To be able to properly ground this in existing foundational
peer reviewed papers will take some time.
To be able to properly ground this in existing foundational
peer reviewed papers will take some time.
On 4/2/2026 3:58 PM, olcott wrote:
To be able to properly ground this in existing foundational
peer reviewed papers will take some time.
To be able to properly ground this in existing foundational
peer reviewed papers will take some time.
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?
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?
On 04/03/2026 12:13 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?
If there are at least three regularities/rulialities,
well-foundedness (Zermelo, Russell) and
well-ordering (Choice, Ono, Zorn) and
well-dispersion (Martin, univalency, the illative, covering, projective determinacy)
and it's readily demonstrable they can be set up against each other,
then it needs be there must be an account of how and why they don't.
All these things have been around
since more than 100 years ago.
On 04/03/2026 11:19 AM, Ross Finlayson wrote:
On 04/03/2026 12:13 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?
If there are at least three regularities/rulialities,
well-foundedness (Zermelo, Russell) and
well-ordering (Choice, Ono, Zorn) and
well-dispersion (Martin, univalency, the illative, covering, projective
determinacy)
and it's readily demonstrable they can be set up against each other,
then it needs be there must be an account of how and why they don't.
All these things have been around
since more than 100 years ago.
Assuming 1) we're not bots, and 2) they are bots,
then perhaps usual bot-ware just follows what it's given,
the blindered hindered course of the invincible ignorance
of the inductive inference directly to inductive impasse,
then as sort of like "garbage in garbage out", "crazy in crazy out".
Since, or if, any sort of individual expression is as well
at least in part as an aspect of psychological projection,
is among reasons why it's a good idea an idea of goodness.
Then the usual account of logic may include that the weaker
variety of logicism is a psychologism, then that Socrates
for example wasn't that profound a technical philosopher,
for what makes sense for the common man, not what makes
a common man of sense.
On 4/3/2026 1:25 PM, Ross Finlayson wrote:
On 04/03/2026 11:19 AM, Ross Finlayson wrote:
On 04/03/2026 12:13 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?
If there are at least three regularities/rulialities,
well-foundedness (Zermelo, Russell) and
well-ordering (Choice, Ono, Zorn) and
well-dispersion (Martin, univalency, the illative, covering, projective
determinacy)
and it's readily demonstrable they can be set up against each other,
then it needs be there must be an account of how and why they don't.
All these things have been around
since more than 100 years ago.
Assuming 1) we're not bots, and 2) they are bots,
then perhaps usual bot-ware just follows what it's given,
the blindered hindered course of the invincible ignorance
of the inductive inference directly to inductive impasse,
then as sort of like "garbage in garbage out", "crazy in crazy out".
Since, or if, any sort of individual expression is as well
at least in part as an aspect of psychological projection,
is among reasons why it's a good idea an idea of goodness.
Then the usual account of logic may include that the weaker
variety of logicism is a psychologism, then that Socrates
for example wasn't that profound a technical philosopher,
for what makes sense for the common man, not what makes
a common man of sense.
When we start with something like the subset of
Russell's "basic facts" that pertain to general
knowledge as axioms and then have semantic entailment
specified syntactically as the only inference step
we derive the entire body of general knowledge that
can be expressed in formal (or formalized natural)
language.
https://plato.stanford.edu/entries/logical-atomism/
On 04/03/2026 12:34 PM, olcott wrote:
On 4/3/2026 1:25 PM, Ross Finlayson wrote:
On 04/03/2026 11:19 AM, Ross Finlayson wrote:
On 04/03/2026 12:13 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? >>>>>
If there are at least three regularities/rulialities,
well-foundedness (Zermelo, Russell) and
well-ordering (Choice, Ono, Zorn) and
well-dispersion (Martin, univalency, the illative, covering, projective >>>> determinacy)
and it's readily demonstrable they can be set up against each other,
then it needs be there must be an account of how and why they don't.
All these things have been around
since more than 100 years ago.
Assuming 1) we're not bots, and 2) they are bots,
then perhaps usual bot-ware just follows what it's given,
the blindered hindered course of the invincible ignorance
of the inductive inference directly to inductive impasse,
then as sort of like "garbage in garbage out", "crazy in crazy out".
Since, or if, any sort of individual expression is as well
at least in part as an aspect of psychological projection,
is among reasons why it's a good idea an idea of goodness.
Then the usual account of logic may include that the weaker
variety of logicism is a psychologism, then that Socrates
for example wasn't that profound a technical philosopher,
for what makes sense for the common man, not what makes
a common man of sense.
When we start with something like the subset of
Russell's "basic facts" that pertain to general
knowledge as axioms and then have semantic entailment
specified syntactically as the only inference step
we derive the entire body of general knowledge that
can be expressed in formal (or formalized natural)
language.
https://plato.stanford.edu/entries/logical-atomism/
Wishful thinking.
That's empiricism with all its faults and baggage
exactly enough as so stated.
I'm not a fan of either of Quine's "dogmas of empiricism",
and there's another for an account of a _stronger_
logicist positivism, alongside a strong mathematical platonism,
since thusly otherwise it's un-founded your well-founding.
Russell's paradox is readily demonstrated in usual accounts
of Russell's theory after Russell's retro-thesis.
It's fine for closed categories, yet, so are
many weaker accounts.
On 4/3/2026 5:10 PM, Ross Finlayson wrote:
On 04/03/2026 12:34 PM, olcott wrote:
On 4/3/2026 1:25 PM, Ross Finlayson wrote:
On 04/03/2026 11:19 AM, Ross Finlayson wrote:
On 04/03/2026 12:13 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? >>>>>>
If there are at least three regularities/rulialities,
well-foundedness (Zermelo, Russell) and
well-ordering (Choice, Ono, Zorn) and
well-dispersion (Martin, univalency, the illative, covering,
projective
determinacy)
and it's readily demonstrable they can be set up against each other, >>>>> then it needs be there must be an account of how and why they don't. >>>>>
All these things have been around
since more than 100 years ago.
Assuming 1) we're not bots, and 2) they are bots,
then perhaps usual bot-ware just follows what it's given,
the blindered hindered course of the invincible ignorance
of the inductive inference directly to inductive impasse,
then as sort of like "garbage in garbage out", "crazy in crazy out".
Since, or if, any sort of individual expression is as well
at least in part as an aspect of psychological projection,
is among reasons why it's a good idea an idea of goodness.
Then the usual account of logic may include that the weaker
variety of logicism is a psychologism, then that Socrates
for example wasn't that profound a technical philosopher,
for what makes sense for the common man, not what makes
a common man of sense.
When we start with something like the subset of
Russell's "basic facts" that pertain to general
knowledge as axioms and then have semantic entailment
specified syntactically as the only inference step
we derive the entire body of general knowledge that
can be expressed in formal (or formalized natural)
language.
https://plato.stanford.edu/entries/logical-atomism/
Wishful thinking.
That's empiricism with all its faults and baggage
exactly enough as so stated.
I am not talking about logical-atomism AT ALL.
I am taking the single notion "atomic fact"
from it and utterly discarding all the rest.
The actual ENTIRE basis for "atomic facts" is
stipulated relations between finite strings.
"cats" <are> "animals"
I'm not a fan of either of Quine's "dogmas of empiricism",
When the otherwise meaningless finite string Bachelor(x) is
stipulated to mean:
Bachelor(x) := ¬Married(x) ∧ Male(x) ∧ Adult(x) ∧ Human(x)
Then Quine's objection to the
analytic/synthetic distinction based on synonymity dissolves.
and there's another for an account of a _stronger_
logicist positivism, alongside a strong mathematical platonism,
since thusly otherwise it's un-founded your well-founding.
You seem to be far too hung up on all of the baggage
that goes with the conventional way of dividing all
these things up. I UTTERLY REJECT ALL THAT BAGGAGE.
Russell's paradox is readily demonstrated in usual accounts
of Russell's theory after Russell's retro-thesis.
ALL PARADOXES are merely incoherence misconstrued.
It's fine for closed categories, yet, so are
many weaker accounts.
My notion of "formal system" contains 100% of ALL
of the details of the entire body of general knowledge
about anything.
On 04/03/2026 04:02 PM, olcott wrote:
On 4/3/2026 5:10 PM, Ross Finlayson wrote:
On 04/03/2026 12:34 PM, olcott wrote:
On 4/3/2026 1:25 PM, Ross Finlayson wrote:
On 04/03/2026 11:19 AM, Ross Finlayson wrote:
On 04/03/2026 12:13 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?
If there are at least three regularities/rulialities,
well-foundedness (Zermelo, Russell) and
well-ordering (Choice, Ono, Zorn) and
well-dispersion (Martin, univalency, the illative, covering,
projective
determinacy)
and it's readily demonstrable they can be set up against each other, >>>>>> then it needs be there must be an account of how and why they don't. >>>>>>
All these things have been around
since more than 100 years ago.
Assuming 1) we're not bots, and 2) they are bots,
then perhaps usual bot-ware just follows what it's given,
the blindered hindered course of the invincible ignorance
of the inductive inference directly to inductive impasse,
then as sort of like "garbage in garbage out", "crazy in crazy out". >>>>>
Since, or if, any sort of individual expression is as well
at least in part as an aspect of psychological projection,
is among reasons why it's a good idea an idea of goodness.
Then the usual account of logic may include that the weaker
variety of logicism is a psychologism, then that Socrates
for example wasn't that profound a technical philosopher,
for what makes sense for the common man, not what makes
a common man of sense.
When we start with something like the subset of
Russell's "basic facts" that pertain to general
knowledge as axioms and then have semantic entailment
specified syntactically as the only inference step
we derive the entire body of general knowledge that
can be expressed in formal (or formalized natural)
language.
https://plato.stanford.edu/entries/logical-atomism/
Wishful thinking.
That's empiricism with all its faults and baggage
exactly enough as so stated.
I am not talking about logical-atomism AT ALL.
I am taking the single notion "atomic fact"
from it and utterly discarding all the rest.
The actual ENTIRE basis for "atomic facts" is
stipulated relations between finite strings.
"cats" <are> "animals"
I'm not a fan of either of Quine's "dogmas of empiricism",
When the otherwise meaningless finite string Bachelor(x) is
stipulated to mean:
Bachelor(x) := ¬Married(x) ∧ Male(x) ∧ Adult(x) ∧ Human(x)
Then Quine's objection to the
analytic/synthetic distinction based on synonymity dissolves.
and there's another for an account of a _stronger_
logicist positivism, alongside a strong mathematical platonism,
since thusly otherwise it's un-founded your well-founding.
You seem to be far too hung up on all of the baggage
that goes with the conventional way of dividing all
these things up. I UTTERLY REJECT ALL THAT BAGGAGE.
Russell's paradox is readily demonstrated in usual accounts
of Russell's theory after Russell's retro-thesis.
ALL PARADOXES are merely incoherence misconstrued.
It's fine for closed categories, yet, so are
many weaker accounts.
My notion of "formal system" contains 100% of ALL
of the details of the entire body of general knowledge
about anything.
Three-legged dog.
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 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.
The above Prolog determines that LP does not
have a "well founded justification tree".
On 4/3/2026 7:53 PM, Ross Finlayson wrote:
On 04/03/2026 04:02 PM, olcott wrote:
On 4/3/2026 5:10 PM, Ross Finlayson wrote:
On 04/03/2026 12:34 PM, olcott wrote:
On 4/3/2026 1:25 PM, Ross Finlayson wrote:
On 04/03/2026 11:19 AM, Ross Finlayson wrote:
On 04/03/2026 12:13 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?
