From Newsgroup: comp.ai.philosophy

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:

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

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

On 11/25/2025 7:29 PM, André G. Isaak wrote: >>>>>>>>>>>>>>>>>>>>>>> On 2025-11-25 17:52, olcott wrote: >>>>>>>>>>>>>>>>>>>>>>>> On 11/25/2025 6:47 PM, Kaz Kylheku wrote: >>>>>>>>>>>>>>>>>>>>>>>>> On 2025-11-25, olcott <polcott333@gmail.com> >>>>>>>>>>>>>>>>>>>>>>>>> wrote:

Gödel incompleteness can only exist in systems >>>>>>>>>>>>>>>>>>>>>>>>>> that divide
their syntax from their semantics ... >>>>>>>>>>>>>>>>>>>>>>>>>

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

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

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

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

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

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

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

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

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

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

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

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

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

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

André

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

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

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

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

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

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

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

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

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

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

This is reframing of the philosophical
The Analytic/Synthetic Distinction https://plato.stanford.edu/entries/analytic-synthetic/
enabling an unequivocal line of demarcation.

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.

--
Copyright 2025 Olcott<br><br>

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

This required establishing a new foundation<br>
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