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 21:11:14 +0000 (UTC)

"Robert Low" <mtx014@linux.services.coventry.ac.uk> wrote in message
news:cfcku7$s0c$1@sunbeam.coventry.ac.uk...
| >parr\(*> <gniKyruaL@tenretnitb.moc> wrote:
| >[Apologies for the top-post but I wanted to leave the original
| >messages intact because they will all have to be addressed. Peter
| >asserts that there are a finite number of essentially different
| >halting problem solutions. I can prove that, if one exists, an
| >uncountable infinity of essentially different ones exist.]
|
| I don't understand what you're claiming here; there are
| only countably many Turing machines, so how can there
| be uncountably many of anything? (Except in the rather
| trivial sense that since there isn't a TM that solves
| the halting problem, assuming that there is one makes
| your system inconsistent and therefore every statement
| is now a theorem.)

There are indeed, a countable infinity of Turing machines.

And you've correctly guessed what happens when you try to find an
upper bound for the number of essentially different halt deciders.
All I did was to apply Peter's own logic. 

--
)>==ss$$%PARR(º>   Parr