From Newsgroup: comp.lang.prolog

On 12/5/2025 3:13 AM, Mikko wrote:

olcott kirjoitti 4.12.2025 klo 16.10:

On 12/4/2025 3:07 AM, Mikko wrote:

olcott kirjoitti 3.12.2025 klo 18.11:

On 12/3/2025 4:53 AM, Mikko wrote:

olcott kirjoitti 26.11.2025 klo 17.13:

On 11/26/2025 3:05 AM, Mikko wrote:

olcott kirjoitti 26.11.2025 klo 5.24:

On 11/25/2025 8:43 PM, Python wrote:

Le 26/11/2025 à 03:41, olcott a écrit :

On 11/25/2025 8:36 PM, André G. Isaak wrote:

On 2025-11-25 19:30, olcott wrote:

On 11/25/2025 8:12 PM, André G. Isaak wrote:

On 2025-11-25 19:08, olcott wrote:

On 11/25/2025 8:00 PM, André G. Isaak wrote:

On 2025-11-25 18:43, olcott wrote:

On 11/25/2025 7:29 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>> On 2025-11-25 17:52, olcott wrote:

On 11/25/2025 6:47 PM, Kaz Kylheku wrote: >>>>>>>>>>>>>>>>>>> On 2025-11-25, olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>> Gödel incompleteness can only exist in systems that >>>>>>>>>>>>>>>>>>>> divide

their syntax from their semantics ...

And, so, just confuse syntax for semantics, and all >>>>>>>>>>>>>>>>>>> is fixed!

Things such as Montague Grammar are outside of your >>>>>>>>>>>>>>>>>> current knowledge. It is called Montague Grammar >>>>>>>>>>>>>>>>>> because it encodes natural language semantics as pure >>>>>>>>>>>>>>>>>> syntax.

You're terribly confused here. Montague Grammar is >>>>>>>>>>>>>>>>> called 'Montague Grammar' because it is due to Richard >>>>>>>>>>>>>>>>> Montague.

Montague Grammar presents a theory of natural language >>>>>>>>>>>>>>>>> (specifically English) semantics expressed in terms of >>>>>>>>>>>>>>>>> logic. Formulae in his system have a syntax. They also >>>>>>>>>>>>>>>>> have a semantics. The two are very much distinct. >>>>>>>>>>>>>>>>>

Montague Grammar is the syntax of English semantics >>>>>>>>>>>>>>>

I can't even make sense of that. It's a *theory* of >>>>>>>>>>>>>>> English semantics.

*Here is a concrete example*
The predicate Bachelor(x) is stipulated to mean ~Married(x) >>>>>>>>>>>>>> where the predicate Married(x) is defined in terms of >>>>>>>>>>>>>> billions
of other things such as all of the details of Human(x). >>>>>>>>>>>>>

A concrete example of what? That's certainly not an example >>>>>>>>>>>>> of 'the syntax of English semantics'. That's simply a >>>>>>>>>>>>> stipulation involving two predicates.

André

It is one concrete example of how a knowledge ontology >>>>>>>>>>>> of trillions of predicates can define the finite set
of atomic facts of the world.

But the topic under discussion was the relationship between >>>>>>>>>>> syntax and semantics in Montague Grammar, not how knowledge >>>>>>>>>>> ontologies are represented. So this isn't an example in >>>>>>>>>>> anyway relevant to the discussion.

*Actually read this, this time*
Kurt Gödel in his 1944 Russell's mathematical logic gave the >>>>>>>>>>>> following definition of the "theory of simple types" in a >>>>>>>>>>>> footnote:

By the theory of simple types I mean the doctrine which says >>>>>>>>>>>> that the objects of thought (or, in another interpretation, >>>>>>>>>>>> the symbolic expressions) are divided into types, namely: >>>>>>>>>>>> individuals, properties of individuals, relations between >>>>>>>>>>>> individuals, properties of such relations

That is the basic infrastructure for defining all *objects >>>>>>>>>>>> of thought*
can be defined in terms of other *objects of thought*

I know full well what a theory of types is. It has nothing to >>>>>>>>>>> do with the relationship between syntax and semantics.

André

That particular theory of types lays out the infrastructure >>>>>>>>>> of how all *objects of thought* can be defined in terms
of other *objects of thought* such that the entire body
of knowledge that can be expressed in language can be encoded >>>>>>>>>> into a single coherent formal system.

Typing “objects of thought” doesn’t make all truths provable —
it only prevents ill-formed expressions.
If your system looks complete, it’s because you threw away >>>>>>>>> every sentence that would have made it incomplete.

When ALL *objects of thought* are defined
in terms of other *objects of thought* then
their truth and their proof is simply walking
the knowledge tree.

When ALL subjects of thoughts are defined
in terms of other subjects of thoughts then
there are no subjects of thoughts.

I am merely elaborating the structure of the
knowledge ontology inheritance hierarchy
tree of knowledge.

When ALL subjects of thoughts are defined in terms of other subjects >>>>> of thoughts the system of ALL subjects of thoughts is either empty
or not a hierarchy. There is no hierarchy where every member is under >>>>> another member.

*I have always been referring to the entire body of general knowledge*

Your condition that ALL objects of thought can be defined in terms of
other objects of thought is false about every non-empyt collection of
objects of thjought, inluding the entire body of general knowledge,
unless your system allows circular definitions that actually don't
define.

Yes circular definitions can be defined syntactically
and are rejected as semantically unsound.

The usual way is to rehject them as syntactically invalid.

Even this simplified version has the same pathological self-reference
(G) F ⊢ GF ↔ ¬ProvF(┌GF┐). https://plato.stanford.edu/entries/goedel-incompleteness/#FirIncTheCom

People incorrectly construe this as non-circular
because of the convoluted mess of calculating Gödel numbers.
The above expression abstracts away this convoluted mess.

If you accept circular definitions as syntactically correct even if semantically unsound

That would be quite nuts

the you can have a nonempty collection of unsound
objects of thought so that ALL objects of thought in that collection
are defined (circularly) in terms of other objects of thought. But
every object of thought defined in terms of an unsound object of
thought is also unsound.

% This sentence is not true.

You mean the one on the foloowing line?

?- LP = not(true(LP)).
LP = not(true(LP)).

The answer by the Prolog system means that it is true according to
the Prolog rules.

When you dishonestly erase the most important
part then it might seem that way to stupid people.

% 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 false means that LP = not(true(LP)).
is semantically unsound.

Colorless green ideas sleep furiously was composed
by Noam Chomsky in his 1957 book Syntactic Structures
as an example of a sentence that is grammatically
well-formed, but semantically nonsensical. https://en.wikipedia.org/wiki/Colorless_green_ideas_sleep_furiously

One of the most brilliant guys on formal languages clearly
proves that it is the semantics that counts.
--
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.lang.prolog

olcott kirjoitti 5.12.2025 klo 19.40:

On 12/5/2025 3:13 AM, Mikko wrote:

olcott kirjoitti 4.12.2025 klo 16.10:

On 12/4/2025 3:07 AM, Mikko wrote:

olcott kirjoitti 3.12.2025 klo 18.11:

On 12/3/2025 4:53 AM, Mikko wrote:

olcott kirjoitti 26.11.2025 klo 17.13:

On 11/26/2025 3:05 AM, Mikko wrote:

olcott kirjoitti 26.11.2025 klo 5.24:

On 11/25/2025 8:43 PM, Python wrote:

Le 26/11/2025 à 03:41, olcott a écrit :

On 11/25/2025 8:36 PM, André G. Isaak wrote:

On 2025-11-25 19:30, olcott wrote:

On 11/25/2025 8:12 PM, André G. Isaak wrote:

On 2025-11-25 19:08, olcott wrote:

On 11/25/2025 8:00 PM, André G. Isaak wrote:

On 2025-11-25 18:43, olcott wrote:

On 11/25/2025 7:29 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>> On 2025-11-25 17:52, olcott wrote:

On 11/25/2025 6:47 PM, Kaz Kylheku wrote: >>>>>>>>>>>>>>>>>>>> On 2025-11-25, olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>> Gödel incompleteness can only exist in systems that >>>>>>>>>>>>>>>>>>>>> divide

their syntax from their semantics ... >>>>>>>>>>>>>>>>>>>>

And, so, just confuse syntax for semantics, and all >>>>>>>>>>>>>>>>>>>> is fixed!

Things such as Montague Grammar are outside of your >>>>>>>>>>>>>>>>>>> current knowledge. It is called Montague Grammar >>>>>>>>>>>>>>>>>>> because it encodes natural language semantics as pure >>>>>>>>>>>>>>>>>>> syntax.

