Re: Refutation of the Halting Problem's Proof (Clarifications Wanted)

From: The Ghost In The Machine (ewill_at_aurigae.athghost7038suus.net)
Date: 08/29/04 

Date: Sun, 29 Aug 2004 00:00:24 GMT

In sci.logic, Peter Olcott
<olcott@worldnet.att.net>
 wrote
on Sat, 28 Aug 2004 10:18:03 GMT
<vZYXc.263150$OB3.102898@bgtnsc05-news.ops.worldnet.att.net>:
>
> "The Ghost In The Machine" <ewill@aurigae.athghost7038suus.net> wrote in message news:2gb502-f7r.ln1@lexi2.athghost7038suus.net...
>> In sci.logic, G Frege
>> <no_spam@aol.com>
>> wrote
>> on Sat, 28 Aug 2004 00:57:01 +0200
>> <s0fvi09o0v62vt6p5edcgv9t09mk5dubvv@4ax.com>:
>> > On Fri, 27 Aug 2004 22:07:32 GMT, "Peter Olcott"
>> > <olcott@worldnet.att.net> wrote:
>> >
>> >>
>> >> So far it has not been shown.
>> >>
>> >
>> > Yes, we know that you are a troll. :-)
>> >
>>
>> Not to mention that I for one would think he *has* been
>> shown, although he might not recognize it yet. :-)
>>
>> But from my standpoint, if he produces a machine with
>> a side effect (at least, of the ones I've identified,
>> which are an extra tape and some blinkylights), I can
>> construct an equivalent machine with no side effect that
>> goes through isomorphic transitions.
>>
>> If he claims his machine correctly computes WillHalt,
>> I claim that my machine, which is isomorphic to his,
>> can be broken by the standard LoopIfHalts transmogrification
>> construction, and therefore his machine may not be quite
>> as correct as he thinks. :-P
>
> I don't think that this can really be done, and I don't
> think that this has been yet shown.

Correct, it has not -- mostly because you've not identified
the side effect you're using for WillHalts to return the
result back to the human, but not to LoopIfHalts.

> The whole local
> transformations thing would not work in the case of
> a TM deriving its own PGP digital signature.

It is not a local transformation. AIUI, the problem is
a level 2 Russell problem (in the sense that WillHalt is
solving a level 1 problem; TMs solve level 0 problems for
the most part -- of course this is a rather artificial
distinction anyway; TMs merely "go through the motions"
if the transition function is correctly specified).

Besides, standard TMs can't derive their own signature, and
an isomorphism from STM1 to STM2 could simply morph the
signature from sig(STM1) to sig(STM2) as well.

I don't see how this helps your proof.

>
>> (Assuming he ever gets around to constructing one. So far
>> his efforts have been primarily aimed at somehow stopping
>> Turing's LoopIfHalts proof.)
>>
>> --
>> #191, ewill3@earthlink.net
>> It's still legal to go .sigless.
>
> 

-- 
#191, ewill3@earthlink.net
It's still legal to go .sigless.

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