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

On 07/05/2025 19:31, olcott wrote:

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.

There isn't a terrible mistake in the Halting Problem.

 

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.

If the code is unreachable, it can't be part of a working program, so simply remove it.

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.

I know precisely what unreachable code is.
Take it out. It's unreachable, so it cannot contribute to the work of the program. Why did you bother to put it in?
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
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