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

On 11/1/24 7:53 AM, olcott wrote:

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.

>

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.
>

 I claims that his whole proof is nonsense until you
provide 1200% concrete proof otherwise.
 All of arithmetic is inherently computable and
any non-arithmetic operation on a number is a type
mismatch error.
 

Doesn't work that way. Your stupidity doesn't affect the truth of his statements.
The proof is either VALID or not based on the truth of itself.
It became part of the general knowledge of the field, when it was reviewed by trusted and knoledgable members in the field who understood it and agreed, combined with the fact that no one has been able to show a step that it uses that is not valid.
That fact you can't understand it has no impact on the proof. The fact you disagree with what the proof shows has no impact on the proof. At best, it shows that there must be something wrong with YOUR logic process to think it must be wrong.
If you really felt there was an error, you would study enough of the thoery of the field to be able to point out the step where he made the error that must be there if he is wrong.
BY DEFINITION, a statement derived by truth perseving operations, from know true statements, is a true statement. Thus, to show it not true, you must show the exact step where he either used an not known to be true statement, or a non-truth perserving operation somewhere in the actual proof. (Your comments about his off-hand comments about the proof don't matter, it is the actual step by step proof that matters).
By your logic, you are admitting that NONE of what you say is true, and in inherently nonsense as you can't even produce a 95% understandable concrete proof of your claims. Thus, by your own rules you are a liar for claiming them to be true.
Yes, arithmetic operations are inherently computable, but statements about arithmetic are not necessarily so.
Statements like "There does not exist a number that ...", or "For ALL number, we can show ...", might not be computable.
Godel's "G" is such a statement, the statement that there does not exist a number g such that it satisfies a particularly define Primiative Recursive Relationship. Such relationship being a computation that in finite work will either show that a given number satisfies it, or that it does't.
His proof is to develop the particular PRR for a logic system (an arbitrary system with a few specific requirements it needs) and then to show that such a number can not exist, and also that in that system, such a result can not be proven (because if you could come up with a proof, then that proof would provide a number that shows the statement to be false because it would satisfy the relationship).
This is based on the fact that he shows that proof verification turns out to be a computable problem, you can with finite work verify that a given proof is either correct, or that it has an error in it.