You're terribly confused here. Montague Grammar is >>>>>>>>>>>>>>>>>> called 'Montague Grammar' because it is due to Richard >>>>>>>>>>>>>>>>>> Montague.

Montague Grammar presents a theory of natural language >>>>>>>>>>>>>>>>>> (specifically English) semantics expressed in terms of >>>>>>>>>>>>>>>>>> logic. Formulae in his system have a syntax. They also >>>>>>>>>>>>>>>>>> have a semantics. The two are very much distinct. >>>>>>>>>>>>>>>>>>

Montague Grammar is the syntax of English semantics >>>>>>>>>>>>>>>>

I can't even make sense of that. It's a *theory* of >>>>>>>>>>>>>>>> English semantics.

*Here is a concrete example*
The predicate Bachelor(x) is stipulated to mean ~Married(x) >>>>>>>>>>>>>>> where the predicate Married(x) is defined in terms of >>>>>>>>>>>>>>> billions
of other things such as all of the details of Human(x). >>>>>>>>>>>>>>

A concrete example of what? That's certainly not an >>>>>>>>>>>>>> example of 'the syntax of English semantics'. That's >>>>>>>>>>>>>> simply a stipulation involving two predicates.

André

It is one concrete example of how a knowledge ontology >>>>>>>>>>>>> of trillions of predicates can define the finite set >>>>>>>>>>>>> of atomic facts of the world.

But the topic under discussion was the relationship between >>>>>>>>>>>> syntax and semantics in Montague Grammar, not how knowledge >>>>>>>>>>>> ontologies are represented. So this isn't an example in >>>>>>>>>>>> anyway relevant to the discussion.

*Actually read this, this time*
Kurt Gödel in his 1944 Russell's mathematical logic gave >>>>>>>>>>>>> the following definition of the "theory of simple types" in >>>>>>>>>>>>> a footnote:

By the theory of simple types I mean the doctrine which >>>>>>>>>>>>> says that the objects of thought (or, in another
interpretation, the symbolic expressions) are divided into >>>>>>>>>>>>> types, namely: individuals, properties of individuals, >>>>>>>>>>>>> relations between individuals, properties of such relations >>>>>>>>>>>>>
That is the basic infrastructure for defining all *objects >>>>>>>>>>>>> of thought*
can be defined in terms of other *objects of thought* >>>>>>>>>>>>

I know full well what a theory of types is. It has nothing >>>>>>>>>>>> to do with the relationship between syntax and semantics. >>>>>>>>>>>>
André

That particular theory of types lays out the infrastructure >>>>>>>>>>> of how all *objects of thought* can be defined in terms
of other *objects of thought* such that the entire body
of knowledge that can be expressed in language can be encoded >>>>>>>>>>> into a single coherent formal system.

Typing “objects of thought” doesn’t make all truths provable —
it only prevents ill-formed expressions.
If your system looks complete, it’s because you threw away >>>>>>>>>> every sentence that would have made it incomplete.

When ALL *objects of thought* are defined
in terms of other *objects of thought* then
their truth and their proof is simply walking
the knowledge tree.

When ALL subjects of thoughts are defined
in terms of other subjects of thoughts then
there are no subjects of thoughts.

I am merely elaborating the structure of the
knowledge ontology inheritance hierarchy
tree of knowledge.

When ALL subjects of thoughts are defined in terms of other subjects >>>>>> of thoughts the system of ALL subjects of thoughts is either empty >>>>>> or not a hierarchy. There is no hierarchy where every member is under >>>>>> another member.

*I have always been referring to the entire body of general knowledge* >>>>

Your condition that ALL objects of thought can be defined in terms of
other objects of thought is false about every non-empyt collection of
objects of thjought, inluding the entire body of general knowledge,
unless your system allows circular definitions that actually don't
define.

Yes circular definitions can be defined syntactically
and are rejected as semantically unsound.

The usual way is to rehject them as syntactically invalid.

Even this simplified version has the same pathological self-reference
(G) F ⊢ GF ↔ ¬ProvF(┌GF┐).

