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

On 07/05/2025 20:35, olcott wrote:

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

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

<snip>

>
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.

If the simulation can't reach code that the directly executed program reaches, then it's not a faithful simulation.
<snip>

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.

Then it's not a correct emulation, so you have a contradiction.

Thus the "proof by contradiction" fails BECAUSE THERE
IS NO CONTRADICTION there never has been.

Whoops, we just found another one.
--
Richard Heathfield
Email: rjh at cpax dot org dot uk
"Usenet is a strange place" - dmr 29 July 1999
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