Re: The proof that I was referring to is on the website
From: Peter Olcott (olcott_at_worldnet.att.net)
Date: 08/11/04
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Date: Tue, 10 Aug 2004 23:14:16 GMT
">parr(*>" <gniKyruaL@tenretnitb.moc> wrote in message news:cfbfhu$hih$3@titan.btinternet.com...
>
> "Peter Olcott" <olcott@worldnet.att.net> wrote in message
> news:q1KRc.415659$Gx4.16777@bgtnsc04-news.ops.worldnet.att.net...
> | If Turing use the diagonalization approach then the basis of my
> refutation
> | would not apply because the pure math version does not permit the
> | equations to have any intelligence. The equations are not allowed
> to
> | refrain from returning a result.
>
> What do you mean 'If Turing use[d]...'?
>
> Here you are, stating as a fact, and doing so repeatedly over a
> period of months, that Turing was wrong, yet you do not have the
> faintest idea what method Turing used.
I read part of the proof last night. He did use the diagonanlization.
>From what I understand this is like a multiplication table. It can not
decide what it will place on the diagonal any more than the 9th column
of the 9th row of a multiplication table can decide to have anything
other than 81.
By limiting his proof to a purely mathematical approach he is implicitly
assuming that the only possible way to determine if a TM halts always
requires the halt analyzer to return its results to every caller.
This shows that his proof does not apply to what it claims that it
applies to.
Quick Summary:
Alan Turing conclusively proved is that it is impossible to construct
a halt analyzer that always returns a correct result back to the program
being analyzed.
Since returning the result back to the program being analyzed is not the
only way to construct a halt analyzer, his proof did not show that
constructing a halt analyzer that works correctly for all input is impossible.
> Which does not surprise me, because you do not even know what the
> title of his paper is.
>
> Anyway, there are two ways of arriving at the same conclusion Turing
> did, firstly by diagonalisation, and secondly by demonstrating a
> paradoxical situation by assuming a halting problem is possible. As
> you accept that diagonalisation is valid, and as you also accept that
> if Turing used that approach, then you are wrong, you must also
> accept that the actual approach Turing used was valid.
>
> What do you mean 'the pure math version'. Turing's conclusion was
> with respect to the behaviour of a computing machine. In order to
> describe the behaviour, and to do so scientifically and rigorously,
> he used Hilbert's [restricted] functional calculus. This calculus
> was specifically designed to describe calculation.
>
> I really do think it's about time you discovered at least the title
> of his paper.
> --
> )>==ss$$%PARR(º> Parr
>
>
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