matters of independence, are lost in quasi-modal logic
(or, contrived, yet readily broken).
On 4/10/2026 7:09 PM, Ross Finlayson wrote:
On 04/10/2026 07:31 AM, olcott wrote:
On 4/10/2026 8:04 AM, Ross Finlayson wrote:
On 04/10/2026 04:18 AM, olcott wrote:
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote:
On 4/3/2026 2:13 AM, Mikko wrote:
On 02/04/2026 23:58, olcott wrote:
To be able to properly ground this in existing >>>>>>>>>>>>>>>>>>>>>> foundationalDo you think 100 years would be enough, or at least >>>>>>>>>>>>>>>>>>>>> some finite time?
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you should have >>>>>>>>>>>>>>>>>>> two examples:
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>>
one with a negative result (as above) and one with a >>>>>>>>>>>>>>>>>>> positive one.
So the above example should be paired with one that has >>>>>>>>>>>>>>>>>>> someting
else in place of not(provable(F, G)) so that the result >>>>>>>>>>>>>>>>>>> will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the >>>>>>>>>>>>>>>>> discussion should
be restricted to Prolog specific things, in this case to >>>>>>>>>>>>>>>>> the Prolog
example above and the contrasting Prolog example not yet >>>>>>>>>>>>>>>>> shown.
In order to elaborate the details of my system >>>>>>>>>>>>>>>> I require some way to formalize natural language. >>>>>>>>>>>>>>>> Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog >>>>>>>>>>>>>>>> are the options that I have been considering.
The notion of how a well-founded justification tree >>>>>>>>>>>>>>>> eliminates undecidability is a key element of my system. >>>>>>>>>>>>>>>> Prolog shows this best.
It is not Prolog computable to determine whether a sentence >>>>>>>>>>>>>>> of Peano
arithmetic has a well-founded justification tree in Peano >>>>>>>>>>>>>>> arithmetic.
A formal language similar to Prolog that can represent >>>>>>>>>>>>>> all of the semantics of PA can be developed so that >>>>>>>>>>>>>> it detects and rejects expressions that lack well-founded >>>>>>>>>>>>>> justification trees.
A language does not detect. For detection you need an >>>>>>>>>>>>> algorithm.
unify_with_occurs_check(LP, not(true(LP))).
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well- >>>>>>>>>>> founded
justification tree is a question about one thing so it needs an >>>>>>>>>>> algrotim that takes only one input but uunify_with_occurs_check >>>>>>>>>>> takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018
If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue.
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine whether >>>>>>>> ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L.
You can't use nify_with_occurs_check/2 to deremine whether True(X, >>>>>>>> L).
If there is a finite back-chained inference path from X
to Γ then X is true.
That does not help if you don't know whether there is a finite
back-chained inference path from X to Γ.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
Besides it that path is insufficient. You must also know that
the inferences are actually truth-preserving and that everything
in Γ is true.
Back-chained inference that reaches the subset of BaseFacts
by semantic entailment specified syntactically proves that
it is true.
Why don't you provide all your references then that
we can put them in a fishbowl and critique them.
This is my most concrete basis. I have the whole paper
yet cannot violate copyright.
https://link.springer.com/article/10.1007/s11245-011-9107-6
My ideas that you referenced above are my own unique
augmentations to the above cited work.
"Anti-realist truth" is an oxymoron.
Yes it is when we ignore the idiomatic
term-of-the-art (TOTA) meaning and go for the
Frege compositional meaning.
I totally ignore all that totally crazy bullshit
and only refer to inferential meaning that I
have reclassified as semantic entailment specified
syntactically.
https://en.wikipedia.org/wiki/Anti-realism
On 4/11/2026 2:30 AM, Mikko wrote:
On 10/04/2026 14:18, olcott wrote:
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:unify_with_occurs_check(LP, not(true(LP))).
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote:
On 4/3/2026 2:13 AM, Mikko wrote:
On 02/04/2026 23:58, olcott wrote:
To be able to properly ground this in existing >>>>>>>>>>>>>>>>>>>> foundationalDo you think 100 years would be enough, or at least >>>>>>>>>>>>>>>>>>> some finite time?
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>> false.
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>> have a "well founded justification tree".
If you want to illustrate with examples you should have >>>>>>>>>>>>>>>>> two examples:
one with a negative result (as above) and one with a >>>>>>>>>>>>>>>>> positive one.
So the above example should be paired with one that has >>>>>>>>>>>>>>>>> someting
else in place of not(provable(F, G)) so that the result >>>>>>>>>>>>>>>>> will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the >>>>>>>>>>>>>>> discussion should
be restricted to Prolog specific things, in this case to >>>>>>>>>>>>>>> the Prolog
example above and the contrasting Prolog example not yet >>>>>>>>>>>>>>> shown.
In order to elaborate the details of my system
I require some way to formalize natural language.
Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog
are the options that I have been considering.
The notion of how a well-founded justification tree >>>>>>>>>>>>>> eliminates undecidability is a key element of my system. >>>>>>>>>>>>>> Prolog shows this best.
It is not Prolog computable to determine whether a sentence >>>>>>>>>>>>> of Peano
arithmetic has a well-founded justification tree in Peano >>>>>>>>>>>>> arithmetic.
A formal language similar to Prolog that can represent >>>>>>>>>>>> all of the semantics of PA can be developed so that
it detects and rejects expressions that lack well-founded >>>>>>>>>>>> justification trees.
A language does not detect. For detection you need an algorithm. >>>>>>>>>>
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well-founded >>>>>>>>> justification tree is a question about one thing so it needs an >>>>>>>>> algrotim that takes only one input but uunify_with_occurs_check >>>>>>>>> takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018
If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue.
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine whether
∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L.
You can't use nify_with_occurs_check/2 to deremine whether True(X, >>>>>> L).
If there is a finite back-chained inference path from X
to Γ then X is true.
That does not help if you don't know whether there is a finite
back-chained inference path from X to Γ.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
And if it does neither ?
It either finds a finite path or finds that no
finite path exists. For the Halting Problem
proof, Gödel's 1931 Incompleteness and Tarski
Undefinability this is trivial.
Besides it that path is insufficient. You must also know that
the inferences are actually truth-preserving and that everything
in Γ is true.
Back-chained inference that reaches the subset of BaseFacts
by semantic entailment specified syntactically proves that
it is true.
Only if all members of the set of Basefacts are true
For the purpose of this thought experiment it is stipulated
that BaseFacts includes every atomic fact of general knowledge.
This includes empirical facts of the actual world and all
analytical facts of math, computer science and logic et cetera.
and all inferences
are truth-preserving. And only if you know or can find one such chain.
There is no method to find one or to determine that there is none.
All inferences are semantic entailment specified
syntactically in a formal language.
"The cat is on the mat" means that this mat
has a cat.
On 4/11/2026 2:30 AM, Mikko wrote:
On 10/04/2026 14:18, olcott wrote:
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:unify_with_occurs_check(LP, not(true(LP))).
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote:
On 4/3/2026 2:13 AM, Mikko wrote:
On 02/04/2026 23:58, olcott wrote:
To be able to properly ground this in existing >>>>>>>>>>>>>>>>>>>> foundationalDo you think 100 years would be enough, or at least >>>>>>>>>>>>>>>>>>> some finite time?
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>> false.
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>> have a "well founded justification tree".
If you want to illustrate with examples you should have >>>>>>>>>>>>>>>>> two examples:
one with a negative result (as above) and one with a >>>>>>>>>>>>>>>>> positive one.
So the above example should be paired with one that has >>>>>>>>>>>>>>>>> someting
else in place of not(provable(F, G)) so that the result >>>>>>>>>>>>>>>>> will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the >>>>>>>>>>>>>>> discussion should
be restricted to Prolog specific things, in this case to >>>>>>>>>>>>>>> the Prolog
example above and the contrasting Prolog example not yet >>>>>>>>>>>>>>> shown.
In order to elaborate the details of my system
I require some way to formalize natural language.
Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog
are the options that I have been considering.
The notion of how a well-founded justification tree >>>>>>>>>>>>>> eliminates undecidability is a key element of my system. >>>>>>>>>>>>>> Prolog shows this best.
It is not Prolog computable to determine whether a sentence >>>>>>>>>>>>> of Peano
arithmetic has a well-founded justification tree in Peano >>>>>>>>>>>>> arithmetic.
A formal language similar to Prolog that can represent >>>>>>>>>>>> all of the semantics of PA can be developed so that
it detects and rejects expressions that lack well-founded >>>>>>>>>>>> justification trees.
A language does not detect. For detection you need an algorithm. >>>>>>>>>>
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well-founded >>>>>>>>> justification tree is a question about one thing so it needs an >>>>>>>>> algrotim that takes only one input but uunify_with_occurs_check >>>>>>>>> takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018
If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue.
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine whether
∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L.
You can't use nify_with_occurs_check/2 to deremine whether True(X, >>>>>> L).
If there is a finite back-chained inference path from X
to Γ then X is true.
That does not help if you don't know whether there is a finite
back-chained inference path from X to Γ.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
And if it does neither ?
It either finds a finite path or finds that no
finite path exists.
On 12/04/2026 16:17, olcott wrote:
On 4/12/2026 4:26 AM, Mikko wrote:
On 11/04/2026 17:14, olcott wrote:
On 4/11/2026 2:30 AM, Mikko wrote:
On 10/04/2026 14:18, olcott wrote:
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote:
On 4/3/2026 2:13 AM, Mikko wrote:
On 02/04/2026 23:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> To be able to properly ground this in existing >>>>>>>>>>>>>>>>>>>>>>> foundational
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>Do you think 100 years would be enough, or at >>>>>>>>>>>>>>>>>>>>>> least some finite time?
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you should >>>>>>>>>>>>>>>>>>>> have two examples:
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>>>
one with a negative result (as above) and one with a >>>>>>>>>>>>>>>>>>>> positive one.
So the above example should be paired with one that >>>>>>>>>>>>>>>>>>>> has someting
else in place of not(provable(F, G)) so that the >>>>>>>>>>>>>>>>>>>> result will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the >>>>>>>>>>>>>>>>>> discussion should
be restricted to Prolog specific things, in this case >>>>>>>>>>>>>>>>>> to the Prolog
example above and the contrasting Prolog example not >>>>>>>>>>>>>>>>>> yet shown.
In order to elaborate the details of my system >>>>>>>>>>>>>>>>> I require some way to formalize natural language. >>>>>>>>>>>>>>>>> Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog >>>>>>>>>>>>>>>>> are the options that I have been considering. >>>>>>>>>>>>>>>>>
The notion of how a well-founded justification tree >>>>>>>>>>>>>>>>> eliminates undecidability is a key element of my system. >>>>>>>>>>>>>>>>> Prolog shows this best.
It is not Prolog computable to determine whether a >>>>>>>>>>>>>>>> sentence of Peano
arithmetic has a well-founded justification tree in >>>>>>>>>>>>>>>> Peano arithmetic.
A formal language similar to Prolog that can represent >>>>>>>>>>>>>>> all of the semantics of PA can be developed so that >>>>>>>>>>>>>>> it detects and rejects expressions that lack well-founded >>>>>>>>>>>>>>> justification trees.
A language does not detect. For detection you need an >>>>>>>>>>>>>> algorithm.
unify_with_occurs_check(LP, not(true(LP))).
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well- >>>>>>>>>>>> founded
justification tree is a question about one thing so it needs an >>>>>>>>>>>> algrotim that takes only one input but uunify_with_occurs_check >>>>>>>>>>>> takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott 2018
If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue.
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine whether >>>>>>>>> ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L.
You can't use nify_with_occurs_check/2 to deremine whether
True(X, L).
If there is a finite back-chained inference path from X
to Γ then X is true.
That does not help if you don't know whether there is a finite
back-chained inference path from X to Γ.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
And if it does neither ?
It either finds a finite path or finds that no
finite path exists.
There is no such it.
This is the it:
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
A goal that is not and cannot be achieved.
The complete structure of this system is now defined.
A miracle can be defined. But can you implement it?
On 4/13/2026 2:03 AM, Mikko wrote:
On 12/04/2026 16:17, olcott wrote:
On 4/12/2026 4:26 AM, Mikko wrote:
On 11/04/2026 17:14, olcott wrote:
On 4/11/2026 2:30 AM, Mikko wrote:
On 10/04/2026 14:18, olcott wrote:
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote:
On 4/3/2026 2:13 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 02/04/2026 23:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> To be able to properly ground this in existing >>>>>>>>>>>>>>>>>>>>>>>> foundational
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>>Do you think 100 years would be enough, or at >>>>>>>>>>>>>>>>>>>>>>> least some finite time?
