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

On 5/7/2025 1:59 PM, Richard Heathfield wrote:

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.
>

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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.
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But you already know all this.
>

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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.
 

It is unreachable by the Halting Problem counter-example
input D when correctly simulated by the simulating
termination analyzer H that it has been defined to thwart.
All the time that people believed that an input could
actually do the opposite of whatever value that its
termination analyzer returns THEY WERE WRONG.

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?
 

It is only unreachable by DD correctly emulated by HHH.
This means that DD cannot possibly do the opposite of
whatever value that HHH returns.
Thus the "proof by contradiction" fails BECAUSE THERE
IS NO CONTRADICTION there never has been.
--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer