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.
On 12/13/2025 5:05 AM, Mikko wrote:
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: >>>>>>>>>>>>>>>>>>>>>>> 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).
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. >>>>>>>>>>>>>>>
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?
member of
the body of general knowledge
that can be expressed in language
On 13/12/2025 17:55, olcott wrote:
On 12/13/2025 5:05 AM, Mikko wrote:
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: >>>>>>>>>>>>>>>>>>>>>>>> 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).
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. >>>>>>>>>>>>>>>>
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?
member of
the body of general knowledge
that can be expressed in language
That matters only if it is syntactically valid in that language.
Is it?
On 12/15/2025 3:52 AM, Mikko wrote:
On 13/12/2025 17:55, olcott wrote:
On 12/13/2025 5:05 AM, Mikko wrote:
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 : >>>>>>>>>>>>>>>>>>> On 11/25/2025 8:36 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>> On 2025-11-25 19:30, olcott wrote:When ALL *objects of thought* are defined
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 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
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. >>>>>>>>>>>>>>>>>
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?
member of
the body of general knowledge
that can be expressed in language
That matters only if it is syntactically valid in that language.
Is it?
I use Montague Grammar fully integrating
semantics directly into the syntax making
unprovable in L simply untrue in L.
When L is the body of general knowledge that
can be expressed in language, then unprovable
in L means not a member of this body.
LLM systems have an easy time with this, it seems
that to everyone everywhere else integrating
semantics directly in syntax is not the way they
were taught thus seems to be nonsense.
LLM systems are not locked in to what they were
taught yet can extrapolate on the basis of what
they were taught.
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