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Re: on mathematical ghosts --- PLO

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On 12/9/2025 6:42 AM, Richard Damon wrote:
> On 12/8/25 11:51 PM, polcott wrote:
>> On 12/8/2025 10:20 PM, Richard Damon wrote:
>>> On 12/8/25 11:00 PM, polcott wrote:
>>>> On 12/8/2025 9:38 PM, dart200 wrote:
>>>>
>>>> *You have support for this in high places*
>>>>
>>>> The Halting Paradox
>>>> Bill Stoddart
>>>>
>>>> 6 Conclusions
>>>> The idea of a universal halting test seems reasonable,
>>>> but cannot be formalised as a consistent specification.
>>>> It has no model and does not exist as a conceptual object.
>>>> Assuming its conceptual existence leads to a paradox.
>>>>
>>>> https://arxiv.org/pdf/1906.05340
>>>>
>>>
>>> Which doesn't prove anything, as there IS a consistant specification 
>>> for the test.
>>>
>>> The problem is you (and Bill) just don't understand it.
>>>
>>> Part of the problem is Bill doesn't understand the nature of Turing 
>>> Complete systems. In particular, he assume there is a UNIQUE encoding 
>>> for every program, which is a false assumption in Turing Complete 
>>> systems.
>>
>> With the text of each program P we associate a
>> unique number ⌈P⌉, known as the program’s encoding,
>> which will stand for the program when we want to
>> use that program as data, e.g. when passing one
>> program to another as an argument.
>>
>> You are just terribly inaccurate in paraphrasing.
>> Perhaps speaking to no one at all is better than
>> talking to you.
>>
> 
> Except there are many texts that create the equivalent program, and thus 
> many numbers for that program.
> 

He is doing this like Gödel numbers, thus a unique
identifier is needed. And again this is merely nit-picky
his point is that the foundations of computer science
are incorrect and I have shown that two different ways.

> Yes, we can convert a program into data, but there are many data values 
> that all represent the same program.
> 

No there are not you are just not being precise enough
in your choice of words. And yet again this is an
irrelevant nit-picky detail.

> This means that Program H can't use a "unique" value of its 
> representation to detect the input using it, as the pathological program 
> can just use an equivalent variation not in the finite list of values 
> that H tests for.

If the finite strings are not identical then the
inputs are not identical.

-- 
Copyright 2025 Olcott

My 28 year goal has been to make
"true on the basis of meaning" computable.

This required establishing a new foundation
for correct reasoning.

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Re: on mathematical ghosts --- PLO polcott <polcott333@gmail.com> - 2025-12-08 22:00 -0600
  Re: on mathematical ghosts --- PLO Richard Damon <Richard@Damon-Family.org> - 2025-12-08 23:20 -0500
    Re: on mathematical ghosts --- PLO polcott <polcott333@gmail.com> - 2025-12-08 22:33 -0600
      Re: on mathematical ghosts --- PLO Richard Damon <Richard@Damon-Family.org> - 2025-12-09 07:42 -0500
        Re: on mathematical ghosts --- PLO polcott <polcott333@gmail.com> - 2025-12-09 09:53 -0600
          Re: on mathematical ghosts --- PLO Richard Damon <Richard@Damon-Family.org> - 2025-12-09 23:02 -0500
    Re: on mathematical ghosts --- PLO polcott <polcott333@gmail.com> - 2025-12-08 22:51 -0600
      Re: on mathematical ghosts --- PLO Richard Damon <Richard@Damon-Family.org> - 2025-12-09 07:42 -0500
        Re: on mathematical ghosts --- PLO polcott <polcott333@gmail.com> - 2025-12-09 09:39 -0600
          Re: on mathematical ghosts --- PLO Richard Damon <Richard@Damon-Family.org> - 2025-12-09 23:02 -0500
  Re: on mathematical ghosts --- PLO dart200 <user7160@newsgrouper.org.invalid> - 2025-12-08 20:54 -0800
    Re: on mathematical ghosts --- PLO polcott <polcott333@gmail.com> - 2025-12-08 23:02 -0600

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