If there are at least three regularities/rulialities,
well-foundedness (Zermelo, Russell) and
well-ordering (Choice, Ono, Zorn) and
well-dispersion (Martin, univalency, the illative, covering,
projective
determinacy)
and it's readily demonstrable they can be set up against each other, >>>>>>> then it needs be there must be an account of how and why they don't. >>>>>>>
All these things have been around
since more than 100 years ago.
Assuming 1) we're not bots, and 2) they are bots,
then perhaps usual bot-ware just follows what it's given,
the blindered hindered course of the invincible ignorance
of the inductive inference directly to inductive impasse,
then as sort of like "garbage in garbage out", "crazy in crazy out". >>>>>>
Since, or if, any sort of individual expression is as well
at least in part as an aspect of psychological projection,
is among reasons why it's a good idea an idea of goodness.
Then the usual account of logic may include that the weaker
variety of logicism is a psychologism, then that Socrates
for example wasn't that profound a technical philosopher,
for what makes sense for the common man, not what makes
a common man of sense.
When we start with something like the subset of
Russell's "basic facts" that pertain to general
knowledge as axioms and then have semantic entailment
specified syntactically as the only inference step
we derive the entire body of general knowledge that
can be expressed in formal (or formalized natural)
language.
https://plato.stanford.edu/entries/logical-atomism/
Wishful thinking.
That's empiricism with all its faults and baggage
exactly enough as so stated.
I am not talking about logical-atomism AT ALL.
I am taking the single notion "atomic fact"
from it and utterly discarding all the rest.
The actual ENTIRE basis for "atomic facts" is
stipulated relations between finite strings.
"cats" <are> "animals"
I'm not a fan of either of Quine's "dogmas of empiricism",
When the otherwise meaningless finite string Bachelor(x) is
stipulated to mean:
Bachelor(x) := ¬Married(x) ∧ Male(x) ∧ Adult(x) ∧ Human(x)
Then Quine's objection to the
analytic/synthetic distinction based on synonymity dissolves.
and there's another for an account of a _stronger_
logicist positivism, alongside a strong mathematical platonism,
since thusly otherwise it's un-founded your well-founding.
You seem to be far too hung up on all of the baggage
that goes with the conventional way of dividing all
these things up. I UTTERLY REJECT ALL THAT BAGGAGE.
Russell's paradox is readily demonstrated in usual accounts
of Russell's theory after Russell's retro-thesis.
ALL PARADOXES are merely incoherence misconstrued.
It's fine for closed categories, yet, so are
many weaker accounts.
My notion of "formal system" contains 100% of ALL
of the details of the entire body of general knowledge
about anything.
Three-legged dog.
In other words you fail to understand that the
body of knowledge expressed in formal language
and formalized natural language is a semantic
tautology expressed as relations between finite
strings.
On 04/04/2026 12:40 AM, olcott wrote:
On 4/3/2026 7:53 PM, Ross Finlayson wrote:
On 04/03/2026 04:02 PM, olcott wrote:
On 4/3/2026 5:10 PM, Ross Finlayson wrote:
On 04/03/2026 12:34 PM, olcott wrote:
On 4/3/2026 1:25 PM, Ross Finlayson wrote:
On 04/03/2026 11:19 AM, Ross Finlayson wrote:
On 04/03/2026 12:13 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?
If there are at least three regularities/rulialities,
well-foundedness (Zermelo, Russell) and
well-ordering (Choice, Ono, Zorn) and
well-dispersion (Martin, univalency, the illative, covering,
projective
determinacy)
and it's readily demonstrable they can be set up against each >>>>>>>> other,
then it needs be there must be an account of how and why they >>>>>>>> don't.
All these things have been around
since more than 100 years ago.
Assuming 1) we're not bots, and 2) they are bots,
then perhaps usual bot-ware just follows what it's given,
the blindered hindered course of the invincible ignorance
of the inductive inference directly to inductive impasse,
then as sort of like "garbage in garbage out", "crazy in crazy out". >>>>>>>
Since, or if, any sort of individual expression is as well
at least in part as an aspect of psychological projection,
is among reasons why it's a good idea an idea of goodness.
Then the usual account of logic may include that the weaker
variety of logicism is a psychologism, then that Socrates
for example wasn't that profound a technical philosopher,
for what makes sense for the common man, not what makes
a common man of sense.
When we start with something like the subset of
Russell's "basic facts" that pertain to general
knowledge as axioms and then have semantic entailment
specified syntactically as the only inference step
we derive the entire body of general knowledge that
can be expressed in formal (or formalized natural)
language.
https://plato.stanford.edu/entries/logical-atomism/
Wishful thinking.
That's empiricism with all its faults and baggage
exactly enough as so stated.
I am not talking about logical-atomism AT ALL.
I am taking the single notion "atomic fact"
from it and utterly discarding all the rest.
The actual ENTIRE basis for "atomic facts" is
stipulated relations between finite strings.
"cats" <are> "animals"
I'm not a fan of either of Quine's "dogmas of empiricism",
When the otherwise meaningless finite string Bachelor(x) is
stipulated to mean:
Bachelor(x) := ¬Married(x) ∧ Male(x) ∧ Adult(x) ∧ Human(x)
Then Quine's objection to the
analytic/synthetic distinction based on synonymity dissolves.
and there's another for an account of a _stronger_
logicist positivism, alongside a strong mathematical platonism,
since thusly otherwise it's un-founded your well-founding.
You seem to be far too hung up on all of the baggage
that goes with the conventional way of dividing all
these things up. I UTTERLY REJECT ALL THAT BAGGAGE.
Russell's paradox is readily demonstrated in usual accounts
of Russell's theory after Russell's retro-thesis.
ALL PARADOXES are merely incoherence misconstrued.
It's fine for closed categories, yet, so are
many weaker accounts.
My notion of "formal system" contains 100% of ALL
of the details of the entire body of general knowledge
about anything.
Three-legged dog.
In other words you fail to understand that the
body of knowledge expressed in formal language
and formalized natural language is a semantic
tautology expressed as relations between finite
strings.
No, I'm saying both that that's a three-legged dog,
and, doesn't know what a three-legged dog is.
On 4/4/2026 10:03 PM, Ross Finlayson wrote:
On 04/04/2026 12:40 AM, olcott wrote:
On 4/3/2026 7:53 PM, Ross Finlayson wrote:
On 04/03/2026 04:02 PM, olcott wrote:
On 4/3/2026 5:10 PM, Ross Finlayson wrote:
On 04/03/2026 12:34 PM, olcott wrote:
On 4/3/2026 1:25 PM, Ross Finlayson wrote:
On 04/03/2026 11:19 AM, Ross Finlayson wrote:
On 04/03/2026 12:13 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?
If there are at least three regularities/rulialities,
well-foundedness (Zermelo, Russell) and
well-ordering (Choice, Ono, Zorn) and
well-dispersion (Martin, univalency, the illative, covering, >>>>>>>>> projective
determinacy)
and it's readily demonstrable they can be set up against each >>>>>>>>> other,
then it needs be there must be an account of how and why they >>>>>>>>> don't.
All these things have been around
since more than 100 years ago.
Assuming 1) we're not bots, and 2) they are bots,
then perhaps usual bot-ware just follows what it's given,
the blindered hindered course of the invincible ignorance
of the inductive inference directly to inductive impasse,
then as sort of like "garbage in garbage out", "crazy in crazy >>>>>>>> out".
Since, or if, any sort of individual expression is as well
at least in part as an aspect of psychological projection,
is among reasons why it's a good idea an idea of goodness.
Then the usual account of logic may include that the weaker
variety of logicism is a psychologism, then that Socrates
for example wasn't that profound a technical philosopher,
for what makes sense for the common man, not what makes
a common man of sense.
When we start with something like the subset of
Russell's "basic facts" that pertain to general
knowledge as axioms and then have semantic entailment
specified syntactically as the only inference step
we derive the entire body of general knowledge that
can be expressed in formal (or formalized natural)
language.
https://plato.stanford.edu/entries/logical-atomism/
Wishful thinking.
That's empiricism with all its faults and baggage
exactly enough as so stated.
I am not talking about logical-atomism AT ALL.
I am taking the single notion "atomic fact"
from it and utterly discarding all the rest.
The actual ENTIRE basis for "atomic facts" is
stipulated relations between finite strings.
"cats" <are> "animals"
I'm not a fan of either of Quine's "dogmas of empiricism",
When the otherwise meaningless finite string Bachelor(x) is
stipulated to mean:
Bachelor(x) := ¬Married(x) ∧ Male(x) ∧ Adult(x) ∧ Human(x)
Then Quine's objection to the
analytic/synthetic distinction based on synonymity dissolves.
and there's another for an account of a _stronger_
logicist positivism, alongside a strong mathematical platonism,
since thusly otherwise it's un-founded your well-founding.
You seem to be far too hung up on all of the baggage
that goes with the conventional way of dividing all
these things up. I UTTERLY REJECT ALL THAT BAGGAGE.
Russell's paradox is readily demonstrated in usual accounts
of Russell's theory after Russell's retro-thesis.
ALL PARADOXES are merely incoherence misconstrued.
It's fine for closed categories, yet, so are
many weaker accounts.
My notion of "formal system" contains 100% of ALL
of the details of the entire body of general knowledge
about anything.
Three-legged dog.
In other words you fail to understand that the
body of knowledge expressed in formal language
and formalized natural language is a semantic
tautology expressed as relations between finite
strings.
No, I'm saying both that that's a three-legged dog,
and, doesn't know what a three-legged dog is.
So you quit being rational.
You do seem rational in your videos.
On 04/04/2026 08:31 PM, olcott wrote:
On 4/4/2026 10:03 PM, Ross Finlayson wrote:
On 04/04/2026 12:40 AM, olcott wrote:
On 4/3/2026 7:53 PM, Ross Finlayson wrote:
On 04/03/2026 04:02 PM, olcott wrote:
On 4/3/2026 5:10 PM, Ross Finlayson wrote:
On 04/03/2026 12:34 PM, olcott wrote:
On 4/3/2026 1:25 PM, Ross Finlayson wrote:
On 04/03/2026 11:19 AM, Ross Finlayson wrote:
On 04/03/2026 12:13 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?
If there are at least three regularities/rulialities,
well-foundedness (Zermelo, Russell) and
well-ordering (Choice, Ono, Zorn) and
well-dispersion (Martin, univalency, the illative, covering, >>>>>>>>>> projective
determinacy)
and it's readily demonstrable they can be set up against each >>>>>>>>>> other,
then it needs be there must be an account of how and why they >>>>>>>>>> don't.
All these things have been around
since more than 100 years ago.
Assuming 1) we're not bots, and 2) they are bots,
then perhaps usual bot-ware just follows what it's given,
the blindered hindered course of the invincible ignorance
of the inductive inference directly to inductive impasse,
then as sort of like "garbage in garbage out", "crazy in crazy >>>>>>>>> out".
Since, or if, any sort of individual expression is as well
at least in part as an aspect of psychological projection,
is among reasons why it's a good idea an idea of goodness.
Then the usual account of logic may include that the weaker
variety of logicism is a psychologism, then that Socrates
for example wasn't that profound a technical philosopher,
for what makes sense for the common man, not what makes
a common man of sense.
When we start with something like the subset of
Russell's "basic facts" that pertain to general
knowledge as axioms and then have semantic entailment
specified syntactically as the only inference step
we derive the entire body of general knowledge that
can be expressed in formal (or formalized natural)
language.
https://plato.stanford.edu/entries/logical-atomism/
Wishful thinking.
That's empiricism with all its faults and baggage
exactly enough as so stated.
I am not talking about logical-atomism AT ALL.
I am taking the single notion "atomic fact"
from it and utterly discarding all the rest.
The actual ENTIRE basis for "atomic facts" is
stipulated relations between finite strings.
