XPost: comp.theory, sci.math
From: mikko.levanto@iki.fi
olcott kirjoitti 3.12.2025 klo 18.13:
> On 12/3/2025 5:17 AM, Mikko wrote:
>> 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.
>
> Unknowns are outside of the body of knowledge.
>
>> 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.
>
> If anyone anywhere knows then it is in the body of general knowledge.
It is not general knowledge as it is not known to anybody outside
North Sentinel Island.
I know the color of my bedroom wall. Is that general knowledge?
--
Mikko
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