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you should >>>>>>>>>>>>>>>>>>>>> have two examples:
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>>>>
one with a negative result (as above) and one with >>>>>>>>>>>>>>>>>>>>> a positive one.
So the above example should be paired with one that >>>>>>>>>>>>>>>>>>>>> has someting
else in place of not(provable(F, G)) so that the >>>>>>>>>>>>>>>>>>>>> result will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the >>>>>>>>>>>>>>>>>>> discussion should
be restricted to Prolog specific things, in this case >>>>>>>>>>>>>>>>>>> to the Prolog
example above and the contrasting Prolog example not >>>>>>>>>>>>>>>>>>> yet shown.
In order to elaborate the details of my system >>>>>>>>>>>>>>>>>> I require some way to formalize natural language. >>>>>>>>>>>>>>>>>> Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog >>>>>>>>>>>>>>>>>> are the options that I have been considering. >>>>>>>>>>>>>>>>>>
The notion of how a well-founded justification tree >>>>>>>>>>>>>>>>>> eliminates undecidability is a key element of my system. >>>>>>>>>>>>>>>>>> Prolog shows this best.
It is not Prolog computable to determine whether a >>>>>>>>>>>>>>>>> sentence of Peano
arithmetic has a well-founded justification tree in >>>>>>>>>>>>>>>>> Peano arithmetic.
A formal language similar to Prolog that can represent >>>>>>>>>>>>>>>> all of the semantics of PA can be developed so that >>>>>>>>>>>>>>>> it detects and rejects expressions that lack well-founded >>>>>>>>>>>>>>>> justification trees.
A language does not detect. For detection you need an >>>>>>>>>>>>>>> algorithm.
unify_with_occurs_check(LP, not(true(LP))).
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well- >>>>>>>>>>>>> founded
justification tree is a question about one thing so it >>>>>>>>>>>>> needs an
algrotim that takes only one input but
uunify_with_occurs_check
takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott
2018
If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue.
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine whether >>>>>>>>>> ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L.
You can't use nify_with_occurs_check/2 to deremine whether >>>>>>>>>> True(X, L).
If there is a finite back-chained inference path from X
to Γ then X is true.
That does not help if you don't know whether there is a finite >>>>>>>> back-chained inference path from X to Γ.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
And if it does neither ?
It either finds a finite path or finds that no
finite path exists.
There is no such it.
This is the it:
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
A goal that is not and cannot be achieved.
All instances of undecidability have either been provably
semantically incoherent input:
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
Or outside of the body of knowledge such as the
truth value of the Goldbach conjecture.
On 13/04/2026 17:24, olcott wrote:
On 4/13/2026 2:03 AM, Mikko wrote:
On 12/04/2026 16:17, olcott wrote:
On 4/12/2026 4:26 AM, Mikko wrote:
On 11/04/2026 17:14, olcott wrote:
On 4/11/2026 2:30 AM, Mikko wrote:
On 10/04/2026 14:18, olcott wrote:
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote:
On 03/04/2026 16:35, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 4/3/2026 2:13 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 02/04/2026 23:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> To be able to properly ground this in existing >>>>>>>>>>>>>>>>>>>>>>>>> foundational
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>>>Do you think 100 years would be enough, or at >>>>>>>>>>>>>>>>>>>>>>>> least some finite time?
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you should >>>>>>>>>>>>>>>>>>>>>> have two examples:
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>>>>>
one with a negative result (as above) and one with >>>>>>>>>>>>>>>>>>>>>> a positive one.
So the above example should be paired with one >>>>>>>>>>>>>>>>>>>>>> that has someting
else in place of not(provable(F, G)) so that the >>>>>>>>>>>>>>>>>>>>>> result will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING
That's mainly true. However, in como.lang.prolog the >>>>>>>>>>>>>>>>>>>> discussion should
be restricted to Prolog specific things, in this >>>>>>>>>>>>>>>>>>>> case to the Prolog
example above and the contrasting Prolog example not >>>>>>>>>>>>>>>>>>>> yet shown.
In order to elaborate the details of my system >>>>>>>>>>>>>>>>>>> I require some way to formalize natural language. >>>>>>>>>>>>>>>>>>> Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog >>>>>>>>>>>>>>>>>>> are the options that I have been considering. >>>>>>>>>>>>>>>>>>>
The notion of how a well-founded justification tree >>>>>>>>>>>>>>>>>>> eliminates undecidability is a key element of my system. >>>>>>>>>>>>>>>>>>> Prolog shows this best.
It is not Prolog computable to determine whether a >>>>>>>>>>>>>>>>>> sentence of Peano
arithmetic has a well-founded justification tree in >>>>>>>>>>>>>>>>>> Peano arithmetic.
A formal language similar to Prolog that can represent >>>>>>>>>>>>>>>>> all of the semantics of PA can be developed so that >>>>>>>>>>>>>>>>> it detects and rejects expressions that lack well-founded >>>>>>>>>>>>>>>>> justification trees.
A language does not detect. For detection you need an >>>>>>>>>>>>>>>> algorithm.
unify_with_occurs_check(LP, not(true(LP))).
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a well- >>>>>>>>>>>>>> founded
justification tree is a question about one thing so it >>>>>>>>>>>>>> needs an
algrotim that takes only one input but
uunify_with_occurs_check
takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright Olcott
2018
If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue. >>>>>>>>>>>>>
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine whether >>>>>>>>>>> ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L. >>>>>>>>>>>
You can't use nify_with_occurs_check/2 to deremine whether >>>>>>>>>>> True(X, L).
If there is a finite back-chained inference path from X
to Γ then X is true.
That does not help if you don't know whether there is a finite >>>>>>>>> back-chained inference path from X to Γ.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
And if it does neither ?
It either finds a finite path or finds that no
finite path exists.
There is no such it.
This is the it:
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
A goal that is not and cannot be achieved.
All instances of undecidability have either been provably
semantically incoherent input:
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
Or outside of the body of knowledge such as the
truth value of the Goldbach conjecture.
It is not known whether there is a finite back-chained inference path
from Goldbach conjecture to the body of knowledge. If there is then
the conjecture is both true and untrue according to your statements
above.
On 4/14/2026 12:55 AM, Mikko wrote:
On 13/04/2026 17:24, olcott wrote:
On 4/13/2026 2:03 AM, Mikko wrote:
On 12/04/2026 16:17, olcott wrote:
On 4/12/2026 4:26 AM, Mikko wrote:
On 11/04/2026 17:14, olcott wrote:
On 4/11/2026 2:30 AM, Mikko wrote:
On 10/04/2026 14:18, olcott wrote:
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote:
On 4/4/2026 2:53 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 03/04/2026 16:35, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 4/3/2026 2:13 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 02/04/2026 23:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> To be able to properly ground this in existing >>>>>>>>>>>>>>>>>>>>>>>>>> foundationalThat's mainly true. However, in como.lang.prolog >>>>>>>>>>>>>>>>>>>>> the discussion should
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>>>>Do you think 100 years would be enough, or at >>>>>>>>>>>>>>>>>>>>>>>>> least some finite time?
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you >>>>>>>>>>>>>>>>>>>>>>> should have two examples:
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>>>>>>
one with a negative result (as above) and one >>>>>>>>>>>>>>>>>>>>>>> with a positive one.
So the above example should be paired with one >>>>>>>>>>>>>>>>>>>>>>> that has someting
else in place of not(provable(F, G)) so that the >>>>>>>>>>>>>>>>>>>>>>> result will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING >>>>>>>>>>>>>>>>>>>>>
be restricted to Prolog specific things, in this >>>>>>>>>>>>>>>>>>>>> case to the Prolog
example above and the contrasting Prolog example >>>>>>>>>>>>>>>>>>>>> not yet shown.
In order to elaborate the details of my system >>>>>>>>>>>>>>>>>>>> I require some way to formalize natural language. >>>>>>>>>>>>>>>>>>>> Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog >>>>>>>>>>>>>>>>>>>> are the options that I have been considering. >>>>>>>>>>>>>>>>>>>>
The notion of how a well-founded justification tree >>>>>>>>>>>>>>>>>>>> eliminates undecidability is a key element of my >>>>>>>>>>>>>>>>>>>> system.
Prolog shows this best.
It is not Prolog computable to determine whether a >>>>>>>>>>>>>>>>>>> sentence of Peano
arithmetic has a well-founded justification tree in >>>>>>>>>>>>>>>>>>> Peano arithmetic.
A formal language similar to Prolog that can represent >>>>>>>>>>>>>>>>>> all of the semantics of PA can be developed so that >>>>>>>>>>>>>>>>>> it detects and rejects expressions that lack well-founded >>>>>>>>>>>>>>>>>> justification trees.
A language does not detect. For detection you need an >>>>>>>>>>>>>>>>> algorithm.
unify_with_occurs_check(LP, not(true(LP))).
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a >>>>>>>>>>>>>>> well- founded
justification tree is a question about one thing so it >>>>>>>>>>>>>>> needs an
algrotim that takes only one input but
uunify_with_occurs_check
takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright >>>>>>>>>>>>>> Olcott 2018
If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue. >>>>>>>>>>>>>>
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine >>>>>>>>>>>> whether
∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L. >>>>>>>>>>>>
You can't use nify_with_occurs_check/2 to deremine whether >>>>>>>>>>>> True(X, L).
If there is a finite back-chained inference path from X
to Γ then X is true.
That does not help if you don't know whether there is a finite >>>>>>>>>> back-chained inference path from X to Γ.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
And if it does neither ?
It either finds a finite path or finds that no
finite path exists.
There is no such it.
This is the it:
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
A goal that is not and cannot be achieved.
All instances of undecidability have either been provably
semantically incoherent input:
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
Or outside of the body of knowledge such as the
truth value of the Goldbach conjecture.
It is not known whether there is a finite back-chained inference path
from Goldbach conjecture to the body of knowledge. If there is then
the conjecture is both true and untrue according to your statements
above.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
On 14/04/2026 16:48, olcott wrote:
On 4/14/2026 12:55 AM, Mikko wrote:
On 13/04/2026 17:24, olcott wrote:
On 4/13/2026 2:03 AM, Mikko wrote:
On 12/04/2026 16:17, olcott wrote:
On 4/12/2026 4:26 AM, Mikko wrote:
On 11/04/2026 17:14, olcott wrote:
On 4/11/2026 2:30 AM, Mikko wrote:
On 10/04/2026 14:18, olcott wrote:
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote:
On 04/04/2026 19:23, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 4/4/2026 2:53 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 03/04/2026 16:35, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 4/3/2026 2:13 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 02/04/2026 23:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> To be able to properly ground this in >>>>>>>>>>>>>>>>>>>>>>>>>>> existing foundational
That's mainly true. However, in como.lang.prolog >>>>>>>>>>>>>>>>>>>>>> the discussion shouldpeer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>>>>>Do you think 100 years would be enough, or at >>>>>>>>>>>>>>>>>>>>>>>>>> least some finite time?
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>>>>>>>>>> of a "well founded justification tree" essentially >>>>>>>>>>>>>>>>>>>>>>>>> means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you >>>>>>>>>>>>>>>>>>>>>>>> should have two examples:
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>>>>>>>
one with a negative result (as above) and one >>>>>>>>>>>>>>>>>>>>>>>> with a positive one.
So the above example should be paired with one >>>>>>>>>>>>>>>>>>>>>>>> that has someting
else in place of not(provable(F, G)) so that the >>>>>>>>>>>>>>>>>>>>>>>> result will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING >>>>>>>>>>>>>>>>>>>>>>
be restricted to Prolog specific things, in this >>>>>>>>>>>>>>>>>>>>>> case to the Prolog
example above and the contrasting Prolog example >>>>>>>>>>>>>>>>>>>>>> not yet shown.
In order to elaborate the details of my system >>>>>>>>>>>>>>>>>>>>> I require some way to formalize natural language. >>>>>>>>>>>>>>>>>>>>> Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog >>>>>>>>>>>>>>>>>>>>> are the options that I have been considering. >>>>>>>>>>>>>>>>>>>>>
The notion of how a well-founded justification tree >>>>>>>>>>>>>>>>>>>>> eliminates undecidability is a key element of my >>>>>>>>>>>>>>>>>>>>> system.
Prolog shows this best.
