XPost: sci.math, comp.theory
From: agisaak@gm.invalid
On 2025-11-25 19:41, olcott wrote:
> 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.
>
Non sequitur. That has nothing to do with anything I wrote.
André
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