Halting Problem proofs appear to be bogus!

From	Mr Flibble <flibble@reddwarf.jmc>
Newsgroups	comp.theory
Subject	Halting Problem proofs appear to be bogus!
Message-ID	<20210716142416.00003996@reddwarf.jmc> (permalink)
Organization	Jupiter Mining Corp
Date	2021-07-16 14:24 +0100

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Hi!

All extant halting problem proofs appear to be predicated on a
misunderstanding of the following contradiction:

	Suppose T[R] is a Boolean function taking a routine
	(or program) R with no formal or free variables as its
	argument and that for all R, T[R] — True if R terminates
	if run and that T[R] = False if R does not terminate. Consider
	the routine P defined as follows 

		rec routine P
			§L :if T[P] goto L
		Return §

	If T[P] = True the routine P will loop, and it will
	only terminate if T[P] = False. In each case T[P] has
	exactly the wrong value, and this contradiction shows
	that the function T cannot exist.

	[Strachey 1965]

T is indeed unable to decide P but for the wrong reason: T[P] is
recursive which means T can never decide if P halts because T never
halts itself; this mistake appears to have been missed by Strachey as
the §L <- L loop can't ever loop due to the recursion.

HOWEVER

Even if we ignore the error of recursion it does NOT follow that for
T[Q], T cannot decide if Q halts where Q is a program that does not
reference T.

[Strachey 1965] shows us that a decider cannot be part of or called by
that which is being decided (a pathological program) and given this it
seems to be unproven that a decider for programs that don't exhibit
this pathology cannot exist.

/Flibble

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Thread

Halting Problem proofs appear to be bogus! Mr Flibble <flibble@reddwarf.jmc> - 2021-07-16 14:24 +0100
  Re: Halting Problem proofs appear to be bogus! Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-16 14:34 +0100
    Re: Halting Problem proofs appear to be bogus! Mr Flibble <flibble@reddwarf.jmc> - 2021-07-16 14:39 +0100
      Re: Halting Problem proofs appear to be bogus! olcott <NoOne@NoWhere.com> - 2021-07-16 09:36 -0500
        Re: Halting Problem proofs appear to be bogus! Mr Flibble <flibble@reddwarf.jmc> - 2021-07-16 15:39 +0100
          Re: Halting Problem proofs appear to be bogus! wij <wyniijj@gmail.com> - 2021-07-16 08:38 -0700
            Re: Halting Problem proofs appear to be bogus! olcott <NoOne@NoWhere.com> - 2021-07-16 11:04 -0500
              Re: Halting Problem proofs appear to be bogus! wij <wyniijj@gmail.com> - 2021-07-16 09:25 -0700
                Re: Halting Problem proofs appear to be bogus! olcott <NoOne@NoWhere.com> - 2021-07-16 12:03 -0500
                Re: Halting Problem proofs appear to be bogus! Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-16 19:50 +0100
        Re: Halting Problem proofs appear to be bogus! Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-16 15:46 +0100
      Re: Halting Problem proofs appear to be bogus! Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-16 15:40 +0100
        Re: Halting Problem proofs appear to be bogus! Mr Flibble <flibble@reddwarf.jmc> - 2021-07-16 15:42 +0100
          Re: Halting Problem proofs appear to be bogus! Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-17 01:06 +0100
            Re: Halting Problem proofs appear to be bogus! olcott <NoOne@NoWhere.com> - 2021-07-17 10:52 -0500
      Re: Halting Problem proofs appear to be bogus! Andy Walker <anw@cuboid.co.uk> - 2021-07-16 16:12 +0100
        Re: Halting Problem proofs appear to be bogus! olcott <NoOne@NoWhere.com> - 2021-07-16 10:52 -0500
          Re: Halting Problem proofs appear to be bogus! wij <wyniijj@gmail.com> - 2021-07-16 09:11 -0700
            Re: Halting Problem proofs appear to be bogus! olcott <NoOne@NoWhere.com> - 2021-07-16 11:15 -0500
    Re: Halting Problem proofs appear to be bogus! olcott <NoOne@NoWhere.com> - 2021-07-16 09:13 -0500
      Re: Halting Problem proofs appear to be bogus! wij <wyniijj@gmail.com> - 2021-07-16 08:32 -0700
      Re: Halting Problem proofs appear to be bogus! Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-17 01:03 +0100
        Re: Halting Problem proofs appear to be bogus! olcott <NoOne@NoWhere.com> - 2021-07-17 10:46 -0500
          Re: Halting Problem proofs appear to be bogus! Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-18 02:32 +0100
            Re: Halting Problem proofs appear to be bogus! olcott <NoOne@NoWhere.com> - 2021-07-19 10:10 -0500
              Re: Halting Problem proofs appear to be bogus! Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-20 01:35 +0100
                Re: Halting Problem proofs appear to be bogus! olcott <NoOne@NoWhere.com> - 2021-07-20 09:24 -0500
                Re: Halting Problem proofs appear to be bogus! Ben Bacarisse <ben.usenet@bsb.me.uk> - 2021-07-21 01:28 +0100
              Re: Halting Problem proofs appear to be bogus! Richard Damon <Richard@Damon-Family.org> - 2021-07-19 20:48 -0700
  Re: Halting Problem proofs appear to be bogus! Peter <peterxpercival@hotmail.com> - 2021-07-16 15:27 +0100
    Re: Halting Problem proofs appear to be bogus! Mr Flibble <flibble@reddwarf.jmc> - 2021-07-16 15:36 +0100
      Re: Halting Problem proofs appear to be bogus! olcott <NoOne@NoWhere.com> - 2021-07-16 10:02 -0500
        Re: Halting Problem proofs appear to be bogus! Peter <peterxpercival@hotmail.com> - 2021-07-16 22:09 +0100
      Re: Halting Problem proofs appear to be bogus! wij <wyniijj@gmail.com> - 2021-07-16 08:46 -0700
      Re: Halting Problem proofs appear to be bogus! Peter <peterxpercival@hotmail.com> - 2021-07-16 22:07 +0100
        Re: Halting Problem proofs appear to be bogus! olcott <NoOne@NoWhere.com> - 2021-07-16 16:20 -0500
          Re: Halting Problem proofs appear to be bogus! Peter <peterxpercival@hotmail.com> - 2021-07-16 22:25 +0100
            Re: Halting Problem proofs appear to be bogus! olcott <NoOne@NoWhere.com> - 2021-07-16 16:32 -0500
              Re: Halting Problem proofs appear to be bogus! Peter <peterxpercival@hotmail.com> - 2021-07-17 11:48 +0100
    Re: Halting Problem proofs appear to be bogus! olcott <NoOne@NoWhere.com> - 2021-07-16 09:44 -0500
      Re: Halting Problem proofs appear to be bogus! Peter <peterxpercival@hotmail.com> - 2021-07-16 22:10 +0100
  Re: Halting Problem proofs appear to be bogus! olcott <NoOne@NoWhere.com> - 2021-07-16 09:32 -0500

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