It is not Prolog computable to determine whether a >>>>>>>>>>>>>>>>>>>> sentence of Peano
arithmetic has a well-founded justification tree in >>>>>>>>>>>>>>>>>>>> Peano arithmetic.
A formal language similar to Prolog that can represent >>>>>>>>>>>>>>>>>>> all of the semantics of PA can be developed so that >>>>>>>>>>>>>>>>>>> it detects and rejects expressions that lack well- >>>>>>>>>>>>>>>>>>> founded
justification trees.
A language does not detect. For detection you need an >>>>>>>>>>>>>>>>>> algorithm.
unify_with_occurs_check(LP, not(true(LP))).
is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a >>>>>>>>>>>>>>>> well- founded
justification tree is a question about one thing so it >>>>>>>>>>>>>>>> needs an
algrotim that takes only one input but
uunify_with_occurs_check
takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected.
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright >>>>>>>>>>>>>>> Olcott 2018
If for any reason a back chained inference does
not reach BaseFacts(L) then the expression is untrue. >>>>>>>>>>>>>>>
CORRECTION:
...then the expression is untrue [within the body
of knowledge that can be expressed in language].
That is not useful unless there are methods to determine >>>>>>>>>>>>> whether
∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L. >>>>>>>>>>>>>
You can't use nify_with_occurs_check/2 to deremine whether >>>>>>>>>>>>> True(X, L).
If there is a finite back-chained inference path from X >>>>>>>>>>>> to Γ then X is true.
That does not help if you don't know whether there is a finite >>>>>>>>>>> back-chained inference path from X to Γ.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
And if it does neither ?
It either finds a finite path or finds that no
finite path exists.
There is no such it.
This is the it:
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
A goal that is not and cannot be achieved.
All instances of undecidability have either been provably
semantically incoherent input:
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
Or outside of the body of knowledge such as the
truth value of the Goldbach conjecture.
It is not known whether there is a finite back-chained inference path
from Goldbach conjecture to the body of knowledge. If there is then
the conjecture is both true and untrue according to your statements
above.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
On 2026-04-15 06:02, olcott wrote:
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
You've said this (or something similar) to several different posters
now; but bear in mind that you yourself only became aware of the
existence of proof-theoretic semantics a few months ago which means that
you have hardly had enough time to become an expert in PTS.
So you're
really not in a position to tell people what an expert in PTS might
claim about any particular issue.
André
On 4/15/2026 11:35 AM, Ross Finlayson wrote:
On 04/15/2026 09:17 AM, olcott wrote:
On 4/15/2026 11:06 AM, Ross Finlayson wrote:
On 04/15/2026 08:49 AM, olcott wrote:
On 4/15/2026 10:15 AM, Ross Finlayson wrote:
On 04/14/2026 05:09 AM, Ross Finlayson wrote:
On 04/13/2026 11:34 PM, Mikko wrote:
On 13/04/2026 17:52, olcott wrote:
On 4/13/2026 2:05 AM, Mikko wrote:
On 12/04/2026 16:22, olcott wrote:
On 4/12/2026 4:32 AM, Mikko wrote:
On 11/04/2026 17:27, olcott wrote:
On 4/11/2026 3:06 AM, Mikko wrote:
On 09/04/2026 16:35, olcott wrote:
On 4/9/2026 4:08 AM, Mikko wrote:
On 08/04/2026 14:52, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>> On 4/5/2026 2:05 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 04/04/2026 19:23, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 4/4/2026 2:53 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 03/04/2026 16:35, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 4/3/2026 2:13 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> On 02/04/2026 23:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>>> To be able to properly ground this in existing >>>>>>>>>>>>>>>>>>>>>>>>>>>>> foundational
That's mainly true. However, in como.lang.prolog >>>>>>>>>>>>>>>>>>>>>>>> thepeer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>>>>>>>Do you think 100 years would be enough, or at >>>>>>>>>>>>>>>>>>>>>>>>>>>> least
some finite time?
I have to carefully study at least a dozen >>>>>>>>>>>>>>>>>>>>>>>>>>> papers
that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>>>>>>>>>>>> of a "well founded justification tree" >>>>>>>>>>>>>>>>>>>>>>>>>>> essentially
means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true. >>>>>>>>>>>>>>>>>>>>>>>>> ?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you >>>>>>>>>>>>>>>>>>>>>>>>>> should
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>>>>>>>>>
have two examples:
one with a negative result (as above) and one >>>>>>>>>>>>>>>>>>>>>>>>>> with a
positive one.
So the above example should be paired with one >>>>>>>>>>>>>>>>>>>>>>>>>> that
has someting
else in place of not(provable(F, G)) so that the >>>>>>>>>>>>>>>>>>>>>>>>>> result will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING >>>>>>>>>>>>>>>>>>>>>>>>
discussion should
be restricted to Prolog specific things, in this >>>>>>>>>>>>>>>>>>>>>>>> case
to the Prolog
example above and the contrasting Prolog example >>>>>>>>>>>>>>>>>>>>>>>> not
yet shown.
In order to elaborate the details of my system >>>>>>>>>>>>>>>>>>>>>>> I require some way to formalize natural language. >>>>>>>>>>>>>>>>>>>>>>> Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog >>>>>>>>>>>>>>>>>>>>>>> are the options that I have been considering. >>>>>>>>>>>>>>>>>>>>>>>
The notion of how a well-founded justification tree >>>>>>>>>>>>>>>>>>>>>>> eliminates undecidability is a key element of my >>>>>>>>>>>>>>>>>>>>>>> system.
Prolog shows this best.
It is not Prolog computable to determine whether a >>>>>>>>>>>>>>>>>>>>>> sentence of Peano
arithmetic has a well-founded justification tree in >>>>>>>>>>>>>>>>>>>>>> Peano
arithmetic.
A formal language similar to Prolog that can represent >>>>>>>>>>>>>>>>>>>>> all of the semantics of PA can be developed so that >>>>>>>>>>>>>>>>>>>>> it detects and rejects expressions that lack >>>>>>>>>>>>>>>>>>>>> well-founded
justification trees.
A language does not detect. For detection you need an >>>>>>>>>>>>>>>>>>>> algorithm.
unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>> is a function of the Prolog language that >>>>>>>>>>>>>>>>>>> implements the algorithm.
No, it is not. The question whether a sentence has a >>>>>>>>>>>>>>>>>> well-founded
justification tree is a question about one thing so it >>>>>>>>>>>>>>>>>> needs an
algrotim that takes only one input but
uunify_with_occurs_check
takes two.
The number of inputs does not matter.
It certainly does. You can't use unify_with_occurs_check to >>>>>>>>>>>>>>>> determine
whether ∀x ∀y (x + y = y + x) has a well-founded >>>>>>>>>>>>>>>> justification
tree.
[00] ∀x
│
└─────> [01] ∀y
│
└─────> [02] Equals
│
├─────> [03] add (Left) >>>>>>>>>>>>>>> │ │
│ ├─────> [05] x <┐ >>>>>>>>>>>>>>> │ │ │ >>>>>>>>>>>>>>> │ └─────> [06] y <┼─┐
│ │ │ (Shared >>>>>>>>>>>>>>> Pointers)
└─────> [04] add (Right) │ │
│ │ │ >>>>>>>>>>>>>>> ├──────> [06] y ─┘ │
│ │ >>>>>>>>>>>>>>> └──────> [05] x ───┘
There are no cycles in this tree
Can we interprete this to mean that you admit that the >>>>>>>>>>>>>> predicate
unify_with_occurs_check is not useful for determination >>>>>>>>>>>>>> whether
∀x ∀y (x + y = y + x) has a well-founded justification tree ?
My example was to merely prove that the Liar Paradox >>>>>>>>>>>>> has never been anything besides incoherent nonsense. >>>>>>>>>>>>> I showed this in an existing well understood logic
programming language.
I.e., yes, we can interprete your diagram to mean that you >>>>>>>>>>>> admit
that
the predicate unify_with_occurs_check is not useful for >>>>>>>>>>>> determination
whether ∀x ∀y (x + y = y + x) has a well-founded justification >>>>>>>>>>>> tree.
Consequently, you agree that your claims to the contrary were >>>>>>>>>>>> false.
I started with the most salient case within
the most well-known language that can prove
my point. T^he above case if my own Minimal Type
Theory.
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
Nice to see that you don't disagree.
When you understand proof theoretic semantics well
enough then you understand that within the coherent
foundation of PTS Gödel 1931 Incompleteness becomes
an instance of incoherent semantics.
An ad-hominem with an unproven premise disqualifies your comment. >>>>>>>> Though an ad-hominem would disqualify it even if the premise were >>>>>>>> proven.
Wikipedia has a page about rhetorical fallacies.
https://en.wikipedia.org/wiki/Fallacy
https://en.wikipedia.org/wiki/List_of_fallacies
These are parts of greater accounts of deductive inference
to allay and prevent failures or sabotage of inductive inference, >>>>>>> the "invincible" ignorance of inductive inference.
This then makes for "two wrongs does not make a right".
The usual account of "axioms" must be distinguished into
at least two kinds: those that "expand comprehension",
and those that "restrict comprehension". Basically one has
that under expansion-of-comprehension, that alternatives
or inverses exist, the other restriction-of-comprehension,
that one or the other doesn't exist.
"Inductive inference" isn't a lie, though, given a lie,
it can't tell the truth.
Then, Wikipedia also has a page about paradox.
https://en.wikipedia.org/wiki/Paradox
https://en.wikipedia.org/wiki/List_of_paradoxes
Then, paradoxes are usually enough given as results of
logic, here about logical paradoxes that would find themselves
in any theory, not about conflicting theories tangentially
relevant each other, those just being a model of conflicting
theories.
So, about resolving the paradoxes of logic, like Russell
and Burali-Forti and Cantor the paradoxes, these being
references to modern accounts of logic, and about the
Barber and the Heap and the Liar, these being references
to classical expositions of logic, has that eventually any
sort of restriction of comprehension in the universe of
logical objects may thusly be found by expansion of comprehension >>>>>>> in the universe of logical objects to be contradicted.
So, it's known since antiquity that any sort of inductive
account can be broken.
Then, these "inductive impasses", must need make for
"analytical bridges", where there's a very particular
account of the primeval of the primary, about a universe
of truth already, else any sort of account of axiomatics
with restriction-of-comprehension is broken, instead of
merely being an example of perspective and thus limited
perspective.
So, the account of Pete Olcott is just a crank's/troll's/bot's
account, adding more restriction-of-comprehension above a
perceived "foundation" that's a false floor, futile and
doomed to fail, while yet simply enough making a claim
that "if it's not wrong it's not wrong", then furthermore
more or less saying "can't tell the difference between
fallacy and paradox and truth".
Here then we may have a modal temporal relevance logic
and a theory where classical logic is modal and excludes
the "material implication" since Chrysippus, and to re-name
the usual account of 20'th century "classical logic" as instead
along the lines of "Philo's Plotinus' Occam's Compte's Boole's
Russell's Carnap's nominalist fictionalist logicist positivist
Tarski's Goedel's quasi-modal account of logic and truth", that
"Olcott's Goedel's" is yet another account of the quasi-modal.
So, it's a crank's/troll's/bot's, sometimes easier just
not to feed it. That said, it's a ready interpretation from
something like modern accounts of inference that simply employ
quasi-modal logic throughout and suggest thusly tabulating fact
after fact as truth, and making the fallacy of calling that
"monotonicity" and "entailment", which would be a lie, or as
with regards to contradicting either the competency or veracity, >>>>>>> of such accounts.
So, PO's futile flailings are just a reflection on the current
intellectual inertia about the quasi-modal logic, which taking
a partial account of a partial account, wronged itself twice.
"The notion of a well-founded justification tree
will be fully elaborated."
A finite back-chained inference from the expression
to its axioms. As shown below in MTT the absence of
cycles in the directed graph of the expressions
evaluation sequence.
% This sentence cannot be proven in F
?- G = not(provable(F, G)).
G = not(provable(F, G)).
?- unify_with_occurs_check(G, not(provable(F, G))).
false.
https://www.swi-prolog.org/pldoc/man?
predicate=unify_with_occurs_check/2
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
No, a deductive account about the possibilities and limits of
inductive inference, helping explain any super-classical result,
not just a rule-sniffing dog that follows its own brown nose.
Goedel's incompleteness result is much simpler after a simple
sort of account of quantification and the old "sputniks of
quantification", that readily demonstrate something like
Russell's paradox in account of ordinary arithmetic, for
what somebody like Mirimanoff calls the "extra-ordinary",
and Skolem constructs for fragments and extensions in the
ordinary account of usual model theory about models of integers,
then that Goedel's incompleteness basically gives limits of
applicability of _claims_, here emphasized the _claims_ as
being the proper word for accounts of inference over usual
sorts of nominalist fictionalist logicist positivists' theories.
Otherwise anybody can just come along and prove Russell wrong,
prove Cantor wrong, and otherwise without a paradox-free reason
its account thereof overall, has that "the notion of a well-founded
justification tree", about e-minimality usually enough, to
be _elaborated_, involves the _diligence_ and the _thoroughness_
of a conscientious account of the extra-ordinary, the super-standard,
and the reasoning for _continuity_, and, _infinity_.
This PO account used to be a bit more open-minded, now it's
quite firmly retro-finitist, the hall-mark of the crank and troll.
So, PO, if there is to be elaborated "well-founded justification
trees",
they live in a domain of discourse with other rulialities
than
well-foundedness/e-minimality/no-infinite-descending-epsilon-chains,
and
somehow in reality and in logic they _do_ all get along.
"E-laborated" means the diligent work was done,
the work was worked out of it, not just "defined" done.
You need an account that rejects quasi-modal logic or
else anyone can easily give innocuous non-facts that
define themselves "true".
It is best understood within the essential framework
of Prolog of back-chained inference from expressions
using Rules to reach Facts.
Prolog itself is far too weak to generalize this,
none-the-less the infrastructure of expressions
anchored in Facts and Rules does provide the complete
essence.
When we do it this way much of what has been misconstrued
as "undecidability" becomes expressions that are rejected
because they remain ungrounded in Facts.
This is not merely the foundations of math and logic
it is alternative foundations for math and logic that
reject and replace the conventional views.
I'd suggest not using the word "understood", with regards
to reasoning about _closures_ and furthermore _completions_,
with regards to things like "infinite limits" the completions.
Facts and rules for rules-engines and the like are very old-hat,
and contradictory rules
Are excluded.
in such accounts given un-true stated
"facts", besides that "facts" in such accounts are stipulated,
with regards to "verum" vis-a-vis "certum" and that it's only
conscientiously a _scientific_ account, con-scient-ious.
I don't speak Latin. These stipulated Facts are actually true
that is all that need be known about them.
The usual account of quasi-modal logic assumes that
_time has stopped and there is no change_,
the quasi-modal account itself is _not_ a temporal logic
and thusly _not_ a modal logic. Furthermore, the quasi-modal
logic's account of "monotonicity" fails, then that also
the "entailment" is not an apropos term, and besides usual
accounts of "garbage-in/garbage-out" is "crazy-in/crazy-out".
All we need to know that that the Facts are true Facts about general knowledge.
So, math and logic have _infinity_ and _infinitary reasoning_,
they are _not_ going away.
Not when restricted to the finite list of true (atomic) Facts of general knowledge.
What you got there is, at best, a calculus of closed-categories,
and if it's not extra-ordinary and super-standard, then it's not.
When closed-categories is referring to the Frege compositional meaning
and not some idiomatic term-of-the-art then yes closed-categories.
About "un-decide-ability", there's furthermore an even stronger
account of _independence_, the mathematical independence, since
I don't need to yet into the nuances of of terms-of-the-art
idiosyncrasies. Either an expression can be resolved to true
or false or it is not a member of the body of knowledge
expressed in language.
there are multiple laws of large numbers, and that measure theory
makes for quasi-invariant measure theory, since doubling/halving
spaces/measures make for the re-Vitali-ization of measure theory
about Vitali and Hausdorff and equi-decomposability, and for
analysts about competing accounts of _convergence_ and _emergence_,
that it is _real_ that some accounts of naive uniqueness instead
are ascribed particular distinctness, about real completions in
the objects of mathematics, beyond "not enough information".
If expressions cannot reach Facts using Rules then they
are out-of-scope. In this case the Rules are full natural
language semantics specified syntactically.
So, your usage of the words is unfortunately poisoned by the
fact that quasi-modal logic makes you think "material implication"
is a thing and that it does the thing, when it is not and does not.
My whole system is constructed entirely on the
basis of A is a necessary consequence of B.
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
Disjunction introduction is totally rejected.
Material implication may be entirely rejected.
Your somewhat convoluted language seems to mostly miss the
point of the barest essence of
"true on the basis of meaning expressed in language"
On 4/15/2026 11:51 AM, André G. Isaak wrote:
On 2026-04-15 06:02, olcott wrote:
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
You've said this (or something similar) to several different posters
now; but bear in mind that you yourself only became aware of the
existence of proof-theoretic semantics a few months ago which means
that you have hardly had enough time to become an expert in PTS.
It turns out that all of my ideas have been fully anchored
in exactly proof theoretic semantics the whole time.
Also
my current ideas have taken the exact PTS basis and extended
them much more.
The current state of PTS seems to still be anchored in
what is essentially propositional logic whereas my system
has been anchored in formalized natural language semantics
for a long time.
So you're really not in a position to tell people what an expert in
PTS might claim about any particular issue.
André
On 2026-04-15 11:24, olcott wrote:
On 4/15/2026 11:51 AM, André G. Isaak wrote:
On 2026-04-15 06:02, olcott wrote:
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
You've said this (or something similar) to several different posters
now; but bear in mind that you yourself only became aware of the
existence of proof-theoretic semantics a few months ago which means
that you have hardly had enough time to become an expert in PTS.
It turns out that all of my ideas have been fully anchored
in exactly proof theoretic semantics the whole time.
They really haven't been.
You stumbled upon a framework which, in your mind, bore some vague resemblance to your own ideas, and then you projected your own ideas
onto that framework. But it's very clear from what you've posted here
that you don't really understand PTS as used by, e.g. Schroeder-Heister
or Francez as you keep attributing things to PTS which they very clearly don't endorse.
Also
my current ideas have taken the exact PTS basis and extended
them much more.
Well, until you actually clarify what *you* think that PTS basis is
(referring to the works of others here won't cut it since as I point out above you seem to have a very different interpretation of PTS than its proponents hold), and until you actually lay out what your "extensions"
are, no one is in any position to discuss your ideas.
André
The current state of PTS seems to still be anchored in
what is essentially propositional logic whereas my system
has been anchored in formalized natural language semantics
for a long time.
So you're really not in a position to tell people what an expert in
PTS might claim about any particular issue.
André
On 4/15/2026 2:13 PM, André G. Isaak wrote:
On 2026-04-15 11:24, olcott wrote:
On 4/15/2026 11:51 AM, André G. Isaak wrote:
On 2026-04-15 06:02, olcott wrote:
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
You've said this (or something similar) to several different posters
now; but bear in mind that you yourself only became aware of the
existence of proof-theoretic semantics a few months ago which means
that you have hardly had enough time to become an expert in PTS.
It turns out that all of my ideas have been fully anchored
in exactly proof theoretic semantics the whole time.
They really haven't been.
You stumbled upon a framework which, in your mind, bore some vague
resemblance to your own ideas, and then you projected your own ideas
onto that framework. But it's very clear from what you've posted here
that you don't really understand PTS as used by, e.g.
Schroeder-Heister or Francez as you keep attributing things to PTS
which they very clearly don't endorse.
Try to explain the details of this.
I am referring to aspects where Professor Dag Prawitz
and professor Peter Schroeder-Heister may have divergent
views. My perspective unifies these divergent views.
Also
my current ideas have taken the exact PTS basis and extended
them much more.
Well, until you actually clarify what *you* think that PTS basis is
I cannot teach my reviewers the entire PTS basis.
(referring to the works of others here won't cut it since as I point
out above you seem to have a very different interpretation of PTS than
its proponents hold), and until you actually lay out what your
"extensions" are, no one is in any position to discuss your ideas.
André
The current state of PTS seems to still be anchored in
what is essentially propositional logic whereas my system
has been anchored in formalized natural language semantics
for a long time.
So you're really not in a position to tell people what an expert in
PTS might claim about any particular issue.
André
On 04/15/2026 01:37 PM, olcott wrote:
On 4/15/2026 2:13 PM, André G. Isaak wrote:
On 2026-04-15 11:24, olcott wrote:
On 4/15/2026 11:51 AM, André G. Isaak wrote:
On 2026-04-15 06:02, olcott wrote:
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
You've said this (or something similar) to several different posters >>>>> now; but bear in mind that you yourself only became aware of the
existence of proof-theoretic semantics a few months ago which means
that you have hardly had enough time to become an expert in PTS.
It turns out that all of my ideas have been fully anchored
in exactly proof theoretic semantics the whole time.
They really haven't been.
You stumbled upon a framework which, in your mind, bore some vague
resemblance to your own ideas, and then you projected your own ideas
onto that framework. But it's very clear from what you've posted here
that you don't really understand PTS as used by, e.g.
Schroeder-Heister or Francez as you keep attributing things to PTS
which they very clearly don't endorse.
Try to explain the details of this.
I am referring to aspects where Professor Dag Prawitz
and professor Peter Schroeder-Heister may have divergent
views. My perspective unifies these divergent views.
Also
my current ideas have taken the exact PTS basis and extended
them much more.
Well, until you actually clarify what *you* think that PTS basis is
I cannot teach my reviewers the entire PTS basis.
(referring to the works of others here won't cut it since as I point
out above you seem to have a very different interpretation of PTS than
its proponents hold), and until you actually lay out what your
"extensions" are, no one is in any position to discuss your ideas.
André
The current state of PTS seems to still be anchored in
what is essentially propositional logic whereas my system
has been anchored in formalized natural language semantics
for a long time.
So you're really not in a position to tell people what an expert in
PTS might claim about any particular issue.
André
If you can't explain it then you don't know it.
On 4/15/2026 2:13 PM, André G. Isaak wrote:
On 2026-04-15 11:24, olcott wrote:
On 4/15/2026 11:51 AM, André G. Isaak wrote:
On 2026-04-15 06:02, olcott wrote:
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
You've said this (or something similar) to several different posters
now; but bear in mind that you yourself only became aware of the
existence of proof-theoretic semantics a few months ago which means
that you have hardly had enough time to become an expert in PTS.
It turns out that all of my ideas have been fully anchored
in exactly proof theoretic semantics the whole time.
They really haven't been.
You stumbled upon a framework which, in your mind, bore some vague
resemblance to your own ideas, and then you projected your own ideas
onto that framework. But it's very clear from what you've posted here
that you don't really understand PTS as used by, e.g.
Schroeder-Heister or Francez as you keep attributing things to PTS
which they very clearly don't endorse.
Try to explain the details of this.
I am referring to aspects where Professor Dag Prawitz
and professor Peter Schroeder-Heister may have divergent
views. My perspective unifies these divergent views.
Also
my current ideas have taken the exact PTS basis and extended
them much more.
Well, until you actually clarify what *you* think that PTS basis is
I cannot teach my reviewers the entire PTS basis.
On 2026-04-15 14:37, olcott wrote:
On 4/15/2026 2:13 PM, André G. Isaak wrote:
On 2026-04-15 11:24, olcott wrote:
On 4/15/2026 11:51 AM, André G. Isaak wrote:
On 2026-04-15 06:02, olcott wrote:
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
You've said this (or something similar) to several different
posters now; but bear in mind that you yourself only became aware
of the existence of proof-theoretic semantics a few months ago
which means that you have hardly had enough time to become an
expert in PTS.
It turns out that all of my ideas have been fully anchored
in exactly proof theoretic semantics the whole time.
They really haven't been.
You stumbled upon a framework which, in your mind, bore some vague
resemblance to your own ideas, and then you projected your own ideas
onto that framework. But it's very clear from what you've posted here
that you don't really understand PTS as used by, e.g. Schroeder-
Heister or Francez as you keep attributing things to PTS which they
very clearly don't endorse.
Try to explain the details of this.
I am referring to aspects where Professor Dag Prawitz
and professor Peter Schroeder-Heister may have divergent
views. My perspective unifies these divergent views.
So what are these divergent views and how exactly have you unified them?
Also
my current ideas have taken the exact PTS basis and extended
them much more.
Well, until you actually clarify what *you* think that PTS basis is
I cannot teach my reviewers the entire PTS basis.
If you ever realize your plans to publish your work, you would be
expected to do just that.
PTS is not sufficiently well-known that you
could get away with simply assuming it in a published paper; you would
need to lay out the details of this theory.
Doing so here would be good practice since its something you will
eventually have to do anyways.
