XPost: comp.theory, sci.math
From: polcott333@gmail.com
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.
--
Copyright 2025 Olcott
My 28 year goal has been to make
"true on the basis of meaning" computable.
This required establishing a new foundation
for correct reasoning.
--- SoupGate-Win32 v1.05
* Origin: you cannot sedate... all the things you hate (1:229/2)
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