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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: Fri, 1 Nov 2024 10:47:42 +0200
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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.

-- 
Mikko