Re: Olcott's theory [ Flibble understands pathological self reference(Olcott 2004) ]

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olcott

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Jul 19, 2021, 3:33:38 PMJul 19
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On 7/10/2021 12:00 PM, Mr Flibble wrote:
> I agree with Olcott that a halt decider can NOT be part of that which
> is being decided (see [Strachey 1965]) which, if Olcott is correct,
> falsifies a collection of proofs (which I don't have the time to
> examine) which rely on that mistake.
>
<snip error>
> /Flibble
>

Pathological Input to a halt decider is defined as any input that was
defined to do the opposite of whatever its corresponding halt decider
decides.

On Sunday, September 5, 2004 at 11:21:57 AM UTC-5, Peter Olcott wrote:
> The Liar Paradox can be shown to be nothing more than
> a incorrectly formed statement because of its pathological
> self-reference. The Halting Problem can only exist because
> of this same sort of pathological self-reference.
https://groups.google.com/g/comp.theory/c/RO9Z9eCabeE/m/Ka8-xS2rdEEJ


--
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre
minds." Einstein

olcott

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Jul 20, 2021, 9:52:39 AMJul 20
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On 7/19/2021 2:40 PM, Peter wrote:
> olcott wrote:
>> On 7/10/2021 12:00 PM, Mr Flibble wrote:
>>> I agree with Olcott that a halt decider can NOT be part of that which
>>> is being decided (see [Strachey 1965]) which, if Olcott is correct,
>>> falsifies a collection of proofs (which I don't have the time to
>>> examine) which rely on that mistake.
>> <snip error>
>>> /Flibble
>>>
>>
>> Pathological Input to a halt decider is defined as any input that was
>> defined to do the opposite of whatever its corresponding halt decider
>> decides.
>
> Then you're not talking about halt deciders as usually understood.  A

Now we construct a new Turing machine D with H as a subroutine. This new
TM calls H to determine what M does when the input to M is its own
description ⟨M⟩. Once D has determined this information, it does the
opposite. (Sipser:1997:165) http://www.liarparadox.org/sipser_165.pdf

Sipser, Michael 1997. Introduction to the Theory of Computation. Boston:
PWS Publishing Company (165-167)


> halt decider takes _any_ TM/tape pair and decides if that TM halts when
> processing that tape.  ('Any' is a harmless exaggeration, obviously the
> tape symbols have to be ones in the TM's langugae.)
>
>>
>> On Sunday, September 5, 2004 at 11:21:57 AM UTC-5, Peter Olcott wrote:
>>  > The Liar Paradox can be shown to be nothing more than
>>  > a incorrectly formed statement because of its pathological
>>  > self-reference. The Halting Problem can only exist because
>>  > of this same sort of pathological self-reference.
>
> Not all self reference is pathological (one reason I chose my sig was to
> illustrate that point).  'Pete Olcott struggles to understand self
> reference' does not mean 'self reference is pathological'.
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