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