XPost: sci.math, comp.theory
From: mikko.levanto@iki.fi
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.
--
Mikko
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