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Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --logically impossible--

Subject	Author
Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	immibis
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	immibis
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	immibis
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	immibis
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	immibis
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	immibis
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	immibis
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	immibis
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior YES/NO	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior YES/NO	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --a	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --a	immibis
H ⟨Ĥ⟩ ⟨Ĥ⟩ is correct when reports on the actual behavior that it sees	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --a	olcott
When H ⟨Ĥ⟩ ⟨Ĥ⟩ reports on the behavior it actually sees then it is correct	olcott
Re: When H ⟨Ĥ⟩ ⟨Ĥ⟩ reports on the behavior it actually sees then it is correct	Mikko
Re: When H ⟨Ĥ⟩ ⟨Ĥ⟩ reports on the behavior it actually sees then it is correct	Richard Damon
Re: When H ⟨Ĥ⟩ ⟨Ĥ⟩ reports on the behavior it actually sees then it is correct	olcott
Re: When H ⟨Ĥ⟩ ⟨Ĥ⟩ reports on the behavior it actually sees then it is correct	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	immibis
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --l	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --a	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	Mikko
H ⟨Ĥ⟩ ⟨Ĥ⟩ is correct when reports on the actual behavior that it sees	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --w	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --O	immibis
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --O	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --w	immibis
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	immibis
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	immibis
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --w	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --O	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --O	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --O	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	immibis
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	Mikko
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	Mikko
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	immibis
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	Mikko
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	immibis
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	Mikko
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	immibis
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	Mikko
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	Mikko
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	immibis
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	immibis
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	Mikko
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --n	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --a	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC	immibis
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC	immibis
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	immibis
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	Richard Damon
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	olcott
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	immibis
Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior	olcott

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Re: ZFC solution to incorrect questions: reject them

<usq57b$1l201$16@i2pn2.org>

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https://www.novabbs.com/devel/article-flat.php?id=54799&group=comp.theory#54799

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Path: i2pn2.org!.POSTED!not-for-mail
From: rich...@damon-family.org (Richard Damon)
Newsgroups: comp.theory
Subject: Re: ZFC solution to incorrect questions: reject them
Date: Tue, 12 Mar 2024 11:00:11 -0700
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by: Richard Damon - Tue, 12 Mar 2024 18:00 UTC

On 3/12/24 8:52 AM, olcott wrote:

> ∀ H ∈ Turing_Machine_Deciders
> ∃ TMD ∈ Turing_Machine_Descriptions |
> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>
> There is some input TMD to every H such that
> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>
> When we disallow decider/input pairs that are incorrect
> questions where both YES and NO are the wrong answer
> (the same way the ZFC disallowed self-referential sets) then
> pathological inputs are not allowed to come into existence.
>
> Does the barber that shaves everyone that does not shave
> themselves shave himself? is rejected as an incorrect question.
> https://en.wikipedia.org/wiki/Barber_paradox#
>

And ZFC says that H is NOT the "Set of Turing Machines" but a single
element of it at a time.

There is no problem with making a H^ from an H, it is built from totally
legal steps.

The fact that it shows that any H you can contruct will get this problem
wrong, proves the Halting Mapping is uncomputable, not non-existant.

Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --new focus--

<usq5eg$1l201$17@i2pn2.org>

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https://www.novabbs.com/devel/article-flat.php?id=54800&group=comp.theory#54800

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by: Richard Damon - Tue, 12 Mar 2024 18:04 UTC

On 3/11/24 8:56 AM, olcott wrote:
> On 3/11/2024 10:36 AM, immibis wrote:
>> On 11/03/24 04:33, olcott wrote:
>>> Then we are back to undecidability being incorrectly construed
>>> as an actual limit to computation.
>>
>> Proof that a certain thing cannot be computed is always a limit to
>> computation.
>>
> Yet in only the same way that the Liar Paradox
> "This sentence is not true."
> does not have a truth value that can be computed.
>
>> For example, you can't compute the colour of the number 4. That is an
>> actual limit to computation.
>>
>
> The inability to to the logically impossible is not any actual limit.
> If we say that the Halting Problem cannot be solved for the same sort
> of reason that Square Circles do not exist then this is not any actual
> limit.

But SHOWING that something is logically impossible reveals the
limitations that were already there.

Yes, the Halting Theorem doesn't MAKE the problem impossible, it shows
that it always was, and gives us knowledge of that.

But, you don't understand the nature of Truth and Knowledge, so that
won't make sense.

>
>> You can't compute the halting problem. That is an actual limit to
>> computation.
>

Re: When H ⟨Ĥ⟩ ⟨Ĥ⟩ reports on the behavior it actually sees then it is correct

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by: Richard Damon - Tue, 12 Mar 2024 18:05 UTC

On 3/11/24 9:08 AM, olcott wrote:
> On 3/11/2024 10:14 AM, Mikko wrote:
>> On 2024-03-11 14:42:30 +0000, olcott said:
>>
>>> On 3/11/2024 5:42 AM, Mikko wrote:
>>>> On 2024-03-11 02:05:53 +0000, olcott said:
>>>>
>>>>> On 3/10/2024 8:52 PM, Richard Damon wrote:
>>>>>> On 3/10/24 6:00 PM, olcott wrote:
>>>>>>> On 3/10/2024 2:23 PM, Richard Damon wrote:
>>>>>>>> On 3/10/24 11:23 AM, olcott wrote:
>>>>>>>>> On 3/10/2024 12:55 PM, Richard Damon wrote:
>>>>>>>>>> On 3/10/24 10:17 AM, olcott wrote:
>>>>>>>>>>> On 3/10/2024 12:08 PM, Richard Damon wrote:
>>>>>>>>>>>> On 3/10/24 9:52 AM, olcott wrote:
>>>>>>>>>>>>> On 3/10/2024 10:50 AM, Richard Damon wrote:
>>>>>>>>>>>>>> On 3/10/24 7:28 AM, olcott wrote:
>>>>>>>>>>>>>>> On 3/10/2024 12:16 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>> On 3/9/24 9:49 PM, olcott wrote:
>>>>>>>>>>>>>>>>> On 3/9/2024 11:36 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>> On 3/9/24 9:14 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>> On 3/9/2024 10:55 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>> On 3/9/24 8:30 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>> On 3/9/2024 7:40 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>> On 10/03/24 02:37, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 3/9/2024 7:32 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 10/03/24 02:29, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 3/9/2024 7:24 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>> On 10/03/24 01:30, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/9/2024 6:24 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 10/03/24 01:22, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/9/2024 5:57 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 10/03/24 00:26, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/9/2024 5:10 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 9/03/24 23:22, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/9/2024 3:50 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 9/03/24 22:34, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What criteria would you use so that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ knows what
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrong answer to provide?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ is stipulated to use the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exact same objective criteria that H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ uses.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Simulating halt deciders must make sure
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that they themselves
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> do not get stuck in infinite execution.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This means that they
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> must abort every simulation that cannot
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> possibly otherwise halt.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This requires Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ to abort its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulation and does not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> require H ⟨Ĥ⟩ ⟨Ĥ⟩ to abort its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulation when Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ aborts
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> its simulation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ does simulate itself in
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> recursive simulation H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> does not simulate itself in recursive
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ is stipulated to use the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exact same objective criteria that H ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> uses.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> *Only because Ĥ.H is embedded within Ĥ
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and H is not*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ can possibly get stuck in
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> recursive simulation and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H ⟨Ĥ⟩ ⟨Ĥ⟩ cannot possibly get stuck in
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> recursive simulation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You dishonestly ignored that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is stipulated to use the exact same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> OBJECTIVE criteria that H ⟨Ĥ⟩ uses.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The above is true no matter what criteria
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that is used
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> as long as H is a simulating halt decider.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> Objective criteria cannot vary based on who
>>>>>>>>>>>>>>>>>>>>>>>>>>>> the subject is. They are objective. The
>>>>>>>>>>>>>>>>>>>>>>>>>>>> answer to different people is the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>> answer if the criteria are objective.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> It is objectively true that Ĥ.H can get stuck
>>>>>>>>>>>>>>>>>>>>>>>>>>> in recursive
>>>>>>>>>>>>>>>>>>>>>>>>>>> simulation because Ĥ copies its input thus
>>>>>>>>>>>>>>>>>>>>>>>>>>> never runs
>>>>>>>>>>>>>>>>>>>>>>>>>>> out of params.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> It is objectively true that Ĥ cannot possibly
>>>>>>>>>>>>>>>>>>>>>>>>>>> get stuck
>>>>>>>>>>>>>>>>>>>>>>>>>>> in recursive because H does not copy its
>>>>>>>>>>>>>>>>>>>>>>>>>>> input thus runs
>>>>>>>>>>>>>>>>>>>>>>>>>>> out of params.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> Wrong. Dead wrong. Stupidly wrong. So wrong
>>>>>>>>>>>>>>>>>>>>>>>>>> that a dead monkey could do better. Write the
>>>>>>>>>>>>>>>>>>>>>>>>>> Olcott machine (not x86utm) code for Ĥ and I
>>>>>>>>>>>>>>>>>>>>>>>>>> would show you.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> *In other words you are denying these verified
>>>>>>>>>>>>>>>>>>>>>>>>> facts*
>>>>>>>>>>>>>>>>>>>>>>>>> *In other words you are denying these verified
>>>>>>>>>>>>>>>>>>>>>>>>> facts*
>>>>>>>>>>>>>>>>>>>>>>>>> *In other words you are denying these verified
>>>>>>>>>>>>>>>>>>>>>>>>> facts*
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ
>>>>>>>>>>>>>>>>>>>>>>>>> applied to ⟨Ĥ⟩ halts
>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn // Ĥ
>>>>>>>>>>>>>>>>>>>>>>>>> applied to ⟨Ĥ⟩ does not halt
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> That's not a verified fact, that's just
>>>>>>>>>>>>>>>>>>>>>>>> something you want to be true.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> ∞ means infinite loop. Infinite loop doesn't
>>>>>>>>>>>>>>>>>>>>>>>> halt. You see how stupid it is, to say that an
>>>>>>>>>>>>>>>>>>>>>>>> infinite loop halts?
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> Execution trace of Ĥ applied to ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>> (a) Ĥ.q0 The input ⟨Ĥ⟩ is copied then
>>>>>>>>>>>>>>>>>>>>>>>>> transitions to Ĥ.H
>>>>>>>>>>>>>>>>>>>>>>>>> (b) Ĥ.H applied ⟨Ĥ⟩ ⟨Ĥ⟩ (input and copy)
>>>>>>>>>>>>>>>>>>>>>>>>> simulates ⟨Ĥ⟩ applied to ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>> (c) which begins at its own simulated ⟨Ĥ.q0⟩ to
>>>>>>>>>>>>>>>>>>>>>>>>> repeat the process
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> Execution trace of H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ BECAUSE
>>>>>>>>>>>>>>>>>>>>>>>> IT IS PRECISELY IDENTICAL TO STEPS B AND C:
>>>>>>>>>>>>>>>>>>>>>>>> > (b) Ĥ.H applied ⟨Ĥ⟩ ⟨Ĥ⟩ (input and copy)
>>>>>>>>>>>>>>>>>>>>>>>> simulates ⟨Ĥ⟩ applied to ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>> > (c) which begins at Ĥ's own simulated ⟨Ĥ.q0⟩
>>>>>>>>>>>>>>>>>>>>>>>> to repeat the process
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> *Yes and the key step of copying its input is
>>>>>>>>>>>>>>>>>>>>>>> left out so*
>>>>>>>>>>>>>>>>>>>>>>> *H ⟨Ĥ⟩ ⟨Ĥ⟩ runs out of params and Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>> never runs out of params*
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> that isn't how any of this works. Do you even know
>>>>>>>>>>>>>>>>>>>>>> what words mean?
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> (b) and (c) are not the same as (1) and (2)
>>>>>>>>>>>>>>>>>>>>> Execution trace of H applied to ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>> (1) H applied ⟨Ĥ⟩ ⟨Ĥ⟩ simulates ⟨Ĥ⟩ applied to ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>> (2) which begins at simulated ⟨Ĥ.q0⟩
>>>>>>>>>>>>>>>>>>>>> (a) Ĥ.q0 The input ⟨Ĥ⟩ is copied then transitions
>>>>>>>>>>>>>>>>>>>>> to Ĥ.H
>>>>>>>>>>>>>>>>>>>>> (b) Ĥ.H applied ⟨Ĥ⟩ ⟨Ĥ⟩ (input and copy) simulates
>>>>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ applied to ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>> (c) which begins at its own simulated ⟨Ĥ.q0⟩ to
>>>>>>>>>>>>>>>>>>>>> repeat the process
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> This means that Turing machine H ⟨Ĥ⟩ ⟨Ĥ⟩ can see
>>>>>>>>>>>>>>>>>>>>> one more execution
>>>>>>>>>>>>>>>>>>>>> trace of Ĥ ⟨Ĥ⟩ than its simulated Turing machine
>>>>>>>>>>>>>>>>>>>>> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ can see.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Nope, your just being stuupid, perhaps intentionally.
>>>>>>>>>>>>>>>>>>>> (c) just moves around to its simulation of a
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> (a) H^.q0 (H^)
>>>>>>>>>>>>>>>>>>>> H^ then makes a copy of its inp
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> (b) H^.H (H^) (H^) == (1) H (H^) (H^)
>>>>>>>>>>>>>>>>>>>> The algorithm of H begins a simulation of its input,
>>>>>>>>>>>>>>>>>>>> watching the behaior of H^ (H^)
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> (c) = (2)
>>>>>>>>>>>>>>>>>>>> Which begins at the simulation of H^.q0 (H^)
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> (d = sim a) = (sim a)
>>>>>>>>>>>>>>>>>>>> Ths Simulated H^.q0 (H^) makes a copy of its input
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> (e = sim b) = (sim b)
>>>>>>>>>>>>>>>>>>>> The Simulated H^.H (H^) (H^) has is H begin the
>>>>>>>>>>>>>>>>>>>> simulation of its input ...
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> and so on.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Both machine see EXACTLY the same level of details.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Yes, the top level H is farther along at any given
>>>>>>>>>>>>>>>>>>>> time then its simulated machine, and that is H's
>>>>>>>>>>>>>>>>>>>> problem, it has to act before it sees how its
>>>>>>>>>>>>>>>>>>>> simulation will respond to its copy of its actions.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Thus, if it stops, it needs to make its decision
>>>>>>>>>>>>>>>>>>>> "blind" and not with an idea of how the machine it
>>>>>>>>>>>>>>>>>>>> is simulating will perform.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> If it doesn't stop, the level of recursion just
>>>>>>>>>>>>>>>>>>>> keeps growing and no answer ever comes out.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> The earliest point that H ⟨Ĥ⟩ ⟨Ĥ⟩ can possibly see to
>>>>>>>>>>>>>>>>>>> abort
>>>>>>>>>>>>>>>>>>> its simulation is immediately before Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>> would begin
>>>>>>>>>>>>>>>>>>> its simulation. Right before its cycle repeats the
>>>>>>>>>>>>>>>>>>> first time.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> So?
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> If it DOES abort there, then so will H^.H when it gets
>>>>>>>>>>>>>>>>>> to that point in its simulation, which will be AFTER
>>>>>>>>>>>>>>>>>> The point that H has stopped simulating it, so H
>>>>>>>>>>>>>>>>>> doesn't know what H^ will do.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Thus, if H DOES abort there, we presume from your
>>>>>>>>>>>>>>>>>> previous answer it will think the input will not halt
>>>>>>>>>>>>>>>>>> and answer qn.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ applied to
>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ halts
>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn // Ĥ applied to
>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ does not halt
>>>>>>>>>>>>>>>>> H ⟨Ĥ⟩ ⟨Ĥ⟩ aborts right after Ĥ.Hq0 before it simulates
>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ ⟨Ĥ⟩.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> And if it does, as I said below, so will H^.H when it is
>>>>>>>>>>>>>>>> run.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Yes.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> And thus, H^.H will give the same answer as H,
>>>>>>>>>>>>>> so H^ will act contrary to what H says,
>>>>>>>>>>>>>> so H will give the wrong answer.
>>>>>>>>>>>>>
>>>>>>>>>>>>> Unlike anything else that anyone else has ever done both H
>>>>>>>>>>>>> ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>> and Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ correctly determine that they must abort
>>>>>>>>>>>>> their own
>>>>>>>>>>>>> simulation to prevent their own infinite execution.
>>>>>>>>>>>>
>>>>>>>>>>>> NOPE.
>>>>>>>>>>>
>>>>>>>>>>> If no source can be cited then the Olcott thesis
>>>>>>>>>>> "that no one did this before" remains unrefuted.
>>>>>>>>>>
>>>>>>>>>> Since, BY THE DEFINITIONS of what H MUST do to be correct, and
>>>>>>>>>> what H^ WILL do by its design, as shown in the Linz Proof.
>>>>>>>>>
>>>>>>>>> If no source can be cited that shows a simulating halt decider can
>>>>>>>>> correctly determine that it must abort its simulation of the
>>>>>>>>> Halting
>>>>>>>>> Problem's pathological input to prevent its own
>>>>>>>>> non-termination, then
>>>>>>>>> innovation remains attributable to me.
>>>>>>>>>
>>>>>>>>> <snip>
>>>>>>>>
>>>>>>>> Of course it can abort its simulation.
>>>>>>>>
>>>>>>>> It just needs some way to get the right answer.
>>>>>>>>
>>>>>>>
>>>>>>> *I have always been using this long before I read about it*
>>>>>>> blind variation and selective retention (BVSR)...
>>>>>>> Two common phenomena characterize BVSR thinking: superfluity and
>>>>>>> backtracking. Superfluity means that the creator generates a
>>>>>>> variety of ideas, one or more of which turn out to be useless.
>>>>>>
>>>>>> But if you have mo idea how things actually works, this seems to
>>>>>> just generate random noise.
>>>>>>
>>>>>>>
>>>>>>> Backtracking signifies that the creator must often return to an
>>>>>>> earlier approach after blindly going off in the wrong direction.
>>>>>>> https://www.scientificamerican.com/article/the-science-of-genius/
>>>>>>>
>>>>>>> *I am aware of no one else that had the idea to apply a
>>>>>>> simulating* *termination analyzer to the halting problem
>>>>>>> counter-example input*
>>>>>>> Professor Hehner had a seed of this idea before I did.
>>>>>>
>>>>>> Nope, I remember talk of that when I was in college, and they
>>>>>> showed why it can't work.
>>>>>>
>>>>>>>
>>>>>>> From a programmer's point of view, if we apply an interpreter to a
>>>>>>> program text that includes a call to that same interpreter with that
>>>>>>> same text as argument, then we have an infinite loop. A halting
>>>>>>> program
>>>>>>> has some of the same character as an interpreter: it applies to
>>>>>>> texts
>>>>>>> through abstract interpretation. Unsurprisingly, if we apply a
>>>>>>> halting
>>>>>>> program to a program text that includes a call to that same halting
>>>>>>> program with that same text as argument, then we have an infinite
>>>>>>> loop. https://www.cs.toronto.edu/~hehner/PHP.pdf
>>>>>>
>>>>>> You THINK so, but if the interpreter is a CONDITIONAL interpreter,
>>>>>> that doesn't hold.
>>>>>>
>>>>>> You seem to miss that fact.
>>>>>>
>>>>>>>
>>>>>>> *Turing Machine and Olcott machine implementations seem to be dead*
>>>>>>> *This the (possibly augmented) RASP machine equivalent of x86*
>>>>>>> Every machine must be able to get its own machine address.
>>>>>>>
>>>>>>
>>>>>> And the reason it is a dead end is they make it too hard for you
>>>>>> to cheat.
>>>>>>
>>>>>> You need to hide that your H is trying to get in some extra
>>>>>> information to hide that the embedded version of H doesn't give
>>>>>> the same answer, which just shows that your H^ is built wrong.
>>>>>
>>>>> My C code proves these two have different behavior:
>>>>> (a) H1(D,D) + H1_machine_address
>>>>> (b) H(D,D) + H_machine_address
>>>>> H1(D,D) does correctly determine the halt status of D(D) because
>>>>> H(D,D) does NOT correctly determine the halt status of D(D).
>>>>>
>>>>> I say:
>>>>> H1(D,D) is isomorphic to H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>> H(D,D) is isomorphic to Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>
>>>>> immibis disagrees.
>>>>> Correct reasoning will show who is correct.
>>>>
>>>> As H does not correctly determine the halt status of D(D) and
>>>> H1 does not correctly determine the halt status of D1(D1) neither
>>>> of them is a halt decider.
>>>>
>>>
>>> *MIT Professor Michael Sipser agreed this verbatim paragraph is correct*
>>> (a) If simulating halt decider H correctly simulates its input D
>>> until H correctly determines that its simulated D would never stop
>>> running unless aborted then
>>> (b) H can abort its simulation of D and correctly report that D
>>> specifies a non-halting sequence of configurations.
>>>
>>> H(D,D) and H ⟨Ĥ⟩ ⟨Ĥ⟩ both report on the behavior that they actually see.
>>> Requiring them to report on different behavior that they actually see is
>>> incorrect.
>>
>> The haltimg problem is well posed. Therefore all requirements it contains
>> are correct.
>>
>
> When simulating halt deciders use the above spec then they
> correctly decide the pathological input.
>
> When they do not use this spec then the are being required
> to report on behavior other than the behavior that they see.
> int sum(int x, int y){ return x + y; }
>
> This is the same as requiring sum(3,4) to report on
> the sum of 5 + 6.
>
>

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Re: H ⟨Ĥ⟩ ⟨Ĥ⟩ is correct when reports on the actual behavior that it sees

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by: Richard Damon - Tue, 12 Mar 2024 18:11 UTC

On 3/11/24 3:10 PM, olcott wrote:
> On 3/11/2024 12:57 PM, Richard Damon wrote:
>> On 3/11/24 8:17 AM, olcott wrote:
>>> On 3/11/2024 6:05 AM, Mikko wrote:
>>>> On 2024-03-11 02:38:30 +0000, olcott said:
>>>>
>>>>> On 3/10/2024 9:04 PM, Richard Damon wrote:
>>>>>> On 3/10/24 6:24 PM, olcott wrote:
>>>>>>> On 3/10/2024 7:40 PM, immibis wrote:
>>>>>>>> On 10/03/24 20:16, olcott wrote:
>>>>>>>>> On 3/10/2024 2:09 PM, immibis wrote:
>>>>>>>>>> On 10/03/24 19:32, olcott wrote:
>>>>>>>>>>> On 3/10/2024 1:08 PM, immibis wrote:
>>>>>>>>>>>> On 10/03/24 18:17, olcott wrote:
>>>>>>>>>>>>> ZFC simply tossed out the Russell's Paradox question as
>>>>>>>>>>>>> unsound.
>>>>>>>>>>>>
>>>>>>>>>>>> So you are saying that some Turing machines are not sound?
>>>>>>>>>>>>
>>>>>>>>>>>>>>> Both H ⟨Ĥ⟩ ⟨Ĥ⟩ and Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ correctly decide that:
>>>>>>>>>>>>>>> (a) Their input halts H.qy
>>>>>>>>>>>>>>> (b) Their input fails to halt or has a pathological
>>>>>>>>>>>>>>> relationship to itself H.qn.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> But the "Pathological Relationship" is ALLOWED.
>>>>>>>>>>>>>>
>>>>>>>>>>>>> ZFC simply tossed out the Russell's Paradox question as
>>>>>>>>>>>>> unsound
>>>>>>>>>>>>> expressly disallowing the "Pathological Relationship".
>>>>>>>>>>>>
>>>>>>>>>>>> So you are saying that some Turing machines are not real
>>>>>>>>>>>> Turing machines?
>>>>>>>>>>>>
>>>>>>>>>>>>> I am only claiming that both H and Ĥ.H correctly say YES
>>>>>>>>>>>>> when their input halts and correctly say NOT YES otherwise.
>>>>>>>>>>>>
>>>>>>>>>>>> well the halting problem requires them to correctly say NO,
>>>>>>>>>>>> so you haven't solved it
>>>>>>>>>>>
>>>>>>>>>>> All decision problem instances of program/input such that both
>>>>>>>>>>> yes and no are the wrong answer toss out the input as invalid.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> all decision problems are defined so that all instances are
>>>>>>>>>> valid or else they are not defined properly
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Not in the case of Russell's Paradox.
>>>>>>>>
>>>>>>>> And now we are back to: Every Turing machine and input pair
>>>>>>>> defines an execution sequence. Every sequence is either finite
>>>>>>>> or infinite. Therefore it is well-defined and there is no paradox.
>>>>>>>>
>>>>>>>> Can you show me a Turing machine that specifies a sequence of
>>>>>>>> configurations that is not finite or infinite?
>>>>>>>
>>>>>>> When we construe every yes/no question that cannot possibly
>>>>>>> have a correct yes/no answer as an incorrect question
>>>>>>>
>>>>>>> then we must correspondingly construe every decider/input
>>>>>>> pair that has no correct yes/no answer as invalid input.
>>>>>>>
>>>>>>
>>>>>> And when you remember that when we posse that ACTUAL question, the
>>>>>> input is a FIXED machine, (not a template that changes by the
>>>>>> decide that it trying to decide it) then there are a LOT of
>>>>>> machines that get the right answer. The key is we know that there
>>>>>> is ONE that doesn't, the one that particular decider was built to
>>>>>> foil. Thus, the problem isn't an invalid question.
>>>>>
>>>>>
>>>>> In computability theory and computational complexity theory,
>>>>> an undecidable problem is a decision problem for which it is
>>>>> proved to be impossible to construct an algorithm that always
>>>>> leads to a correct yes-or-no answer.
>>>>> https://en.wikipedia.org/wiki/Undecidable_problem
>>>>>
>>>>> If the only reason that a machine does not get a correct yes/no answer
>>>>> for this machine/input pair is that both yes and no are the wrong
>>>>> answer
>>>>> for this machine/input pair then this machine/input pair is a yes/no
>>>>> question that has no correct yes/no answer for this machine/input
>>>>> pair.
>>>>>
>>>>> The exact same word-for-word question:
>>>>> Are you a little girl?
>>>>> Has a different meaning depending on who is asked.
>>>>
>>>> It is semantically different question as the meaning of "you" varies.
>>> Exactly my point.
>>>
>>>> Teh interpretations of "little" and "girl" may vary, too.
>>>>
>>>>> The exact same word-for-word question:
>>>>> Does your input halt on its input?
>>>>> Has a different meaning depending on who is asked.
>>>>
>>>> Likewise, because of "you".
>>> Exactly my point.
>>>
>>>> Also depens on when it is asked
>>>> if the input is replaced. And can be an incorrect question
>>>> if the input or the input of the input does not exist or
>>>> the input is something that cannot be said to "halt" (e.g.,
>>>> a number).
>>>>
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>>>
>>>>> When every Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ is asked this question:
>>>>> Does your input halt on its input?
>>>>> It is an incorrect question.
>>>>
>>>> Yes, so no need say anything about it. A correct question
>>>> is "Does Ĥ ⟨Ĥ⟩ halt?".
>>>>
>>>
>>> Is a subjective specification because the behavior depends on
>>> the agent that performs it.
>>
>> The only agent that performs "Does H^ (H^) Halt?" is the H^ that is
>> being executed.
>>
>> The decider might try to simulate that behavior to see the answer, but
>> the behavior asked about it the actual objective behavior of the
>> machine describe by the input.
>>
>> You seem to thing that reality is subjective
>>
>>>
>>> This is more clearly seen by my H1(D,D) versus H(D,D).
>>> The behavior of D(D) varies depending on the presence of
>>> the "twisted self-reference" in H(D,D) or the lack of it
>>> in H1(D,D).
>>
>> No, their simulation of the behavior varies, because H makes an
>> incorrect presumption of the behavior of the input.
>>
>>>
>>> Objective and Subjective Specifications
>>> A specification is objective if the specified behavior does not
>>> depend on the agent that performs it, and subjective if it does.
>>> https://www.cs.toronto.edu/~hehner/OSS.pdf
>>>
>> And since the ACTUAL behavior of H^ (H^) doesn't depend on who is
>> trying to look at it or simulate it, the question is OBJECTIVE.
>>
>> If some machine does a simulation that indicates a different results,
>> that simulation, or the analysis of it, is just incorrect.
>>
>> So, you are just proving you are either a pathological liar, or a
>> totally ignorant person, or both (most likely).
>>
>
> That is what it would take to disagree with this:
> Objectively every implementation of the Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ gets the wrong
> answer and not every implementation of H1 ⟨Ĥ⟩ ⟨Ĥ⟩ gets the wrong answer.
>