"cats" <are> "animals"
I'm not a fan of either of Quine's "dogmas of empiricism",
When the otherwise meaningless finite string Bachelor(x) is
stipulated to mean:
Bachelor(x) := ¬Married(x) ∧ Male(x) ∧ Adult(x) ∧ Human(x)
Then Quine's objection to the
analytic/synthetic distinction based on synonymity dissolves.
and there's another for an account of a _stronger_
logicist positivism, alongside a strong mathematical platonism,
since thusly otherwise it's un-founded your well-founding.
You seem to be far too hung up on all of the baggage
that goes with the conventional way of dividing all
these things up. I UTTERLY REJECT ALL THAT BAGGAGE.
Russell's paradox is readily demonstrated in usual accounts
of Russell's theory after Russell's retro-thesis.
ALL PARADOXES are merely incoherence misconstrued.
It's fine for closed categories, yet, so are
many weaker accounts.
My notion of "formal system" contains 100% of ALL
of the details of the entire body of general knowledge
about anything.
Three-legged dog.
In other words you fail to understand that the
body of knowledge expressed in formal language
and formalized natural language is a semantic
tautology expressed as relations between finite
strings.
No, I'm saying both that that's a three-legged dog,
and, doesn't know what a three-legged dog is.
So you quit being rational.
You do seem rational in your videos.
Perhaps you've heard of particle/wave duality,
it's a super-classical concept in quantum mechanics.
Then, how about the radical/rational?
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:I have to carefully study at least a dozen papers
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? >>>>
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.
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:I have to carefully study at least a dozen papers
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? >>>>>
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.
On 4/4/2026 10:44 PM, Ross Finlayson wrote:
On 04/04/2026 08:31 PM, olcott wrote:
On 4/4/2026 10:03 PM, Ross Finlayson wrote:
On 04/04/2026 12:40 AM, olcott wrote:
On 4/3/2026 7:53 PM, Ross Finlayson wrote:
On 04/03/2026 04:02 PM, olcott wrote:
On 4/3/2026 5:10 PM, Ross Finlayson wrote:
On 04/03/2026 12:34 PM, olcott wrote:
On 4/3/2026 1:25 PM, Ross Finlayson wrote:
On 04/03/2026 11:19 AM, Ross Finlayson wrote:
On 04/03/2026 12:13 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?
If there are at least three regularities/rulialities,
well-foundedness (Zermelo, Russell) and
well-ordering (Choice, Ono, Zorn) and
well-dispersion (Martin, univalency, the illative, covering, >>>>>>>>>>> projective
determinacy)
and it's readily demonstrable they can be set up against each >>>>>>>>>>> other,
then it needs be there must be an account of how and why they >>>>>>>>>>> don't.
All these things have been around
since more than 100 years ago.
Assuming 1) we're not bots, and 2) they are bots,
then perhaps usual bot-ware just follows what it's given,
the blindered hindered course of the invincible ignorance
of the inductive inference directly to inductive impasse,
then as sort of like "garbage in garbage out", "crazy in crazy >>>>>>>>>> out".
Since, or if, any sort of individual expression is as well >>>>>>>>>> at least in part as an aspect of psychological projection, >>>>>>>>>> is among reasons why it's a good idea an idea of goodness. >>>>>>>>>>
Then the usual account of logic may include that the weaker >>>>>>>>>> variety of logicism is a psychologism, then that Socrates
for example wasn't that profound a technical philosopher,
for what makes sense for the common man, not what makes
a common man of sense.
When we start with something like the subset of
Russell's "basic facts" that pertain to general
knowledge as axioms and then have semantic entailment
specified syntactically as the only inference step
we derive the entire body of general knowledge that
can be expressed in formal (or formalized natural)
language.
https://plato.stanford.edu/entries/logical-atomism/
Wishful thinking.
That's empiricism with all its faults and baggage
exactly enough as so stated.
I am not talking about logical-atomism AT ALL.
I am taking the single notion "atomic fact"
from it and utterly discarding all the rest.
The actual ENTIRE basis for "atomic facts" is
stipulated relations between finite strings.
"cats" <are> "animals"
I'm not a fan of either of Quine's "dogmas of empiricism",
When the otherwise meaningless finite string Bachelor(x) is
stipulated to mean:
Bachelor(x) := ¬Married(x) ∧ Male(x) ∧ Adult(x) ∧ Human(x) >>>>>>>
Then Quine's objection to the
analytic/synthetic distinction based on synonymity dissolves.
and there's another for an account of a _stronger_
logicist positivism, alongside a strong mathematical platonism, >>>>>>>> since thusly otherwise it's un-founded your well-founding.
You seem to be far too hung up on all of the baggage
that goes with the conventional way of dividing all
these things up. I UTTERLY REJECT ALL THAT BAGGAGE.
Russell's paradox is readily demonstrated in usual accounts
of Russell's theory after Russell's retro-thesis.
ALL PARADOXES are merely incoherence misconstrued.
It's fine for closed categories, yet, so are
many weaker accounts.
My notion of "formal system" contains 100% of ALL
of the details of the entire body of general knowledge
about anything.
Three-legged dog.
In other words you fail to understand that the
body of knowledge expressed in formal language
and formalized natural language is a semantic
tautology expressed as relations between finite
strings.
No, I'm saying both that that's a three-legged dog,
and, doesn't know what a three-legged dog is.
So you quit being rational.
You do seem rational in your videos.
Perhaps you've heard of particle/wave duality,
it's a super-classical concept in quantum mechanics.
Then, how about the radical/rational?
That would seem to have nothing to do with a
finite list of atomic facts of general knowledge.
On 04/05/2026 04:15 AM, olcott wrote:
On 4/4/2026 10:44 PM, Ross Finlayson wrote:
On 04/04/2026 08:31 PM, olcott wrote:
On 4/4/2026 10:03 PM, Ross Finlayson wrote:
On 04/04/2026 12:40 AM, olcott wrote:
On 4/3/2026 7:53 PM, Ross Finlayson wrote:
On 04/03/2026 04:02 PM, olcott wrote:
On 4/3/2026 5:10 PM, Ross Finlayson wrote:
On 04/03/2026 12:34 PM, olcott wrote:
On 4/3/2026 1:25 PM, Ross Finlayson wrote:
On 04/03/2026 11:19 AM, Ross Finlayson wrote:
On 04/03/2026 12:13 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?
If there are at least three regularities/rulialities,
well-foundedness (Zermelo, Russell) and
well-ordering (Choice, Ono, Zorn) and
well-dispersion (Martin, univalency, the illative, covering, >>>>>>>>>>>> projective
determinacy)
and it's readily demonstrable they can be set up against each >>>>>>>>>>>> other,
then it needs be there must be an account of how and why they >>>>>>>>>>>> don't.
All these things have been around
since more than 100 years ago.
Assuming 1) we're not bots, and 2) they are bots,
then perhaps usual bot-ware just follows what it's given, >>>>>>>>>>> the blindered hindered course of the invincible ignorance >>>>>>>>>>> of the inductive inference directly to inductive impasse, >>>>>>>>>>> then as sort of like "garbage in garbage out", "crazy in crazy >>>>>>>>>>> out".
Since, or if, any sort of individual expression is as well >>>>>>>>>>> at least in part as an aspect of psychological projection, >>>>>>>>>>> is among reasons why it's a good idea an idea of goodness. >>>>>>>>>>>
Then the usual account of logic may include that the weaker >>>>>>>>>>> variety of logicism is a psychologism, then that Socrates >>>>>>>>>>> for example wasn't that profound a technical philosopher, >>>>>>>>>>> for what makes sense for the common man, not what makes
a common man of sense.
When we start with something like the subset of
Russell's "basic facts" that pertain to general
knowledge as axioms and then have semantic entailment
specified syntactically as the only inference step
we derive the entire body of general knowledge that
can be expressed in formal (or formalized natural)
language.
https://plato.stanford.edu/entries/logical-atomism/
Wishful thinking.
That's empiricism with all its faults and baggage
exactly enough as so stated.
I am not talking about logical-atomism AT ALL.
I am taking the single notion "atomic fact"
from it and utterly discarding all the rest.
The actual ENTIRE basis for "atomic facts" is
stipulated relations between finite strings.
"cats" <are> "animals"
I'm not a fan of either of Quine's "dogmas of empiricism",
When the otherwise meaningless finite string Bachelor(x) is
stipulated to mean:
Bachelor(x) := ¬Married(x) ∧ Male(x) ∧ Adult(x) ∧ Human(x) >>>>>>>>
Then Quine's objection to the
analytic/synthetic distinction based on synonymity dissolves.
and there's another for an account of a _stronger_
logicist positivism, alongside a strong mathematical platonism, >>>>>>>>> since thusly otherwise it's un-founded your well-founding.
You seem to be far too hung up on all of the baggage
that goes with the conventional way of dividing all
these things up. I UTTERLY REJECT ALL THAT BAGGAGE.
Russell's paradox is readily demonstrated in usual accounts
of Russell's theory after Russell's retro-thesis.
ALL PARADOXES are merely incoherence misconstrued.
It's fine for closed categories, yet, so are
many weaker accounts.
My notion of "formal system" contains 100% of ALL
of the details of the entire body of general knowledge
about anything.
Three-legged dog.
In other words you fail to understand that the
body of knowledge expressed in formal language
and formalized natural language is a semantic
tautology expressed as relations between finite
strings.
No, I'm saying both that that's a three-legged dog,
and, doesn't know what a three-legged dog is.
So you quit being rational.
You do seem rational in your videos.
Perhaps you've heard of particle/wave duality,
it's a super-classical concept in quantum mechanics.
Then, how about the radical/rational?
That would seem to have nothing to do with a
finite list of atomic facts of general knowledge.
No it wouldn't, just add it as another fact.
The usual account of material implication about
monotonicity and entailment is that "material
implication" is neither material nor implication,
and furthermore doesn't entail entailment and
isn't monotone about monotonicity.
I'll agree that one can count to five on the usual
fingers on a usual hand, then here that besides
that the left hand does know what the right hand
is doing, stop hitting yourself.
On 04/05/2026 04:25 AM, 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.
Montague was a hipster flake and about the
worst sort of snide hypocrite.
Herbrand on the other hand has a much more
thorough account of that abstract symbolic
language and natural language are equi-interpretable.
Otherwise your account of weak logicist positivism
has that there's a stronger account of a strong
logicist positivism that includes for the like of
Derrida and Husserl an accommodation of the strong
mathematical platonism and including its super-classical
concepts and results.
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:I have to carefully study at least a dozen papers
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? >>>>>
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.
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.
It's seems that PO has it that given an infinitely
fast and infinitely large computer, that he can
compute some change in cash and most of the steps
of a pizza delivery order.
I suppose congratulation are in order,
that'll make a great pizza delivery driver.
"Pete Olcott: the pizza man."
On 4/5/2026 8:30 AM, Ross Finlayson wrote:
[...]
It's seems that PO has it that given an infinitely
fast and infinitely large computer, that he can
compute some change in cash and most of the steps
of a pizza delivery order.
I suppose congratulation are in order,
that'll make a great pizza delivery driver.
"Pete Olcott: the pizza man."
PO is strange. A low life pedo, and thinks he is god.
On 04/06/2026 12:09 PM, Chris M. Thomasson wrote:
On 4/5/2026 8:30 AM, Ross Finlayson wrote:
[...]
It's seems that PO has it that given an infinitely
fast and infinitely large computer, that he can
compute some change in cash and most of the steps
of a pizza delivery order.
I suppose congratulation are in order,
that'll make a great pizza delivery driver.
"Pete Olcott: the pizza man."
PO is strange. A low life pedo, and thinks he is god.
You know, since the 90's or so and "think of the children",
I blame the Redcoats and Limeys for making "terrorists"
and "pedophiles" the boogey-men and unclean abominations
that taint matters of the violation of liberties with
the excrable pathological psychologism of filth and dirt.
Furthermore, the correct word for child molesters would
be "pederast", since "pedophile" simply means those who
love children, then that the conflation of "love" and "lust"
is another dirty, dark algorithm, since besides "cropophiles"
and "necrophiles" that most accounts of -philia are the
platonic variety.
So, think of the children, and boogey-man word-wavers can
go directly straight to hell, anybody who abuses the
words "terrorist" or "pedo" can go eat a box of dicks.
Not that there's necessarily anything wrong with that, ....
So, the next person who uses the word "terrorist" or
"pedo", tell them those mean just "enemy" and "abuser",
and that they're abusers of words the enemies of good people.
On 04/06/2026 12:26 PM, Ross Finlayson wrote:
On 04/06/2026 12:09 PM, Chris M. Thomasson wrote:
On 4/5/2026 8:30 AM, Ross Finlayson wrote:
[...]
It's seems that PO has it that given an infinitely
fast and infinitely large computer, that he can
compute some change in cash and most of the steps
of a pizza delivery order.
I suppose congratulation are in order,
that'll make a great pizza delivery driver.
"Pete Olcott: the pizza man."
PO is strange. A low life pedo, and thinks he is god.
You know, since the 90's or so and "think of the children",
I blame the Redcoats and Limeys for making "terrorists"
and "pedophiles" the boogey-men and unclean abominations
that taint matters of the violation of liberties with
the excrable pathological psychologism of filth and dirt.
Furthermore, the correct word for child molesters would
be "pederast", since "pedophile" simply means those who
love children, then that the conflation of "love" and "lust"
is another dirty, dark algorithm, since besides "cropophiles"
and "necrophiles" that most accounts of -philia are the
platonic variety.
So, think of the children, and boogey-man word-wavers can
go directly straight to hell, anybody who abuses the
words "terrorist" or "pedo" can go eat a box of dicks.
Not that there's necessarily anything wrong with that, ....
So, the next person who uses the word "terrorist" or
"pedo", tell them those mean just "enemy" and "abuser",
and that they're abusers of words the enemies of good people.
More correct usage would be along the lines of
"Donald Trump is an alleged _pederast_, and his
bombastic belligerence exhibits _terroristic_ tendencies",
or for something like "Fudd Bibi was a genocidal monomaniac."
On 04/06/2026 12:09 PM, Chris M. Thomasson wrote:
On 4/5/2026 8:30 AM, Ross Finlayson wrote:
[...]
It's seems that PO has it that given an infinitely
fast and infinitely large computer, that he can
compute some change in cash and most of the steps
of a pizza delivery order.
I suppose congratulation are in order,
that'll make a great pizza delivery driver.
"Pete Olcott: the pizza man."
PO is strange. A low life pedo, and thinks he is god.
You know, since the 90's or so and "think of the children",
I blame the Redcoats and Limeys for making "terrorists"
and "pedophiles" the boogey-men
and unclean abominations
that taint matters of the violation of liberties with
the excrable pathological psychologism of filth and dirt.
Furthermore, the correct word for child molesters would
be "pederast", since "pedophile" simply means those who
love children, then that the conflation of "love" and "lust"
is another dirty, dark algorithm, since besides "cropophiles"
and "necrophiles" that most accounts of -philia are the
platonic variety.
So, think of the children, and boogey-man word-wavers can
go directly straight to hell, anybody who abuses the
words "terrorist" or "pedo" can go eat a box of dicks.
Not that there's necessarily anything wrong with that, ....
So, the next person who uses the word "terrorist" or
"pedo", tell them those mean just "enemy" and "abuser",
and that they're abusers of words the enemies of good people.
On 04/06/2026 12:35 PM, Ross Finlayson wrote:
On 04/06/2026 12:26 PM, Ross Finlayson wrote:
On 04/06/2026 12:09 PM, Chris M. Thomasson wrote:
On 4/5/2026 8:30 AM, Ross Finlayson wrote:
[...]
It's seems that PO has it that given an infinitely
fast and infinitely large computer, that he can
compute some change in cash and most of the steps
of a pizza delivery order.
I suppose congratulation are in order,
that'll make a great pizza delivery driver.
"Pete Olcott: the pizza man."
PO is strange. A low life pedo, and thinks he is god.
You know, since the 90's or so and "think of the children",
I blame the Redcoats and Limeys for making "terrorists"
and "pedophiles" the boogey-men and unclean abominations
that taint matters of the violation of liberties with
the excrable pathological psychologism of filth and dirt.
Furthermore, the correct word for child molesters would
be "pederast", since "pedophile" simply means those who
love children, then that the conflation of "love" and "lust"
is another dirty, dark algorithm, since besides "cropophiles"
and "necrophiles" that most accounts of -philia are the
platonic variety.
So, think of the children, and boogey-man word-wavers can
go directly straight to hell, anybody who abuses the
words "terrorist" or "pedo" can go eat a box of dicks.
Not that there's necessarily anything wrong with that, ....
So, the next person who uses the word "terrorist" or
"pedo", tell them those mean just "enemy" and "abuser",
and that they're abusers of words the enemies of good people.
More correct usage would be along the lines of
"Donald Trump is an alleged _pederast_, and his
bombastic belligerence exhibits _terroristic_ tendencies",
or for something like "Fudd Bibi was a genocidal monomaniac."
My dick has a rather limited vocabulary,
and only a modicum of intelligence,
with the theory that the gonads of both
sexes involve their own grey cells besides
hormones. Tt doesn't much know the difference
between a crotch in a tree and a large-mouth bass.
That said, it doesn't much like cringing at
each mention of "sex crimes". It rather
considers "sex crimes" as "sex offenses".
Neither does my rectum, yet it only has one job.
Children: not to be confused with juveniles.
Terrorists get a sort of automatic death penalty.
P.S.: I hate pimps.
On 4/6/2026 1:46 PM, Ross Finlayson wrote:
On 04/06/2026 12:35 PM, Ross Finlayson wrote:
On 04/06/2026 12:26 PM, Ross Finlayson wrote:
On 04/06/2026 12:09 PM, Chris M. Thomasson wrote:
On 4/5/2026 8:30 AM, Ross Finlayson wrote:
[...]
It's seems that PO has it that given an infinitely
fast and infinitely large computer, that he can
compute some change in cash and most of the steps
of a pizza delivery order.
I suppose congratulation are in order,
that'll make a great pizza delivery driver.
"Pete Olcott: the pizza man."
PO is strange. A low life pedo, and thinks he is god.
You know, since the 90's or so and "think of the children",
I blame the Redcoats and Limeys for making "terrorists"
and "pedophiles" the boogey-men and unclean abominations
that taint matters of the violation of liberties with
the excrable pathological psychologism of filth and dirt.
Furthermore, the correct word for child molesters would
be "pederast", since "pedophile" simply means those who
love children, then that the conflation of "love" and "lust"
is another dirty, dark algorithm, since besides "cropophiles"
and "necrophiles" that most accounts of -philia are the
platonic variety.
So, think of the children, and boogey-man word-wavers can
go directly straight to hell, anybody who abuses the
words "terrorist" or "pedo" can go eat a box of dicks.
Not that there's necessarily anything wrong with that, ....
So, the next person who uses the word "terrorist" or
"pedo", tell them those mean just "enemy" and "abuser",
and that they're abusers of words the enemies of good people.
More correct usage would be along the lines of
"Donald Trump is an alleged _pederast_, and his
bombastic belligerence exhibits _terroristic_ tendencies",
or for something like "Fudd Bibi was a genocidal monomaniac."
My dick has a rather limited vocabulary,
and only a modicum of intelligence,
with the theory that the gonads of both
sexes involve their own grey cells besides
hormones. Tt doesn't much know the difference
between a crotch in a tree and a large-mouth bass.
That said, it doesn't much like cringing at
each mention of "sex crimes". It rather
considers "sex crimes" as "sex offenses".
Neither does my rectum, yet it only has one job.
Children: not to be confused with juveniles.
Terrorists get a sort of automatic death penalty.
P.S.: I hate pimps.
You should turn yourself into the authorities now before you harm anybody?
On 04/06/2026 03:31 PM, Chris M. Thomasson wrote:
On 4/6/2026 1:46 PM, Ross Finlayson wrote:
On 04/06/2026 12:35 PM, Ross Finlayson wrote:
On 04/06/2026 12:26 PM, Ross Finlayson wrote:
On 04/06/2026 12:09 PM, Chris M. Thomasson wrote:
On 4/5/2026 8:30 AM, Ross Finlayson wrote:
[...]
It's seems that PO has it that given an infinitely
fast and infinitely large computer, that he can
compute some change in cash and most of the steps
of a pizza delivery order.
I suppose congratulation are in order,
that'll make a great pizza delivery driver.
"Pete Olcott: the pizza man."
PO is strange. A low life pedo, and thinks he is god.
You know, since the 90's or so and "think of the children",
I blame the Redcoats and Limeys for making "terrorists"
and "pedophiles" the boogey-men and unclean abominations
that taint matters of the violation of liberties with
the excrable pathological psychologism of filth and dirt.
Furthermore, the correct word for child molesters would
be "pederast", since "pedophile" simply means those who
love children, then that the conflation of "love" and "lust"
is another dirty, dark algorithm, since besides "cropophiles"
and "necrophiles" that most accounts of -philia are the
platonic variety.
So, think of the children, and boogey-man word-wavers can
go directly straight to hell, anybody who abuses the
words "terrorist" or "pedo" can go eat a box of dicks.
Not that there's necessarily anything wrong with that, ....
So, the next person who uses the word "terrorist" or
"pedo", tell them those mean just "enemy" and "abuser",
and that they're abusers of words the enemies of good people.
More correct usage would be along the lines of
"Donald Trump is an alleged _pederast_, and his
bombastic belligerence exhibits _terroristic_ tendencies",
or for something like "Fudd Bibi was a genocidal monomaniac."
My dick has a rather limited vocabulary,
and only a modicum of intelligence,
with the theory that the gonads of both
sexes involve their own grey cells besides
hormones. Tt doesn't much know the difference
between a crotch in a tree and a large-mouth bass.
That said, it doesn't much like cringing at
each mention of "sex crimes". It rather
considers "sex crimes" as "sex offenses".
Neither does my rectum, yet it only has one job.
Children: not to be confused with juveniles.
Terrorists get a sort of automatic death penalty.
P.S.: I hate pimps.
You should turn yourself into the authorities now before you harm
anybody?
Hit the wrong nerve?
On 4/6/26 5:14 PM, Ross Finlayson wrote:
On 04/06/2026 03:31 PM, Chris M. Thomasson wrote:
On 4/6/2026 1:46 PM, Ross Finlayson wrote:
On 04/06/2026 12:35 PM, Ross Finlayson wrote:
On 04/06/2026 12:26 PM, Ross Finlayson wrote:
On 04/06/2026 12:09 PM, Chris M. Thomasson wrote:
On 4/5/2026 8:30 AM, Ross Finlayson wrote:
[...]
It's seems that PO has it that given an infinitely
fast and infinitely large computer, that he can
compute some change in cash and most of the steps
of a pizza delivery order.
I suppose congratulation are in order,
that'll make a great pizza delivery driver.
"Pete Olcott: the pizza man."
PO is strange. A low life pedo, and thinks he is god.
You know, since the 90's or so and "think of the children",
I blame the Redcoats and Limeys for making "terrorists"
and "pedophiles" the boogey-men and unclean abominations
that taint matters of the violation of liberties with
the excrable pathological psychologism of filth and dirt.
Furthermore, the correct word for child molesters would
be "pederast", since "pedophile" simply means those who
love children, then that the conflation of "love" and "lust"
is another dirty, dark algorithm, since besides "cropophiles"
and "necrophiles" that most accounts of -philia are the
platonic variety.
