XPost: comp.theory, sci.math
From: mikko.levanto@iki.fi
olcott kirjoitti 8.12.2025 klo 21.05:
> On 12/8/2025 3:08 AM, Mikko wrote:
>> olcott kirjoitti 7.12.2025 klo 19.15:
>>> On 12/7/2025 4:50 AM, Mikko wrote:
>>>> olcott kirjoitti 6.12.2025 klo 14.46:
>>>>> 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
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