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From: joes <noreply@example.org>
Newsgroups: comp.theory
Subject: Re: =?iso-8859-1?Q?G=F6del's?= actual proof and deriving all of the
 digits of the actual =?iso-8859-1?B?R/ZkZWw=?= numbers
Date: Thu, 31 Oct 2024 14:00:42 -0000 (UTC)
Organization: i2pn2 (i2pn.org)
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Am Thu, 31 Oct 2024 07:15:42 -0500 schrieb olcott:
> On 10/31/2024 4:45 AM, Mikko wrote:
>> On 2024-10-30 12:13:43 +0000, olcott said:
>>> On 10/30/2024 4:57 AM, Mikko wrote:
>>>> On 2024-10-29 13:25:34 +0000, olcott said:
>>>>> On 10/29/2024 2:38 AM, Mikko wrote:
>>>>>> On 2024-10-28 14:04:24 +0000, olcott said:
>>>>>>> On 10/28/2024 3:35 AM, Mikko wrote:
>>>>>>>> On 2024-10-27 14:29:22 +0000, olcott said:
>>>>>>>>> On 10/27/2024 4:02 AM, Mikko wrote:

>>>>>>> https://www.liarparadox.org/G%C3%B6del_Sentence(1931).pdf
>>>>>> That page is not relevant to our immediate context. Note that it
>>>>>> uses symbols that are already defined earlier in the opus.
>>>>> I think that the assumption that it is anchored in arithmetic is
>>>>> incorrect until I see the details of it anchored in actual
>>>>> arithmetic.
>>>> Depends on what you mean by "it" and "anchored".
>>> Exactly what additional basic operations are require besides this to
>>> actual algorithmically perform every step of his whole proof? char*
>>> sum(x, char* y)
>>> char* product(x, char* y)
>>> char* exponent(x, char* y)
>> In those operations x should have a type. More specifically, the same
>> type as y and the function.
> Yet arithmetic does not have types and the proof is supposed to be about
> numbers.
Code has types.

>> In addition to these operations you need comparisons:
>> bool equal(char* x, char* y)
>> bool greater(char* x, char* y)
>> Formulas and in particular the undecidable formulas contain universal
>> and existential quantifiers. THere is no way to iimplement those in C.
>> But Gödel numbers can be computed and proofs checked without them.
-- 
Am Sat, 20 Jul 2024 12:35:31 +0000 schrieb WM in sci.math:
It is not guaranteed that n+1 exists for every n.