Re: Foundation for a Formal Refutation of the Original Halting Problem?

From: >parr\(*> (gniKyruaL_at_tenretnitb.moc)
Date: 08/11/04 

Date: Wed, 11 Aug 2004 21:39:58 +0000 (UTC)

"Peter Olcott" <olcott@worldnet.att.net> wrote in message
news:gwmSc.427662$Gx4.84040@bgtnsc04-news.ops.worldnet.att.net...
|
| ">parr(*>" <gniKyruaL@tenretnitb.moc> wrote in message
news:cfcgeh$pig$1@titan.btinternet.com...
[my original post, which follows, has been trimmed slightly]

| > Here's the story on this point so far:
| > ============
| >
| > Background: Given the existence of one halt
| > decider, an infinity can be constructed
| > by adding null statements, this Peter
| > accepts. But Peter's work so far does
| > not take into account that a Halt decider
| > must handle an infinite number of Halt
| > deciders.
| >
| > Parr> 2. How do you square the existence of
| > an infinity of halting problem solutions
| > with your thesis?
| >
| > Peter> There are not an infinity of Halting
| > Problem solutions that are different in
| > essence.
| >
| > Parr> How do you know? I see no statement
| > to that effect in any of your work. You
| > have conceived of a single one [halt
| > decider]. Other heads may pinpoint many
| > more angles.
| >
| > Peter> I have constructed a thought
| > experiment that shows that omniscience is
| > itself finite. The universal set of all
| > knowledge (conceptual and otherwise) (If
| > one does not count repeats as new
| > knowledge) is finite. This is off-topic.
| > =========
| >
| > You answer that by including the word 'omniscience'[**]. I did
not
| > use that word. You talk about the set of all knowledge. 'All
| > knowledge' is not relevant. What is relevant is 'the set of all
| > possible essentially diffeent halt deciders'. Let me stress,
_ALL
| > POSSIBLE_, not all currently known (=0).
|
| If the universal set of all knowledge is finite then it logically
| follows that any subset of this set is also finite.

Of course.

But I still fail to see the relevance of talking about 'knowledge'.
We are talking about Turing's paper of 1936 (with 1937 amendments),
are we not?

And you still have not said how many essentially different halt
deciders there are. Is it 1? Is it 2? Is it 97?

I put it to you that you not only do not have a clue, but that you
have not the foggiest idea how to work it out.

But why should you bother?

I'll tell you.

The longer you take getting to grips with Turing's original paper,
the more chance there is that someone who has read and understood its
35 pages will step in and come up with a version of what you're
claiming. However, you will not be able to do a thing about it
because you have been frightened of trying to learn how to read what
he wrote, and frightened to try to understanding what he wrote
sufficiently well to pinpoint the flaw in his argument.

The paper is frighteningly long. It is frighteningly full of
definitions and complicated looking formulae. It takes a long time
to get to grips with it, particularly if you're faffing about
trolling a newsgroup for hours at a time.

Personally, I've lost interes..... 

--
)>==ss$$%PARR(º>   Parr

Relevant Pages

  • Re: Foundation for a Formal Refutation of the Original Halting Problem?
    ... "Peter Olcott" wrote in message ... Given the existence of one halt ... |> not take into account that a Halt decider ... |> an infinity of halting problem solutions ...
    (sci.logic)
  • Re: Exploiting limitations of Turing machines in Turing tests?
    ... halts providing the correct answer or doesn't halt. ... My point is that if there exists a finite set A of decider programs ... a decider program in A which halts on input X. ... The self-referential halting problem of that program would be ...
    (comp.ai.philosophy)
  • Re: A challenge to Peter Olcott
    ... | to an arbitrarily large tape (if the tape symbols are ... by Peter. ... |> when it has found the lowest odd perfect number. ... |> The challenge is, Peter, what decision does your halt ...
    (sci.logic)
  • Re: Disproof of the Halting Problems Conclusion
    ... > Peter> that both of these functions derive results that have the ... line-by-line execution trace of a specific counter-example proving you wrong. ... string InputData) ... Line 21) SecureOutput("The Program Will Not Halt"); ...
    (sci.logic)
  • Re: Disproof of the Halting Problems Conclusion
    ... > Peter> that both of these functions derive results that have the ... line-by-line execution trace of a specific counter-example proving you wrong. ... string InputData) ... Line 21) SecureOutput("The Program Will Not Halt"); ...
    (comp.theory)