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.
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.
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*
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:A concrete example of what? That's certainly not an example >>>>>>>>>>> of 'the syntax of English semantics'. That's simply a
On 2025-11-25 18:43, olcott wrote:
On 11/25/2025 7:29 PM, André G. Isaak wrote:I can't even make sense of that. It's a *theory* of English >>>>>>>>>>>>> semantics.
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 >>>>>>>>>>>>>
*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). >>>>>>>>>>>
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.
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: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.
On 2025-11-25 18:43, olcott wrote:
On 11/25/2025 7:29 PM, André G. Isaak wrote:I can't even make sense of that. It's a *theory* of >>>>>>>>>>>>>> English semantics.
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 >>>>>>>>>>>>>>
*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). >>>>>>>>>>>>
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.
% This sentence is not true.
?- LP = not(true(LP)).
LP = not(true(LP)).
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: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.
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:I can't even make sense of that. It's a *theory* of >>>>>>>>>>>>>>> English semantics.
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 >>>>>>>>>>>>>>>
*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). >>>>>>>>>>>>>
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.
If you accept circular definitions as syntactically correct even if semantically unsound
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.
Le 26/11/2025 à 03:34, olcott a écrit :
On 11/25/2025 8:09 PM, Python wrote:
Le 26/11/2025 à 03:03, olcott a écrit :
On 11/25/2025 7:45 PM, Python wrote:
Le 26/11/2025 à 02:43, olcott a écrit :
Montague Grammar is the syntax of English semantics
that is why he called it Montague Grammar. This is
all anchored in Rudolf Carnap meaning postulates
Peter, Montague Grammar does not make truth = provability.
It maps English into logic — it does not turn logic into a magic
incompleteness-proof shredder.
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).
Two Dogmas of Empiricism by Willard Van Orman had no idea
how we know that Bachelors are unmarried. Basically we
just look it up in the type hierarchy, that is the simple
proof of its truth.
If your claim were right, every linguist using Montague’s system
would have accidentally solved Godel’s theorem in the 1970s.
They didn’t.
I spoke with many people very interested in linguistics
on sci.lang for many years. Even ordinary semantics
freaks them out.
None of them ever had the slightest clue about Montague
Grammar. Except for one they all had very severe math
phobia. Formal semantics got them very aggravated.
Because encoding semantics as syntax does not erase diagonalization >>>>> — it just gives it nicer types.
G ↔ ¬Prov(⌜G⌝)
Directed Graph of evaluation sequence
00 ↔ 01 02
01 G
02 ¬ 03
03 Prov 04
04 Gödel_Number_of 01 // cycle
Proves that the evaluation of the above G is stuck
in an infinite loop whether you understand this or not.
Montague built a translation function.
You’re treating it like a trapdoor that makes unprovable truths
disappear.
It doesn’t.
Only your theory does that.
When True(L,x) is exactly one and the same thing as
Provable(L,x) then if you are honest you will admit
that they cannot possibly diverge thus within this
system Gödel incompleteness cannot possibly exist.
Seeing how this makes perfect sense and is absolutely
not any sort of ruse may take much more dialogue.
Réponse proposée (courte, mordante, ASCII-safe)
Peter, you keep repeating the same pattern:
Because you utterly refuse to pay enough attention.
Take a normal semantic fact (like bachelor = unmarried).
Declare that because some meanings can be defined, all meaning
reduces to proof.
All *objects of thought* can be defined in terms of other
*objects of thought*
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, etc.
Then insist that since in your system True = Provable by definition,
Godel “cannot possibly exist.”
But that is not a refutation — that is simply renaming the problem
out of existence.
Your “directed graph infinite loop” does not show an error in Godel; >>> it shows that Prolog refuses cyclic terms.
Mathematics does not.
That you fail to understand that it conclusively
proves that the expression is semantically
unsound is your ignorance on not my mistake.
Peter, your entire argument now rests on one mistake:
You think that a self-referential fixed point is “semantically unsound” because Prolog refuses to unify a cyclic term.
But Prolog’s occurs-check does not detect “semantic unsoundness.”
