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From: Richard Damon <richard@damon-family.org>
Newsgroups: comp.theory,comp.ai.philosophy
Subject: Re: Hypothetical possibilities V2
Date: Mon, 22 Jul 2024 20:01:04 -0400
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On 7/22/24 12:08 PM, olcott wrote:
> void DDD()
> {
>    HHH(DDD);
>    return;
> }
> 
> int main()
> {
>    HHH(DDD);
> }
> 
> Of the two hypothetical possible ways that HHH can be encoded:
> (a) HHH(DDD) is encoded to abort its simulation.
> (b) HHH(DDD) is encoded to never abort its simulation.
> 
> We can know that (b) is wrong because this fails to meet the design 
> requirement that HHH must itself halt.
> 
> We also know that any simulation that must be aborted to prevent the 
> infinite execution of the simulator is necessarily a non-halting input.
> 
> 

Remember, every HHH crreates a DIFFERENT "PROGRAM" DDD to decide on, and 
thus you don't have a case you can apply the property of the excluded 
middle.

In case (a) HHH(DDD) aborts and returns, so it returns to DDD and DDD 
Halts, so if HHH returned 0, it was wrong.

In case (b) HHH(DDD) never aborts, and as you admit, fails to be a decider.

We can show that for (a), that HHH was wrong by giving that same DDD 
(which still calls that HHH) to another emulator (like the (b) case) put 
in an unused location of memory, and it WILL emulate that input to the 
final state, thus proving you wrong.

This is what you HHH1 shows,