Given a single Turing machine T, is there a decider D which takes the description of T as its input, and returns "true" if T halts and "false" if T does not? Well certainly there is: either the constant machine D_t that always returns "true", or else the constant machine D_f which always returns "false", does the job. There's no algorithm to decide which of these is actually the right D for the given T, but one of them definitely is. On Sun, Nov 9, 2014 at 10:31 PM, Warren D Smith <warren.wds@gmail.com> wrote:

I do not see the basis for APG's claim for for any particular turing machine T, it is decidable whether it halts. Au contraire, it is decidable IF it halts, but if it does not halt, then why is it decidable?

Similarly, particular propositions like the RH are decidable if false, but might be undecidable if true.

So I do not see APG's claim that only CLASSES of propositions undecidable.

-- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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