XPost: sci.math, comp.theory
From: mikko.levanto@iki.fi
olcott kirjoitti 29.11.2025 klo 18.40:
> On 11/29/2025 3:44 AM, Mikko wrote:
>> olcott kirjoitti 28.11.2025 klo 17.16:
>>> On 11/28/2025 2:35 AM, Mikko wrote:
>>>> olcott kirjoitti 27.11.2025 klo 17.16:
>>>>> On 11/27/2025 1:30 AM, Mikko wrote:
>>>>>> olcott kirjoitti 26.11.2025 klo 16.58:
>>>>>>> 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 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.
>>>>>>>
>>>>>>> Kurt Gödel explains the details of how *objects of thought*
>>>>>>> are 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,
>>>>>>
>>>>>> That is irrelevant to the point that you cannot define ALL
>>>>>> subjects of
>>>>>> thoughts in terms of other subject of thoughts.
>>>>>
>>>>> One cannot possibly exhaustively define individual
>>>>> living human beings at all.
>>>>
>>>> True, as already pointed out by Aristotle; but irrelevant to the point
>>>> that if all objects of thought are defined by other objects of thought
>>>> there are not objects of thought at all.
>>>
>>> So you never heard of a type hierarchy that
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