There is no self reference there. F is a formal system. A formal system
is not a reference. GF is an uninterpreted sentence in the language of
F that is constructed earlier. Because it is uninterpreted it cannot
refer. ProvF is the provability predicate that the caunter-assumption
assumes to exist. ┌GF┐ is the Gödel number of GF. A number does not
refer.
--
Mikko
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.lang.prolog

On 12/6/2025 3:19 AM, Mikko wrote:

olcott kirjoitti 5.12.2025 klo 19.40:

On 12/5/2025 3:13 AM, Mikko wrote:

olcott kirjoitti 4.12.2025 klo 16.10:

On 12/4/2025 3:07 AM, Mikko wrote:

olcott kirjoitti 3.12.2025 klo 18.11:

On 12/3/2025 4:53 AM, Mikko wrote:

olcott kirjoitti 26.11.2025 klo 17.13:

On 11/26/2025 3:05 AM, Mikko wrote:

olcott kirjoitti 26.11.2025 klo 5.24:

On 11/25/2025 8:43 PM, Python wrote:

Le 26/11/2025 à 03:41, olcott a écrit :

On 11/25/2025 8:36 PM, André G. Isaak wrote:

On 2025-11-25 19:30, olcott wrote:

On 11/25/2025 8:12 PM, André G. Isaak wrote:

On 2025-11-25 19:08, olcott wrote:

On 11/25/2025 8:00 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>> On 2025-11-25 18:43, olcott wrote:

On 11/25/2025 7:29 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>> On 2025-11-25 17:52, olcott wrote:

On 11/25/2025 6:47 PM, Kaz Kylheku wrote: >>>>>>>>>>>>>>>>>>>>> On 2025-11-25, olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>> Gödel incompleteness can only exist in systems >>>>>>>>>>>>>>>>>>>>>> that divide

their syntax from their semantics ... >>>>>>>>>>>>>>>>>>>>>

And, so, just confuse syntax for semantics, and all >>>>>>>>>>>>>>>>>>>>> is fixed!

Things such as Montague Grammar are outside of your >>>>>>>>>>>>>>>>>>>> current knowledge. It is called Montague Grammar >>>>>>>>>>>>>>>>>>>> because it encodes natural language semantics as pure >>>>>>>>>>>>>>>>>>>> syntax.

You're terribly confused here. Montague Grammar is >>>>>>>>>>>>>>>>>>> called 'Montague Grammar' because it is due to >>>>>>>>>>>>>>>>>>> Richard Montague.

Montague Grammar presents a theory of natural >>>>>>>>>>>>>>>>>>> language (specifically English) semantics expressed >>>>>>>>>>>>>>>>>>> in terms of logic. Formulae in his system have a >>>>>>>>>>>>>>>>>>> syntax. They also have a semantics. The two are very >>>>>>>>>>>>>>>>>>> much distinct.

Montague Grammar is the syntax of English semantics >>>>>>>>>>>>>>>>>

I can't even make sense of that. It's a *theory* of >>>>>>>>>>>>>>>>> English semantics.

*Here is a concrete example*
The predicate Bachelor(x) is stipulated to mean ~Married(x) >>>>>>>>>>>>>>>> where the predicate Married(x) is defined in terms of >>>>>>>>>>>>>>>> billions
of other things such as all of the details of Human(x). >>>>>>>>>>>>>>>

A concrete example of what? That's certainly not an >>>>>>>>>>>>>>> example of 'the syntax of English semantics'. That's >>>>>>>>>>>>>>> simply a stipulation involving two predicates.

André

It is one concrete example of how a knowledge ontology >>>>>>>>>>>>>> of trillions of predicates can define the finite set >>>>>>>>>>>>>> of atomic facts of the world.

But the topic under discussion was the relationship between >>>>>>>>>>>>> syntax and semantics in Montague Grammar, not how knowledge >>>>>>>>>>>>> ontologies are represented. So this isn't an example in >>>>>>>>>>>>> anyway relevant to the discussion.

*Actually read this, this time*
Kurt Gödel in his 1944 Russell's mathematical logic gave >>>>>>>>>>>>>> the following definition of the "theory of simple types" >>>>>>>>>>>>>> in a footnote:

By the theory of simple types I mean the doctrine which >>>>>>>>>>>>>> says that the objects of thought (or, in another
interpretation, the symbolic expressions) are divided into >>>>>>>>>>>>>> types, namely: individuals, properties of individuals, >>>>>>>>>>>>>> relations between individuals, properties of such relations >>>>>>>>>>>>>>
That is the basic infrastructure for defining all *objects >>>>>>>>>>>>>> of thought*
can be defined in terms of other *objects of thought* >>>>>>>>>>>>>

I know full well what a theory of types is. It has nothing >>>>>>>>>>>>> to do with the relationship between syntax and semantics. >>>>>>>>>>>>>
André

That particular theory of types lays out the infrastructure >>>>>>>>>>>> of how all *objects of thought* can be defined in terms >>>>>>>>>>>> of other *objects of thought* such that the entire body >>>>>>>>>>>> of knowledge that can be expressed in language can be encoded >>>>>>>>>>>> into a single coherent formal system.