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Re: ZFC solution to incorrect questions: reject them

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From: polco...@gmail.com (olcott)
Newsgroups: comp.theory
Subject: Re: ZFC solution to incorrect questions: reject them
Date: Tue, 12 Mar 2024 11:00:11 -0700
Organization: i2pn2 (i2pn.org)
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by: olcott - Tue, 12 Mar 2024 18:13 UTC

On 3/12/2024 1:00 PM, Richard Damon wrote:
> On 3/12/24 8:52 AM, olcott wrote:
>
>> ∀ H ∈ Turing_Machine_Deciders
>> ∃ TMD ∈ Turing_Machine_Descriptions |
>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>
>> There is some input TMD to every H such that
>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>
>> When we disallow decider/input pairs that are incorrect
>> questions where both YES and NO are the wrong answer
>> (the same way the ZFC disallowed self-referential sets) then
>> pathological inputs are not allowed to come into existence.
>>
>> Does the barber that shaves everyone that does not shave
>> themselves shave himself? is rejected as an incorrect question.
>> https://en.wikipedia.org/wiki/Barber_paradox#
>>
>
> And ZFC says that H is NOT the "Set of Turing Machines" but a single
> element of it at a time.
>
> There is no problem with making a H^ from an H, it is built from totally
> legal steps.
>
> The fact that it shows that any H you can contruct will get this problem
> wrong, proves the Halting Mapping is uncomputable, not non-existant.

*This discussion has moved to my new post*
[ZFC solution to incorrect questions: reject them]

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

Re: H ⟨Ĥ⟩ ⟨Ĥ⟩ is correct when reports on the actual behavior that it sees

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by: Richard Damon - Tue, 12 Mar 2024 18:14 UTC

On 3/12/24 8:03 AM, olcott wrote:
> On 3/12/2024 4:27 AM, Mikko wrote:
>> On 2024-03-11 15:17:42 +0000, olcott said:
>>
>>> On 3/11/2024 6:05 AM, Mikko wrote:
>>>> On 2024-03-11 02:38:30 +0000, olcott said:
>>>>
>>>>> On 3/10/2024 9:04 PM, Richard Damon wrote:
>>>>>> On 3/10/24 6:24 PM, olcott wrote:
>>>>>>> On 3/10/2024 7:40 PM, immibis wrote:
>>>>>>>> On 10/03/24 20:16, olcott wrote:
>>>>>>>>> On 3/10/2024 2:09 PM, immibis wrote:
>>>>>>>>>> On 10/03/24 19:32, olcott wrote:
>>>>>>>>>>> On 3/10/2024 1:08 PM, immibis wrote:
>>>>>>>>>>>> On 10/03/24 18:17, olcott wrote:
>>>>>>>>>>>>> ZFC simply tossed out the Russell's Paradox question as
>>>>>>>>>>>>> unsound.
>>>>>>>>>>>>
>>>>>>>>>>>> So you are saying that some Turing machines are not sound?
>>>>>>>>>>>>
>>>>>>>>>>>>>>> Both H ⟨Ĥ⟩ ⟨Ĥ⟩ and Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ correctly decide that:
>>>>>>>>>>>>>>> (a) Their input halts H.qy
>>>>>>>>>>>>>>> (b) Their input fails to halt or has a pathological
>>>>>>>>>>>>>>> relationship to itself H.qn.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> But the "Pathological Relationship" is ALLOWED.
>>>>>>>>>>>>>>
>>>>>>>>>>>>> ZFC simply tossed out the Russell's Paradox question as
>>>>>>>>>>>>> unsound
>>>>>>>>>>>>> expressly disallowing the "Pathological Relationship".
>>>>>>>>>>>>
>>>>>>>>>>>> So you are saying that some Turing machines are not real
>>>>>>>>>>>> Turing machines?
>>>>>>>>>>>>
>>>>>>>>>>>>> I am only claiming that both H and Ĥ.H correctly say YES
>>>>>>>>>>>>> when their input halts and correctly say NOT YES otherwise.
>>>>>>>>>>>>
>>>>>>>>>>>> well the halting problem requires them to correctly say NO,
>>>>>>>>>>>> so you haven't solved it
>>>>>>>>>>>
>>>>>>>>>>> All decision problem instances of program/input such that both
>>>>>>>>>>> yes and no are the wrong answer toss out the input as invalid.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> all decision problems are defined so that all instances are
>>>>>>>>>> valid or else they are not defined properly
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Not in the case of Russell's Paradox.
>>>>>>>>
>>>>>>>> And now we are back to: Every Turing machine and input pair
>>>>>>>> defines an execution sequence. Every sequence is either finite
>>>>>>>> or infinite. Therefore it is well-defined and there is no paradox.
>>>>>>>>
>>>>>>>> Can you show me a Turing machine that specifies a sequence of
>>>>>>>> configurations that is not finite or infinite?
>>>>>>>
>>>>>>> When we construe every yes/no question that cannot possibly
>>>>>>> have a correct yes/no answer as an incorrect question
>>>>>>>
>>>>>>> then we must correspondingly construe every decider/input
>>>>>>> pair that has no correct yes/no answer as invalid input.
>>>>>>>
>>>>>>
>>>>>> And when you remember that when we posse that ACTUAL question, the
>>>>>> input is a FIXED machine, (not a template that changes by the
>>>>>> decide that it trying to decide it) then there are a LOT of
>>>>>> machines that get the right answer. The key is we know that there
>>>>>> is ONE that doesn't, the one that particular decider was built to
>>>>>> foil. Thus, the problem isn't an invalid question.
>>>>>
>>>>>
>>>>> In computability theory and computational complexity theory,
>>>>> an undecidable problem is a decision problem for which it is
>>>>> proved to be impossible to construct an algorithm that always
>>>>> leads to a correct yes-or-no answer.
>>>>> https://en.wikipedia.org/wiki/Undecidable_problem
>>>>>
>>>>> If the only reason that a machine does not get a correct yes/no answer
>>>>> for this machine/input pair is that both yes and no are the wrong
>>>>> answer
>>>>> for this machine/input pair then this machine/input pair is a yes/no
>>>>> question that has no correct yes/no answer for this machine/input
>>>>> pair.
>>>>>
>>>>> The exact same word-for-word question:
>>>>> Are you a little girl?
>>>>> Has a different meaning depending on who is asked.
>>>>
>>>> It is semantically different question as the meaning of "you" varies.
>>> Exactly my point.
>>>
>>>> Teh interpretations of "little" and "girl" may vary, too.
>>>>
>>>>> The exact same word-for-word question:
>>>>> Does your input halt on its input?
>>>>> Has a different meaning depending on who is asked.
>>>>
>>>> Likewise, because of "you".
>>> Exactly my point.
>>>
>>>> Also depens on when it is asked
>>>> if the input is replaced. And can be an incorrect question
>>>> if the input or the input of the input does not exist or
>>>> the input is something that cannot be said to "halt" (e.g.,
>>>> a number).
>>>>
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>>>
>>>>> When every Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ is asked this question:
>>>>> Does your input halt on its input?
>>>>> It is an incorrect question.
>>>>
>>>> Yes, so no need say anything about it. A correct question
>>>> is "Does Ĥ ⟨Ĥ⟩ halt?".
>>>>
>>>
>>> Is a subjective specification because the behavior depends on
>>> the agent that performs it.
>>
>> The specified behaviour of halting decider does not.
>>
>
> Because the specification of a the halting problem allows pathological
> inputs this proves that this specification is subjective[Hehner].
>

Nope.

SInce the behavior of the machine/input described, which is of a
SPECIFIC H^ built on a SPECIFIC H, its behavior is fixed and independent
of the decider looking at it.

The input doesn't "referece" the decider, it uses a copy of it, so if
you apply program modulation thinking (talking about changing the
machine) the input doesn't change, like your logic has it do.

Re: H ⟨Ĥ⟩ ⟨Ĥ⟩ is correct when reports on the actual behavior that it sees

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by: Richard Damon - Tue, 12 Mar 2024 18:15 UTC

On 3/11/24 8:51 AM, olcott wrote:
> On 3/11/2024 10:34 AM, immibis wrote:
>> On 11/03/24 03:38, olcott wrote:
>>> If the only reason that a machine does not get a correct yes/no answer
>>> for this machine/input pair is that both yes and no are the wrong answer
>>> for this machine/input pair then this machine/input pair is a yes/no
>>> question that has no correct yes/no answer for this machine/input pair.
>>
>> This is bullshit, because the question has a correct yes/no answer,
>> and you know this, so stop lying.
>>
>
> When you ignore the context of {who is asked} then the halting
> problem question incorrectly seems to always have a correct answer.

And show me an actual Turing Machine that changes its behavior based on
who is looking at it.

