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Re: on mathematical ghosts --- PLO

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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.

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

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.

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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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