XPost: comp.theory, sci.math
From: polcott333@gmail.com
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 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?
>
The most famous guy on Formal Languages write this
https://en.wikipedia.org/wiki/Colorless_green_ideas_sleep_furiously
--
Copyright 2025 Olcott
My 28 year goal has been to make
"true on the basis of meaning" computable.
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