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Re: Peer-reviewed arguments against Cantor Diagonalization
Posted:
Oct 29, 2012 4:30 PM
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On Monday, October 29, 2012 2:04:42 PM UTC-5, JRStern wrote:
> On Mon, 29 Oct 2012 09:14:02 -0700 (PDT), Arturo Magidin
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> <magidin@member.ams.org> wrote:
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> >> >The government doesn't like it when I read minds without a
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> >> >warrant, so I try not to do it, you see.
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> >>
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> >> There are constructivist objections to the whole enterprise. If
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> >> nothing else, I was hoping to see something like these addressed
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> >> against the diagonal argument piecemeal.
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> >
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> >In a constructivist universe, you cannot have a function defined
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> >on the natural numbers, and you cannot have a set of real numbers at all.
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> >The very premise ("Suppose f:N-->(0,1) is a function") is considered
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> >nonsensical in the constructivist point of view.
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> >
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> >You can only talk about a "rule" that will allow you, in principle,
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> >to compute f(n) up to any degree of exactness that you care to specify.
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> >You can encode the procedure in the proof given assuming that the
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> >function f is given by Turing Machine which, when given n as an input,
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> >will give you the number of a Turing machine that computes f(n).
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> >Then you can establish the existence of a Turing machine r which,
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> >when given as input the number of a Turing machine that computes
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> >a function f as described above, will produce as an output the
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> >sequence b_n which is not equal to the output of any Turing machine
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> >whose number is produced by the Turing machine corresponding to f.
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> >That much is allowable within the computational universe.
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> Doesn't this sound rather like what some of the "cranks" hereabouts
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> are trying to say?
Which "cranks", and what specifically do they say that you find "rather like" exactly which part of the above?
Yet again: one cannot give you an exact answer if you insist on presenting nothing but vague statements that have little or no actual content. I certainly have no desire to waste my time discussing phantoms and ephemerals, so perhaps you can stop being vague and wishy-washy, and give some specifics? If you can't, then stop trying to think about math. Now. Stop. Yes. You. Stop it. There is absolutely no point in discussing mathematics on the basis of vague pronouncements, vague statements, vague "feelings", and vague impressions; because, whatever it is you end up doing, it's not mathematics.
--
Arturo Magidin
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> J.
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