XPost: sci.logic, sci.math, comp.theory
From: mikko.levanto@iki.fi
On 08/12/2025 21:56, olcott wrote:
> On 12/7/2025 5:08 AM, Mikko wrote:
>> 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.
>
> That is the same as disagreeing with arithmetic.
Not really. That you have done both does not mean they are the same.
--
Mikko
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