Remember, H^ is a SPECIFIC implementation based on a SPECIFIC
implemetation of H, and thus doesn't change, if you try a "different H"
on it (which will be a different machine, and not the H that H^ was
built on)

>
> Alan Turing's Halting Problem is incorrectly formed (PART-TWO) sci.logic
> On 6/20/2004 11:31 AM, Peter Olcott wrote:
> > PREMISES:
> > (1) The Halting Problem was specified in such a way that a solution
> > was defined to be impossible.
> >
> > (2) The set of questions that are defined to not have any possible
> > correct answer(s) forms a proper subset of all possible questions.
> > …
> > CONCLUSION:
> > Therefore the Halting Problem is an ill-formed question.
> >
> USENET Message-ID:
> <kZiBc.103407$Gx4.18142@bgtnsc04-news.ops.worldnet.att.net>
>
> *Direct Link to original message*
> http://al.howardknight.net/?STYPE=msgid&MSGI=%3CkZiBc.103407%24Gx4.18142%40bgtnsc04-news.ops.worldnet.att.net%3E+
>
>

Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --logically impossible--

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by: olcott - Tue, 12 Mar 2024 18:16 UTC

On 3/12/2024 1:04 PM, Richard Damon wrote:
> On 3/11/24 8:56 AM, olcott wrote:
>> On 3/11/2024 10:36 AM, immibis wrote:
>>> On 11/03/24 04:33, olcott wrote:
>>>> Then we are back to undecidability being incorrectly construed
>>>> as an actual limit to computation.
>>>
>>> Proof that a certain thing cannot be computed is always a limit to
>>> computation.
>>>
>> Yet in only the same way that the Liar Paradox
>> "This sentence is not true."
>> does not have a truth value that can be computed.
>>
>>> For example, you can't compute the colour of the number 4. That is an
>>> actual limit to computation.
>>>
>>
>> The inability to to the logically impossible is not any actual limit.
>> If we say that the Halting Problem cannot be solved for the same sort
>> of reason that Square Circles do not exist then this is not any actual
>> limit.
>
> But SHOWING that something is logically impossible reveals the
> limitations that were already there.
>
> Yes, the Halting Theorem doesn't MAKE the problem impossible, it shows
> that it always was, and gives us knowledge of that.
>

The halting problem does not derive a limit to computation
any more than the inability of CAD systems to draw square
circles places a limit on computation.

> But, you don't understand the nature of Truth and Knowledge, so that
> won't make sense.
>
>>
>>> You can't compute the halting problem. That is an actual limit to
>>> computation.
>>
>

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

Re: When H ⟨Ĥ⟩ ⟨Ĥ⟩ reports on the behavior it actually sees then it is correct

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by: olcott - Tue, 12 Mar 2024 18:17 UTC

On 3/12/2024 1:05 PM, Richard Damon wrote:
> On 3/11/24 9:08 AM, olcott wrote:
>> On 3/11/2024 10:14 AM, Mikko wrote:
>>> On 2024-03-11 14:42:30 +0000, olcott said:
>>>
>>>> On 3/11/2024 5:42 AM, Mikko wrote:
>>>>> On 2024-03-11 02:05:53 +0000, olcott said:
>>>>>
>>>>>> On 3/10/2024 8:52 PM, Richard Damon wrote:
>>>>>>> On 3/10/24 6:00 PM, olcott wrote:
>>>>>>>> On 3/10/2024 2:23 PM, Richard Damon wrote:
>>>>>>>>> On 3/10/24 11:23 AM, olcott wrote:
>>>>>>>>>> On 3/10/2024 12:55 PM, Richard Damon wrote:
>>>>>>>>>>> On 3/10/24 10:17 AM, olcott wrote:
>>>>>>>>>>>> On 3/10/2024 12:08 PM, Richard Damon wrote:
>>>>>>>>>>>>> On 3/10/24 9:52 AM, olcott wrote:
>>>>>>>>>>>>>> On 3/10/2024 10:50 AM, Richard Damon wrote:
>>>>>>>>>>>>>>> On 3/10/24 7:28 AM, olcott wrote:
>>>>>>>>>>>>>>>> On 3/10/2024 12:16 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>> On 3/9/24 9:49 PM, olcott wrote:
>>>>>>>>>>>>>>>>>> On 3/9/2024 11:36 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>> On 3/9/24 9:14 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>> On 3/9/2024 10:55 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>> On 3/9/24 8:30 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>> On 3/9/2024 7:40 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 10/03/24 02:37, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 3/9/2024 7:32 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 10/03/24 02:29, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/9/2024 7:24 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>> On 10/03/24 01:30, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/9/2024 6:24 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 10/03/24 01:22, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/9/2024 5:57 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 10/03/24 00:26, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/9/2024 5:10 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 9/03/24 23:22, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/9/2024 3:50 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 9/03/24 22:34, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What criteria would you use so that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ knows what
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrong answer to provide?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ is stipulated to use the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exact same objective criteria that H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ uses.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Simulating halt deciders must make
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> sure that they themselves
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> do not get stuck in infinite
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> execution. This means that they
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> must abort every simulation that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> cannot possibly otherwise halt.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This requires Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ to abort its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulation and does not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> require H ⟨Ĥ⟩ ⟨Ĥ⟩ to abort its
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulation when Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ aborts
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> its simulation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ does simulate itself in
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> recursive simulation H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> does not simulate itself in recursive
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ is stipulated to use the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> exact same objective criteria that H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ uses.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> *Only because Ĥ.H is embedded within Ĥ
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> and H is not*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ can possibly get stuck in
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> recursive simulation and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H ⟨Ĥ⟩ ⟨Ĥ⟩ cannot possibly get stuck in
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> recursive simulation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You dishonestly ignored that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> is stipulated to use the exact same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> OBJECTIVE criteria that H ⟨Ĥ⟩ uses.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The above is true no matter what criteria
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> that is used
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> as long as H is a simulating halt decider.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Objective criteria cannot vary based on who
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> the subject is. They are objective. The
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> answer to different people is the same
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> answer if the criteria are objective.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is objectively true that Ĥ.H can get
>>>>>>>>>>>>>>>>>>>>>>>>>>>> stuck in recursive
>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulation because Ĥ copies its input thus
>>>>>>>>>>>>>>>>>>>>>>>>>>>> never runs
>>>>>>>>>>>>>>>>>>>>>>>>>>>> out of params.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is objectively true that Ĥ cannot
>>>>>>>>>>>>>>>>>>>>>>>>>>>> possibly get stuck
>>>>>>>>>>>>>>>>>>>>>>>>>>>> in recursive because H does not copy its
>>>>>>>>>>>>>>>>>>>>>>>>>>>> input thus runs
>>>>>>>>>>>>>>>>>>>>>>>>>>>> out of params.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> Wrong. Dead wrong. Stupidly wrong. So wrong
>>>>>>>>>>>>>>>>>>>>>>>>>>> that a dead monkey could do better. Write the
>>>>>>>>>>>>>>>>>>>>>>>>>>> Olcott machine (not x86utm) code for Ĥ and I
>>>>>>>>>>>>>>>>>>>>>>>>>>> would show you.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> *In other words you are denying these verified
>>>>>>>>>>>>>>>>>>>>>>>>>> facts*
>>>>>>>>>>>>>>>>>>>>>>>>>> *In other words you are denying these verified
>>>>>>>>>>>>>>>>>>>>>>>>>> facts*
>>>>>>>>>>>>>>>>>>>>>>>>>> *In other words you are denying these verified
>>>>>>>>>>>>>>>>>>>>>>>>>> facts*
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ
>>>>>>>>>>>>>>>>>>>>>>>>>> applied to ⟨Ĥ⟩ halts
>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn // Ĥ
>>>>>>>>>>>>>>>>>>>>>>>>>> applied to ⟨Ĥ⟩ does not halt
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> That's not a verified fact, that's just
>>>>>>>>>>>>>>>>>>>>>>>>> something you want to be true.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> ∞ means infinite loop. Infinite loop doesn't
>>>>>>>>>>>>>>>>>>>>>>>>> halt. You see how stupid it is, to say that an
>>>>>>>>>>>>>>>>>>>>>>>>> infinite loop halts?
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> Execution trace of Ĥ applied to ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>> (a) Ĥ.q0 The input ⟨Ĥ⟩ is copied then
>>>>>>>>>>>>>>>>>>>>>>>>>> transitions to Ĥ.H
>>>>>>>>>>>>>>>>>>>>>>>>>> (b) Ĥ.H applied ⟨Ĥ⟩ ⟨Ĥ⟩ (input and copy)
>>>>>>>>>>>>>>>>>>>>>>>>>> simulates ⟨Ĥ⟩ applied to ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>> (c) which begins at its own simulated ⟨Ĥ.q0⟩
>>>>>>>>>>>>>>>>>>>>>>>>>> to repeat the process
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> Execution trace of H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ BECAUSE
>>>>>>>>>>>>>>>>>>>>>>>>> IT IS PRECISELY IDENTICAL TO STEPS B AND C:
>>>>>>>>>>>>>>>>>>>>>>>>> > (b) Ĥ.H applied ⟨Ĥ⟩ ⟨Ĥ⟩ (input and copy)
>>>>>>>>>>>>>>>>>>>>>>>>> simulates ⟨Ĥ⟩ applied to ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>> > (c) which begins at Ĥ's own simulated ⟨Ĥ.q0⟩
>>>>>>>>>>>>>>>>>>>>>>>>> to repeat the process
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> *Yes and the key step of copying its input is
>>>>>>>>>>>>>>>>>>>>>>>> left out so*
>>>>>>>>>>>>>>>>>>>>>>>> *H ⟨Ĥ⟩ ⟨Ĥ⟩ runs out of params and Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>> never runs out of params*
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> that isn't how any of this works. Do you even
>>>>>>>>>>>>>>>>>>>>>>> know what words mean?
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> (b) and (c) are not the same as (1) and (2)
>>>>>>>>>>>>>>>>>>>>>> Execution trace of H applied to ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>> (1) H applied ⟨Ĥ⟩ ⟨Ĥ⟩ simulates ⟨Ĥ⟩ applied to ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>> (2) which begins at simulated ⟨Ĥ.q0⟩
>>>>>>>>>>>>>>>>>>>>>> (a) Ĥ.q0 The input ⟨Ĥ⟩ is copied then transitions
>>>>>>>>>>>>>>>>>>>>>> to Ĥ.H
>>>>>>>>>>>>>>>>>>>>>> (b) Ĥ.H applied ⟨Ĥ⟩ ⟨Ĥ⟩ (input and copy) simulates
>>>>>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ applied to ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>> (c) which begins at its own simulated ⟨Ĥ.q0⟩ to
>>>>>>>>>>>>>>>>>>>>>> repeat the process
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> This means that Turing machine H ⟨Ĥ⟩ ⟨Ĥ⟩ can see
>>>>>>>>>>>>>>>>>>>>>> one more execution
>>>>>>>>>>>>>>>>>>>>>> trace of Ĥ ⟨Ĥ⟩ than its simulated Turing machine
>>>>>>>>>>>>>>>>>>>>>> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ can see.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Nope, your just being stuupid, perhaps intentionally.
>>>>>>>>>>>>>>>>>>>>> (c) just moves around to its simulation of a
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> (a) H^.q0 (H^)
>>>>>>>>>>>>>>>>>>>>> H^ then makes a copy of its inp
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> (b) H^.H (H^) (H^) == (1) H (H^) (H^)
>>>>>>>>>>>>>>>>>>>>> The algorithm of H begins a simulation of its
>>>>>>>>>>>>>>>>>>>>> input, watching the behaior of H^ (H^)
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> (c) = (2)
>>>>>>>>>>>>>>>>>>>>> Which begins at the simulation of H^.q0 (H^)
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> (d = sim a) = (sim a)
>>>>>>>>>>>>>>>>>>>>> Ths Simulated H^.q0 (H^) makes a copy of its input
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> (e = sim b) = (sim b)
>>>>>>>>>>>>>>>>>>>>> The Simulated H^.H (H^) (H^) has is H begin the
>>>>>>>>>>>>>>>>>>>>> simulation of its input ...
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> and so on.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Both machine see EXACTLY the same level of details.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Yes, the top level H is farther along at any given
>>>>>>>>>>>>>>>>>>>>> time then its simulated machine, and that is H's
>>>>>>>>>>>>>>>>>>>>> problem, it has to act before it sees how its
>>>>>>>>>>>>>>>>>>>>> simulation will respond to its copy of its actions.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Thus, if it stops, it needs to make its decision
>>>>>>>>>>>>>>>>>>>>> "blind" and not with an idea of how the machine it
>>>>>>>>>>>>>>>>>>>>> is simulating will perform.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> If it doesn't stop, the level of recursion just
>>>>>>>>>>>>>>>>>>>>> keeps growing and no answer ever comes out.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> The earliest point that H ⟨Ĥ⟩ ⟨Ĥ⟩ can possibly see
>>>>>>>>>>>>>>>>>>>> to abort
>>>>>>>>>>>>>>>>>>>> its simulation is immediately before Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>> would begin
>>>>>>>>>>>>>>>>>>>> its simulation. Right before its cycle repeats the
>>>>>>>>>>>>>>>>>>>> first time.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> So?
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> If it DOES abort there, then so will H^.H when it
>>>>>>>>>>>>>>>>>>> gets to that point in its simulation, which will be
>>>>>>>>>>>>>>>>>>> AFTER The point that H has stopped simulating it, so
>>>>>>>>>>>>>>>>>>> H doesn't know what H^ will do.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Thus, if H DOES abort there, we presume from your
>>>>>>>>>>>>>>>>>>> previous answer it will think the input will not halt
>>>>>>>>>>>>>>>>>>> and answer qn.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ applied to
>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ halts
>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn // Ĥ applied to
>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ does not halt
>>>>>>>>>>>>>>>>>> H ⟨Ĥ⟩ ⟨Ĥ⟩ aborts right after Ĥ.Hq0 before it simulates
>>>>>>>>>>>>>>>>>> ⟨Ĥ⟩ ⟨Ĥ⟩.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> And if it does, as I said below, so will H^.H when it
>>>>>>>>>>>>>>>>> is run.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Yes.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> And thus, H^.H will give the same answer as H,
>>>>>>>>>>>>>>> so H^ will act contrary to what H says,
>>>>>>>>>>>>>>> so H will give the wrong answer.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Unlike anything else that anyone else has ever done both H
>>>>>>>>>>>>>> ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>> and Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ correctly determine that they must abort
>>>>>>>>>>>>>> their own
>>>>>>>>>>>>>> simulation to prevent their own infinite execution.
>>>>>>>>>>>>>
>>>>>>>>>>>>> NOPE.
>>>>>>>>>>>>
>>>>>>>>>>>> If no source can be cited then the Olcott thesis
>>>>>>>>>>>> "that no one did this before" remains unrefuted.
>>>>>>>>>>>
>>>>>>>>>>> Since, BY THE DEFINITIONS of what H MUST do to be correct,
>>>>>>>>>>> and what H^ WILL do by its design, as shown in the Linz Proof.
>>>>>>>>>>
>>>>>>>>>> If no source can be cited that shows a simulating halt decider
>>>>>>>>>> can
>>>>>>>>>> correctly determine that it must abort its simulation of the
>>>>>>>>>> Halting
>>>>>>>>>> Problem's pathological input to prevent its own
>>>>>>>>>> non-termination, then
>>>>>>>>>> innovation remains attributable to me.
>>>>>>>>>>
>>>>>>>>>> <snip>
>>>>>>>>>
>>>>>>>>> Of course it can abort its simulation.
>>>>>>>>>
>>>>>>>>> It just needs some way to get the right answer.
>>>>>>>>>
>>>>>>>>
>>>>>>>> *I have always been using this long before I read about it*
>>>>>>>> blind variation and selective retention (BVSR)...
>>>>>>>> Two common phenomena characterize BVSR thinking: superfluity and
>>>>>>>> backtracking. Superfluity means that the creator generates a
>>>>>>>> variety of ideas, one or more of which turn out to be useless.
>>>>>>>
>>>>>>> But if you have mo idea how things actually works, this seems to
>>>>>>> just generate random noise.
>>>>>>>
>>>>>>>>
>>>>>>>> Backtracking signifies that the creator must often return to an
>>>>>>>> earlier approach after blindly going off in the wrong direction.
>>>>>>>> https://www.scientificamerican.com/article/the-science-of-genius/
>>>>>>>>
>>>>>>>> *I am aware of no one else that had the idea to apply a
>>>>>>>> simulating* *termination analyzer to the halting problem
>>>>>>>> counter-example input*
>>>>>>>> Professor Hehner had a seed of this idea before I did.
>>>>>>>
>>>>>>> Nope, I remember talk of that when I was in college, and they
>>>>>>> showed why it can't work.
>>>>>>>
>>>>>>>>
>>>>>>>> From a programmer's point of view, if we apply an interpreter to a
>>>>>>>> program text that includes a call to that same interpreter with
>>>>>>>> that
>>>>>>>> same text as argument, then we have an infinite loop. A halting
>>>>>>>> program
>>>>>>>> has some of the same character as an interpreter: it applies to
>>>>>>>> texts
>>>>>>>> through abstract interpretation. Unsurprisingly, if we apply a
>>>>>>>> halting
>>>>>>>> program to a program text that includes a call to that same halting
>>>>>>>> program with that same text as argument, then we have an
>>>>>>>> infinite loop. https://www.cs.toronto.edu/~hehner/PHP.pdf
>>>>>>>
>>>>>>> You THINK so, but if the interpreter is a CONDITIONAL
>>>>>>> interpreter, that doesn't hold.
>>>>>>>
>>>>>>> You seem to miss that fact.
>>>>>>>
>>>>>>>>
>>>>>>>> *Turing Machine and Olcott machine implementations seem to be dead*
>>>>>>>> *This the (possibly augmented) RASP machine equivalent of x86*
>>>>>>>> Every machine must be able to get its own machine address.
>>>>>>>>
>>>>>>>
>>>>>>> And the reason it is a dead end is they make it too hard for you
>>>>>>> to cheat.
>>>>>>>
>>>>>>> You need to hide that your H is trying to get in some extra
>>>>>>> information to hide that the embedded version of H doesn't give
>>>>>>> the same answer, which just shows that your H^ is built wrong.
>>>>>>
>>>>>> My C code proves these two have different behavior:
>>>>>> (a) H1(D,D) + H1_machine_address
>>>>>> (b) H(D,D) + H_machine_address
>>>>>> H1(D,D) does correctly determine the halt status of D(D) because
>>>>>> H(D,D) does NOT correctly determine the halt status of D(D).
>>>>>>
>>>>>> I say:
>>>>>> H1(D,D) is isomorphic to H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>> H(D,D) is isomorphic to Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>
>>>>>> immibis disagrees.
>>>>>> Correct reasoning will show who is correct.
>>>>>
>>>>> As H does not correctly determine the halt status of D(D) and
>>>>> H1 does not correctly determine the halt status of D1(D1) neither
>>>>> of them is a halt decider.
>>>>>
>>>>
>>>> *MIT Professor Michael Sipser agreed this verbatim paragraph is
>>>> correct*
>>>> (a) If simulating halt decider H correctly simulates its input D
>>>> until H correctly determines that its simulated D would never stop
>>>> running unless aborted then
>>>> (b) H can abort its simulation of D and correctly report that D
>>>> specifies a non-halting sequence of configurations.
>>>>
>>>> H(D,D) and H ⟨Ĥ⟩ ⟨Ĥ⟩ both report on the behavior that they actually
>>>> see.
>>>> Requiring them to report on different behavior that they actually
>>>> see is
>>>> incorrect.
>>>
>>> The haltimg problem is well posed. Therefore all requirements it
>>> contains
>>> are correct.
>>>
>>
>> When simulating halt deciders use the above spec then they
>> correctly decide the pathological input.
>>
>> When they do not use this spec then the are being required
>> to report on behavior other than the behavior that they see.
>> int sum(int x, int y){ return x + y; }
>>
>> This is the same as requiring sum(3,4) to report on
>> the sum of 5 + 6.
>>
>>
>
> In other words, you think strawmen are valid, and it is ok to lie.