So, think of the children, and boogey-man word-wavers can
go directly straight to hell, anybody who abuses the
words "terrorist" or "pedo" can go eat a box of dicks.
Not that there's necessarily anything wrong with that, ....
So, the next person who uses the word "terrorist" or
"pedo", tell them those mean just "enemy" and "abuser",
and that they're abusers of words the enemies of good people.
More correct usage would be along the lines of
"Donald Trump is an alleged _pederast_, and his
bombastic belligerence exhibits _terroristic_ tendencies",
or for something like "Fudd Bibi was a genocidal monomaniac."
My dick has a rather limited vocabulary,
and only a modicum of intelligence,
with the theory that the gonads of both
sexes involve their own grey cells besides
hormones. Tt doesn't much know the difference
between a crotch in a tree and a large-mouth bass.
That said, it doesn't much like cringing at
each mention of "sex crimes". It rather
considers "sex crimes" as "sex offenses".
Neither does my rectum, yet it only has one job.
Children: not to be confused with juveniles.
Terrorists get a sort of automatic death penalty.
P.S.: I hate pimps.
You should turn yourself into the authorities now before you harm
anybody?
Hit the wrong nerve?
chris is shallow af retard who can't handle the heat he pathetically
tries to dish out,
ofc u hit a nerve suggesting the status quo boogie men are overblown,
the dud doesn't have critical thinking faculties
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.
On 04/06/2026 08:00 PM, dart200 wrote:
On 4/6/26 5:14 PM, Ross Finlayson wrote:
On 04/06/2026 03:31 PM, Chris M. Thomasson wrote:
On 4/6/2026 1:46 PM, Ross Finlayson wrote:
On 04/06/2026 12:35 PM, Ross Finlayson wrote:
On 04/06/2026 12:26 PM, Ross Finlayson wrote:
On 04/06/2026 12:09 PM, Chris M. Thomasson wrote:
On 4/5/2026 8:30 AM, Ross Finlayson wrote:
[...]
It's seems that PO has it that given an infinitely
fast and infinitely large computer, that he can
compute some change in cash and most of the steps
of a pizza delivery order.
I suppose congratulation are in order,
that'll make a great pizza delivery driver.
"Pete Olcott: the pizza man."
PO is strange. A low life pedo, and thinks he is god.
You know, since the 90's or so and "think of the children",
I blame the Redcoats and Limeys for making "terrorists"
and "pedophiles" the boogey-men and unclean abominations
that taint matters of the violation of liberties with
the excrable pathological psychologism of filth and dirt.
Furthermore, the correct word for child molesters would
be "pederast", since "pedophile" simply means those who
love children, then that the conflation of "love" and "lust"
is another dirty, dark algorithm, since besides "cropophiles"
and "necrophiles" that most accounts of -philia are the
platonic variety.
So, think of the children, and boogey-man word-wavers can
go directly straight to hell, anybody who abuses the
words "terrorist" or "pedo" can go eat a box of dicks.
Not that there's necessarily anything wrong with that, ....
So, the next person who uses the word "terrorist" or
"pedo", tell them those mean just "enemy" and "abuser",
and that they're abusers of words the enemies of good people.
More correct usage would be along the lines of
"Donald Trump is an alleged _pederast_, and his
bombastic belligerence exhibits _terroristic_ tendencies",
or for something like "Fudd Bibi was a genocidal monomaniac."
My dick has a rather limited vocabulary,
and only a modicum of intelligence,
with the theory that the gonads of both
sexes involve their own grey cells besides
hormones. Tt doesn't much know the difference
between a crotch in a tree and a large-mouth bass.
That said, it doesn't much like cringing at
each mention of "sex crimes". It rather
considers "sex crimes" as "sex offenses".
Neither does my rectum, yet it only has one job.
Children: not to be confused with juveniles.
Terrorists get a sort of automatic death penalty.
P.S.: I hate pimps.
You should turn yourself into the authorities now before you harm
anybody?
Hit the wrong nerve?
chris is shallow af retard who can't handle the heat he pathetically
tries to dish out,
ofc u hit a nerve suggesting the status quo boogie men are overblown,
the dud doesn't have critical thinking faculties
philia-phobes <-> phobia-philes
Since I'm not an axe murderer, I'd rather be generous and
figure that if he didn't show abject fear at the mere
mention of bucking the "child protective services" that
he'd worry that they'd kidnap his offspring. It's easy
to understand the fear and anxiety tied up in the closest
(or, closets) of bonds.
I.e., the people who suffer the most from demonization
of unlikely occurrences are vulnerable themselves,
while of course it's better if children are innocents
and don't need to grow up too soon and have no reason
to think so. Not un-protected, just, not over-protected.
Then, if philia-phobes are those that are driven to
fear normal sorts of situations like being polite and
talking to the neighbors and the sending the children outside
to play, and then phobia-philes are those who get off on
the fears of others, then the world would be better off
with less of both of them. This would be for the
alleviating the unreasonable anxiety of philia-phobes,
which would naturally shrivel up phobia-philes.
The "child-parent-adult" account of psychology is usual.
The phobia-philes, or phoba-philes or phobo-philes,
basically are terrorists by definition.
Then, "regardless", where "regardless" was a term
introduced in pop-psychology for behavior in the '80s,
regardless of where Donald Trump touched the dolly,
the open corruption is obscene.
Here, then, though, the "ad hominem" is not only irrelevant,
it's insulting, since what's under discussion are
matters of logic.
Now, I'm going to remark about the ideas of this
closed-minded "well-founded justification tree",
about what's going on in "synthetic mathematics"
these days, which is contradictions, that even
mechanical reference reasoners are readily provided
that destroy said ignorances of contradictions of
"synthetic mathematics". Or, "PO and similar troll-bots"
aren't doing "synthetic mathematics", since mathematics
is a whole, those are "ignorant inductive impasses".
On 4/7/2026 12:07 AM, Ross Finlayson wrote:
On 04/06/2026 08:00 PM, dart200 wrote:
On 4/6/26 5:14 PM, Ross Finlayson wrote:
On 04/06/2026 03:31 PM, Chris M. Thomasson wrote:
On 4/6/2026 1:46 PM, Ross Finlayson wrote:
On 04/06/2026 12:35 PM, Ross Finlayson wrote:
On 04/06/2026 12:26 PM, Ross Finlayson wrote:
On 04/06/2026 12:09 PM, Chris M. Thomasson wrote:
On 4/5/2026 8:30 AM, Ross Finlayson wrote:
[...]
It's seems that PO has it that given an infinitely
fast and infinitely large computer, that he can
compute some change in cash and most of the steps
of a pizza delivery order.
I suppose congratulation are in order,
that'll make a great pizza delivery driver.
"Pete Olcott: the pizza man."
PO is strange. A low life pedo, and thinks he is god.
You know, since the 90's or so and "think of the children",
I blame the Redcoats and Limeys for making "terrorists"
and "pedophiles" the boogey-men and unclean abominations
that taint matters of the violation of liberties with
the excrable pathological psychologism of filth and dirt.
Furthermore, the correct word for child molesters would
be "pederast", since "pedophile" simply means those who
love children, then that the conflation of "love" and "lust"
is another dirty, dark algorithm, since besides "cropophiles"
and "necrophiles" that most accounts of -philia are the
platonic variety.
So, think of the children, and boogey-man word-wavers can
go directly straight to hell, anybody who abuses the
words "terrorist" or "pedo" can go eat a box of dicks.
Not that there's necessarily anything wrong with that, ....
So, the next person who uses the word "terrorist" or
"pedo", tell them those mean just "enemy" and "abuser",
and that they're abusers of words the enemies of good people.
More correct usage would be along the lines of
"Donald Trump is an alleged _pederast_, and his
bombastic belligerence exhibits _terroristic_ tendencies",
or for something like "Fudd Bibi was a genocidal monomaniac."
My dick has a rather limited vocabulary,
and only a modicum of intelligence,
with the theory that the gonads of both
sexes involve their own grey cells besides
hormones. Tt doesn't much know the difference
between a crotch in a tree and a large-mouth bass.
That said, it doesn't much like cringing at
each mention of "sex crimes". It rather
considers "sex crimes" as "sex offenses".
Neither does my rectum, yet it only has one job.
Children: not to be confused with juveniles.
Terrorists get a sort of automatic death penalty.
P.S.: I hate pimps.
You should turn yourself into the authorities now before you harm
anybody?
Hit the wrong nerve?
chris is shallow af retard who can't handle the heat he pathetically
tries to dish out,
ofc u hit a nerve suggesting the status quo boogie men are overblown,
the dud doesn't have critical thinking faculties
philia-phobes <-> phobia-philes
Since I'm not an axe murderer, I'd rather be generous and
figure that if he didn't show abject fear at the mere
mention of bucking the "child protective services" that
he'd worry that they'd kidnap his offspring. It's easy
to understand the fear and anxiety tied up in the closest
(or, closets) of bonds.
I.e., the people who suffer the most from demonization
of unlikely occurrences are vulnerable themselves,
while of course it's better if children are innocents
and don't need to grow up too soon and have no reason
to think so. Not un-protected, just, not over-protected.
Then, if philia-phobes are those that are driven to
fear normal sorts of situations like being polite and
talking to the neighbors and the sending the children outside
to play, and then phobia-philes are those who get off on
the fears of others, then the world would be better off
with less of both of them. This would be for the
alleviating the unreasonable anxiety of philia-phobes,
which would naturally shrivel up phobia-philes.
The "child-parent-adult" account of psychology is usual.
The phobia-philes, or phoba-philes or phobo-philes,
basically are terrorists by definition.
Then, "regardless", where "regardless" was a term
introduced in pop-psychology for behavior in the '80s,
regardless of where Donald Trump touched the dolly,
the open corruption is obscene.
Here, then, though, the "ad hominem" is not only irrelevant,
it's insulting, since what's under discussion are
matters of logic.
Now, I'm going to remark about the ideas of this
closed-minded "well-founded justification tree",
about what's going on in "synthetic mathematics"
these days, which is contradictions, that even
mechanical reference reasoners are readily provided
that destroy said ignorances of contradictions of
"synthetic mathematics". Or, "PO and similar troll-bots"
aren't doing "synthetic mathematics", since mathematics
is a whole, those are "ignorant inductive impasses".
Why are seemingly trying to justify pedo's?
Why are seemingly trying to justify pedo's?
On 04/07/2026 12:19 PM, Chris M. Thomasson wrote:
On 4/7/2026 12:07 AM, Ross Finlayson wrote:
On 04/06/2026 08:00 PM, dart200 wrote:
On 4/6/26 5:14 PM, Ross Finlayson wrote:
On 04/06/2026 03:31 PM, Chris M. Thomasson wrote:
On 4/6/2026 1:46 PM, Ross Finlayson wrote:
On 04/06/2026 12:35 PM, Ross Finlayson wrote:
On 04/06/2026 12:26 PM, Ross Finlayson wrote:
On 04/06/2026 12:09 PM, Chris M. Thomasson wrote:
On 4/5/2026 8:30 AM, Ross Finlayson wrote:
[...]
It's seems that PO has it that given an infinitely
fast and infinitely large computer, that he can
compute some change in cash and most of the steps
of a pizza delivery order.
I suppose congratulation are in order,
that'll make a great pizza delivery driver.
"Pete Olcott: the pizza man."
PO is strange. A low life pedo, and thinks he is god.
You know, since the 90's or so and "think of the children",
I blame the Redcoats and Limeys for making "terrorists"
and "pedophiles" the boogey-men and unclean abominations
that taint matters of the violation of liberties with
the excrable pathological psychologism of filth and dirt.