It detects infinite data structures in Prolog.
Mathematics is not Prolog.
Lambda calculus allows fixed points.
Type theory allows fixed points.
Arithmetic allows fixed points.
Diagonalization is a fixed point.
G <-> not Prov(F,G)
cycle -> therefore invalid
My calculator overflows on 10^100
therefore big integers are semantically unsound.
My calculator overflows on 10^100
therefore big integers are semantically unsound.
No, Peter.
It is your implementation that cannot handle the structure, not the mathematics.
As for “objects of thought are typed,” yes — and typed systems also have
Godel-style incompleteness theorems.
HOL, type theory, Montague-style semantics, all of them.
Typing does not prevent diagonalization.
It just prevents nonsense terms like phi(phi).
Godel’s construction never uses those.
You are not proving G is “semantically unsound.”
You are proving that your framework cannot express diagonalization.
But any framework that cannot express diagonalization also cannot
express arithmetic — and therefore cannot be “the entire body of objects of thought.”
In short:
You didn’t refute Godel.
You refuted your own system’s ability to model arithmetic.
Le 26/11/2025 à 03:34, olcott a écrit :
On 11/25/2025 8:09 PM, Python wrote:
Le 26/11/2025 à 03:03, olcott a écrit :
On 11/25/2025 7:45 PM, Python wrote:
Le 26/11/2025 à 02:43, olcott a écrit :
Montague Grammar is the syntax of English semantics
that is why he called it Montague Grammar. This is
all anchored in Rudolf Carnap meaning postulates
Peter, Montague Grammar does not make truth = provability.
It maps English into logic — it does not turn logic into a magic
incompleteness-proof shredder.
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).
Two Dogmas of Empiricism by Willard Van Orman had no idea
how we know that Bachelors are unmarried. Basically we
just look it up in the type hierarchy, that is the simple
proof of its truth.
If your claim were right, every linguist using Montague’s system
would have accidentally solved Godel’s theorem in the 1970s.
They didn’t.
I spoke with many people very interested in linguistics
on sci.lang for many years. Even ordinary semantics
freaks them out.
None of them ever had the slightest clue about Montague
Grammar. Except for one they all had very severe math
phobia. Formal semantics got them very aggravated.
Because encoding semantics as syntax does not erase diagonalization >>>>> — it just gives it nicer types.
G ↔ ¬Prov(⌜G⌝)
Directed Graph of evaluation sequence
00 ↔ 01 02
01 G
02 ¬ 03
03 Prov 04
04 Gödel_Number_of 01 // cycle
Proves that the evaluation of the above G is stuck
in an infinite loop whether you understand this or not.
Montague built a translation function.
You’re treating it like a trapdoor that makes unprovable truths
disappear.
It doesn’t.
Only your theory does that.
When True(L,x) is exactly one and the same thing as
Provable(L,x) then if you are honest you will admit
that they cannot possibly diverge thus within this
system Gödel incompleteness cannot possibly exist.
Seeing how this makes perfect sense and is absolutely
not any sort of ruse may take much more dialogue.
Réponse proposée (courte, mordante, ASCII-safe)
Peter, you keep repeating the same pattern:
Because you utterly refuse to pay enough attention.
Take a normal semantic fact (like bachelor = unmarried).
Declare that because some meanings can be defined, all meaning
reduces to proof.
All *objects of thought* can be defined in terms of other
*objects of thought*
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, etc.
Then insist that since in your system True = Provable by definition,
Godel “cannot possibly exist.”
But that is not a refutation — that is simply renaming the problem
out of existence.
Your “directed graph infinite loop” does not show an error in Godel; >>> it shows that Prolog refuses cyclic terms.
Mathematics does not.
That you fail to understand that it conclusively
proves that the expression is semantically
unsound is your ignorance on not my mistake.
Peter, your entire argument now rests on one mistake:
You think that a self-referential fixed point is “semantically unsound” because Prolog refuses to unify a cyclic term.
But Prolog’s occurs-check does not detect “semantic unsoundness.”