Typing “objects of thought” doesn’t make all truths provable >>>>>>>>>>> — it only prevents ill-formed expressions.
If your system looks complete, it’s because you threw away >>>>>>>>>>> every sentence that would have made it incomplete.

When ALL *objects of thought* are defined
in terms of other *objects of thought* then
their truth and their proof is simply walking
the knowledge tree.

When ALL subjects of thoughts are defined
in terms of other subjects of thoughts then
there are no subjects of thoughts.

I am merely elaborating the structure of the
knowledge ontology inheritance hierarchy
tree of knowledge.

When ALL subjects of thoughts are defined in terms of other subjects >>>>>>> of thoughts the system of ALL subjects of thoughts is either empty >>>>>>> or not a hierarchy. There is no hierarchy where every member is >>>>>>> under
another member.

*I have always been referring to the entire body of general
knowledge*

Your condition that ALL objects of thought can be defined in terms of >>>>> other objects of thought is false about every non-empyt collection of >>>>> objects of thjought, inluding the entire body of general knowledge,
unless your system allows circular definitions that actually don't
define.

Yes circular definitions can be defined syntactically
and are rejected as semantically unsound.

The usual way is to rehject them as syntactically invalid.

Even this simplified version has the same pathological self-reference
(G) F ⊢ GF ↔ ¬ProvF(┌GF┐).

There is no self reference there. F is a formal system. A formal system
is not a reference. GF is an uninterpreted sentence in the language of
F that is constructed earlier. Because it is uninterpreted it cannot
refer. ProvF is the provability predicate that the caunter-assumption
assumes to exist. ┌GF┐ is the Gödel number of GF. A number does not refer.

...We are therefore confronted with a proposition which asserts its own unprovability. 15 … (Gödel 1931:40-41)

Gödel, Kurt 1931.
On Formally Undecidable Propositions of Principia Mathematica And
Related Systems

He says there is and the above expression fails the
unify_with_occurs_check. That you don't understand
what this means is not a rebuttal.

% 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.
--
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.lang.prolog

olcott kirjoitti 6.12.2025 klo 14.45:

On 12/6/2025 3:19 AM, Mikko wrote:

olcott kirjoitti 5.12.2025 klo 19.40:

On 12/5/2025 3:13 AM, Mikko wrote:

olcott kirjoitti 4.12.2025 klo 16.10:

On 12/4/2025 3:07 AM, Mikko wrote:

olcott kirjoitti 3.12.2025 klo 18.11:

On 12/3/2025 4:53 AM, Mikko wrote:

olcott kirjoitti 26.11.2025 klo 17.13:

On 11/26/2025 3:05 AM, Mikko wrote:

olcott kirjoitti 26.11.2025 klo 5.24:

On 11/25/2025 8:43 PM, Python wrote:

Le 26/11/2025 à 03:41, olcott a écrit :

On 11/25/2025 8:36 PM, André G. Isaak wrote:

On 2025-11-25 19:30, olcott wrote:

On 11/25/2025 8:12 PM, André G. Isaak wrote:

On 2025-11-25 19:08, olcott wrote:

On 11/25/2025 8:00 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>> On 2025-11-25 18:43, olcott wrote:

On 11/25/2025 7:29 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>> On 2025-11-25 17:52, olcott wrote:

On 11/25/2025 6:47 PM, Kaz Kylheku wrote: >>>>>>>>>>>>>>>>>>>>>> On 2025-11-25, olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>> Gödel incompleteness can only exist in systems >>>>>>>>>>>>>>>>>>>>>>> that divide

their syntax from their semantics ... >>>>>>>>>>>>>>>>>>>>>>

And, so, just confuse syntax for semantics, and >>>>>>>>>>>>>>>>>>>>>> all is fixed!

