Re: Can the 'Turing Problem' be deflated?

Jesse F. Hughes wrote:
J Jones <jonescardiff@xxxxxxx> writes:

"The TM either halts or does not engage in computation."

That should suffice. The statement is analytic - its proof is
self-evident.

You are just adorable!

But I'm a bit unsure how to understand this brilliant new analysis.
According to the insight you've provided, the Halting problem:

(a) is not a problem at all.
(b) is solved.
(c) is ill-posed.
(d) is self-evident.

Much thanks for a prompt reply, so that I can keep score here at home.


OK. Off the cuff, here it is:

(a)IF Turing wants to address a particular problem, THEN it may be the case that the way he tackles it through the 'halting problem' doesn't actually address it. So "The Turing Problem MAY be a problem", but IF it is a problem, THEN the problem is not addressed in the form in which it is cast in the halting problem.
(b) I say that "the Turing Problem is not solved", because the parameters in which a solution is cast are the same as those in which the problem is cast, and those parameters have been put in doubt.
(c) I do not know if the Turing Problem is ill-posed. From (a), above, the halting problem may ACCURATELY mirror Turing's real problem if he has one, whether or not that latter problem is ill-posed. As I don't know what Turing's original, central concern is, if indeed there is a more basic problem he wishes to address, then I can't say whether the halting problem is either well-posed but unsound, or ill-posed and unsound.
(d) An analytic statement, such as the one I presented, is self-evident, that is, we do not need to step into the synthetic domain to consider it. However, an analytic statement still needs to be presented, even if it is self-evident. Now, because it is not presented in the Turing halting problem per se, then there is nothing of which we can ask 'is the solution to the halting problem self-evident or not'.

I propose instead that the Halting Problem
(e) is dissolved. A 'dissolution' might be of what I think Conant calls "mere nonsense" . Don't quote me on that as I can't find Conant's paper ("was Wittgenstein whistling it?"). There are grades of nonsense (there is also a 'substantial nonsense'), but I can't find that paper, and its bed-time.
.

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