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Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --new focus--

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From: new...@immibis.com (immibis)
Newsgroups: comp.theory
Subject: Re: ZFC solution to incorrect questions: reject them
Date: Tue, 12 Mar 2024 11:00:11 -0700
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by: immibis - Tue, 12 Mar 2024 18:27 UTC

On 12/03/24 18:46, olcott wrote:
> On 3/12/2024 12:36 PM, Richard Damon wrote:
>> On 3/12/24 9:02 AM, olcott wrote:
>>> On 3/11/2024 10:57 PM, Richard Damon wrote:
>>>> On 3/11/24 8:37 PM, olcott wrote:
>>>>> On 3/11/2024 10:31 PM, Richard Damon wrote:
>>>>>> On 3/11/24 7:52 PM, olcott wrote:
>>>>>>> On 3/11/2024 9:32 PM, immibis wrote:
>>>>>>>> On 12/03/24 03:24, olcott wrote:
>>>>>> \
>>>>>>>>> Troll detected.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Once we understand that either YES or NO is the right answer
>>>>>>>
>>>>>>> Not for this decider/input question: Ĥ.H / ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>> For that decider/input question both YES and NO are the wrong
>>>>>>> answer.
>>>>>>
>>>>>> The problem that you keeep on missing is that by the point we can
>>>>>> ask this question, H and H^ are FULLY CODED, and thus we know
>>>>>> their behavirs.
>>>>>
>>>>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy // Ĥ applied to ⟨Ĥ⟩ halts
>>>>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>>>
>>>>> Since you know that is false why lie?
>>>>> ⊢* specifies an infinite set of encodings.
>>>>
>>>> Nope, read him again, not just skim and assume.
>>>>
>>>
>>> *Here is the proof that I am correct*
>>> ∀ H ∈ Turing_Machine_Deciders
>>> ∃ TMD ∈ Turing_Machine_Descriptions |
>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>
>>>
>>
>> So, H, being an ELEMENT of Turing Machine Deciders, is a SINGLE
>> INSTANCE of it, it is NOT the set itself.
>
> ∀ H ∈ Turing_Machine_Deciders *DOES NOT REFER TO A SINGLE INSTANCE*

Yes it does. It means that if H is a single instance, no matter which
one it is, the rest of the sentence is true.

Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior --Foundations--

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by: Richard Damon - Tue, 12 Mar 2024 18:32 UTC