Things such as Montague Grammar are outside of your >>>>>>>>>>>>>>>>>>>>> current knowledge. It is called Montague Grammar >>>>>>>>>>>>>>>>>>>>> because it encodes natural language semantics as pure >>>>>>>>>>>>>>>>>>>>> syntax.

You're terribly confused here. Montague Grammar is >>>>>>>>>>>>>>>>>>>> called 'Montague Grammar' because it is due to >>>>>>>>>>>>>>>>>>>> Richard Montague.

Montague Grammar presents a theory of natural >>>>>>>>>>>>>>>>>>>> language (specifically English) semantics expressed >>>>>>>>>>>>>>>>>>>> in terms of logic. Formulae in his system have a >>>>>>>>>>>>>>>>>>>> syntax. They also have a semantics. The two are very >>>>>>>>>>>>>>>>>>>> much distinct.

Montague Grammar is the syntax of English semantics >>>>>>>>>>>>>>>>>>

I can't even make sense of that. It's a *theory* of >>>>>>>>>>>>>>>>>> English semantics.

*Here is a concrete example*
The predicate Bachelor(x) is stipulated to mean >>>>>>>>>>>>>>>>> ~Married(x)
where the predicate Married(x) is defined in terms of >>>>>>>>>>>>>>>>> billions
of other things such as all of the details of Human(x). >>>>>>>>>>>>>>>>

A concrete example of what? That's certainly not an >>>>>>>>>>>>>>>> example of 'the syntax of English semantics'. That's >>>>>>>>>>>>>>>> simply a stipulation involving two predicates. >>>>>>>>>>>>>>>>
André

It is one concrete example of how a knowledge ontology >>>>>>>>>>>>>>> of trillions of predicates can define the finite set >>>>>>>>>>>>>>> of atomic facts of the world.

But the topic under discussion was the relationship >>>>>>>>>>>>>> between syntax and semantics in Montague Grammar, not how >>>>>>>>>>>>>> knowledge ontologies are represented. So this isn't an >>>>>>>>>>>>>> example in anyway relevant to the discussion.

*Actually read this, this time*
Kurt Gödel in his 1944 Russell's mathematical logic gave >>>>>>>>>>>>>>> the following definition of the "theory of simple types" >>>>>>>>>>>>>>> in a footnote:

By the theory of simple types I mean the doctrine which >>>>>>>>>>>>>>> says that the objects of thought (or, in another >>>>>>>>>>>>>>> interpretation, the symbolic expressions) are divided >>>>>>>>>>>>>>> into types, namely: individuals, properties of
individuals, relations between individuals, properties of >>>>>>>>>>>>>>> such relations

That is the basic infrastructure for defining all >>>>>>>>>>>>>>> *objects of thought*
can be defined in terms of other *objects of thought* >>>>>>>>>>>>>>

I know full well what a theory of types is. It has nothing >>>>>>>>>>>>>> to do with the relationship between syntax and semantics. >>>>>>>>>>>>>>
André

That particular theory of types lays out the infrastructure >>>>>>>>>>>>> of how all *objects of thought* can be defined in terms >>>>>>>>>>>>> of other *objects of thought* such that the entire body >>>>>>>>>>>>> of knowledge that can be expressed in language can be encoded >>>>>>>>>>>>> into a single coherent formal system.

Typing “objects of thought” doesn’t make all truths provable
— it only prevents ill-formed expressions.
If your system looks complete, it’s because you threw away >>>>>>>>>>>> every sentence that would have made it incomplete.

When ALL *objects of thought* are defined
in terms of other *objects of thought* then
their truth and their proof is simply walking
the knowledge tree.

When ALL subjects of thoughts are defined
in terms of other subjects of thoughts then
there are no subjects of thoughts.

I am merely elaborating the structure of the
knowledge ontology inheritance hierarchy
tree of knowledge.

When ALL subjects of thoughts are defined in terms of other
subjects
of thoughts the system of ALL subjects of thoughts is either empty >>>>>>>> or not a hierarchy. There is no hierarchy where every member is >>>>>>>> under
another member.

*I have always been referring to the entire body of general
knowledge*

Your condition that ALL objects of thought can be defined in terms of >>>>>> other objects of thought is false about every non-empyt collection of >>>>>> objects of thjought, inluding the entire body of general knowledge, >>>>>> unless your system allows circular definitions that actually don't >>>>>> define.

