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From: olcott <polcott333@gmail.com>
Newsgroups: comp.theory
Subject: Re: Peano Axioms anchored in First Grade Arithmetic on ASCII Digit
 String pairs
Date: Sun, 3 Nov 2024 07:11:09 -0600
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On 11/3/2024 3:10 AM, Mikko wrote:
> On 2024-11-02 11:05:20 +0000, olcott said:
> 
>> On 11/2/2024 3:29 AM, Mikko wrote:
>>> On 2024-11-01 11:53:00 +0000, olcott said:
>>>
>>>> On 11/1/2024 3:47 AM, Mikko wrote:
>>>>> On 2024-10-31 14:18:40 +0000, olcott said:
>>>>>
>>>>>> 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.
>>>>>
>>>>> 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.
>>>
>>> Crackpots claim all all sorts of things. There is no way to change that
>>> so there is no point to try.
>>>
>>>> All of arithmetic is inherently computable and
>>>> any non-arithmetic operation on a number is a type
>>>> mismatch error.
>>>
>>> There are arithmetic functions and predicates that are not Turing
>>> computable. For example, Busy Beaver.
>>
>> Not computable because of self-reference is a different class
>> than not computable for other reasons.
> 
> There is no self reference in Busy Beaver. Anyway, not Turing computable
> is not Turing computable, whatever the reason.
> 

Computing the square root of a pile of actual mud
is not Truing computable yet does not prove any
actual limit to computation. Likewise for simply
counting to infinity.

>> The Goldbach conjecture seems not computable only because it seems to
>> require an infinite number of steps.
> 
> It seems so but that is not really known.
> 

We do know that an infinite number of steps would
provide the correct answer after an infinite amount
of time. There is no after an infinite amount of time.

-- 
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer