Re: [PO] Re: Proving a negative is hard

From: Mitch Harris (harrisq_at_tcs.inf.tu-dresden.de)
Date: 08/23/04 

Date: Mon, 23 Aug 2004 10:24:57 +0200

Peter Olcott wrote:
>
> No one has even attempted to show that there is more than
> one case. Some people have claimed that there is more than
> one case, yet never provided any supporting reasoning.

I think some people have described other cases in general
terms. I will do so again. In creating a Diag TM (a
LoopIfHalts program), you can add on extraneous do-nothing
operations (compute some arbitrary digits of pi, solve some
linear equations, whatever). Or you could even modify the
real action of what happens after calling Halt: if the
return is true, then instead of "while(true) ;" you could
call Diag again with the same parameters (and deduce that
this would cause an infinite loop). There might be other
ways of creating a Diag TM, but my imagination is a bit
lacking. The burden of proof for you would be to show that
it is not my imagination that is limited but reality.

> If there was only one case that shows the undecidability of
> the Halting Problem, (it sure looks like there is only one case,
> no one has ever provided evidence otherwise), and I refute
> this single case,

-all- these cases, possibly treated as an equivalence class.

> then I have refuted the proof of the undecidability
> of the Halting Problem.

Yes, but you still will not have shown anything about the
claim itself. There might be other ways of proving it. 

-- 
Mitch Harris
(remove q to reply)

Relevant Pages

  • Re: [PO] Re: Proving a negative is hard
    ... Peter Olcott wrote: ... In creating a Diag TM (a ... it is not my imagination that is limited but reality. ... > the Halting Problem, (it sure looks like there is only one case, ...
    (sci.logic)
  • Re: [PO] Re: Proving a negative is hard
    ... > Peter Olcott wrote: ... In creating a Diag TM (a ... Undecidability can not be shown to exist. ... >> no one has ever provided evidence otherwise), and I refute ...
    (sci.logic)
  • Re: [PO] Re: Proving a negative is hard
    ... > Peter Olcott wrote: ... In creating a Diag TM (a ... Undecidability can not be shown to exist. ... >> no one has ever provided evidence otherwise), and I refute ...
    (comp.theory)