André
On 2026-04-15 14:37, olcott wrote:
On 4/15/2026 2:13 PM, André G. Isaak wrote:
On 2026-04-15 11:24, olcott wrote:
On 4/15/2026 11:51 AM, André G. Isaak wrote:
On 2026-04-15 06:02, olcott wrote:
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
You've said this (or something similar) to several different
posters now; but bear in mind that you yourself only became aware
of the existence of proof-theoretic semantics a few months ago
which means that you have hardly had enough time to become an
expert in PTS.
It turns out that all of my ideas have been fully anchored
in exactly proof theoretic semantics the whole time.
They really haven't been.
You stumbled upon a framework which, in your mind, bore some vague
resemblance to your own ideas, and then you projected your own ideas
onto that framework. But it's very clear from what you've posted here
that you don't really understand PTS as used by, e.g. Schroeder-
Heister or Francez as you keep attributing things to PTS which they
very clearly don't endorse.
Try to explain the details of this.
I am referring to aspects where Professor Dag Prawitz
and professor Peter Schroeder-Heister may have divergent
views. My perspective unifies these divergent views.
So what are these divergent views and how exactly have you unified them?
Also
my current ideas have taken the exact PTS basis and extended
them much more.
Well, until you actually clarify what *you* think that PTS basis is
I cannot teach my reviewers the entire PTS basis.
If you ever realize your plans to publish your work, you would be
expected to do just that. PTS is not sufficiently well-known that you
could get away with simply assuming it in a published paper; you would
need to lay out the details of this theory.
Doing so here would be good practice since its something you will
eventually have to do anyways.
André
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
On 4/14/2026 12:55 AM, Mikko wrote:
On 13/04/2026 17:24, olcott wrote:
On 4/13/2026 2:03 AM, Mikko wrote:
On 12/04/2026 16:17, olcott wrote:
On 4/12/2026 4:26 AM, Mikko wrote:
On 11/04/2026 17:14, olcott wrote:
On 4/11/2026 2:30 AM, Mikko wrote:
On 10/04/2026 14:18, olcott wrote:
On 4/10/2026 2:30 AM, Mikko wrote:
On 09/04/2026 16:34, olcott wrote:
On 4/9/2026 4:17 AM, Mikko wrote:
On 08/04/2026 17:13, olcott wrote:
On 4/8/2026 6:52 AM, olcott wrote:
On 4/8/2026 2:08 AM, Mikko wrote:
On 07/04/2026 17:49, olcott wrote:
On 4/7/2026 3:00 AM, Mikko wrote:
On 06/04/2026 14:21, olcott wrote:
On 4/6/2026 3:27 AM, Mikko wrote:
On 05/04/2026 14:25, olcott wrote:
On 4/5/2026 2:05 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>> On 04/04/2026 19:23, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 4/4/2026 2:53 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 03/04/2026 16:35, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>> On 4/3/2026 2:13 AM, Mikko wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>> On 02/04/2026 23:58, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>>>>>> To be able to properly ground this in >>>>>>>>>>>>>>>>>>>>>>>>>>>> existing foundational
That's mainly true. However, in como.lang.prolog >>>>>>>>>>>>>>>>>>>>>>> the discussion shouldpeer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>>>>>>Do you think 100 years would be enough, or at >>>>>>>>>>>>>>>>>>>>>>>>>>> least some finite time?
I have to carefully study at least a dozen papers >>>>>>>>>>>>>>>>>>>>>>>>>> that may average 15 pages each. The basic notion >>>>>>>>>>>>>>>>>>>>>>>>>> of a "well founded justification tree" >>>>>>>>>>>>>>>>>>>>>>>>>> essentially
means the Proof Theoretic notion of reduction to >>>>>>>>>>>>>>>>>>>>>>>>>> a Canonical proof.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
?- unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>>>>>>>> false.
If you want to illustrate with examples you >>>>>>>>>>>>>>>>>>>>>>>>> should have two examples:
The above Prolog determines that LP does not >>>>>>>>>>>>>>>>>>>>>>>>>> have a "well founded justification tree". >>>>>>>>>>>>>>>>>>>>>>>>>
one with a negative result (as above) and one >>>>>>>>>>>>>>>>>>>>>>>>> with a positive one.
So the above example should be paired with one >>>>>>>>>>>>>>>>>>>>>>>>> that has someting
else in place of not(provable(F, G)) so that >>>>>>>>>>>>>>>>>>>>>>>>> the result will not be
false.
THIS IS NOT A PROLOG SPECIFIC THING >>>>>>>>>>>>>>>>>>>>>>>
be restricted to Prolog specific things, in this >>>>>>>>>>>>>>>>>>>>>>> case to the Prolog
example above and the contrasting Prolog example >>>>>>>>>>>>>>>>>>>>>>> not yet shown.
In order to elaborate the details of my system >>>>>>>>>>>>>>>>>>>>>> I require some way to formalize natural language. >>>>>>>>>>>>>>>>>>>>>> Montague Grammar, Rudolf Carnap Meaning Postulates, >>>>>>>>>>>>>>>>>>>>>> the CycL language of the Cyc project and Prolog >>>>>>>>>>>>>>>>>>>>>> are the options that I have been considering. >>>>>>>>>>>>>>>>>>>>>>
The notion of how a well-founded justification tree >>>>>>>>>>>>>>>>>>>>>> eliminates undecidability is a key element of my >>>>>>>>>>>>>>>>>>>>>> system.
Prolog shows this best.
It is not Prolog computable to determine whether a >>>>>>>>>>>>>>>>>>>>> sentence of Peano
arithmetic has a well-founded justification tree in >>>>>>>>>>>>>>>>>>>>> Peano arithmetic.
A formal language similar to Prolog that can represent >>>>>>>>>>>>>>>>>>>> all of the semantics of PA can be developed so that >>>>>>>>>>>>>>>>>>>> it detects and rejects expressions that lack well- >>>>>>>>>>>>>>>>>>>> founded
justification trees.
A language does not detect. For detection you need an >>>>>>>>>>>>>>>>>>> algorithm.
unify_with_occurs_check(LP, not(true(LP))). >>>>>>>>>>>>>>>>>> is a function of the Prolog language that
implements the algorithm.
No, it is not. The question whether a sentence has a >>>>>>>>>>>>>>>>> well- founded
justification tree is a question about one thing so it >>>>>>>>>>>>>>>>> needs an
algrotim that takes only one input but
uunify_with_occurs_check
takes two.
The number of inputs does not matter.
If BY ANY MEANS a cycle is detected in the
directed graph of the evaluation sequence of
the expression then the expression is rejected. >>>>>>>>>>>>>>>>
True(L, X) := ∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) // copyright >>>>>>>>>>>>>>>> Olcott 2018
If for any reason a back chained inference does >>>>>>>>>>>>>>>> not reach BaseFacts(L) then the expression is untrue. >>>>>>>>>>>>>>>>
CORRECTION:
...then the expression is untrue [within the body >>>>>>>>>>>>>>> of knowledge that can be expressed in language].
That is not useful unless there are methods to determine >>>>>>>>>>>>>> whether
∃Γ ⊆ BaseFacts(L) (Γ ⊢ X) for every X in some L. >>>>>>>>>>>>>>
You can't use nify_with_occurs_check/2 to deremine whether >>>>>>>>>>>>>> True(X, L).
If there is a finite back-chained inference path from X >>>>>>>>>>>>> to Γ then X is true.
That does not help if you don't know whether there is a finite >>>>>>>>>>>> back-chained inference path from X to Γ.
You simply do the back-chained inference and it reaches
the subset of BaseFacts or it does not. If it reaches
a loop then it is rejected as semantically incoherent.
And if it does neither ?
It either finds a finite path or finds that no
finite path exists.
There is no such it.
This is the it:
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
A goal that is not and cannot be achieved.
All instances of undecidability have either been provably
semantically incoherent input:
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
Or outside of the body of knowledge such as the
truth value of the Goldbach conjecture.
It is not known whether there is a finite back-chained inference path
from Goldbach conjecture to the body of knowledge. If there is then
the conjecture is both true and untrue according to your statements
above.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
On 15/04/2026 15:02, olcott wrote:
On 4/15/2026 2:07 AM, Mikko wrote:
But it is indeed true that I don't believe in conclusions if it
is not known whether the premises are true. And I don't believe
that ad-hominem can be a part of a valid argument, although it
might be a basis to reject a testimnoy.
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
Not quite. I will remain a wonderer. You will remain clueless.
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers. https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers. https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:The current path is not finite.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach >>>>>>> conjecture to the body of knowledge then how it is out of scope ? >>>>>>
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number,
then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
On 04/16/2026 10:47 AM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:The current path is not finite.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach >>>>>>>> conjecture to the body of knowledge then how it is out of scope ? >>>>>>>
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number,
then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
There's a thread here about 2003 "Factorial/Exponential Identity,
Infinity" where I arrived at not only an infinitary
factorial/exponential identity, also a new approximation for factorial,
then show that "Borel versus Combinatorics" makes that set theory's
account of descriptive set theory has conflicting ordinary accounts
of "Borel versus Combinatorics" about how many almost all/none of
infinite {0,1} sequences are absolutely normal, this shows that
whether "Borel" or "Combinatorics" holds is independent the
ordinary set theory's descriptive account of Archimedean numbers,
and naturally.
https://groups.google.com/g/sci.math/c/3AH5LXl76Cw
So, "Borel versus Combinatorics", then I later make it "Borel vis-a-vis Combinatorics", and make constructive developments that then live in the applied, while then I can take any account that invokes van der Waerden
or Roth and the like or Ramsey theory, and make it two theories.
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:The current path is not finite.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach >>>>>>> conjecture to the body of knowledge then how it is out of scope ? >>>>>>
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number,
then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
On 04/16/2026 10:47 AM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:The current path is not finite.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach >>>>>>>> conjecture to the body of knowledge then how it is out of scope ? >>>>>>>
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number,
then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
There's a thread here about 2003 "Factorial/Exponential Identity,
Infinity" where I arrived at not only an infinitary
factorial/exponential identity, also a new approximation for factorial,
then show that "Borel versus Combinatorics" makes that set theory's
account of descriptive set theory has conflicting ordinary accounts
of "Borel versus Combinatorics" about how many almost all/none of
infinite {0,1} sequences are absolutely normal, this shows that
whether "Borel" or "Combinatorics" holds is independent the
ordinary set theory's descriptive account of Archimedean numbers,
and naturally.
https://groups.google.com/g/sci.math/c/3AH5LXl76Cw
So, "Borel versus Combinatorics", then I later make it "Borel vis-a-vis Combinatorics", and make constructive developments that then live in the applied, while then I can take any account that invokes van der Waerden
or Roth and the like or Ramsey theory, and make it two theories.
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:The current path is not finite.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach >>>>>>>> conjecture to the body of knowledge then how it is out of scope ? >>>>>>>
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number,
then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:The current path is not finite.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach >>>>>>>>> conjecture to the body of knowledge then how it is out of scope ? >>>>>>>>
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number,
then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem".
I suppose you could omit _all_ super-classical results from mathematics, since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:The current path is not finite.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach >>>>>>>>> conjecture to the body of knowledge then how it is out of scope ? >>>>>>>>
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number,
then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem".
I suppose you could omit _all_ super-classical results from mathematics, since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:The current path is not finite.
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach >>>>>>>>>> conjecture to the body of knowledge then how it is out of scope ? >>>>>>>>>
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number,
then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem".
I suppose you could omit _all_ super-classical results from mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from >>>>>>>>>>> Goldbach
conjecture to the body of knowledge then how it is out of >>>>>>>>>>> scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number,
then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem".
I suppose you could omit _all_ super-classical results from mathematics, >>> since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
On 4/16/2026 3:33 AM, Mikko wrote:
On 15/04/2026 15:02, olcott wrote:
On 4/15/2026 2:07 AM, Mikko wrote:
But it is indeed true that I don't believe in conclusions if it
is not known whether the premises are true. And I don't believe
that ad-hominem can be a part of a valid argument, although it
might be a basis to reject a testimnoy.
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
Not quite. I will remain a wonderer. You will remain clueless.
It will soon be an easily verified fact that all
my ideas have always been fully anchored in modern
Proof Theoretic Semantics.
I will write a new paper that specifically anchors
each of my ideas point-by-point and item-by-item
in direct quotes from foundational papers in Proof
Theoretic Semantics. This is easy to do, yet takes
time to get it exactly right.
