XPost: sci.math, comp.theory
From: polcott333@gmail.com
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
>> has as its root: {thing}
>
> Of course I have. Such type hierarcy has a structure that is different
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