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

From: Peter Olcott (olcott_at_worldnet.att.net)
Date: 08/24/04 

Date: Tue, 24 Aug 2004 01:46:59 GMT

"Mitch Harris" <harrisq@tcs.inf.tu-dresden.de> wrote in message news:2otnupFeje1sU1@uni-berlin.de...
> 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

No No No. Substantially different, different in substance.

> 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.

No it becomes the Olcott thesis:
Undecidability can not be shown to exist.

> > 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.

I have cut off all possible paths to undecidability.

> --
> 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 ... Undecidability can not be shown to exist. ... >> no one has ever provided evidence otherwise), and I refute ...
    (comp.theory)
  • Incredible Result from Olcott-Reasoning
    ... As followers of this group have seen, Peter Olcott re-cast the ... simpler than Turing's construction to show the halting problem ... That undecidability result was already known. ...
    (sci.logic)
  • Re: [PO] Re: Proving a negative is hard
    ... >> Peter Olcott says... ... It is provably false that there is a program ... >If you make this assumption then eliminating the undecidability ... 1, we derive a contradiction, and we conclude that 1 is false. ...
    (sci.logic)
  • Re: [PO] Re: Proving a negative is hard
    ... >> Peter Olcott says... ... It is provably false that there is a program ... >If you make this assumption then eliminating the undecidability ... 1, we derive a contradiction, and we conclude that 1 is false. ...
    (comp.theory)
  • 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, ...
    (comp.theory)