Furthermore, the correct word for child molesters would
be "pederast", since "pedophile" simply means those who
love children, then that the conflation of "love" and "lust" >>>>>>>>> is another dirty, dark algorithm, since besides "cropophiles" >>>>>>>>> and "necrophiles" that most accounts of -philia are the
platonic variety.
So, think of the children, and boogey-man word-wavers can
go directly straight to hell, anybody who abuses the
words "terrorist" or "pedo" can go eat a box of dicks.
Not that there's necessarily anything wrong with that, ....
So, the next person who uses the word "terrorist" or
"pedo", tell them those mean just "enemy" and "abuser",
and that they're abusers of words the enemies of good people. >>>>>>>>>
More correct usage would be along the lines of
"Donald Trump is an alleged _pederast_, and his
bombastic belligerence exhibits _terroristic_ tendencies",
or for something like "Fudd Bibi was a genocidal monomaniac."
My dick has a rather limited vocabulary,
and only a modicum of intelligence,
with the theory that the gonads of both
sexes involve their own grey cells besides
hormones. Tt doesn't much know the difference
between a crotch in a tree and a large-mouth bass.
That said, it doesn't much like cringing at
each mention of "sex crimes". It rather
considers "sex crimes" as "sex offenses".
Neither does my rectum, yet it only has one job.
Children: not to be confused with juveniles.
Terrorists get a sort of automatic death penalty.
P.S.: I hate pimps.
You should turn yourself into the authorities now before you harm
anybody?
Hit the wrong nerve?
chris is shallow af retard who can't handle the heat he pathetically
tries to dish out,
ofc u hit a nerve suggesting the status quo boogie men are overblown,
the dud doesn't have critical thinking faculties
philia-phobes <-> phobia-philes
Since I'm not an axe murderer, I'd rather be generous and
figure that if he didn't show abject fear at the mere
mention of bucking the "child protective services" that
he'd worry that they'd kidnap his offspring. It's easy
to understand the fear and anxiety tied up in the closest
(or, closets) of bonds.
I.e., the people who suffer the most from demonization
of unlikely occurrences are vulnerable themselves,
while of course it's better if children are innocents
and don't need to grow up too soon and have no reason
to think so. Not un-protected, just, not over-protected.
Then, if philia-phobes are those that are driven to
fear normal sorts of situations like being polite and
talking to the neighbors and the sending the children outside
to play, and then phobia-philes are those who get off on
the fears of others, then the world would be better off
with less of both of them. This would be for the
alleviating the unreasonable anxiety of philia-phobes,
which would naturally shrivel up phobia-philes.
The "child-parent-adult" account of psychology is usual.
The phobia-philes, or phoba-philes or phobo-philes,
basically are terrorists by definition.
Then, "regardless", where "regardless" was a term
introduced in pop-psychology for behavior in the '80s,
regardless of where Donald Trump touched the dolly,
the open corruption is obscene.
Here, then, though, the "ad hominem" is not only irrelevant,
it's insulting, since what's under discussion are
matters of logic.
Now, I'm going to remark about the ideas of this
closed-minded "well-founded justification tree",
about what's going on in "synthetic mathematics"
these days, which is contradictions, that even
mechanical reference reasoners are readily provided
that destroy said ignorances of contradictions of
"synthetic mathematics". Or, "PO and similar troll-bots"
aren't doing "synthetic mathematics", since mathematics
is a whole, those are "ignorant inductive impasses".
Why are seemingly trying to justify pedo's?
No, I'm anti-terrorist.
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.
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.
Why are seemingly trying to justify pedo's?
No, I'm anti-terrorist.
In comp.theory Chris M. Thomasson <chris.m.thomasson.1@gmail.com> wrote:
[ .... ]
Why are seemingly trying to justify pedo's?
You're the sort of person who, 90 years ago in Europe, would be asking
"why are you trying to justify Jews?".
On 4/7/2026 12:46 PM, Alan Mackenzie wrote:
In comp.theory Chris M. Thomasson <chris.m.thomasson.1@gmail.com> wrote:
[ .... ]
Why are seemingly trying to justify pedo's?
You're the sort of person who, 90 years ago in Europe, would be asking
"why are you trying to justify Jews?".
Strange! pedo vs a person who is jewish?
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.
On 4/7/2026 12:46 PM, Alan Mackenzie wrote:
In comp.theory Chris M. Thomasson <chris.m.thomasson.1@gmail.com> wrote:
[ .... ]
Why are seemingly trying to justify pedo's?
You're the sort of person who, 90 years ago in Europe, would be asking
"why are you trying to justify Jews?".
Strange! pedo vs a person who is jewish?
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 >>>>>>>>>>>>>> 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.
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.
In sci.math Chris M. Thomasson <chris.m.thomasson.1@gmail.com> wrote:
On 4/7/2026 12:46 PM, Alan Mackenzie wrote:
In comp.theory Chris M. Thomasson <chris.m.thomasson.1@gmail.com> wrote:
[ .... ]
Why are seemingly trying to justify pedo's?
You're the sort of person who, 90 years ago in Europe, would be asking
"why are you trying to justify Jews?".
Strange! pedo vs a person who is jewish?
I just don't believe you're dumb enough not to see the analogy. We're talking about two groups of people who aren't popular in popular culture
(of whatever time), and bullies like you think that justifies them in harrassing members of those groups with degrading epithets.
You used the term "low-life pedo" in this thread, implying that the
target of your nastiness was less than human. I suggest you reconsider
all the implications, and then apologise publicly to Peter Olcott in
this thread.
Besides everything else, individuals' sexual psychology is not on topic
in the newsgroups this thread is posted to.
In sci.math Chris M. Thomasson <chris.m.thomasson.1@gmail.com> wrote:
On 4/7/2026 12:46 PM, Alan Mackenzie wrote:
In comp.theory Chris M. Thomasson <chris.m.thomasson.1@gmail.com> wrote:
[ .... ]
Why are seemingly trying to justify pedo's?
You're the sort of person who, 90 years ago in Europe, would be asking
"why are you trying to justify Jews?".
Strange! pedo vs a person who is jewish?
I just don't believe you're dumb enough not to see the analogy. We're talking about two groups of people who aren't popular in popular culture
(of whatever time), and bullies like you think that justifies them in harrassing members of those groups with degrading epithets.
You used the term "low-life pedo" in this thread, implying that the
target of your nastiness was less than human. I suggest you reconsider
all the implications, and then apologise publicly to Peter Olcott in
this thread.
Besides everything else, individuals' sexual psychology is not on topic
in the newsgroups this thread is posted to.
On 04/09/2026 05:46 AM, Alan Mackenzie wrote:
In sci.math Chris M. Thomasson <chris.m.thomasson.1@gmail.com> wrote:
On 4/7/2026 12:46 PM, Alan Mackenzie wrote:
In comp.theory Chris M. Thomasson <chris.m.thomasson.1@gmail.com>
wrote:
[ .... ]
Why are seemingly trying to justify pedo's?
You're the sort of person who, 90 years ago in Europe, would be asking >>>> "why are you trying to justify Jews?".
Strange! pedo vs a person who is jewish?
I just don't believe you're dumb enough not to see the analogy. We're
talking about two groups of people who aren't popular in popular culture
(of whatever time), and bullies like you think that justifies them in
harrassing members of those groups with degrading epithets.
You used the term "low-life pedo" in this thread, implying that the
target of your nastiness was less than human. I suggest you reconsider
all the implications, and then apologise publicly to Peter Olcott in
this thread.
Besides everything else, individuals' sexual psychology is not on topic
in the newsgroups this thread is posted to.
"Otherism" as a usual account is sometimes demonizing specters and then threatening sympathy with association, and furthermore threatening the rejection of otherism as association with the demonized, besides the
wider accounts of "otherism" and "we-think" and "in-group" types of
pecking and the like, then furthermore is the association with "thought police" and the like, here vis-a-vis "thought crimes" and "real crimes".
So, besides "un-popular", it's a gross bludgeon.
Let us recall the stories we'd tell youth, or give youth to discover,
the fable.
https://en.wikipedia.org/wiki/Fable https://en.wikipedia.org/wiki/Aesop%27s_Fables#Select_fables
Now, plenty of these fables have consequences,
and some invoke a specter like "the boogey-man"
as variously threatens irresponsibility or the unwary,
or, punishes misbehavior, and even, when that
invoking the specter, invokes the specter.
https://en.wikipedia.org/wiki/The_Boy_Who_Cried_Wolf
The psycho-sexual in the psycho-logical, is an aspect
of thinking and feeling beings, largely biological.
Anyways children should be more concerned with if anybody
in their class likes them, not whether the world is full
of monsters, after them. (Nor that they'll become one.)
There is not a monster under the bed,
there is not a monster in the closet,
there is not a monster in the basement,
there is not a monster in the yard.
"The only thing to fear is fear itself."
"So, first of all, let me assert my firm belief that the only thing we
have to fear is fear itself — nameless, unreasoning, unjustified terror which paralyzes needed efforts to convert retreat into advance." -- FDR
There is not a monster in your mind.
Then, basically it's insulting to make "ad hominem" fallacy.
I read a good book a few years ago about identity and including
a chapter on otherism, and how easy it is to see through it,
I'm thinking it was an "Ian B." or so, if I don't recall,
something about "politics of identity" or "psychology of identity"
or along these lines, in the philosophy section though as about
psychology. If I recall it I'll note it here.
Anyways, we still need a word for "loves children".
Thanks for writing.
On 4/9/2026 10:14 AM, Ross Finlayson wrote:
On 04/09/2026 05:46 AM, Alan Mackenzie wrote:
In sci.math Chris M. Thomasson <chris.m.thomasson.1@gmail.com> wrote:
On 4/7/2026 12:46 PM, Alan Mackenzie wrote:
In comp.theory Chris M. Thomasson <chris.m.thomasson.1@gmail.com>
wrote:
[ .... ]
Why are seemingly trying to justify pedo's?
You're the sort of person who, 90 years ago in Europe, would be asking >>>>> "why are you trying to justify Jews?".
Strange! pedo vs a person who is jewish?
I just don't believe you're dumb enough not to see the analogy. We're
talking about two groups of people who aren't popular in popular culture >>> (of whatever time), and bullies like you think that justifies them in
harrassing members of those groups with degrading epithets.
You used the term "low-life pedo" in this thread, implying that the
target of your nastiness was less than human. I suggest you reconsider
all the implications, and then apologise publicly to Peter Olcott in
this thread.
Besides everything else, individuals' sexual psychology is not on topic
in the newsgroups this thread is posted to.
"Otherism" as a usual account is sometimes demonizing specters and then
threatening sympathy with association, and furthermore threatening the
rejection of otherism as association with the demonized, besides the
wider accounts of "otherism" and "we-think" and "in-group" types of
pecking and the like, then furthermore is the association with "thought
police" and the like, here vis-a-vis "thought crimes" and "real crimes".
So, besides "un-popular", it's a gross bludgeon.
Let us recall the stories we'd tell youth, or give youth to discover,
the fable.
https://en.wikipedia.org/wiki/Fable
https://en.wikipedia.org/wiki/Aesop%27s_Fables#Select_fables
Now, plenty of these fables have consequences,
and some invoke a specter like "the boogey-man"
as variously threatens irresponsibility or the unwary,
or, punishes misbehavior, and even, when that
invoking the specter, invokes the specter.
https://en.wikipedia.org/wiki/The_Boy_Who_Cried_Wolf
The psycho-sexual in the psycho-logical, is an aspect
of thinking and feeling beings, largely biological.
Anyways children should be more concerned with if anybody
in their class likes them, not whether the world is full
of monsters, after them. (Nor that they'll become one.)
There is not a monster under the bed,
there is not a monster in the closet,
there is not a monster in the basement,
there is not a monster in the yard.
