XPost: sci.math, comp.theory
From: mikko.levanto@iki.fi
olcott kirjoitti 28.11.2025 klo 17.16:
> On 11/28/2025 2:35 AM, Mikko wrote:
>> olcott kirjoitti 27.11.2025 klo 17.16:
>>> On 11/27/2025 1:30 AM, Mikko wrote:
>>>> 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.
>>>
>>> One cannot possibly exhaustively define individual
>>> living human beings at all.
>>
>> True, as already pointed out by Aristotle; but irrelevant to the point
>> that if all objects of thought are defined by other objects of thought
>> there are not objects of thought at all.
>
> So you never heard of a type hierarchy that
> has as its root: {thing}
Of course I have. Such type hierarcy has a structure that is different
from the structure where ALL subjects of thoughts are defined in terms
of other subjects of thoughts.
--
Mikko
--- SoupGate-Win32 v1.05
* Origin: you cannot sedate... all the things you hate (1:229/2)
|
