Re: Attempt to Refute the Halting Problem's Refutation

From: Peter Olcott (olcott_at_worldnet.att.net)
Date: 08/14/04 

Date: Sat, 14 Aug 2004 14:47:46 GMT

"Daryl McCullough" <daryl@atc-nycorp.com> wrote in message news:cfk0380on6@drn.newsguy.com...
> Peter Olcott says...
>
> >Statement of what I have achieved
>
> You haven't achieved anything, Peter. Turing's proof still
> stands, as always, and you've done nothing but confuse yourself
> about it.
>
> The fact is: there is no program H(x,y) such that for any pair
> of strings x and y, *always* returns 1 if x is the code for a
> program that halts on input y, and *always* returns 0 otherwise.
>
> --
> Daryl McCullough
> Ithaca, NY
>
Yet this was not in the definition of the problem it was merely an
assumption of the proof, thus when the proof is applied to the
actual problem, the proof fails to correspond.

The specific error that Turing made was that the assumption
made in the proof retained its 1-1 mapping to the definition of
the problem itself. Since it did not, he erred. It is completely
obvious that he and most of the rest of the world made this
same mistake. Every instance of the specific definition of the
problem (that I have encountered) takes on essentailly this same
meaning:

No program can ever be written to determine whether any
arbitrary program will halt

Even Turing's own definition of the problem takes on this same meaning.

Halting Problem according to Alan Turing:
The problem of finding out whether a given number is the D.N of
a circle-free machine, and we have no general process for doing
this in a finite number of steps. In fact, by applying the diagonal
process argument correctly, we can show that there cannot be any
such general solution.

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