Yes circular definitions can be defined syntactically
and are rejected as semantically unsound.

The usual way is to rehject them as syntactically invalid.

Even this simplified version has the same pathological self-reference
(G) F ⊢ GF ↔ ¬ProvF(┌GF┐).

There is no self reference there. F is a formal system. A formal system
is not a reference. GF is an uninterpreted sentence in the language of
F that is constructed earlier. Because it is uninterpreted it cannot
refer. ProvF is the provability predicate that the caunter-assumption
assumes to exist. ┌GF┐ is the Gödel number of GF. A number does not
refer.

...We are therefore confronted with a proposition which asserts its own unprovability. 15 … (Gödel 1931:40-41)

Here Gödel refers to a non-arithmetic interpretation of an arithmetic sentence. But there is no self-reference in the arithmetic meaning
of the sentence.
--
Mikko
--- Synchronet 3.21a-Linux NewsLink 1.2

From Newsgroup: comp.lang.prolog

On 12/7/2025 4:55 AM, Mikko wrote:

olcott kirjoitti 6.12.2025 klo 14.45:

On 12/6/2025 3:19 AM, Mikko wrote:

olcott kirjoitti 5.12.2025 klo 19.40:

On 12/5/2025 3:13 AM, Mikko wrote:

olcott kirjoitti 4.12.2025 klo 16.10:

On 12/4/2025 3:07 AM, Mikko wrote:

olcott kirjoitti 3.12.2025 klo 18.11:

On 12/3/2025 4:53 AM, Mikko wrote:

olcott kirjoitti 26.11.2025 klo 17.13:

On 11/26/2025 3:05 AM, Mikko wrote:

olcott kirjoitti 26.11.2025 klo 5.24:

On 11/25/2025 8:43 PM, Python wrote:

Le 26/11/2025 à 03:41, olcott a écrit :

On 11/25/2025 8:36 PM, André G. Isaak wrote:

On 2025-11-25 19:30, olcott wrote:

On 11/25/2025 8:12 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>> On 2025-11-25 19:08, olcott wrote:

On 11/25/2025 8:00 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>> On 2025-11-25 18:43, olcott wrote:

On 11/25/2025 7:29 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>> On 2025-11-25 17:52, olcott wrote:

On 11/25/2025 6:47 PM, Kaz Kylheku wrote: >>>>>>>>>>>>>>>>>>>>>>> On 2025-11-25, olcott <polcott333@gmail.com> wrote: >>>>>>>>>>>>>>>>>>>>>>>> Gödel incompleteness can only exist in systems >>>>>>>>>>>>>>>>>>>>>>>> that divide

their syntax from their semantics ... >>>>>>>>>>>>>>>>>>>>>>>

And, so, just confuse syntax for semantics, and >>>>>>>>>>>>>>>>>>>>>>> all is fixed!

Things such as Montague Grammar are outside of your >>>>>>>>>>>>>>>>>>>>>> current knowledge. It is called Montague Grammar >>>>>>>>>>>>>>>>>>>>>> because it encodes natural language semantics as pure >>>>>>>>>>>>>>>>>>>>>> syntax.

You're terribly confused here. Montague Grammar is >>>>>>>>>>>>>>>>>>>>> called 'Montague Grammar' because it is due to >>>>>>>>>>>>>>>>>>>>> Richard Montague.

Montague Grammar presents a theory of natural >>>>>>>>>>>>>>>>>>>>> language (specifically English) semantics expressed >>>>>>>>>>>>>>>>>>>>> in terms of logic. Formulae in his system have a >>>>>>>>>>>>>>>>>>>>> syntax. They also have a semantics. The two are >>>>>>>>>>>>>>>>>>>>> very much distinct.

Montague Grammar is the syntax of English semantics >>>>>>>>>>>>>>>>>>>

I can't even make sense of that. It's a *theory* of >>>>>>>>>>>>>>>>>>> English semantics.

*Here is a concrete example*
The predicate Bachelor(x) is stipulated to mean >>>>>>>>>>>>>>>>>> ~Married(x)
where the predicate Married(x) is defined in terms of >>>>>>>>>>>>>>>>>> billions
of other things such as all of the details of Human(x). >>>>>>>>>>>>>>>>>

A concrete example of what? That's certainly not an >>>>>>>>>>>>>>>>> example of 'the syntax of English semantics'. That's >>>>>>>>>>>>>>>>> simply a stipulation involving two predicates. >>>>>>>>>>>>>>>>>
André

It is one concrete example of how a knowledge ontology >>>>>>>>>>>>>>>> of trillions of predicates can define the finite set >>>>>>>>>>>>>>>> of atomic facts of the world.