It detects infinite data structures in Prolog.
Mathematics is not Prolog.
Lambda calculus allows fixed points.
Type theory allows fixed points.
Arithmetic allows fixed points.
Diagonalization is a fixed point.
G <-> not Prov(F,G)
cycle -> therefore invalid
My calculator overflows on 10^100
therefore big integers are semantically unsound.
My calculator overflows on 10^100
therefore big integers are semantically unsound.
No, Peter.
It is your implementation that cannot handle the structure, not the mathematics.
As for “objects of thought are typed,” yes — and typed systems also have
Godel-style incompleteness theorems.
HOL, type theory, Montague-style semantics, all of them.
Typing does not prevent diagonalization.
It just prevents nonsense terms like phi(phi).
Godel’s construction never uses those.
You are not proving G is “semantically unsound.”
You are proving that your framework cannot express diagonalization.
But any framework that cannot express diagonalization also cannot
express arithmetic — and therefore cannot be “the entire body of objects of thought.”
In short:
You didn’t refute Godel.
You refuted your own system’s ability to model arithmetic.
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:Your condition that ALL objects of thought can be defined in terms of
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: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.
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:I can't even make sense of that. It's a *theory* of >>>>>>>>>>>>>>>> English semantics.
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 >>>>>>>>>>>>>>>>
*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). >>>>>>>>>>>>>>
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* >>>>
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┐).
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: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.
On 2025-11-25 18:43, olcott wrote:
On 11/25/2025 7:29 PM, André G. Isaak wrote:I can't even make sense of that. It's a *theory* of >>>>>>>>>>>>>> English semantics.
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 >>>>>>>>>>>>>>
*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). >>>>>>>>>>>>
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.
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: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.
On 11/25/2025 7:29 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>> On 2025-11-25 17:52, olcott wrote:I can't even make sense of that. It's a *theory* of >>>>>>>>>>>>>>>>> English semantics.
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 >>>>>>>>>>>>>>>>>
*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). >>>>>>>>>>>>>>>
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.
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: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.
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:I can't even make sense of that. It's a *theory* of >>>>>>>>>>>>>>> English semantics.
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 >>>>>>>>>>>>>>>
*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). >>>>>>>>>>>>>
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.
If they are syntactically valid then what does "reject" mean?
What consequences does not have?
On 12/6/2025 3:21 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:Your condition that ALL objects of thought can be defined in terms of
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: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.
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:I can't even make sense of that. It's a *theory* of >>>>>>>>>>>>>>>> English semantics.
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 >>>>>>>>>>>>>>>>
*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). >>>>>>>>>>>>>>
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* >>>>
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.
If they are syntactically valid then what does "reject" mean?
What consequences does not have?
The most famous guy on Formal Languages write this https://en.wikipedia.org/wiki/Colorless_green_ideas_sleep_furiously
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: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. >>>>>>>>>>>>>>>>
On 11/25/2025 7:29 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>> On 2025-11-25 17:52, olcott wrote:I can't even make sense of that. It's a *theory* of >>>>>>>>>>>>>>>>>> English semantics.
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 >>>>>>>>>>>>>>>>>>
*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). >>>>>>>>>>>>>>>>
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)
olcott kirjoitti 6.12.2025 klo 14.46:
On 12/6/2025 3:21 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: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.
On 11/25/2025 7:29 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>> On 2025-11-25 17:52, olcott wrote:I can't even make sense of that. It's a *theory* of >>>>>>>>>>>>>>>>> English semantics.
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 >>>>>>>>>>>>>>>>>
*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). >>>>>>>>>>>>>>>
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.
If they are syntactically valid then what does "reject" mean?
What consequences does not have?
The most famous guy on Formal Languages write this
https://en.wikipedia.org/wiki/Colorless_green_ideas_sleep_furiously
Don't use the word if you don't know what it means.
On 12/7/2025 4:50 AM, Mikko wrote:
olcott kirjoitti 6.12.2025 klo 14.46:
On 12/6/2025 3:21 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: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. >>>>>>>>>>>>>>>>
On 11/25/2025 7:29 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>> On 2025-11-25 17:52, olcott wrote:I can't even make sense of that. It's a *theory* of >>>>>>>>>>>>>>>>>> English semantics.
