Re: Attempt to Refute the Halting Problem's Refutation

From: Chris Menzel (cmenzel_at_remove-this.tamu.edu)
Date: 08/24/04 

Date: 24 Aug 2004 10:13:29 GMT

On Tue, 24 Aug 2004 01:47:01 GMT, Peter Olcott <olcott@worldnet.att.net> said:
>
> "Chris Menzel" <cmenzel@remove-this.tamu.edu> wrote in message
> news:slrncijuko.ag2.cmenzel@philebus.tamu.edu...
>> On Sun, 22 Aug 2004 16:45:43 GMT, Peter Olcott
>> <olcott@worldnet.att.net> said:
>> >
>> > "peter_douglass" <baisly@gis.net> wrote in message
>> > news:9ZGVc.290598$a24.281796@attbi_s03...
>> >> "Marc Goodman" <marc.goodman@comcast.net> wrote in message
>> >> news:H3BVc.200346$eM2.91747@attbi_s51...
>> >>
>> >> > It's more accurate to say, "I found an ambiguity in the problem
>> >> > description that allowed me to define the problem in such a way
>> >> > as to eliminate a specific case that shows the Halting Problem
>> >> > is undecidable."
>> >>
>> >> He has failed to to even that.
>> >>
>> >> --PeterD
>> >
>> > Then attempt to prove that I have failed to do even that.
>>
>> You miss the point -- it would be a waste of time. Even if you *had*
>> proved even that, it is utterly trivial and has absolutely no bearing on
>> unsolvability of the halting problem.
>
> I have proved more than this.
> I have correctly refuted every existing proof that the Undecidability
> of the Halting Problem ever actually existed.

You are pathetically mistaken; not to mention horribly confused about the
basic subject matter (as your description of what you think you've done
bears witness).

>> > Note, that you must take into consideration the much higher burden of
>> > proof of "proving a negative".
>>
>> You really need to get over this. A proof is a proof. Some proofs are
>> easy. Some are hard. There is no "higher burden" involved in proving a
>> negative --
>
> Proving a positive provides only showing a single example.
> proving a negative requires showing that no example can possibly
> exist, it must categorically exhaustively consider every possibility.

Alas, you haven't a clue as to how an argument by reductio ad absurdum
works. Quite sad, really.

>> i.e., proving that nothing has a certain well-defined property. You
>> just need a sound proof. As others have noted, typical proofs of the
>> unsolvability of the Halting Problem proceed by reductio. Such proofs
>> show in *one fell swoop* that all attempts to construct something with
>> a given property must necessarily fail:
>>
>> 1. Assume something has property P.
>> 2. Show this assumption entails a contradiction.
>> 3. Conclude (by reductio) that nothing has property P.
>
> 95% of the people here screwed up the second step,

No, they didn't. Turing didn't. I didn't: http://tinyurl.com/6ow6c.

> and then presumed the third step from the incorrect second step. If my
> proof is correct, (and no one has correctly shown that it isn't)

Actually, they have, many times. Here is the proof: Turing proved the
halting problem is unsolvable. Therefore, your proof is incorrect. QED

> then even Turing himself failed to prove this negative.

Vide supra.

>> In the case at hand, P is the property of being a TM that -- by whatever
>> means -- computes the function Halts, and the contradiction that follows
>> from the assumption that something has this property is that there is a
>> TM with impossible properties (it halts iff it doesn't). So no TM
>> computes Halts.
>
> But then this was merely a lack of precision in taking the semantic
> meaning of what was specified. No TM Halts if it doesn't, this is true.
> Its not about halting if you don't halt. Its about not halting if you
> ARE TOLD that you will halt. It about return values.

I'll light a candle for you.

>> Why you can't see, in light of much clear and simple instruction, that
>> this shows that your project is either trivial or hopeless is sad,
>> perplexing, and, alas, rather morbidly fascinating.

-cm

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