XPost: comp.lang.prolog, comp.theory, sci.math
From: mikko.levanto@iki.fi
olcott kirjoitti 6.12.2025 klo 14.45:
> On 12/6/2025 3:19 AM, Mikko wrote:
>> olcott kirjoitti 5.12.2025 klo 19.40:
>>> On 12/5/2025 3:13 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
>>>>>>>> another member.
>>>>>>>
>>>>>>> *I have always been referring to the entire body of general
>>>>>>> knowledge*
>>>>>>
>>>>>> Your condition that ALL objects of thought can be defined in terms of
>>>>>> other objects of thought is false about every non-empyt collection of
>>>>>> objects of thjought, inluding the entire body of general knowledge,
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