On 3/11/24 1:56 PM, olcott wrote:
> On 3/11/2024 1:49 PM, Richard Damon wrote:
>> On 3/11/24 7:25 AM, olcott wrote:
>>> On 3/11/2024 1:17 AM, Richard Damon wrote:
>>>> On 3/10/24 10:40 PM, olcott wrote:
>>>>> On 3/11/2024 12:07 AM, Richard Damon wrote:
>>>>>> On 3/10/24 9:33 PM, olcott wrote:
>>>>>>> On 3/10/2024 10:07 PM, Richard Damon wrote:
>>>>>>>> On 3/10/24 7:47 PM, olcott wrote:
>>>>>>>>> On 3/10/2024 9:08 PM, Richard Damon wrote:
>>>>>>>>>> On 3/10/24 5:32 PM, olcott wrote:
>>>>>>>>>>> On 3/10/2024 2:16 PM, immibis wrote:
>>>>>>>>>>>> On 10/03/24 19:32, olcott wrote:
>>>>>>>>>>>>> On 3/10/2024 1:08 PM, immibis wrote:
>>>>>>>>>>>>>> On 10/03/24 18:17, olcott wrote:
>>>>>>>>>>>>>>> ZFC simply tossed out the Russell's Paradox question as
>>>>>>>>>>>>>>> unsound.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> So you are saying that some Turing machines are not sound?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Both H ⟨Ĥ⟩ ⟨Ĥ⟩ and Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ correctly decide that:
>>>>>>>>>>>>>>>>> (a) Their input halts H.qy
>>>>>>>>>>>>>>>>> (b) Their input fails to halt or has a pathological
>>>>>>>>>>>>>>>>> relationship to itself H.qn.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> But the "Pathological Relationship" is ALLOWED.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> ZFC simply tossed out the Russell's Paradox question as
>>>>>>>>>>>>>>> unsound
>>>>>>>>>>>>>>> expressly disallowing the "Pathological Relationship".
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> So you are saying that some Turing machines are not real
>>>>>>>>>>>>>> Turing machines?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> I am only claiming that both H and Ĥ.H correctly say YES
>>>>>>>>>>>>>>> when their input halts and correctly say NOT YES otherwise.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> well the halting problem requires them to correctly say
>>>>>>>>>>>>>> NO, so you haven't solved it
>>>>>>>>>>>>>
>>>>>>>>>>>>> All decision problem instances of program/input such that both
>>>>>>>>>>>>> yes and no are the wrong answer toss out the input as invalid.
>>>>>>>>>>>>
>>>>>>>>>>>> I noticed that you gave up on Olcott machines and now you
>>>>>>>>>>>> are back to your old bullshit ways of pretending that the
>>>>>>>>>>>> same machine can produce two different execution traces on
>>>>>>>>>>>> the same input. Why don't you show us an execution trace
>>>>>>>>>>>> where that happens? Both traces must show the first
>>>>>>>>>>>> instruction that is different in both traces and I recommend
>>>>>>>>>>>> showing 20 more instructions after that, but you can abort
>>>>>>>>>>>> one after that time, if it doesn't halt, to prevent the
>>>>>>>>>>>> trace getting infinitely long.
>>>>>>>>>>>
>>>>>>>>>>> Turing Machines and Olcott machines cannot properly implement
>>>>>>>>>>> H1(D,D) and H(D,D) that know their own machine address.
>>>>>>>>>>>
>>>>>>>>>>> My C code proves these two have different behavior:
>>>>>>>>>>> (a) H1(D,D) + H1_machine_address
>>>>>>>>>>> (b) H(D,D) + H_machine_address
>>>>>>>>>>>
>>>>>>>>>>> Because they are different computations they are
>>>>>>>>>>> not required to have the same behavior.
>>>>>>>>>>
>>>>>>>>>> Right, but it also means that since the dfference is because
>>>>>>>>>> of a "Hidden" input none of them qualify as a Halt Decider.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> The key input (the machines own address) is not hidden
>>>>>>>>> merely unavailable to Turing machine and Olcott machines.
>>>>>>>>
>>>>>>>> And if it isn't hidden, then the other copies that take use a
>>>>>>>> different address become different computations and can't claim
>>>>>>>> to fill in for THE H.
>>>>>>>>
>>>>>>>> You then prove each copy wrong by giving it the version of H^/D
>>>>>>>> that is built on it, which it will get wrong.
>>>>>>>>
>>>>>>>> All the other ones might get it right, showing that there IS a
>>>>>>>> correct answer.
>>>>>>>>
>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> H(D,D) immediately sees the first time it calls itself
>>>>>>>>>>> with its same inputs.
>>>>>>>>>>>
>>>>>>>>>>> H1(D,D) never sees it call itself with its same inputs.
>>>>>>>>>>>
>>>>>>>>>>> Full Execution trace of H1(D,D)
>>>>>>>>>>> (a) main() invokes H1(D,D)
>>>>>>>>>>> (b) H1(D,D) simulates D(D)
>>>>>>>>>>> (c) Simulated D(D) calls simulated H(D,D)
>>>>>>>>>>> (d) Simulated H(D,D) simulates another D(D)
>>>>>>>>>>> (e) Simulated H(D,D) aborts this D(D) when it would call itself
>>>>>>>>>>> (f) Simulated H(D,D) returns 0 to simulated caller D(D)
>>>>>>>>>>> (g) Simulated caller D(D) returns to H1(D,D)
>>>>>>>>>>> (h) H1(D,D) returns 1 to main()
>>>>>>>>>>>
>>>>>>>>>>> They cannot be implemented as Turing Machines or Olcott
>>>>>>>>>>> Machines. They can be implemented as RASP machines proven
>>>>>>>>>>> by the fact that they are implemented as C functions.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Right, which proves your C functions also were never the
>>>>>>>>>> required computation, as they has an extra "hidden" input. As
>>>>>>>>>> has been told to you many times in the past.
>>>>>>>>>
>>>>>>>>> When I specify that every machine can know its own machine address
>>>>>>>>> in x86 machines and (possibly augmented) RASP machines then it is
>>>>>>>>> not hidden and an explicitly part of the input to the computation.
>>>>>>>>
>>>>>>>> And if it isn't hidden, then the other copies that take use a
>>>>>>>> different address become different computations and can't claim
>>>>>>>> to fill in for THE H.
>>>>>>>>
>>>>>>>> You then prove each copy wrong by giving it the version of H^/D
>>>>>>>> that is built on it, which it will get wrong.
>>>>>>>>
>>>>>>>> All the other ones might get it right, showing that there IS a
>>>>>>>> correct answer.
>>>>>>>>
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> So, you just admitted that you hae just been lying for all
>>>>>>>>>> these years, and you are no closer to your fantasy goal then
>>>>>>>>>> you ever were.
>>>>>>>>>>
>>>>>>>>>> Sorry, you just don't know enough to do this problem.
>>>>>>>>>
>>>>>>>>> I just admitted that it took me about two years to translate my
>>>>>>>>> intuitions into words that address your objections.
>>>>>>>>>
>>>>>>>>> For these two years you and many other people claimed that H1(D,D)
>>>>>>>>> could not possibly do what it actually did actually do. This has
>>>>>>>>> always been the same thing as disagreeing with arithmetic.
>>>>>>>>>
>>>>>>>>
>>>>>>>> It can't do it and be the SAME COMPUTATION as H, which is what
>>>>>>>> you were claiming.
>>>>>>>>
>>>>>>>
>>>>>>> It did actually do exactly what I claimed and everyone wanted
>>>>>>> to stick to their opinion and deny the actual facts that it
>>>>>>> did actually do what I said.
>>>>>>
>>>>>> It might have done what you THOUGHT you were saying, but it
>>>>>> doesn't do what you ACTUALLY SAID.
>>>>>>
>>>>>
>>>>> I always claimed that H1(D,D) returns 1 and H(D,D) returns 0 and you
>>>>> always said it was impossible even though that is what actual code
>>>>> actually did. The code always discloses that H and H1 have their
>>>>> own address.
>>>>
>>>> No, we said it was impossible if they were the COMPUTATIONS you were
>>>> claiming them to be.
>>>>
>>>
>>> I never ever claimed that they were the same computation.
>>
>> yes you did. You problem don't remember because the word computation
>> doesn't seem to have a real meaning to you.
>>
>
> I have known the meaning of theory of computation meaning of computation
> for two years. It was very difficult to correctly adapt this to account
> for C functions. I finally did and had it checked over by quite a few
> people and for C functions to be computable functions they must be this
> notion of a pure function.
>
> https://en.wikipedia.org/wiki/Pure_function

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Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --infinite set--

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by: olcott - Tue, 12 Mar 2024 18:34 UTC

On 3/12/2024 1:27 PM, immibis wrote:
> On 12/03/24 18:46, olcott wrote:
>> On 3/12/2024 12:36 PM, Richard Damon wrote:
>>> On 3/12/24 9:02 AM, olcott wrote:
>>>> On 3/11/2024 10:57 PM, Richard Damon wrote:
>>>>> On 3/11/24 8:37 PM, olcott wrote:
>>>>>> On 3/11/2024 10:31 PM, Richard Damon wrote:
>>>>>>> On 3/11/24 7:52 PM, olcott wrote:
>>>>>>>> On 3/11/2024 9:32 PM, immibis wrote:
>>>>>>>>> On 12/03/24 03:24, olcott wrote:
>>>>>>> \
>>>>>>>>>> Troll detected.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Once we understand that either YES or NO is the right answer
>>>>>>>>
>>>>>>>> Not for this decider/input question: Ĥ.H / ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>> For that decider/input question both YES and NO are the wrong
>>>>>>>> answer.
>>>>>>>
>>>>>>> The problem that you keeep on missing is that by the point we can
>>>>>>> ask this question, H and H^ are FULLY CODED, and thus we know
>>>>>>> their behavirs.
>>>>>>
>>>>>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy // Ĥ applied to ⟨Ĥ⟩ halts
>>>>>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>>>>
>>>>>> Since you know that is false why lie?
>>>>>> ⊢* specifies an infinite set of encodings.
>>>>>
>>>>> Nope, read him again, not just skim and assume.
>>>>>
>>>>
>>>> *Here is the proof that I am correct*
>>>> ∀ H ∈ Turing_Machine_Deciders
>>>> ∃ TMD ∈ Turing_Machine_Descriptions |
>>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>>
>>>>
>>>
>>> So, H, being an ELEMENT of Turing Machine Deciders, is a SINGLE
>>> INSTANCE of it, it is NOT the set itself.
>>
>> ∀ H ∈ Turing_Machine_Deciders *DOES NOT REFER TO A SINGLE INSTANCE*
>
> Yes it does. It means that if H is a single instance, no matter which
> one it is, the rest of the sentence is true.

*Richard updated his incorrect words*
On 3/12/2024 12:50 PM, Richard Damon wrote:
> Of COURSE "H" referes to just a single instance at a time.

More correctly
"H" refers to just a single instance at a time
of the elements of the infinite set specified by
∀ H ∈ Turing_Machine_Deciders

*This discussion has moved to my new post*
[Proving my 2004 claim that some decider/input pairs are incorrect
questions]

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

Re: ZFC solution to incorrect questions: reject them

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From: ross.a.f...@gmail.com (Ross Finlayson)
Newsgroups: comp.theory
Subject: Re: ZFC solution to incorrect questions: reject them
Date: Tue, 12 Mar 2024 11:00:11 -0700
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by: Ross Finlayson - Tue, 12 Mar 2024 19:08 UTC

On 03/12/2024 08:52 AM, olcott wrote:

People learn about ZFC when their mathematical curiousity
brings them to questions of foundations.

Then it's understood that it's an axiomatic theory,
and that axioms are rules, and in an axiomatic theory,
there result theorems derived from axioms, with axioms
themselves being considered theorems, and that no theorems
break any axioms.

This is that axioms are somehow "true", and in the theory
they're defined to be true, meaning they're never contradicted.

This is with the usual notion of contradiction and
non-contradiction, about opposition and juxtaposition,
where it's established usually that there is "true" or
there is "false" and there is no middle ground, that
a third case or tertium does not exist in the world,
"tertium non datur", the laws of excluded middle, the
principle of excluded middle, which in this axiomatic
theory, is somehow always a theorem, as it results
from the plain contemplation or consideration, that
axioms are "true", in the theory, in what is almost
always these days, a "meta-theory", that's undefined,
except that axioms are true and none of their theorems
contradict each other, saying "both true and false",
which is tertium and non datur.

So anyways ZFC is a theory where there's only one relation,
it's "elt". There's only one kind of object, it's "set".
For any given set P and any given set Q, either P elt Q
or Q elt P, or neither, and, not both. Then you might
wonder, "well why not both?", and it's because, one of
the axioms of ZFC is "not both".

The axioms of ZFC either _expand_ comprehension, meaning,
"no reason why not, so, it's so", or _restrict_ comprehension,
meaning, "not: because this axiom is true in this theory,
and says no".

This introduces the concept of "independence" of axioms,
that axioms that are independent say nothing about the
theorems of otherwise independent axioms, and that axioms
that are not independent, contradict each other, and that
restriction is defined to always win, in any case of otherwise
contradiction, when axioms aren't independent, in ZFC,
that axioms of _restriction_ of comprehension aren't
necessarily independent each other, or, the independent
axioms of _expansion_ of comprehension.

So, ZFC has various axioms of restriction of comprehension,
what boil down to the "Axiom of Regularity" also known as
the "Axiom of Well-Foundedness" or "Axiom of Foundation",
that for any two sets P elt Q or Q elt P, or neither,
but not both. This is where otherwise the axioms of
expansion of comprehension, would otherwise result,
"no reason why not", except that eventually certain
theorems _desired_, of the theory, would either not be
evident or would see contradictions.

So, yeah, "ZFC solution to incorrect questions: reject them",
is what's called "restriction of comprehension" and then
what you do is get into all the various combinations of
otherwise the expansion of comprehension, then get into
why the models of the universe of the objects so related,
is a wider theory where ZFC, or ZF, set theory, is variously
considerable as either a fragment or an extension,
the universe of the objects of ZF and ZFC set theories,
in all theory in all comprehension according to what's, "true".

Or, you know, "not false".

So of course there are names for all these things and
studies of all these things and criteria for all these
things, what basically results for "Set Theory" what's
called "Class/Set Distinction", a sort of, meta-theory,
about set theory, where "elt" has a sort of complement
"members" reflects "elt's sets are contained in sets"
while "members' classes contain classes", that also the
Class/Set distinction reflects objects as of the,
"Inconsistent Multiplicities", of set theory, that
one can relate to the, "Indeterminate Forms", of
mathematics, that variously kind of do or don't have
structure, "models" in the "model theory", where a
theory has a model and a model has a theory is the meta-theory,
helping explain why the wider world of theory knows that
ZFC, or ZF, set theory, is a fragment of the universe of
the objects of ZF set theory, which is its model in
the wider model theory,

Theory of ZF, of course, doesn't actually acknowledge,
"a universe of objects of ZF, the domain of discourse"
not so much as it's axiomatic "there is no universe of
objects in ZF set theory", but that it's a theorem that's
a consequence of restriction of comprehension, "foundational
well-foundedness", which follows from otherwise a very
useful result called "uncountability", .

Now, "Regularity" means "the Rulial", it rules or defines
a rule, so other theories otherwise about sets can have
their own sorts rulial definitions, just saying that the
theory where Well-Foundedness is rulial, just indicates
that this is moreso "ZF's axiom that establishes ZF's
main restriction of comprehension as ruliality, AoR
the Axiom of Regularity, is particular to ZF, and it's
called Well-Foundedness or Foundation, to reflect that
theories without it are called Non-Well-Founded or
sometimes Anti-Well-Founded, with regards to the regular
or rulial the ruliality of what may be other theories,
of sets, which are defined by one relation, elt".

So anyways, there are others.

