Re: Halting Problem proofs appear to be bogus!

From	Mr Flibble <flibble@reddwarf.jmc>
Newsgroups	comp.theory
Subject	Re: Halting Problem proofs appear to be bogus!
Message-ID	<20210716143926.000052ae@reddwarf.jmc> (permalink)
References	<20210716142416.00003996@reddwarf.jmc> <871r7ys7pd.fsf@bsb.me.uk>
Organization	Jupiter Mining Corp
Date	2021-07-16 14:39 +0100

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On Fri, 16 Jul 2021 14:34:54 +0100
Ben Bacarisse <ben.usenet@bsb.me.uk> wrote:

> Mr Flibble <flibble@reddwarf.jmc> writes:
> 
> > All extant halting problem proofs appear to be predicated on a
> > misunderstanding of the following contradiction:
> 
> I don't think you've read any actual proofs, let along all of them.
> Why you would even say such a thing?
> 
> > 	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
> 
> T[P] is not recursive.  Maybe you don't understand what the CPL means?

Of course it is recursive, such is obvious even to the casual reader
who is unfamiliar with the CPL language (a clue: read the paragraph
before the definition of P again).

> 
> Further, this argument must fail for any of the actual proofs that are
> based on Turing machine because TMs have not functions, not calls and
> no recursion.

Depends on whether or not there is an isomorphic equivalence.

/Flibble

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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