But the topic under discussion was the relationship >>>>>>>>>>>>>>> between syntax and semantics in Montague Grammar, not how >>>>>>>>>>>>>>> knowledge ontologies are represented. So this isn't an >>>>>>>>>>>>>>> example in anyway relevant to the discussion.

*Actually read this, this time*
Kurt Gödel in his 1944 Russell's mathematical logic gave >>>>>>>>>>>>>>>> the following definition of the "theory of simple types" >>>>>>>>>>>>>>>> in a footnote:

By the theory of simple types I mean the doctrine which >>>>>>>>>>>>>>>> says that the objects of thought (or, in another >>>>>>>>>>>>>>>> interpretation, the symbolic expressions) are divided >>>>>>>>>>>>>>>> into types, namely: individuals, properties of >>>>>>>>>>>>>>>> individuals, relations between individuals, properties >>>>>>>>>>>>>>>> of such relations

That is the basic infrastructure for defining all >>>>>>>>>>>>>>>> *objects of thought*
can be defined in terms of other *objects of thought* >>>>>>>>>>>>>>>

I know full well what a theory of types is. It has >>>>>>>>>>>>>>> nothing to do with the relationship between syntax and >>>>>>>>>>>>>>> semantics.

André

That particular theory of types lays out the infrastructure >>>>>>>>>>>>>> of how all *objects of thought* can be defined in terms >>>>>>>>>>>>>> of other *objects of thought* such that the entire body >>>>>>>>>>>>>> of knowledge that can be expressed in language can be encoded >>>>>>>>>>>>>> into a single coherent formal system.

Typing “objects of thought” doesn’t make all truths >>>>>>>>>>>>> provable — it only prevents ill-formed expressions. >>>>>>>>>>>>> If your system looks complete, it’s because you threw away >>>>>>>>>>>>> every sentence that would have made it incomplete.

When ALL *objects of thought* are defined
in terms of other *objects of thought* then
their truth and their proof is simply walking
the knowledge tree.

When ALL subjects of thoughts are defined
in terms of other subjects of thoughts then
there are no subjects of thoughts.

I am merely elaborating the structure of the
knowledge ontology inheritance hierarchy
tree of knowledge.

When ALL subjects of thoughts are defined in terms of other >>>>>>>>> subjects
of thoughts the system of ALL subjects of thoughts is either empty >>>>>>>>> or not a hierarchy. There is no hierarchy where every member is >>>>>>>>> under
another member.

*I have always been referring to the entire body of general
knowledge*

Your condition that ALL objects of thought can be defined in
terms of
other objects of thought is false about every non-empyt
collection of
objects of thjought, inluding the entire body of general knowledge, >>>>>>> unless your system allows circular definitions that actually don't >>>>>>> define.

Yes circular definitions can be defined syntactically
and are rejected as semantically unsound.

The usual way is to rehject them as syntactically invalid.

Even this simplified version has the same pathological self-reference
(G) F ⊢ GF ↔ ¬ProvF(┌GF┐).

There is no self reference there. F is a formal system. A formal system
is not a reference. GF is an uninterpreted sentence in the language of
F that is constructed earlier. Because it is uninterpreted it cannot
refer. ProvF is the provability predicate that the caunter-assumption
assumes to exist. ┌GF┐ is the Gödel number of GF. A number does not >>> refer.

...We are therefore confronted with a proposition which asserts its
own unprovability. 15 … (Gödel 1931:40-41)

Here Gödel refers to a non-arithmetic interpretation of an arithmetic sentence. But there is no self-reference in the arithmetic meaning
of the sentence.

(G) F ⊢ GF ↔ ¬ProvF(┌GF┐).
The arithmetic can simply be represented
Gödel_Number_of(GF) still showing pathological
self reference(Olcott 2004) that cannot be
resolved to a truth value.
--
Copyright 2025 Olcott<br><br>

My 28 year goal has been to make <br>
"true on the basis of meaning" computable.<br><br>

This required establishing a new foundation<br>
--- Synchronet 3.21a-Linux NewsLink 1.2