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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory
Subject: Re: Peano Axioms anchored in First Grade Arithmetic on ASCII Digit
 String pairs
Date: Thu, 31 Oct 2024 19:08:53 -0400
Organization: i2pn2 (i2pn.org)
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On 10/31/24 10:18 AM, olcott wrote:
> 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.

But that isn't "just" what Z-F did. (note ZFC isn't a person, so it 
doesn't actively DO anything).

> 
>>>>> It might be the case that one number fills 100 books of 1000 pages
>>>>> each.
>>>> You fill find out when you evaluate the expressions. If you use Gödel's
>>>> original numbering you will need larger numbers than strictly
>>>> necessary. If you first encode symbols with a finite set of characters
>>>> you can encode everything with finite set of characters.
>>> A book a trillion light years deep?
>> Is finite.
>>
>>>> Then you can encode those character strings as integers. The number of
>>>> digits can be determined from the length of the character strings.
>>>> Besides, computations are much faster than with Gödel's powers of
>>>> primes.
> 
>