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path from >>>>>>>>>>>> Goldbach
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language" >>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>
conjecture to the body of knowledge then how it is out of >>>>>>>>>>>> scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity >>>>>> in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number,
then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem".
I suppose you could omit _all_ super-classical results from
mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
On 04/16/2026 05:41 PM, olcott wrote:
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:It states that every even natural number greater
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path from >>>>>>>>>>>>> Goldbach
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>
conjecture to the body of knowledge then how it is out of >>>>>>>>>>>>> scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where
they are not, that they are "independent" the "standard model" >>>>>>>>
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity >>>>>>> in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number,
then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem".
I suppose you could omit _all_ super-classical results from
mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
It's actually an exercise in _reading comprehension_.
Reading as an exercise involves multiple passes of
parsing. There is no actual finality in statement.
It's un-scientific to presume declarative fact.
Text is always a fragment. The context is always
existent, and the text is always outside of it.
On 16/04/2026 15:36, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
Nice to see that you agree.
But you still havn't answered the question.
On 16/04/2026 15:52, olcott wrote:
On 4/16/2026 3:33 AM, Mikko wrote:
On 15/04/2026 15:02, olcott wrote:
On 4/15/2026 2:07 AM, Mikko wrote:
But it is indeed true that I don't believe in conclusions if it
is not known whether the premises are true. And I don't believe
that ad-hominem can be a part of a valid argument, although it
might be a basis to reject a testimnoy.
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
Not quite. I will remain a wonderer. You will remain clueless.
It will soon be an easily verified fact that all
my ideas have always been fully anchored in modern
Proof Theoretic Semantics.
Does that "soon" mean less than 50 years ?
I will write a new paper that specifically anchors
each of my ideas point-by-point and item-by-item
in direct quotes from foundational papers in Proof
Theoretic Semantics. This is easy to do, yet takes
time to get it exactly right.
A good paper would not give any reason to think that the author may
be stupid or ignorant.
On 4/17/2026 2:49 AM, Ross Finlayson wrote:
On 04/16/2026 05:41 PM, olcott wrote:
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:It states that every even natural number greater
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path from >>>>>>>>>>>>>> Goldbach
It is known that the truth value of the Goldbach >>>>>>>>>>>>>>> conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>
conjecture to the body of knowledge then how it is out of >>>>>>>>>>>>>> scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where >>>>>>>>>> they are not, that they are "independent" the "standard model" >>>>>>>>>
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity >>>>>>>> in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number, >>>>>>>> then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem".
I suppose you could omit _all_ super-classical results from
mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
It's actually an exercise in _reading comprehension_.
Reading as an exercise involves multiple passes of
parsing. There is no actual finality in statement.
It's un-scientific to presume declarative fact.
Text is always a fragment. The context is always
existent, and the text is always outside of it.
It seems to be a dishonest dodge way from this point
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
All that I am establishing is that there are
some expressions of language that have truth
values that do not exist within the body of
knowledge.
You keep talking in endless circles around
this single precise point.
On 04/17/2026 07:04 AM, olcott wrote:
On 4/17/2026 2:49 AM, Ross Finlayson wrote:
On 04/16/2026 05:41 PM, olcott wrote:
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:It states that every even natural number greater
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path from >>>>>>>>>>>>>>> Goldbach
It is known that the truth value of the Goldbach >>>>>>>>>>>>>>>> conjecture is unknown this is out-of-scope for >>>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>
conjecture to the body of knowledge then how it is out of >>>>>>>>>>>>>>> scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models >>>>>>>>>>> of integers where they are so and models of integers where >>>>>>>>>>> they are not, that they are "independent" the "standard model" >>>>>>>>>>
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at- >>>>>>>>> infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number, >>>>>>>>> then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't. >>>>>>>>>
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem".
I suppose you could omit _all_ super-classical results from
mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
It's actually an exercise in _reading comprehension_.
Reading as an exercise involves multiple passes of
parsing. There is no actual finality in statement.
It's un-scientific to presume declarative fact.
Text is always a fragment. The context is always
existent, and the text is always outside of it.
It seems to be a dishonest dodge way from this point
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
All that I am establishing is that there are
some expressions of language that have truth
values that do not exist within the body of
knowledge.
You keep talking in endless circles around
this single precise point.
So, the previous posts have much about this
that you just snipped, that _snipping_ is
On 4/17/2026 2:49 AM, Ross Finlayson wrote:
On 04/16/2026 05:41 PM, olcott wrote:
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:It states that every even natural number greater
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path from >>>>>>>>>>>>>> Goldbach
It is known that the truth value of the Goldbach >>>>>>>>>>>>>>> conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>
conjecture to the body of knowledge then how it is out of >>>>>>>>>>>>>> scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models
of integers where they are so and models of integers where >>>>>>>>>> they are not, that they are "independent" the "standard model" >>>>>>>>>
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at-infinity >>>>>>>> in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number, >>>>>>>> then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't.
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem".
I suppose you could omit _all_ super-classical results from
mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
It's actually an exercise in _reading comprehension_.
Reading as an exercise involves multiple passes of
parsing. There is no actual finality in statement.
It's un-scientific to presume declarative fact.
Text is always a fragment. The context is always
existent, and the text is always outside of it.
It seems to be a dishonest dodge way from this point
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
All that I am establishing is that there are
some expressions of language that have truth
values that do not exist within the body of
knowledge.
You keep talking in endless circles around
this single precise point.
On 4/17/2026 9:52 AM, Ross Finlayson wrote:
On 04/17/2026 07:04 AM, olcott wrote:
On 4/17/2026 2:49 AM, Ross Finlayson wrote:
On 04/16/2026 05:41 PM, olcott wrote:
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:It states that every even natural number greater
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path from >>>>>>>>>>>>>>>> Goldbach
It is known that the truth value of the Goldbach >>>>>>>>>>>>>>>>> conjecture is unknown this is out-of-scope for >>>>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>>
conjecture to the body of knowledge then how it is out of >>>>>>>>>>>>>>>> scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language" >>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside >>>>>>>>>>>>> the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models >>>>>>>>>>>> of integers where they are so and models of integers where >>>>>>>>>>>> they are not, that they are "independent" the "standard model" >>>>>>>>>>>
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point, >>>>>>>>>> whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at- >>>>>>>>>> infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number, >>>>>>>>>> then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example >>>>>>>>>> about notions like as from p-adic integers, where they don't. >>>>>>>>>>
For example, the direct-sum of the infinitely-many integers >>>>>>>>>> would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem". >>>>>>>>
I suppose you could omit _all_ super-classical results from
mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
It's actually an exercise in _reading comprehension_.
Reading as an exercise involves multiple passes of
parsing. There is no actual finality in statement.
It's un-scientific to presume declarative fact.
Text is always a fragment. The context is always
existent, and the text is always outside of it.
It seems to be a dishonest dodge way from this point
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
All that I am establishing is that there are
some expressions of language that have truth
values that do not exist within the body of
knowledge.
You keep talking in endless circles around
this single precise point.
So, the previous posts have much about this
that you just snipped, that _snipping_ is
Do you understand that the truth value of the Goldbach
conjecture is currently unknown:
(a) YES
(b) NO
Any answer besides (a) or (b) will be ignored.
On 4/17/26 10:04 AM, olcott wrote:
On 4/17/2026 2:49 AM, Ross Finlayson wrote:
On 04/16/2026 05:41 PM, olcott wrote:
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:It states that every even natural number greater
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path from >>>>>>>>>>>>>>> Goldbach
It is known that the truth value of the Goldbach >>>>>>>>>>>>>>>> conjecture is unknown this is out-of-scope for >>>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>
conjecture to the body of knowledge then how it is out of >>>>>>>>>>>>>>> scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models >>>>>>>>>>> of integers where they are so and models of integers where >>>>>>>>>>> they are not, that they are "independent" the "standard model" >>>>>>>>>>
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples,
whether the naturals are compact and make for fixed-point,
whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a
point-at-infinity
in "the naturals", naturally, whether you like it or not,
there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number, >>>>>>>>> then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example
about notions like as from p-adic integers, where they don't. >>>>>>>>>
For example, the direct-sum of the infinitely-many integers
would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem".
I suppose you could omit _all_ super-classical results from
mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
It's actually an exercise in _reading comprehension_.
Reading as an exercise involves multiple passes of
parsing. There is no actual finality in statement.
It's un-scientific to presume declarative fact.
Text is always a fragment. The context is always
existent, and the text is always outside of it.
It seems to be a dishonest dodge way from this point
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
All that I am establishing is that there are
some expressions of language that have truth
values that do not exist within the body of
knowledge.
You keep talking in endless circles around
this single precise point.
Right, because "Knowledge" and "Truth" are different things.
It seems you just admitted that you goal is unatainable, that there
*ARE* statements with a truth value (like the Goldbach Conjecture) that
can not be actually proven based on our current knowledge.
It isn't that the Goldbach Conjecture doesn't have a meaning, but it expresses something whose answer is currently not known, and might never
be known.
The problem is you can not exhaustively search the possible space it discusses to rule out that there is a counter example. No matter how
high you test, there are still larger numbers where a counter example
might be found. So unless you happen to be able to find an actual proof
of its truth, it might be unknowable.
This is the whole concept of incompleteness, a term I don't think you understand. Being "incomplete" doesn't make a system less usefull, and
in fact comes out of the fact that the power of the system to exprss
thins grew too rapidly for it to be able to analyize EVERYTHING, but it
still does more than a lessor system that can analyize everything it can express.
On 04/17/2026 07:58 AM, olcott wrote:
On 4/17/2026 9:52 AM, Ross Finlayson wrote:
On 04/17/2026 07:04 AM, olcott wrote:
On 4/17/2026 2:49 AM, Ross Finlayson wrote:
On 04/16/2026 05:41 PM, olcott wrote:
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:It states that every even natural number greater
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:My 28 year goal has been to make
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path from >>>>>>>>>>>>>>>>> Goldbach
It is known that the truth value of the Goldbach >>>>>>>>>>>>>>>>>> conjecture is unknown this is out-of-scope for >>>>>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>>>
conjecture to the body of knowledge then how it is out of >>>>>>>>>>>>>>>>> scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question, >>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside >>>>>>>>>>>>>> the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models >>>>>>>>>>>>> of integers where they are so and models of integers where >>>>>>>>>>>>> they are not, that they are "independent" the "standard model" >>>>>>>>>>>>
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples, >>>>>>>>>>> whether the naturals are compact and make for fixed-point, >>>>>>>>>>> whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at- >>>>>>>>>>> infinity
in "the naturals", naturally, whether you like it or not, >>>>>>>>>>> there's a prime at infinity or a composite at infinity,
whether or not according to the operations it's an even number, >>>>>>>>>>> then as with regards to whether or not that is or isn't
a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example >>>>>>>>>>> about notions like as from p-adic integers, where they don't. >>>>>>>>>>>
For example, the direct-sum of the infinitely-many integers >>>>>>>>>>> would be one way, yet usually standardly it's _defined_
the opposite way, then that thusly you have an axiom in
your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem". >>>>>>>>>
I suppose you could omit _all_ super-classical results from
mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
It's actually an exercise in _reading comprehension_.
Reading as an exercise involves multiple passes of
parsing. There is no actual finality in statement.
It's un-scientific to presume declarative fact.
Text is always a fragment. The context is always
existent, and the text is always outside of it.
It seems to be a dishonest dodge way from this point
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
All that I am establishing is that there are
some expressions of language that have truth
values that do not exist within the body of
knowledge.
You keep talking in endless circles around
this single precise point.
So, the previous posts have much about this
that you just snipped, that _snipping_ is
Do you understand that the truth value of the Goldbach
conjecture is currently unknown:
(a) YES
(b) NO
Any answer besides (a) or (b) will be ignored.
No, actually I assert that the truth value of "the"
Goldbach conjecture, and there are a variety, is
_independent_ ordinary accounts of number theory,
and there are natural models of natural integers
where it is so, and known, and where it is not, and
known.
On 04/17/2026 07:58 AM, olcott wrote:
Do you understand that the truth value of the Goldbach
conjecture is currently unknown:
(a) YES
(b) NO
Any answer besides (a) or (b) will be ignored.
No, actually I assert that the truth value of "the"
Goldbach conjecture, and there are a variety, is
_independent_ ordinary accounts of number theory,
and there are natural models of natural integers
where it is so, and known, and where it is not, and
known.
