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From: Mikko <mikko.levanto@iki.fi>
Newsgroups: comp.theory
Subject: Re: Peano Axioms anchored in First Grade Arithmetic on ASCII Digit String pairs
Date: Sun, 3 Nov 2024 11:10:41 +0200
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On 2024-11-02 11:05:20 +0000, olcott said:

> On 11/2/2024 3:29 AM, Mikko wrote:
>> On 2024-11-01 11:53:00 +0000, olcott said:
>> 
>>> On 11/1/2024 3:47 AM, Mikko wrote:
>>>> On 2024-10-31 14:18:40 +0000, olcott said:
>>>> 
>>>>> On 10/31/2024 8:58 AM, joes wrote:
>>>>>> Am Thu, 31 Oct 2024 07:19:18 -0500 schrieb olcott:
>>>>>>> On 10/31/2024 5:34 AM, Mikko wrote:
>>>>>>>> On 2024-10-30 12:16:02 +0000, olcott said:
>>>>>>>>> On 10/30/2024 5:02 AM, Mikko wrote:
>>>>>>>>>> On 2024-10-27 14:21:25 +0000, olcott said:
>>>>>>>>>>> On 10/27/2024 3:37 AM, Mikko wrote:
>>>>>>>>>>>> On 2024-10-26 13:17:52 +0000, olcott said:
>>>>>>>>>>>> 
>>>>>>>>>>>>> Just imagine c functions that have enough memory to compute sums
>>>>>>>>>>>>> and products of ASCII strings of digits using the same method that
>>>>>>>>>>>>> people do.
>>>>>>>>>>>> Why just imagein? That is fairly easy to make. In some other
>>>>>>>>>>>> lanugages (e.g. Python, Javascript) it is alread in the library or
>>>>>>>>>>>> as a built-in feature.
>>>>>>>>>>> OK next I want to see the actual Godel numbers and the arithmetic
>>>>>>>>>>> steps used to derive them.
>>>>>>>>>> They can be found in any textbook of logic that discusses
>>>>>>>>>> undecidability.
>>>>>>>>>> If you need to ask about details tell us which book you are using.
>>>>>>>>> Every single digit of the entire natural numbers not any symbolic name
>>>>>>>>> for such a number.
>>>>>>>> Just evaluate the expressions shown in the books.
>>>>>>> To me they are all nonsense gibberish. How one can convert a proof about
>>>>>>> arithmetic into a proof about provability seems to be flatly false.
>>>>> 
>>>>>> The key is selfreference. There is a number that encodes the sentence
>>>>>> "the sentence with the number [the number that this sentence encodes to]
>>>>>> is not provable".
>>>>> 
>>>>> Can you please hit return before you reply?
>>>>> Your reply is always buried too close to what you are replying to.
>>>>> 
>>>>> We simply reject pathological self-reference lie
>>>>> ZFC did and the issue ends.
>>>> 
>>>> You cannot reject any number from atrithmetic. If you do the result is
>>>> not arithmetic anymore.
>>> 
>>> I claims that his whole proof is nonsense until you
>>> provide 1200% concrete proof otherwise.
>> 
>> Crackpots claim all all sorts of things. There is no way to change that
>> so there is no point to try.
>> 
>>> All of arithmetic is inherently computable and
>>> any non-arithmetic operation on a number is a type
>>> mismatch error.
>> 
>> There are arithmetic functions and predicates that are not Turing
>> computable. For example, Busy Beaver.
> 
> Not computable because of self-reference is a different class
> than not computable for other reasons.

There is no self reference in Busy Beaver. Anyway, not Turing computable
is not Turing computable, whatever the reason.

> The Goldbach conjecture seems not computable only because it seems to
> require an infinite number of steps.

It seems so but that is not really known.

-- 
Mikko