XPost: sci.math, comp.theory
From: polcott333@gmail.com
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. They are the subject of
thought from the Zen Buddhist subject/object dichotomy
at the heart of Anattā.
https://en.wikipedia.org/wiki/Anatt%C4%81
On the other hand *objects of thought* are the
set of every element of every thought that anyone
can ever have when this thought is expressed in
language.
> 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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