"The only thing to fear is fear itself."
"So, first of all, let me assert my firm belief that the only thing we
have to fear is fear itself — nameless, unreasoning, unjustified terror
which paralyzes needed efforts to convert retreat into advance." -- FDR
There is not a monster in your mind.
Then, basically it's insulting to make "ad hominem" fallacy.
I read a good book a few years ago about identity and including
a chapter on otherism, and how easy it is to see through it,
I'm thinking it was an "Ian B." or so, if I don't recall,
something about "politics of identity" or "psychology of identity"
or along these lines, in the philosophy section though as about
psychology. If I recall it I'll note it here.
Anyways, we still need a word for "loves children".
Thanks for writing.
A parent loves their children, indeed. Or at least they should? Olcott,
might love them too much? Oh shit, there I go again.
On 04/09/2026 12:55 PM, Chris M. Thomasson wrote:
On 4/9/2026 10:14 AM, Ross Finlayson wrote:
On 04/09/2026 05:46 AM, Alan Mackenzie wrote:
In sci.math Chris M. Thomasson <chris.m.thomasson.1@gmail.com> wrote: >>>>> On 4/7/2026 12:46 PM, Alan Mackenzie wrote:
In comp.theory Chris M. Thomasson <chris.m.thomasson.1@gmail.com>
wrote:
[ .... ]
Why are seemingly trying to justify pedo's?
You're the sort of person who, 90 years ago in Europe, would be
asking
"why are you trying to justify Jews?".
Strange! pedo vs a person who is jewish?
I just don't believe you're dumb enough not to see the analogy. We're >>>> talking about two groups of people who aren't popular in popular
culture
(of whatever time), and bullies like you think that justifies them in
harrassing members of those groups with degrading epithets.
You used the term "low-life pedo" in this thread, implying that the
target of your nastiness was less than human. I suggest you reconsider >>>> all the implications, and then apologise publicly to Peter Olcott in
this thread.
Besides everything else, individuals' sexual psychology is not on topic >>>> in the newsgroups this thread is posted to.
"Otherism" as a usual account is sometimes demonizing specters and then
threatening sympathy with association, and furthermore threatening the
rejection of otherism as association with the demonized, besides the
wider accounts of "otherism" and "we-think" and "in-group" types of
pecking and the like, then furthermore is the association with "thought
police" and the like, here vis-a-vis "thought crimes" and "real crimes". >>> So, besides "un-popular", it's a gross bludgeon.
Let us recall the stories we'd tell youth, or give youth to discover,
the fable.
https://en.wikipedia.org/wiki/Fable
https://en.wikipedia.org/wiki/Aesop%27s_Fables#Select_fables
Now, plenty of these fables have consequences,
and some invoke a specter like "the boogey-man"
as variously threatens irresponsibility or the unwary,
or, punishes misbehavior, and even, when that
invoking the specter, invokes the specter.
https://en.wikipedia.org/wiki/The_Boy_Who_Cried_Wolf
The psycho-sexual in the psycho-logical, is an aspect
of thinking and feeling beings, largely biological.
Anyways children should be more concerned with if anybody
in their class likes them, not whether the world is full
of monsters, after them. (Nor that they'll become one.)
There is not a monster under the bed,
there is not a monster in the closet,
there is not a monster in the basement,
there is not a monster in the yard.
"The only thing to fear is fear itself."
"So, first of all, let me assert my firm belief that the only thing we
have to fear is fear itself — nameless, unreasoning, unjustified terror >>> which paralyzes needed efforts to convert retreat into advance." -- FDR
There is not a monster in your mind.
Then, basically it's insulting to make "ad hominem" fallacy.
I read a good book a few years ago about identity and including
a chapter on otherism, and how easy it is to see through it,
I'm thinking it was an "Ian B." or so, if I don't recall,
something about "politics of identity" or "psychology of identity"
or along these lines, in the philosophy section though as about
psychology. If I recall it I'll note it here.
Anyways, we still need a word for "loves children".
Thanks for writing.
A parent loves their children, indeed. Or at least they should? Olcott,
might love them too much? Oh shit, there I go again.
Try minding your own business and the old "innocent until proven
guilty", and not be sham "operant-conditioning" that is still
back on pigeons and dogs.
If your actual interests are "protecting the children", and everybody
else, from dangers real or imagined, how about investigating "ad-tech"
for billions of counts and counting of "luring", "corruption of a
minor", "child endangerment", and not even getting into slander and
libel, "identity theft", "computer crimes", and so on. The "ad-tech"
is not "social media", it's got no "safe harbor", and having
algorithm'ed itself it's poisoned itself and pierced its own veil.
Then, about what used to be "special services", these days with
the "surveillance tech" making it more like "secret stasis",
then that's also for busting surveillance tech. That and
busting all the "seals" covering all kinds of "mistakes".
Yes, let's protect the children by busting ad-tech and surveillance
tech. For example, they're liable for anything they know.
Sometimes: ignorance _is_ a defense.
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 >>>>>>>>>>>>>>> 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.
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
my wife just gave birth to a boy 6 hours ago, and i'm unsure of how to > protect him from that during his childhood 😕
On 4/9/2026 11:01 PM, dart200 wrote:
Why are seemingly trying to justify pedo's?
my wife just gave birth to a boy 6 hours ago, and i'm unsure of how to
protect him from that during his childhood 😕
Don't ever let him onto the internet. It's addictive. Case in point.
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 >>>>>>>>>>>>>>> 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.
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
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 >>>>>>>>>>>>>>>> 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.
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 ?
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: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.
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.
This simple little example tosses the whole Tarski
Undefinability theorem out on its ass.
The above is Olcott's Minimal Type Theory that
was intentionally designed to analyze a larger
body of expressions specifically for detecting
cycles in the directed graph of evaluation
sequence of input expressions. That is ALL that
the current MTT does.
It was created using YACC and LEX, it just parses
expressions into their directed graph.
On 4/9/26 5:43 PM, Ross Finlayson wrote:
On 04/09/2026 12:55 PM, Chris M. Thomasson wrote:
On 4/9/2026 10:14 AM, Ross Finlayson wrote:
On 04/09/2026 05:46 AM, Alan Mackenzie wrote:
In sci.math Chris M. Thomasson <chris.m.thomasson.1@gmail.com> wrote: >>>>>> On 4/7/2026 12:46 PM, Alan Mackenzie wrote:
In comp.theory Chris M. Thomasson <chris.m.thomasson.1@gmail.com> >>>>>>> wrote:
[ .... ]
Why are seemingly trying to justify pedo's?
You're the sort of person who, 90 years ago in Europe, would be >>>>>>> asking
"why are you trying to justify Jews?".
Strange! pedo vs a person who is jewish?
I just don't believe you're dumb enough not to see the analogy. We're >>>>> talking about two groups of people who aren't popular in popular
culture
(of whatever time), and bullies like you think that justifies them in >>>>> harrassing members of those groups with degrading epithets.
You used the term "low-life pedo" in this thread, implying that the
target of your nastiness was less than human. I suggest you
reconsider
all the implications, and then apologise publicly to Peter Olcott in >>>>> this thread.
Besides everything else, individuals' sexual psychology is not on
topic
in the newsgroups this thread is posted to.
"Otherism" as a usual account is sometimes demonizing specters and then >>>> threatening sympathy with association, and furthermore threatening the >>>> rejection of otherism as association with the demonized, besides the
wider accounts of "otherism" and "we-think" and "in-group" types of
pecking and the like, then furthermore is the association with "thought >>>> police" and the like, here vis-a-vis "thought crimes" and "real
crimes".
So, besides "un-popular", it's a gross bludgeon.
Let us recall the stories we'd tell youth, or give youth to discover,
the fable.
https://en.wikipedia.org/wiki/Fable
https://en.wikipedia.org/wiki/Aesop%27s_Fables#Select_fables
Now, plenty of these fables have consequences,
and some invoke a specter like "the boogey-man"
as variously threatens irresponsibility or the unwary,
or, punishes misbehavior, and even, when that
invoking the specter, invokes the specter.
https://en.wikipedia.org/wiki/The_Boy_Who_Cried_Wolf
The psycho-sexual in the psycho-logical, is an aspect
of thinking and feeling beings, largely biological.
Anyways children should be more concerned with if anybody
in their class likes them, not whether the world is full
of monsters, after them. (Nor that they'll become one.)
There is not a monster under the bed,
there is not a monster in the closet,
there is not a monster in the basement,
there is not a monster in the yard.
"The only thing to fear is fear itself."
"So, first of all, let me assert my firm belief that the only thing we >>>> have to fear is fear itself — nameless, unreasoning, unjustified terror >>>> which paralyzes needed efforts to convert retreat into advance." -- FDR >>>>
There is not a monster in your mind.
Then, basically it's insulting to make "ad hominem" fallacy.
I read a good book a few years ago about identity and including
a chapter on otherism, and how easy it is to see through it,
I'm thinking it was an "Ian B." or so, if I don't recall,
something about "politics of identity" or "psychology of identity"
or along these lines, in the philosophy section though as about
psychology. If I recall it I'll note it here.
Anyways, we still need a word for "loves children".
Thanks for writing.
A parent loves their children, indeed. Or at least they should? Olcott,
might love them too much? Oh shit, there I go again.
Try minding your own business and the old "innocent until proven
guilty", and not be sham "operant-conditioning" that is still
back on pigeons and dogs.
If your actual interests are "protecting the children", and everybody
else, from dangers real or imagined, how about investigating "ad-tech"
for billions of counts and counting of "luring", "corruption of a
minor", "child endangerment", and not even getting into slander and
libel, "identity theft", "computer crimes", and so on. The "ad-tech"
is not "social media", it's got no "safe harbor", and having
algorithm'ed itself it's poisoned itself and pierced its own veil.
Then, about what used to be "special services", these days with
the "surveillance tech" making it more like "secret stasis",
then that's also for busting surveillance tech. That and
busting all the "seals" covering all kinds of "mistakes".
Yes, let's protect the children by busting ad-tech and surveillance
tech. For example, they're liable for anything they know.
Sometimes: ignorance _is_ a defense.
idk if u've used the rest of the internet in the last decade or so,
but pedos are basically the ultimately boogieman that somehow sit below literal serial killers and mass murders on the social media hierarchy,
usenet (which i only joined last year) is the only place i've ever seen
any amount of nuance applied to subject, probably because censorship
doesn't really exist here, and therefore the discussion cannot be shaped
by the fear of people in charge
imo this is likely a reflection of an incredibly amount of systemic
sexual trauma we've received by how modern society represses sexuality during childhood, which i think is an appendage of how religion used to repress it, that somehow snuck it's way into secular society...
my wife just gave birth to a boy 6 hours ago, and i'm unsure of how to protect him from that during his childhood 😕
On 4/9/2026 11:01 PM, dart200 wrote:
Why are seemingly trying to justify pedo's?
my wife just gave birth to a boy 6 hours ago, and i'm unsure of how to
protect him from that during his childhood 😕
Don't ever let him onto the internet. It's addictive. Case in point.
On 4/10/2026 4:24 PM, Dude wrote:
On 4/9/2026 11:01 PM, dart200 wrote:
Why are seemingly trying to justify pedo's?
;Don't ever let him onto the internet. It's addictive. Case in point.
my wife just gave birth to a boy 6 hours ago, and i'm unsure of how
to > protect him from that during his childhood 😕
;
Scary. He has to be able to use the internet, but its the wild west
filled with predators. Sigh.
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: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.
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.
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: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.
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.
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: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.
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
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: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.
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.
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 >>>>>>>>>>>>>>>>>>>>> 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.
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.
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 >>>>>>>>>>>>>>>>>>>>> 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.
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.
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 >>>>>>>>>>>>>>>>>>>>> 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.
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.
