XPost: comp.theory, sci.math
From: mikko.levanto@iki.fi
olcott kirjoitti 2.12.2025 klo 16.07:
> On 12/2/2025 3:56 AM, Mikko wrote:
>> olcott kirjoitti 1.12.2025 klo 14.19:
>>> On 12/1/2025 4:31 AM, Mikko wrote:
>>>> Alan Mackenzie kirjoitti 29.11.2025 klo 13.55:
>>>>> [ Followup-To: set ]
>>>>>
>>>>> In comp.theory olcott wrote:
>>>>>> On 11/28/2025 4:54 PM, Alan Mackenzie wrote:
>>>>>
>>>>>>> In comp.theory olcott wrote:
>>>>>>>> On 11/28/2025 3:08 PM, Alan Mackenzie wrote:
>>>>>>>>> dart200 wrote:
>>>>>
>>>>> [ .... ]
>>>>>
>>>>>>>> *Within A new foundation for correct reasoning*
>>>>>
>>>>>>>> (a) Every element of the body of knowledge that can
>>>>>>>> be expressed in language is entirely composed of
>>>>>>>> (1) A finite set of atomic facts
>>>>>>>> (2) Every expression of language that is semantically
>>>>>>>> entailed by (1)
>>>>>>>> (b) a formal language based on Rudolf Carnap Meaning
>>>>>>>> Postulates combined with The Kurt Gödel definition
>>>>>>>> of the "theory of simple types"
>>>>>>>> https://en.wikipedia.org/wiki/
>>>>>>>> History_of_type_theory#G%C3%B6del_1944
>>>>>>>> Where every semantic meaning is fully encoded syntactically
>>>>>>>> as one fully integrated whole not needing model theory
>>>>>
>>>>>>>> We have now totally overcome Gödel Incompleteness
>>>>>>>> and Tarski Undefinability for the entire body if
>>>>>>>> knowledge that can be expressed in language. It
>>>>>>>> is now a giant semantic tautology.
>>>>>
>>>>>>> You can't "overcome" these theorems, since they're not obstacles.
>>>>>>> They're fundamental truths.
>>>>>
>>>>>> I just showed the detailed steps making both of
>>>>>> them impossible in the system that I just specified.
>>>>>> A counter-example is categorically impossible.
>>>>>
>>>>> Your construction is impossible, as proven by Gödel's Incompleteness
>>>>> Theorem.
>>>>
>>>> Doesn't a theory that has no theorems satisfy all above stated
>>>> requriements?
>>>
>>> Every element of the body of knowledge
>>> is not such a formal system.
>>
>> That's right, the body of knowledge is irrelevant here.
>
> If we are not talking about elements of the body
> of knowledge that are missing or unknown truths
> then there is no notion of actual incompleteness
> that remains.
The body of knowledge includes that certain quesstions have answers
but doesn't include now what those answers are. For example, we
know that North Sentinel Island is population but we don't know
what language is spoken there. This and other examples show that
the body of knowledge is incomplete.
--
Mikko
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