XPost: sci.math, comp.theory
From: mikko.levanto@iki.fi
olcott kirjoitti 28.11.2025 klo 17.18:
> On 11/28/2025 2:36 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.
>>
>> If the structure is empty there is no need to elaborate.
>
> Every thought that anyone can possibly have
> has its place in a knowledge ontology inheritance
> hierarchy.
But none of them is in the colloection of subjects of thoughts where
ALL subjects of thoughts are defined in terms of other subjects of
thoughts.
--
Mikko
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