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:My example was to merely prove that the Liar Paradox
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 >>>>>>>>>>>>>>>>>>>>>> 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.
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 ? >>>>>>
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.
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:My example was to merely prove that the Liar Paradox
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 >>>>>>>>>>>>>>>>>>>>>> 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.
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 ? >>>>>>
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.
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:My example was to merely prove that the Liar Paradox
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 >>>>>>>>>>>>>>>>>>>>>> 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.
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 ? >>>>>>
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.
PTS is irrelevant to GÖdel's incompleteness theorem, which is about
formal logic, not about PTS.
Whether there is something similar in
PTS is another problem.
Perhaps, if you would know more about PTS than just its name you might
be able to say something meaningful about it. Perhaps.
On 4/14/2026 12:59 AM, 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:My example was to merely prove that the Liar Paradox
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
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.
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 ? >>>>>>>
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.
PTS is irrelevant to GÖdel's incompleteness theorem, which is about
formal logic, not about PTS.
PTS replaces the foundation of model theory and this
changes everything.
On 4/14/2026 1:34 AM, 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:My example was to merely prove that the Liar Paradox
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
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.
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 ? >>>>>>>
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.
You keep arguing on the basis of ignorance of proof
theoretic semantics, like a kindergarten kid that
says I just don't believe in algebra.
On 14/04/2026 16:50, olcott wrote:
On 4/14/2026 12:59 AM, 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:My example was to merely prove that the Liar Paradox
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
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.
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 ? >>>>>>>>
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.
PTS is irrelevant to GÖdel's incompleteness theorem, which is about
formal logic, not about PTS.
PTS replaces the foundation of model theory and this
changes everything.
Only for PTS. It changes nothing for those who use model theory.
But both are irrelevant to the incompleteness theorem, which is
derived from logic and arithmetic with truth preserving inferences.
On 14/04/2026 16:45, olcott wrote:
On 4/14/2026 1:34 AM, 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:My example was to merely prove that the Liar Paradox
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
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.
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 ? >>>>>>>>
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.
You keep arguing on the basis of ignorance of proof
theoretic semantics, like a kindergarten kid that
says I just don't believe in algebra.
You are the one who is like a kindergarten kid that says "I just
don't believe in algebra". Instead of algebra, you just don't
believe in logic.
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.
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:My example was to merely prove that the Liar Paradox
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
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.
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 ? >>>>>>>
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.
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:My example was to merely prove that the Liar Paradox
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
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.
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 ? >>>>>>>>
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."
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:My example was to merely prove that the Liar Paradox
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
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.
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 ? >>>>>>>>>
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
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:My example was to merely prove that the Liar Paradox
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 >>>>>>>>>>>>>>>>>>>>>>>>>> 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.
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 ? >>>>>>>>>>
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".
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:My example was to merely prove that the Liar Paradox
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 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.
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 ? >>>>>>>>>>>
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.
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:My example was to merely prove that the Liar Paradox
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 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.
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 ? >>>>>>>>>>>>
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 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.
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".
So, math and logic have _infinity_ and _infinitary reasoning_,
they are _not_ going away.
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.
About "un-decide-ability", there's furthermore an even stronger
account of _independence_, the mathematical independence, since
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".
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.
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 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:My example was to merely prove that the Liar Paradox
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 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.
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 ? >>>>>>>>>>>>
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
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.
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".
So, math and logic have _infinity_ and _infinitary reasoning_,
they are _not_ going away.
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.
About "un-decide-ability", there's furthermore an even stronger
account of _independence_, the mathematical independence, since
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".
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.
On 04/15/2026 10:18 AM, olcott wrote:
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
That's mainly true. However, in como.lang.prolog >>>>>>>>>>>>>>>>>>>>>>>>> thefoundationalDo you think 100 years would be enough, or at >>>>>>>>>>>>>>>>>>>>>>>>>>>>> least
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>
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"
That's a usual account of "true" in common sense,
then though _all_ the mathematics and logic of
the infinite and infinitary bring _all_ their
matters of rigor resolving paradox for _any_
sorts formal accounts.
Or, "math is hard".
"True on the basis of meaning is true" is a sort
of coherent, pragmatist, correspondence definition
of truth, while though here there's always that
"is" is what "is" is.
Saying that a system is "whole" does not give that
it's "complete". Furthermore, matters of the
continuous and infinite must make for the "replete".
On 4/15/2026 12:33 PM, Ross Finlayson wrote:
On 04/15/2026 10:18 AM, olcott wrote:
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
That's mainly true. However, in como.lang.prolog >>>>>>>>>>>>>>>>>>>>>>>>>> thefoundationalDo you think 100 years would be enough, or at >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> least
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
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"
That's a usual account of "true" in common sense,
then though _all_ the mathematics and logic of
the infinite and infinitary bring _all_ their
matters of rigor resolving paradox for _any_
sorts formal accounts.
Or, "math is hard".
"True on the basis of meaning is true" is a sort
of coherent, pragmatist, correspondence definition
of truth, while though here there's always that
"is" is what "is" is.
It took me 27 years to come up with this bridge between coherence/correspondence analytic/synthetic unifying
them into on single exact and precise perspective.
"true on the basis of meaning expressed in language"
expressed in language
expressed in language
expressed in language
Saying that a system is "whole" does not give that
it's "complete". Furthermore, matters of the
continuous and infinite must make for the "replete".
every single detail of general knowledge
"EXPRESSED IN LANGUAGE" can be encoded in my system
thus as complete as complete can possibly be.
Much of this must be algorithmically compressed
to make it finite.
On 04/15/2026 10:43 AM, olcott wrote:
On 4/15/2026 12:33 PM, Ross Finlayson wrote:
On 04/15/2026 10:18 AM, olcott wrote:
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
That's mainly true. However, in como.lang.prolog >>>>>>>>>>>>>>>>>>>>>>>>>>> theI have to carefully study at least a dozen >>>>>>>>>>>>>>>>>>>>>>>>>>>>>> papersfoundationalDo you think 100 years would be enough, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or at
peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
least
some finite time? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
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"
That's a usual account of "true" in common sense,
then though _all_ the mathematics and logic of
the infinite and infinitary bring _all_ their
matters of rigor resolving paradox for _any_
sorts formal accounts.
Or, "math is hard".
"True on the basis of meaning is true" is a sort
of coherent, pragmatist, correspondence definition
of truth, while though here there's always that
"is" is what "is" is.
It took me 27 years to come up with this bridge between
coherence/correspondence analytic/synthetic unifying
them into on single exact and precise perspective.
"true on the basis of meaning expressed in language"
expressed in language
expressed in language
expressed in language
Saying that a system is "whole" does not give that
it's "complete". Furthermore, matters of the
continuous and infinite must make for the "replete".
every single detail of general knowledge
"EXPRESSED IN LANGUAGE" can be encoded in my system
thus as complete as complete can possibly be.
Much of this must be algorithmically compressed
to make it finite.
The use of the words "anchor" or "Goedelian anchor"
or any mention of "delve" or "crucial" and recently
enough "compression" sure sounds like a bot to me.
The compression has at least two kinds:
loss-less and loss-y.
"Methods of exhaustion" are _not_ the completions themselves,
and naive inductive accounts do _not_ complete themselves.
Making "claims" absent "proofs" isn't quite use-less,
though it is illogical.
Perhaps it would help if you posted all your ramblings
with your bot bros instead of just posting the same
snippet a hundreds times and since it's malformed
saying that it's profound.
On 4/15/2026 12:51 PM, Ross Finlayson wrote:
On 04/15/2026 10:43 AM, olcott wrote:
On 4/15/2026 12:33 PM, Ross Finlayson wrote:
On 04/15/2026 10:18 AM, olcott wrote:
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:It certainly does. You can't use
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
That's mainly true. However, in >>>>>>>>>>>>>>>>>>>>>>>>>>>> como.lang.prologI have to carefully study at least a dozen >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> papersfoundational >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> peer reviewed papers will take some time. >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>Do you think 100 years would be enough, >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> or at
least
some finite time? >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
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 >>>>>>>>>>>>>>>>>>>>>>>>>>>>
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. >>>>>>>>>>>>>>>>>>>>
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"
That's a usual account of "true" in common sense,
then though _all_ the mathematics and logic of
the infinite and infinitary bring _all_ their
matters of rigor resolving paradox for _any_
sorts formal accounts.
Or, "math is hard".
"True on the basis of meaning is true" is a sort
of coherent, pragmatist, correspondence definition
of truth, while though here there's always that
"is" is what "is" is.
It took me 27 years to come up with this bridge between
coherence/correspondence analytic/synthetic unifying
them into on single exact and precise perspective.
"true on the basis of meaning expressed in language"
expressed in language
expressed in language
expressed in language
Saying that a system is "whole" does not give that
it's "complete". Furthermore, matters of the
continuous and infinite must make for the "replete".
every single detail of general knowledge
"EXPRESSED IN LANGUAGE" can be encoded in my system
thus as complete as complete can possibly be.
Much of this must be algorithmically compressed
to make it finite.
The use of the words "anchor" or "Goedelian anchor"
or any mention of "delve" or "crucial" and recently
enough "compression" sure sounds like a bot to me.
The compression has at least two kinds:
loss-less and loss-y.
"Methods of exhaustion" are _not_ the completions themselves,
and naive inductive accounts do _not_ complete themselves.
Making "claims" absent "proofs" isn't quite use-less,
though it is illogical.
Perhaps it would help if you posted all your ramblings
with your bot bros instead of just posting the same
snippet a hundreds times and since it's malformed
saying that it's profound.
In other words you are merely another learned-by-rote
guy and find philosophical underpinnings to be complete
nonsense within your rote memorization of the conventional
view perspective.
On 4/15/2026 1:58 AM, Mikko wrote:
On 14/04/2026 16:50, olcott wrote:
On 4/14/2026 12:59 AM, 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:My example was to merely prove that the Liar Paradox
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
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.
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 ? >>>>>>>>>
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.
PTS is irrelevant to GÖdel's incompleteness theorem, which is about
formal logic, not about PTS.
PTS replaces the foundation of model theory and this
changes everything.
Only for PTS. It changes nothing for those who use model theory.
Likewise modern medicine changes nothing for
those with the evil spirit theory of disease.
On 4/15/2026 2:07 AM, Mikko wrote:
On 14/04/2026 16:45, olcott wrote:
On 4/14/2026 1:34 AM, 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:My example was to merely prove that the Liar Paradox
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
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.
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 ? >>>>>>>>>
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.
You keep arguing on the basis of ignorance of proof
theoretic semantics, like a kindergarten kid that
says I just don't believe in algebra.
You are the one who is like a kindergarten kid that says "I just
don't believe in algebra". Instead of algebra, you just don't
believe in logic.
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.
On 4/15/2026 1:58 AM, Mikko wrote:
On 14/04/2026 16:50, olcott wrote:
On 4/14/2026 12:59 AM, 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:My example was to merely prove that the Liar Paradox
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
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.
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 ? >>>>>>>>>
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.
PTS is irrelevant to GÖdel's incompleteness theorem, which is about
formal logic, not about PTS.
PTS replaces the foundation of model theory and this
changes everything.
Only for PTS. It changes nothing for those who use model theory.
Likewise modern medicine changes nothing for
those with the evil spirit theory of disease.
But both are irrelevant to the incompleteness theorem, which is
derived from logic and arithmetic with truth preserving inferences.
| Sysop: | DaiTengu |
|---|---|
| Location: | Appleton, WI |
| Users: | 1,113 |
| Nodes: | 10 (0 / 10) |
| Uptime: | 492335:43:58 |
| Calls: | 14,238 |
| Files: | 186,312 |
| D/L today: |
3,558 files (1,159M bytes) |
| Messages: | 2,514,865 |