Re: Formal systems that cannot possibly be incomplete except for unknowns and unknowable

On 5/7/2025 1:14 PM, Richard Heathfield wrote:

On 07/05/2025 18:55, olcott wrote:

When THERE IS NO CONTRADICTION then proof by contradiction fails.
How do you not get that?

 I do. You must be talking about the Olcott Problem again, because the contradiction is inherent in the Halting Problem.
 

Not when its terrible mistake is corrected.

It starts with the assumption that a universal halt decider can be written, and then shows that such a decider can be used to devise a program that the 'universal' decider can't decide --- a contradiction.
 But you already know all this.
 

I already know that the contradictory part of the
counter-example input has always been unreachable code.
Thus PROOF BY CONTRADICTION FAILS because there never
was any actual contradiction. It has been a false assumption
that there has been a contradiction for 90 years.
If you have no idea what unreachable code is you won't
get this.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer