Re: Peano Axioms anchored in First Grade Arithmetic on ASCII Digit String pairs

On 11/2/24 7:05 AM, olcott wrote:

On 11/2/2024 3:29 AM, Mikko wrote:

On 2024-11-01 11:53:00 +0000, olcott said:
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On 11/1/2024 3:47 AM, Mikko wrote:

On 2024-10-31 14:18:40 +0000, olcott said:
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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:
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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.

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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".

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Can you please hit return before you reply?
Your reply is always buried too close to what you are replying to.
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We simply reject pathological self-reference lie
ZFC did and the issue ends.

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You cannot reject any number from atrithmetic. If you do the result is
not arithmetic anymore.

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I claims that his whole proof is nonsense until you
provide 1200% concrete proof otherwise.

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Crackpots claim all all sorts of things. There is no way to change that
so there is no point to try.
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All of arithmetic is inherently computable and
any non-arithmetic operation on a number is a type
mismatch error.

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There are arithmetic functions and predicates that are not Turing
computable. For example, Busy Beaver.
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 Not computable because of self-reference is a different class
than not computable for other reasons. The Goldbach conjecture
seems not computable only because it seems to require an infinite
number of steps.
 

No, because the ability to form self-reference is totally inherent in the nature of Turing Complete computation systems.
The essential fact that infinity is not finite is the core reason for both non-computable natures.
Note, we don't know if Goldbach is non-computable, and in fact, if we did, we would have the answer, and thus it can not be proven to be non-computable, as the proof of truth of Goldback being non-computable would be a proof that it was true, as if the Goldback conjecture is false, there is a compuation that proves that.