Re: ZFC solution to incorrect questions: reject them

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by: olcott - Tue, 12 Mar 2024 19:32 UTC

On 3/12/2024 2:08 PM, Ross Finlayson wrote:
> On 03/12/2024 08:52 AM, olcott wrote:
>
>> ∀ H ∈ Turing_Machine_Deciders
>> ∃ TMD ∈ Turing_Machine_Descriptions |
>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>
>> There is some input TMD to every H such that
>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>
>> When we disallow decider/input pairs that are incorrect
>> questions where both YES and NO are the wrong answer
>> (the same way the ZFC disallowed self-referential sets) then
>> pathological inputs are not allowed to come into existence.
>>
>> Does the barber that shaves everyone that does not shave
>> themselves shave himself? is rejected as an incorrect question.
>> https://en.wikipedia.org/wiki/Barber_paradox#
>>
>
>
> People learn about ZFC when their mathematical curiousity
> brings them to questions of foundations.
>
> Then it's understood that it's an axiomatic theory,
> and that axioms are rules, and in an axiomatic theory,
> there result theorems derived from axioms, with axioms
> themselves being considered theorems, and that no theorems
> break any axioms.
>
> This is that axioms are somehow "true", and in the theory
> they're defined to be true, meaning they're never contradicted.
>
That is a great insight that you and Haskell Curry and
very few others agree on.
https://www.liarparadox.org/Haskell_Curry_45.pdf

> This is with the usual notion of contradiction and
> non-contradiction, about opposition and juxtaposition,
> where it's established usually that there is "true" or
> there is "false" and there is no middle ground, that
> a third case or tertium does not exist in the world,
> "tertium non datur", the laws of excluded middle, the
> principle of excluded middle, which in this axiomatic
> theory, is somehow always a theorem, as it results
> from the plain contemplation or consideration, that
> axioms are "true", in the theory, in what is almost
> always these days, a "meta-theory", that's undefined,
> except that axioms are true and none of their theorems
> contradict each other, saying "both true and false",
> which is tertium and non datur.
>
>
> So anyways ZFC is a theory where there's only one relation,
> it's "elt". There's only one kind of object, it's "set".

I have no idea what "elt" means.

> For any given set P and any given set Q, either P elt Q
> or Q elt P, or neither, and, not both. Then you might
> wonder, "well why not both?", and it's because, one of
> the axioms of ZFC is "not both".
>
> The axioms of ZFC either _expand_ comprehension, meaning,
> "no reason why not, so, it's so", or _restrict_ comprehension,
> meaning, "not: because this axiom is true in this theory,
> and says no".
>
> This introduces the concept of "independence" of axioms,
> that axioms that are independent say nothing about the
> theorems of otherwise independent axioms, and that axioms
> that are not independent, contradict each other, and that
> restriction is defined to always win, in any case of otherwise
> contradiction, when axioms aren't independent, in ZFC,
> that axioms of _restriction_ of comprehension aren't
> necessarily independent each other, or, the independent
> axioms of _expansion_ of comprehension.
>
>
>
> So, ZFC has various axioms of restriction of comprehension,
Yes, no set can be defined that contains itself.

> what boil down to the "Axiom of Regularity" also known as
> the "Axiom of Well-Foundedness" or "Axiom of Foundation",
Yes that one

> that for any two sets P elt Q or Q elt P, or neither,
> but not both. This is where otherwise the axioms of
> expansion of comprehension, would otherwise result,
> "no reason why not", except that eventually certain
> theorems _desired_, of the theory, would either not be
> evident or would see contradictions.
>
>
> So, yeah, "ZFC solution to incorrect questions: reject them",
> is what's called "restriction of comprehension" and then
Great !!!

> what you do is get into all the various combinations of
> otherwise the expansion of comprehension, then get into
> why the models of the universe of the objects so related,
> is a wider theory where ZFC, or ZF, set theory, is variously
> considerable as either a fragment or an extension,
> the universe of the objects of ZF and ZFC set theories,
> in all theory in all comprehension according to what's, "true".
>
>
> Or, you know, "not false".
>
>
>
> So of course there are names for all these things and
> studies of all these things and criteria for all these
> things, what basically results for "Set Theory" what's
> called "Class/Set Distinction", a sort of, meta-theory,
NBG set theory
https://www.britannica.com/science/proper-class

> about set theory, where "elt" has a sort of complement
> "members" reflects "elt's sets are contained in sets"
> while "members' classes contain classes", that also the
> Class/Set distinction reflects objects as of the,
> "Inconsistent Multiplicities", of set theory, that
> one can relate to the, "Indeterminate Forms", of
> mathematics, that variously kind of do or don't have
> structure, "models" in the "model theory", where a
> theory has a model and a model has a theory is the meta-theory,
> helping explain why the wider world of theory knows that
> ZFC, or ZF, set theory, is a fragment of the universe of
> the objects of ZF set theory, which is its model in
> the wider model theory,
>
> Theory of ZF, of course, doesn't actually acknowledge,
> "a universe of objects of ZF, the domain of discourse"
> not so much as it's axiomatic "there is no universe of
> objects in ZF set theory", but that it's a theorem that's
> a consequence of restriction of comprehension, "foundational
> well-foundedness", which follows from otherwise a very
> useful result called "uncountability", .
>
> Now, "Regularity" means "the Rulial", it rules or defines
> a rule, so other theories otherwise about sets can have
> their own sorts rulial definitions, just saying that the
> theory where Well-Foundedness is rulial, just indicates
> that this is moreso "ZF's axiom that establishes ZF's
> main restriction of comprehension as ruliality, AoR
> the Axiom of Regularity, is particular to ZF, and it's
> called Well-Foundedness or Foundation, to reflect that
> theories without it are called Non-Well-Founded or
> sometimes Anti-Well-Founded, with regards to the regular
Yes I get that and have known about it for some years.

> or rulial the ruliality of what may be other theories,
> of sets, which are defined by one relation, elt".
>
>
>
> So anyways, there are others.

*Your knowledge of these things seem truly superb*
I had forgotten many of the details that you referenced.

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --logically impossible--

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by: Richard Damon - Tue, 12 Mar 2024 19:33 UTC

On 3/12/24 11:16 AM, olcott wrote:
> On 3/12/2024 1:04 PM, Richard Damon wrote:

>> But SHOWING that something is logically impossible reveals the
>> limitations that were already there.
>>
>> Yes, the Halting Theorem doesn't MAKE the problem impossible, it shows
>> that it always was, and gives us knowledge of that.
>>
>
> The halting problem does not derive a limit to computation
> any more than the inability of CAD systems to draw square
> circles places a limit on computation.
>

But shows the limitation that already existed in compuations.

You don't seem to understand that.

Computation can only do what Computation do.

One of the LIMITS of Computations, is they can not determine is the
halting state us any and all algoritms + data.

They may be able to determine it for a subset of all possible,
but not for all possible.

That IS a limit of Computations REVEALED by the Halting Theorem.

Re: ZFC solution to incorrect questions: reject them

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by: Ross Finlayson - Tue, 12 Mar 2024 19:59 UTC

On 03/12/2024 12:32 PM, olcott wrote:
> On 3/12/2024 2:08 PM, Ross Finlayson wrote:
>> On 03/12/2024 08:52 AM, olcott wrote:
>>
>>> ∀ H ∈ Turing_Machine_Deciders
>>> ∃ TMD ∈ Turing_Machine_Descriptions |
>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>
>>> There is some input TMD to every H such that
>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>
>>> When we disallow decider/input pairs that are incorrect
>>> questions where both YES and NO are the wrong answer
>>> (the same way the ZFC disallowed self-referential sets) then
>>> pathological inputs are not allowed to come into existence.
>>>
>>> Does the barber that shaves everyone that does not shave
>>> themselves shave himself? is rejected as an incorrect question.
>>> https://en.wikipedia.org/wiki/Barber_paradox#
>>>
>>
>>
>> People learn about ZFC when their mathematical curiousity
>> brings them to questions of foundations.
>>
>> Then it's understood that it's an axiomatic theory,
>> and that axioms are rules, and in an axiomatic theory,
>> there result theorems derived from axioms, with axioms
>> themselves being considered theorems, and that no theorems
>> break any axioms.
>>
>> This is that axioms are somehow "true", and in the theory
>> they're defined to be true, meaning they're never contradicted.
>>
> That is a great insight that you and Haskell Curry and
> very few others agree on.
> https://www.liarparadox.org/Haskell_Curry_45.pdf
>
>> This is with the usual notion of contradiction and
>> non-contradiction, about opposition and juxtaposition,
>> where it's established usually that there is "true" or
>> there is "false" and there is no middle ground, that
>> a third case or tertium does not exist in the world,
>> "tertium non datur", the laws of excluded middle, the
>> principle of excluded middle, which in this axiomatic
>> theory, is somehow always a theorem, as it results
>> from the plain contemplation or consideration, that
>> axioms are "true", in the theory, in what is almost
>> always these days, a "meta-theory", that's undefined,
>> except that axioms are true and none of their theorems
>> contradict each other, saying "both true and false",
>> which is tertium and non datur.
>>
>>
>> So anyways ZFC is a theory where there's only one relation,
>> it's "elt". There's only one kind of object, it's "set".
>
> I have no idea what "elt" means.
>
>> For any given set P and any given set Q, either P elt Q
>> or Q elt P, or neither, and, not both. Then you might
>> wonder, "well why not both?", and it's because, one of
>> the axioms of ZFC is "not both".
>>
>> The axioms of ZFC either _expand_ comprehension, meaning,
>> "no reason why not, so, it's so", or _restrict_ comprehension,
>> meaning, "not: because this axiom is true in this theory,
>> and says no".
>>
>> This introduces the concept of "independence" of axioms,
>> that axioms that are independent say nothing about the
>> theorems of otherwise independent axioms, and that axioms
>> that are not independent, contradict each other, and that
>> restriction is defined to always win, in any case of otherwise
>> contradiction, when axioms aren't independent, in ZFC,
>> that axioms of _restriction_ of comprehension aren't
>> necessarily independent each other, or, the independent
>> axioms of _expansion_ of comprehension.
>>
>>
>>
>> So, ZFC has various axioms of restriction of comprehension,
> Yes, no set can be defined that contains itself.
>
>> what boil down to the "Axiom of Regularity" also known as
>> the "Axiom of Well-Foundedness" or "Axiom of Foundation",
> Yes that one
>
>> that for any two sets P elt Q or Q elt P, or neither,
>> but not both. This is where otherwise the axioms of
>> expansion of comprehension, would otherwise result,
>> "no reason why not", except that eventually certain
>> theorems _desired_, of the theory, would either not be
>> evident or would see contradictions.
>>
>>
>> So, yeah, "ZFC solution to incorrect questions: reject them",
>> is what's called "restriction of comprehension" and then
> Great !!!
>
>> what you do is get into all the various combinations of
>> otherwise the expansion of comprehension, then get into
>> why the models of the universe of the objects so related,
>> is a wider theory where ZFC, or ZF, set theory, is variously
>> considerable as either a fragment or an extension,
>> the universe of the objects of ZF and ZFC set theories,
>> in all theory in all comprehension according to what's, "true".
>>
>>
>> Or, you know, "not false".
>>
>>
>>
>> So of course there are names for all these things and
>> studies of all these things and criteria for all these
>> things, what basically results for "Set Theory" what's
>> called "Class/Set Distinction", a sort of, meta-theory,
> NBG set theory
> https://www.britannica.com/science/proper-class
>
>> about set theory, where "elt" has a sort of complement
>> "members" reflects "elt's sets are contained in sets"
>> while "members' classes contain classes", that also the
>> Class/Set distinction reflects objects as of the,
>> "Inconsistent Multiplicities", of set theory, that
>> one can relate to the, "Indeterminate Forms", of
>> mathematics, that variously kind of do or don't have
>> structure, "models" in the "model theory", where a
>> theory has a model and a model has a theory is the meta-theory,
>> helping explain why the wider world of theory knows that
>> ZFC, or ZF, set theory, is a fragment of the universe of
>> the objects of ZF set theory, which is its model in
>> the wider model theory,
>>
>> Theory of ZF, of course, doesn't actually acknowledge,
>> "a universe of objects of ZF, the domain of discourse"
>> not so much as it's axiomatic "there is no universe of
>> objects in ZF set theory", but that it's a theorem that's
>> a consequence of restriction of comprehension, "foundational
>> well-foundedness", which follows from otherwise a very
>> useful result called "uncountability", .
>>
>> Now, "Regularity" means "the Rulial", it rules or defines
>> a rule, so other theories otherwise about sets can have
>> their own sorts rulial definitions, just saying that the
>> theory where Well-Foundedness is rulial, just indicates
>> that this is moreso "ZF's axiom that establishes ZF's
>> main restriction of comprehension as ruliality, AoR
>> the Axiom of Regularity, is particular to ZF, and it's
>> called Well-Foundedness or Foundation, to reflect that
>> theories without it are called Non-Well-Founded or
>> sometimes Anti-Well-Founded, with regards to the regular
> Yes I get that and have known about it for some years.
>
>> or rulial the ruliality of what may be other theories,
>> of sets, which are defined by one relation, elt".
>>
>>
>>
>> So anyways, there are others.
>
> *Your knowledge of these things seem truly superb*
> I had forgotten many of the details that you referenced.
>

Well, yeah, my mathematical curiousity brought me
to questions of foundations.

