XPost: sci.math, comp.theory
From: polcott333@gmail.com
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}
>>> In order to define
>>> subjects of thoughts in terms of other subjects of thoughts you need a
>>> subject of thoughts that is not defined in terms of other subjects of
>>> thoughts. Unless, of course, your ALL subjects of thoughts is no
>>> subjects thoughts.
>
--
Copyright 2025 Olcott
My 28 year goal has been to make
"true on the basis of meaning" computable.
This required establishing a new foundation
for correct reasoning.
--- SoupGate-Win32 v1.05
* Origin: you cannot sedate... all the things you hate (1:229/2)
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