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