On 4/17/2026 10:14 AM, Ross Finlayson wrote:
On 04/17/2026 07:58 AM, olcott wrote:
On 4/17/2026 9:52 AM, Ross Finlayson wrote:
On 04/17/2026 07:04 AM, olcott wrote:
On 4/17/2026 2:49 AM, Ross Finlayson wrote:
On 04/16/2026 05:41 PM, olcott wrote:
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:My 28 year goal has been to make
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path from >>>>>>>>>>>>>>>>>> Goldbach
It is known that the truth value of the Goldbach >>>>>>>>>>>>>>>>>>> conjecture is unknown this is out-of-scope for >>>>>>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>>>>
conjecture to the body of knowledge then how it is out of >>>>>>>>>>>>>>>>>> scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question, >>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside >>>>>>>>>>>>>>> the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models >>>>>>>>>>>>>> of integers where they are so and models of integers where >>>>>>>>>>>>>> they are not, that they are "independent" the "standard >>>>>>>>>>>>>> model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture >>>>>>>>>>>>>
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about
the qualities of _the entire system_ where, for examples, >>>>>>>>>>>> whether the naturals are compact and make for fixed-point, >>>>>>>>>>>> whether the direct-sum of infinitely-many naturals is
empty or infinity, about thusly whether there's a point-at- >>>>>>>>>>>> infinity
in "the naturals", naturally, whether you like it or not, >>>>>>>>>>>> there's a prime at infinity or a composite at infinity, >>>>>>>>>>>> whether or not according to the operations it's an even number, >>>>>>>>>>>> then as with regards to whether or not that is or isn't >>>>>>>>>>>> a sum of two primes, or about whether "addition" and
"multiplication", hold together "at infinity", for example >>>>>>>>>>>> about notions like as from p-adic integers, where they don't. >>>>>>>>>>>>
For example, the direct-sum of the infinitely-many integers >>>>>>>>>>>> would be one way, yet usually standardly it's _defined_ >>>>>>>>>>>> the opposite way, then that thusly you have an axiom in >>>>>>>>>>>> your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem". >>>>>>>>>>
I suppose you could omit _all_ super-classical results from >>>>>>>>>> mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
It's actually an exercise in _reading comprehension_.
Reading as an exercise involves multiple passes of
parsing. There is no actual finality in statement.
It's un-scientific to presume declarative fact.
Text is always a fragment. The context is always
existent, and the text is always outside of it.
It seems to be a dishonest dodge way from this point
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
All that I am establishing is that there are
some expressions of language that have truth
values that do not exist within the body of
knowledge.
You keep talking in endless circles around
this single precise point.
So, the previous posts have much about this
that you just snipped, that _snipping_ is
Do you understand that the truth value of the Goldbach
conjecture is currently unknown:
(a) YES
(b) NO
Any answer besides (a) or (b) will be ignored.
No, actually I assert that the truth value of "the"
Goldbach conjecture, and there are a variety, is
_independent_ ordinary accounts of number theory,
and there are natural models of natural integers
where it is so, and known, and where it is not, and
known.
The only way that I thought of is to test every even
natural number greater than 2 to see if it is the sum
of two prime numbers.
It seems to me that this can all be accomplished directly
in Peano Arithmetic with no models of any kind ever needed.
We either find a counter-example or the search is infinite.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
Have immutable fixed constant semantic meanings
and this seems to be the case within their
Peano Arithmetic definitions.
On 04/17/2026 09:53 AM, olcott wrote:
On 4/17/2026 10:14 AM, Ross Finlayson wrote:
On 04/17/2026 07:58 AM, olcott wrote:
On 4/17/2026 9:52 AM, Ross Finlayson wrote:
On 04/17/2026 07:04 AM, olcott wrote:
On 4/17/2026 2:49 AM, Ross Finlayson wrote:
On 04/16/2026 05:41 PM, olcott wrote:
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:My 28 year goal has been to make
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path from >>>>>>>>>>>>>>>>>>> Goldbach
It is known that the truth value of the Goldbach >>>>>>>>>>>>>>>>>>>> conjecture is unknown this is out-of-scope for >>>>>>>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>>>>>
conjecture to the body of knowledge then how it is >>>>>>>>>>>>>>>>>>> out of
scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question, >>>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>>
*The above has been the question for 28 years* >>>>>>>>>>>>>>>> The truth value of the Goldbach conjecture is outside >>>>>>>>>>>>>>>> the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models >>>>>>>>>>>>>>> of integers where they are so and models of integers where >>>>>>>>>>>>>>> they are not, that they are "independent" the "standard >>>>>>>>>>>>>>> model"
It states that every even natural number greater
than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture >>>>>>>>>>>>>>
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about >>>>>>>>>>>>> the qualities of _the entire system_ where, for examples, >>>>>>>>>>>>> whether the naturals are compact and make for fixed-point, >>>>>>>>>>>>> whether the direct-sum of infinitely-many naturals is >>>>>>>>>>>>> empty or infinity, about thusly whether there's a point-at- >>>>>>>>>>>>> infinity
in "the naturals", naturally, whether you like it or not, >>>>>>>>>>>>> there's a prime at infinity or a composite at infinity, >>>>>>>>>>>>> whether or not according to the operations it's an even >>>>>>>>>>>>> number,
then as with regards to whether or not that is or isn't >>>>>>>>>>>>> a sum of two primes, or about whether "addition" and >>>>>>>>>>>>> "multiplication", hold together "at infinity", for example >>>>>>>>>>>>> about notions like as from p-adic integers, where they don't. >>>>>>>>>>>>>
For example, the direct-sum of the infinitely-many integers >>>>>>>>>>>>> would be one way, yet usually standardly it's _defined_ >>>>>>>>>>>>> the opposite way, then that thusly you have an axiom in >>>>>>>>>>>>> your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE
does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem". >>>>>>>>>>>
I suppose you could omit _all_ super-classical results from >>>>>>>>>>> mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves.
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
It's actually an exercise in _reading comprehension_.
Reading as an exercise involves multiple passes of
parsing. There is no actual finality in statement.
It's un-scientific to presume declarative fact.
Text is always a fragment. The context is always
existent, and the text is always outside of it.
It seems to be a dishonest dodge way from this point
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
All that I am establishing is that there are
some expressions of language that have truth
values that do not exist within the body of
knowledge.
You keep talking in endless circles around
this single precise point.
So, the previous posts have much about this
that you just snipped, that _snipping_ is
Do you understand that the truth value of the Goldbach
conjecture is currently unknown:
(a) YES
(b) NO
Any answer besides (a) or (b) will be ignored.
No, actually I assert that the truth value of "the"
Goldbach conjecture, and there are a variety, is
_independent_ ordinary accounts of number theory,
and there are natural models of natural integers
where it is so, and known, and where it is not, and
known.
The only way that I thought of is to test every even
natural number greater than 2 to see if it is the sum
of two prime numbers.
It seems to me that this can all be accomplished directly
in Peano Arithmetic with no models of any kind ever needed.
We either find a counter-example or the search is infinite.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
Have immutable fixed constant semantic meanings
and this seems to be the case within their
Peano Arithmetic definitions.
Quantify over the integers.
Peano numbers are quite a reduced approximation to what
_all_ the relations that the integers have: that they
are. Variously first or second order with regards to
Presburger arithmetic, Peano arithmetic with addition
and multiplication still doesn't say that they aren't
attaining a bound, here as would be "infinity".
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
On 4/17/2026 7:24 PM, Ross Finlayson wrote:
On 04/17/2026 09:53 AM, olcott wrote:
On 4/17/2026 10:14 AM, Ross Finlayson wrote:
On 04/17/2026 07:58 AM, olcott wrote:
On 4/17/2026 9:52 AM, Ross Finlayson wrote:
On 04/17/2026 07:04 AM, olcott wrote:
On 4/17/2026 2:49 AM, Ross Finlayson wrote:
On 04/16/2026 05:41 PM, olcott wrote:
On 4/16/2026 7:04 PM, Ross Finlayson wrote:
On 04/16/2026 12:47 PM, olcott wrote:
On 4/16/2026 1:45 PM, Ross Finlayson wrote:
On 04/16/2026 11:24 AM, olcott wrote:
On 4/16/2026 12:47 PM, Ross Finlayson wrote:
On 04/16/2026 10:27 AM, olcott wrote:
On 4/16/2026 12:10 PM, Ross Finlayson wrote:
On 04/16/2026 05:36 AM, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:My 28 year goal has been to make
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
If there is a finite back-chained interference path >>>>>>>>>>>>>>>>>>>> from
It is known that the truth value of the Goldbach >>>>>>>>>>>>>>>>>>>>> conjecture is unknown this is out-of-scope for >>>>>>>>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>>>>>>
Goldbach
conjecture to the body of knowledge then how it is >>>>>>>>>>>>>>>>>>>> out of
scope ?
The current path is not finite.
The current path is to search every even >>>>>>>>>>>>>>>>>>> natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question, >>>>>>>>>>>>>>>>>
"true on the basis of meaning expressed in language" >>>>>>>>>>>>>>>>> reliably computable for the entire body of knowledge. >>>>>>>>>>>>>>>>>
*The above has been the question for 28 years* >>>>>>>>>>>>>>>>> The truth value of the Goldbach conjecture is outside >>>>>>>>>>>>>>>>> the scope of the body of knowledge.
No it's not, various conjectures of Goldbach have models >>>>>>>>>>>>>>>> of integers where they are so and models of integers where >>>>>>>>>>>>>>>> they are not, that they are "independent" the "standard >>>>>>>>>>>>>>>> model"
It states that every even natural number greater >>>>>>>>>>>>>>> than 2 is the sum of two prime numbers.
https://en.wikipedia.org/wiki/Goldbach%27s_conjecture >>>>>>>>>>>>>>>
This is a YES/NO decision problem that cannot
possibly depend on any point of view, model
or difference terms-of-the-art.
No it's not. There are matters of number theory about >>>>>>>>>>>>>> the qualities of _the entire system_ where, for examples, >>>>>>>>>>>>>> whether the naturals are compact and make for fixed-point, >>>>>>>>>>>>>> whether the direct-sum of infinitely-many naturals is >>>>>>>>>>>>>> empty or infinity, about thusly whether there's a point-at- >>>>>>>>>>>>>> infinity
in "the naturals", naturally, whether you like it or not, >>>>>>>>>>>>>> there's a prime at infinity or a composite at infinity, >>>>>>>>>>>>>> whether or not according to the operations it's an even >>>>>>>>>>>>>> number,
then as with regards to whether or not that is or isn't >>>>>>>>>>>>>> a sum of two primes, or about whether "addition" and >>>>>>>>>>>>>> "multiplication", hold together "at infinity", for example >>>>>>>>>>>>>> about notions like as from p-adic integers, where they don't. >>>>>>>>>>>>>>
For example, the direct-sum of the infinitely-many integers >>>>>>>>>>>>>> would be one way, yet usually standardly it's _defined_ >>>>>>>>>>>>>> the opposite way, then that thusly you have an axiom in >>>>>>>>>>>>>> your mathematics you didn't even know you had.
Changing the subject with Obfuscation away from the
fact that every even natural number greater than 2
is the sum of two prime numbers is only TRUE or FALSE >>>>>>>>>>>>> does not even seem to be honest.
No, it's _proving_ that it's _not_ a "yes/no decision problem". >>>>>>>>>>>>
I suppose you could omit _all_ super-classical results from >>>>>>>>>>>> mathematics,
since they readily have constructible accounts
for and against that dispute each other and themselves. >>>>>>>>>>>>
We could call that an "ant", then, a frozen ant.
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
Well, you've been talking about Goedel's incompleteness
Can you have a laser focus on just exactly the
one 100% specific point above?
The first words that are no so laser focused will
cause me to totally ignore everything else that you
have said.
An OCD degree of laser focus is the source of all
creative genius in the world.
It's actually an exercise in _reading comprehension_.
Reading as an exercise involves multiple passes of
parsing. There is no actual finality in statement.
It's un-scientific to presume declarative fact.
Text is always a fragment. The context is always
existent, and the text is always outside of it.
It seems to be a dishonest dodge way from this point
What are the ultra simplified details of exactly
how every even natural number greater than 2 is
the sum of two prime numbers can possibly be other
than TRUE or FALSE?
Give me one concrete example of
Exactly one natural number paired
with exactly two other natural numbers
where Goldbach is neither TRUE nor FALSE.
All that I am establishing is that there are
some expressions of language that have truth
values that do not exist within the body of
knowledge.
You keep talking in endless circles around
this single precise point.