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 >>>>>>>>>>>>>>>>>>
*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). >>>>>>>>>>>>>>>>
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.
If they are syntactically valid then what does "reject" mean?
What consequences does not have?
Does not semantically follow is exactly what I mean.
olcott kirjoitti 7.12.2025 klo 19.15:
On 12/7/2025 4:50 AM, Mikko wrote:
olcott kirjoitti 6.12.2025 klo 14.46:
On 12/6/2025 3:21 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: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. >>>>>>>>>>>>>>>>>
On 11/25/2025 7:29 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>> On 2025-11-25 17:52, olcott wrote:I can't even make sense of that. It's a *theory* of >>>>>>>>>>>>>>>>>>> English semantics.
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 >>>>>>>>>>>>>>>>>>>
*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). >>>>>>>>>>>>>>>>>
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.
If they are syntactically valid then what does "reject" mean?
What consequences does not have?
Does not semantically follow is exactly what I mean.
That is quite far from the usual meaning of "reject".
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: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. >>>>>>>>>>>>>>>>>
On 11/25/2025 7:29 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>> On 2025-11-25 17:52, olcott wrote:I can't even make sense of that. It's a *theory* of >>>>>>>>>>>>>>>>>>> English semantics.
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 >>>>>>>>>>>>>>>>>>>
*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). >>>>>>>>>>>>>>>>>
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.
On 12/8/2025 3:08 AM, Mikko wrote:
olcott kirjoitti 7.12.2025 klo 19.15:
On 12/7/2025 4:50 AM, Mikko wrote:
olcott kirjoitti 6.12.2025 klo 14.46:
On 12/6/2025 3:21 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: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. >>>>>>>>>>>>>>>>>>
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 divideI can't even make sense of that. It's a *theory* of >>>>>>>>>>>>>>>>>>>> English semantics.
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 >>>>>>>>>>>>>>>>>>>>
*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). >>>>>>>>>>>>>>>>>>
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.
If they are syntactically valid then what does "reject" mean?
What consequences does not have?
Does not semantically follow is exactly what I mean.
That is quite far from the usual meaning of "reject".
Is this gibberish nonsense: "iho iu,78r GYU(UY OPJ OJOJ"
a member of the body of general knowledge that can be
expressed in language? Reject means not a member.
olcott kirjoitti 8.12.2025 klo 21.05:
On 12/8/2025 3:08 AM, Mikko wrote:
olcott kirjoitti 7.12.2025 klo 19.15:
On 12/7/2025 4:50 AM, Mikko wrote:
olcott kirjoitti 6.12.2025 klo 14.46:
On 12/6/2025 3:21 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 :When ALL *objects of thought* are defined
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: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. >>>>>>>>>>>>>>>>>>>
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:I can't even make sense of that. It's a *theory* of >>>>>>>>>>>>>>>>>>>>> English semantics.
Gödel incompleteness can only exist in systems >>>>>>>>>>>>>>>>>>>>>>>>>> that divideAnd, so, just confuse syntax for semantics, and >>>>>>>>>>>>>>>>>>>>>>>>> all is fixed!
their syntax from their semantics ... >>>>>>>>>>>>>>>>>>>>>>>>>
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 >>>>>>>>>>>>>>>>>>>>>
*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). >>>>>>>>>>>>>>>>>>>
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. >>>>>>>>>>>>>>
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.
If they are syntactically valid then what does "reject" mean?
What consequences does not have?
Does not semantically follow is exactly what I mean.
That is quite far from the usual meaning of "reject".
Is this gibberish nonsense: "iho iu,78r GYU(UY OPJ OJOJ"
a member of the body of general knowledge that can be
expressed in language? Reject means not a member.
Not a memebr of what?
You want to accept a circular defintion as
symtactically valid so it is a member of the language (which is
a set of finite strings). It is also a valid premmise in a proof
because it is a definition.
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