Re: Gödel's actual proof and deriving all of the digits of the actual Gödel numbers

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.