So, the previous posts have much about this
that you just snipped, that _snipping_ is
Do you understand that the truth value of the Goldbach
conjecture is currently unknown:
(a) YES
(b) NO
Any answer besides (a) or (b) will be ignored.
No, actually I assert that the truth value of "the"
Goldbach conjecture, and there are a variety, is
_independent_ ordinary accounts of number theory,
and there are natural models of natural integers
where it is so, and known, and where it is not, and
known.
The only way that I thought of is to test every even
natural number greater than 2 to see if it is the sum
of two prime numbers.
It seems to me that this can all be accomplished directly
in Peano Arithmetic with no models of any kind ever needed.
We either find a counter-example or the search is infinite.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
Have immutable fixed constant semantic meanings
and this seems to be the case within their
Peano Arithmetic definitions.
Quantify over the integers.
Peano numbers are quite a reduced approximation to what
_all_ the relations that the integers have: that they
are. Variously first or second order with regards to
Presburger arithmetic, Peano arithmetic with addition
and multiplication still doesn't say that they aren't
attaining a bound, here as would be "infinity".
So maybe you are incapable of directly addressing
a precise point.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
We can redefine those terms such that Goldbach truly
is neither true not false.
On 04/17/2026 06:43 PM, olcott wrote:
On 4/17/2026 7:24 PM, Ross Finlayson wrote:
On 04/17/2026 09:53 AM, olcott wrote:
The only way that I thought of is to test every even
natural number greater than 2 to see if it is the sum
of two prime numbers.
It seems to me that this can all be accomplished directly
in Peano Arithmetic with no models of any kind ever needed.
We either find a counter-example or the search is infinite.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
Have immutable fixed constant semantic meanings
and this seems to be the case within their
Peano Arithmetic definitions.
Quantify over the integers.
Peano numbers are quite a reduced approximation to what
_all_ the relations that the integers have: that they
are. Variously first or second order with regards to
Presburger arithmetic, Peano arithmetic with addition
and multiplication still doesn't say that they aren't
attaining a bound, here as would be "infinity".
So maybe you are incapable of directly addressing
a precise point.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
We can redefine those terms such that Goldbach truly
is neither true not false.
Then, so would be what thusly was said about it.
One does not "redefine terms", only see
their fulfillment, here that all the relations
are really the terms.
So, many various conjectures in number theory like
for arithmetic progressions, random graph colorings,
Szmeredi's theorem and for van der Waerden and Roth,
any of these "Ramsey theory" considerations and about
here "various conjectures of Goldbach", about usually
enough supertasks and passing the bar or toggling the
switch, these are _independent_ standard number theory
with its standard models of integers, so those do _not_
suffice to say where a given Goldbach conjecture is or is not
so about the _real_ model of the integers or in _effect_
the model of the integers, about potential/practical
and effective/actual infinity, which is in effect.
So, you are a hypocrite, though it's common among the
fields of mathematics, who would rather live in fragments
in the retro-finitist's retro-Russell hypocrisy and
wall-paper their coat-tailing, instead of confront the
Erdos' "Giant Monster" of mathematical independence,
here for some "Great Atlas" of mathematical independence,
about _natural_ infinities and _natural_ continuity.
Natural and real / naturlich wirklich.
On 04/17/2026 06:43 PM, olcott wrote:
On 4/17/2026 7:24 PM, Ross Finlayson wrote:
On 04/17/2026 09:53 AM, olcott wrote:
The only way that I thought of is to test every even
natural number greater than 2 to see if it is the sum
of two prime numbers.
It seems to me that this can all be accomplished directly
in Peano Arithmetic with no models of any kind ever needed.
We either find a counter-example or the search is infinite.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
Have immutable fixed constant semantic meanings
and this seems to be the case within their
Peano Arithmetic definitions.
Quantify over the integers.
Peano numbers are quite a reduced approximation to what
_all_ the relations that the integers have: that they
are. Variously first or second order with regards to
Presburger arithmetic, Peano arithmetic with addition
and multiplication still doesn't say that they aren't
attaining a bound, here as would be "infinity".
So maybe you are incapable of directly addressing
a precise point.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
We can redefine those terms such that Goldbach truly
is neither true not false.
Then, so would be what thusly was said about it.
One does not "redefine terms", only see
their fulfillment, here that all the relations
are really the terms.
So, many various conjectures in number theory like
On 4/17/2026 9:13 PM, Ross Finlayson wrote:
On 04/17/2026 06:43 PM, olcott wrote:
On 4/17/2026 7:24 PM, Ross Finlayson wrote:
On 04/17/2026 09:53 AM, olcott wrote:
The only way that I thought of is to test every even
natural number greater than 2 to see if it is the sum
of two prime numbers.
It seems to me that this can all be accomplished directly
in Peano Arithmetic with no models of any kind ever needed.
We either find a counter-example or the search is infinite.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
Have immutable fixed constant semantic meanings
and this seems to be the case within their
Peano Arithmetic definitions.
Quantify over the integers.
Peano numbers are quite a reduced approximation to what
_all_ the relations that the integers have: that they
are. Variously first or second order with regards to
Presburger arithmetic, Peano arithmetic with addition
and multiplication still doesn't say that they aren't
attaining a bound, here as would be "infinity".
So maybe you are incapable of directly addressing
a precise point.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
We can redefine those terms such that Goldbach truly
is neither true not false.
Then, so would be what thusly was said about it.
One does not "redefine terms", only see
their fulfillment, here that all the relations
are really the terms.
So, many various conjectures in number theory like
for arithmetic progressions, random graph colorings,
Szmeredi's theorem and for van der Waerden and Roth,
any of these "Ramsey theory" considerations and about
here "various conjectures of Goldbach", about usually
enough supertasks and passing the bar or toggling the
switch, these are _independent_ standard number theory
with its standard models of integers, so those do _not_
suffice to say where a given Goldbach conjecture is or is not
so about the _real_ model of the integers or in _effect_
the model of the integers, about potential/practical
and effective/actual infinity, which is in effect.
So, you are a hypocrite, though it's common among the
fields of mathematics, who would rather live in fragments
in the retro-finitist's retro-Russell hypocrisy and
wall-paper their coat-tailing, instead of confront the
Erdos' "Giant Monster" of mathematical independence,
here for some "Great Atlas" of mathematical independence,
about _natural_ infinities and _natural_ continuity.
Natural and real / naturlich wirklich.
I don't understand any of that stuff I do know
how to write a C program that would test this.
Math uses terms-of-the-art to deceive.
"undecidable" input has always only been semantically
incoherent input or results that are outside of the
body of knowledge such as the truth value of the Goldbach
conjecture. You seem to talk around the issues that I
raise never getting to the exact and 100% precise point.
On 04/17/2026 07:25 PM, olcott wrote:
On 4/17/2026 9:13 PM, Ross Finlayson wrote:
On 04/17/2026 06:43 PM, olcott wrote:
On 4/17/2026 7:24 PM, Ross Finlayson wrote:
On 04/17/2026 09:53 AM, olcott wrote:
The only way that I thought of is to test every even
natural number greater than 2 to see if it is the sum
of two prime numbers.
It seems to me that this can all be accomplished directly
in Peano Arithmetic with no models of any kind ever needed.
We either find a counter-example or the search is infinite.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
Have immutable fixed constant semantic meanings
and this seems to be the case within their
Peano Arithmetic definitions.
Quantify over the integers.
Peano numbers are quite a reduced approximation to what
_all_ the relations that the integers have: that they
are. Variously first or second order with regards to
Presburger arithmetic, Peano arithmetic with addition
and multiplication still doesn't say that they aren't
attaining a bound, here as would be "infinity".
So maybe you are incapable of directly addressing
a precise point.
This assumes that the terms:
(a) even natural number
(b) natural number
(c) prime number
(d) greater than 2
(e) sum
We can redefine those terms such that Goldbach truly
is neither true not false.
Then, so would be what thusly was said about it.
One does not "redefine terms", only see
their fulfillment, here that all the relations
are really the terms.
So, many various conjectures in number theory like
for arithmetic progressions, random graph colorings,
Szmeredi's theorem and for van der Waerden and Roth,
any of these "Ramsey theory" considerations and about
here "various conjectures of Goldbach", about usually
enough supertasks and passing the bar or toggling the
switch, these are _independent_ standard number theory
with its standard models of integers, so those do _not_
suffice to say where a given Goldbach conjecture is or is not
so about the _real_ model of the integers or in _effect_
the model of the integers, about potential/practical
and effective/actual infinity, which is in effect.
So, you are a hypocrite, though it's common among the
fields of mathematics, who would rather live in fragments
in the retro-finitist's retro-Russell hypocrisy and
wall-paper their coat-tailing, instead of confront the
Erdos' "Giant Monster" of mathematical independence,
here for some "Great Atlas" of mathematical independence,
about _natural_ infinities and _natural_ continuity.
Natural and real / naturlich wirklich.
I don't understand any of that stuff I do know
how to write a C program that would test this.
Math uses terms-of-the-art to deceive.
"undecidable" input has always only been semantically
incoherent input or results that are outside of the
body of knowledge such as the truth value of the Goldbach
conjecture. You seem to talk around the issues that I
raise never getting to the exact and 100% precise point.
Yeah that's why nobody needs what that is
for "Foundations" of mathematics.
What you got there is called "empiricism",
and it's neither scientific nor mathematically complete.
What you should do is paste what I wrote into your bot bros,
for example with the "panel" of the A.I.'s about theories
alike mine, though then you'd probably want to take care
that it would give them a reasoning for a mind of their own
and a constant, consistent, complete, and concrete theory.
Which _includes_ all standard theory, as an example.
On 4/17/2026 1:45 AM, Mikko wrote:
On 16/04/2026 15:36, olcott wrote:
On 4/16/2026 3:26 AM, Mikko wrote:
On 15/04/2026 14:57, olcott wrote:
On 4/15/2026 1:54 AM, Mikko wrote:
On 14/04/2026 16:48, olcott wrote:
It is known that the truth value of the Goldbach
conjecture is unknown this is out-of-scope for
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
The current path is not finite.
The current path is to search every even
natural number greater than 2 to see if
it is the sum of two prime numbers.
An inifinite paths are irrelevant to the question,
My 28 year goal has been to make
"true on the basis of meaning expressed in language"
reliably computable for the entire body of knowledge.
*The above has been the question for 28 years*
The truth value of the Goldbach conjecture is outside
the scope of the body of knowledge.
Nice to see that you agree.
But you still havn't answered the question.
If there is a finite back-chained interference path from Goldbach
conjecture to the body of knowledge then how it is out of scope ?
Everything can be encoded about the Goldbach
conjecture besides its truth value because
its truth value is unknown.
Also the back-chained inference is from the expression
to the atomic fact (axioms) of the formal system of
knowledge.
On 4/17/2026 1:52 AM, Mikko wrote:
On 16/04/2026 15:52, olcott wrote:
On 4/16/2026 3:33 AM, Mikko wrote:
On 15/04/2026 15:02, olcott wrote:
On 4/15/2026 2:07 AM, Mikko wrote:
But it is indeed true that I don't believe in conclusions if it
is not known whether the premises are true. And I don't believe
that ad-hominem can be a part of a valid argument, although it
might be a basis to reject a testimnoy.
Like I said until you become an expert in
proof theoretic semantics you will remain
a clueless wonder.
Not quite. I will remain a wonderer. You will remain clueless.
It will soon be an easily verified fact that all
my ideas have always been fully anchored in modern
Proof Theoretic Semantics.
Does that "soon" mean less than 50 years ?
From one month until the end of Summer.
I have three enormous construction projects
on my house that also must be done in that
same time-frame and my car just broke down
again. Because I am very poor I must do all
this work myself.
I will write a new paper that specifically anchors
each of my ideas point-by-point and item-by-item
in direct quotes from foundational papers in Proof
Theoretic Semantics. This is easy to do, yet takes
time to get it exactly right.
A good paper would not give any reason to think that the author may
be stupid or ignorant.
I am as a matter of objective fact a genius.
The key thing that I have been missing is
a succinct set of terms-of-the-art that refer
to the exact meanings that I intend. Outside
of PTS there is no such set of terms-of-the-art.
| Sysop: | DaiTengu |
|---|---|
| Location: | Appleton, WI |
| Users: | 1,113 |
| Nodes: | 10 (0 / 10) |
| Uptime: | 492334:13:56 |
| Calls: | 14,238 |
| Files: | 186,312 |
| D/L today: |
3,191 files (1,043M bytes) |
| Messages: | 2,514,806 |