XPost: comp.theory, sci.math
From: mikko.levanto@iki.fi
olcott kirjoitti 6.12.2025 klo 14.53:
> On 12/6/2025 3:39 AM, Mikko wrote:
>> olcott kirjoitti 5.12.2025 klo 19.31:
>>> On 12/5/2025 3:03 AM, Mikko wrote:
>>>> olcott kirjoitti 4.12.2025 klo 16.18:
>>>>> On 12/4/2025 3:29 AM, Mikko wrote:
>>>>>> 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?
>>>>
>>>>> To simply things the body of general knowledge
>>>>> can be everything written down in any published
>>>>> book or published paper. Also anything that can
>>>>> be deduced from these sources.
>>>>
>>>> General knowledge also includes that there are claims that might be
>>>> deducible from published knowledge or might be not, and it is not
>>>> yet known whether or how. Examples of such claims can be found in
>>>> published sources.
>>
>>> Yes this is correct.
>>
>> Therefore it is not correct to say that all claims decucible from
>> general knowledge
>
> I never said that they were.
Above you said that
>>>>> To simply things the body of general knowledge
>>>>> can be everything written down in any published
>>>>> book or published paper. Also anything that can
>>>>> be deduced from these sources.
As I just inferred, it is not correct to say so.
>> are in general knoledge. The claims that are
>> deducible from general knoledge but neither known to be deducible from
>> the common knowledge nor ottherwise knwon are not in general knowledge.
>> This is an incompleteness in general knowledge.
>>
>
> Claims that can be deduced from published knowledge
> can be construed to be the body of general knowledge.
And here you say it again.
--
Mikko
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