"Question" is a word, and it's kind of loaded. For
example, the German language has two different words
for "question-able", "fraglich", as, dubious, and,
"question-providing", "fragwuerdig", as, profound.

I.e., the profound, opens new questions, vis-a-vis
the interrogable, which may or may not.

I'm reading about this in Steiner on Heidegger as
of from old Roger Bacon. (I've sort of got a
trio of anti-Plato's in Wittgenstein, Nietzsche,
and Heidegger as various rejections of logical
positivism in the accommodation of logical positivism
after their compensation in search of teleology
after the breakwater of ontology, that of course
they're each strong Platonists in otherwise a
world of mundane, subjective, inauthentic,
Existentialists, the adrift logical positivists.
Of course that's for a strong logical positivism
overall, with re-attaching the silver thread, or cord.)

Click here to read the complete article

Re: ZFC solution to incorrect questions: reject them

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by: olcott - Tue, 12 Mar 2024 20:28 UTC

On 3/12/2024 2:59 PM, Ross Finlayson wrote:
> On 03/12/2024 12:32 PM, olcott wrote:
>> On 3/12/2024 2:08 PM, Ross Finlayson wrote:
>>> On 03/12/2024 08:52 AM, olcott wrote:
>>>
>>>> ∀ H ∈ Turing_Machine_Deciders
>>>> ∃ TMD ∈ Turing_Machine_Descriptions |
>>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>>
>>>> There is some input TMD to every H such that
>>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>>
>>>> When we disallow decider/input pairs that are incorrect
>>>> questions where both YES and NO are the wrong answer
>>>> (the same way the ZFC disallowed self-referential sets) then
>>>> pathological inputs are not allowed to come into existence.
>>>>
>>>> Does the barber that shaves everyone that does not shave
>>>> themselves shave himself? is rejected as an incorrect question.
>>>> https://en.wikipedia.org/wiki/Barber_paradox#
>>>>
>>>
>>>
>>> People learn about ZFC when their mathematical curiousity
>>> brings them to questions of foundations.
>>>
>>> Then it's understood that it's an axiomatic theory,
>>> and that axioms are rules, and in an axiomatic theory,
>>> there result theorems derived from axioms, with axioms
>>> themselves being considered theorems, and that no theorems
>>> break any axioms.
>>>
>>> This is that axioms are somehow "true", and in the theory
>>> they're defined to be true, meaning they're never contradicted.
>>>
>> That is a great insight that you and Haskell Curry and
>> very few others agree on.
>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>
>>> This is with the usual notion of contradiction and
>>> non-contradiction, about opposition and juxtaposition,
>>> where it's established usually that there is "true" or
>>> there is "false" and there is no middle ground, that
>>> a third case or tertium does not exist in the world,
>>> "tertium non datur", the laws of excluded middle, the
>>> principle of excluded middle, which in this axiomatic
>>> theory, is somehow always a theorem, as it results
>>> from the plain contemplation or consideration, that
>>> axioms are "true", in the theory, in what is almost
>>> always these days, a "meta-theory", that's undefined,
>>> except that axioms are true and none of their theorems
>>> contradict each other, saying "both true and false",
>>> which is tertium and non datur.
>>>
>>>
>>> So anyways ZFC is a theory where there's only one relation,
>>> it's "elt". There's only one kind of object, it's "set".
>>
>> I have no idea what "elt" means.
>>
>>> For any given set P and any given set Q, either P elt Q
>>> or Q elt P, or neither, and, not both. Then you might
>>> wonder, "well why not both?", and it's because, one of
>>> the axioms of ZFC is "not both".
>>>
>>> The axioms of ZFC either _expand_ comprehension, meaning,
>>> "no reason why not, so, it's so", or _restrict_ comprehension,
>>> meaning, "not: because this axiom is true in this theory,
>>> and says no".
>>>
>>> This introduces the concept of "independence" of axioms,
>>> that axioms that are independent say nothing about the
>>> theorems of otherwise independent axioms, and that axioms
>>> that are not independent, contradict each other, and that
>>> restriction is defined to always win, in any case of otherwise
>>> contradiction, when axioms aren't independent, in ZFC,
>>> that axioms of _restriction_ of comprehension aren't
>>> necessarily independent each other, or, the independent
>>> axioms of _expansion_ of comprehension.
>>>
>>>
>>>
>>> So, ZFC has various axioms of restriction of comprehension,
>> Yes, no set can be defined that contains itself.
>>
>>> what boil down to the "Axiom of Regularity" also known as
>>> the "Axiom of Well-Foundedness" or "Axiom of Foundation",
>> Yes that one
>>
>>> that for any two sets P elt Q or Q elt P, or neither,
>>> but not both. This is where otherwise the axioms of
>>> expansion of comprehension, would otherwise result,
>>> "no reason why not", except that eventually certain
>>> theorems _desired_, of the theory, would either not be
>>> evident or would see contradictions.
>>>
>>>
>>> So, yeah, "ZFC solution to incorrect questions: reject them",
>>> is what's called "restriction of comprehension" and then
>> Great !!!
>>
>>> what you do is get into all the various combinations of
>>> otherwise the expansion of comprehension, then get into
>>> why the models of the universe of the objects so related,
>>> is a wider theory where ZFC, or ZF, set theory, is variously
>>> considerable as either a fragment or an extension,
>>> the universe of the objects of ZF and ZFC set theories,
>>> in all theory in all comprehension according to what's, "true".
>>>
>>>
>>> Or, you know, "not false".
>>>
>>>
>>>
>>> So of course there are names for all these things and
>>> studies of all these things and criteria for all these
>>> things, what basically results for "Set Theory" what's
>>> called "Class/Set Distinction", a sort of, meta-theory,
>> NBG set theory
>> https://www.britannica.com/science/proper-class
>>
>>> about set theory, where "elt" has a sort of complement
>>> "members" reflects "elt's sets are contained in sets"
>>> while "members' classes contain classes", that also the
>>> Class/Set distinction reflects objects as of the,
>>> "Inconsistent Multiplicities", of set theory, that
>>> one can relate to the, "Indeterminate Forms", of
>>> mathematics, that variously kind of do or don't have
>>> structure, "models" in the "model theory", where a
>>> theory has a model and a model has a theory is the meta-theory,
>>> helping explain why the wider world of theory knows that
>>> ZFC, or ZF, set theory, is a fragment of the universe of
>>> the objects of ZF set theory, which is its model in
>>> the wider model theory,
>>>
>>> Theory of ZF, of course, doesn't actually acknowledge,
>>> "a universe of objects of ZF, the domain of discourse"
>>> not so much as it's axiomatic "there is no universe of
>>> objects in ZF set theory", but that it's a theorem that's
>>> a consequence of restriction of comprehension, "foundational
>>> well-foundedness", which follows from otherwise a very
>>> useful result called "uncountability", .
>>>
>>> Now, "Regularity" means "the Rulial", it rules or defines
>>> a rule, so other theories otherwise about sets can have
>>> their own sorts rulial definitions, just saying that the
>>> theory where Well-Foundedness is rulial, just indicates
>>> that this is moreso "ZF's axiom that establishes ZF's
>>> main restriction of comprehension as ruliality, AoR
>>> the Axiom of Regularity, is particular to ZF, and it's
>>> called Well-Foundedness or Foundation, to reflect that
>>> theories without it are called Non-Well-Founded or
>>> sometimes Anti-Well-Founded, with regards to the regular
>> Yes I get that and have known about it for some years.
>>
>>> or rulial the ruliality of what may be other theories,
>>> of sets, which are defined by one relation, elt".
>>>
>>>
>>>
>>> So anyways, there are others.
>>
>> *Your knowledge of these things seem truly superb*
>> I had forgotten many of the details that you referenced.
>>
>
> Well, yeah, my mathematical curiousity brought me
> to questions of foundations.
>
I love foundations because I noticed errors in the understanding
of the notion of true_on_the_basis_of_semantic_meaning(x) back
in 2004.

Click here to read the complete article

Re: ZFC solution to incorrect questions: reject them

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by: Ross Finlayson - Tue, 12 Mar 2024 22:50 UTC

On 03/12/2024 01:28 PM, olcott wrote:
> On 3/12/2024 2:59 PM, Ross Finlayson wrote:
>> On 03/12/2024 12:32 PM, olcott wrote:
>>> On 3/12/2024 2:08 PM, Ross Finlayson wrote:
>>>> On 03/12/2024 08:52 AM, olcott wrote:
>>>>
>>>>> ∀ H ∈ Turing_Machine_Deciders
>>>>> ∃ TMD ∈ Turing_Machine_Descriptions |
>>>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>>>
>>>>> There is some input TMD to every H such that
>>>>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>>>>>
>>>>> When we disallow decider/input pairs that are incorrect
>>>>> questions where both YES and NO are the wrong answer
>>>>> (the same way the ZFC disallowed self-referential sets) then
>>>>> pathological inputs are not allowed to come into existence.
>>>>>
>>>>> Does the barber that shaves everyone that does not shave
>>>>> themselves shave himself? is rejected as an incorrect question.
>>>>> https://en.wikipedia.org/wiki/Barber_paradox#
>>>>>
>>>>
>>>>
>>>> People learn about ZFC when their mathematical curiousity
>>>> brings them to questions of foundations.
>>>>
>>>> Then it's understood that it's an axiomatic theory,
>>>> and that axioms are rules, and in an axiomatic theory,
>>>> there result theorems derived from axioms, with axioms
>>>> themselves being considered theorems, and that no theorems
>>>> break any axioms.
>>>>
>>>> This is that axioms are somehow "true", and in the theory
>>>> they're defined to be true, meaning they're never contradicted.
>>>>
>>> That is a great insight that you and Haskell Curry and
>>> very few others agree on.
>>> https://www.liarparadox.org/Haskell_Curry_45.pdf
>>>
>>>> This is with the usual notion of contradiction and
>>>> non-contradiction, about opposition and juxtaposition,
>>>> where it's established usually that there is "true" or
>>>> there is "false" and there is no middle ground, that
>>>> a third case or tertium does not exist in the world,
>>>> "tertium non datur", the laws of excluded middle, the
>>>> principle of excluded middle, which in this axiomatic
>>>> theory, is somehow always a theorem, as it results
>>>> from the plain contemplation or consideration, that
>>>> axioms are "true", in the theory, in what is almost
>>>> always these days, a "meta-theory", that's undefined,
>>>> except that axioms are true and none of their theorems
>>>> contradict each other, saying "both true and false",
>>>> which is tertium and non datur.
>>>>
>>>>
>>>> So anyways ZFC is a theory where there's only one relation,
>>>> it's "elt". There's only one kind of object, it's "set".
>>>
>>> I have no idea what "elt" means.
>>>
>>>> For any given set P and any given set Q, either P elt Q
>>>> or Q elt P, or neither, and, not both. Then you might
>>>> wonder, "well why not both?", and it's because, one of
>>>> the axioms of ZFC is "not both".
>>>>
>>>> The axioms of ZFC either _expand_ comprehension, meaning,
>>>> "no reason why not, so, it's so", or _restrict_ comprehension,
>>>> meaning, "not: because this axiom is true in this theory,
>>>> and says no".
>>>>
>>>> This introduces the concept of "independence" of axioms,
>>>> that axioms that are independent say nothing about the
>>>> theorems of otherwise independent axioms, and that axioms
>>>> that are not independent, contradict each other, and that
>>>> restriction is defined to always win, in any case of otherwise
>>>> contradiction, when axioms aren't independent, in ZFC,
>>>> that axioms of _restriction_ of comprehension aren't
>>>> necessarily independent each other, or, the independent
>>>> axioms of _expansion_ of comprehension.
>>>>
>>>>
>>>>
>>>> So, ZFC has various axioms of restriction of comprehension,
>>> Yes, no set can be defined that contains itself.
>>>
>>>> what boil down to the "Axiom of Regularity" also known as
>>>> the "Axiom of Well-Foundedness" or "Axiom of Foundation",
>>> Yes that one
>>>
>>>> that for any two sets P elt Q or Q elt P, or neither,
>>>> but not both. This is where otherwise the axioms of
>>>> expansion of comprehension, would otherwise result,
>>>> "no reason why not", except that eventually certain
>>>> theorems _desired_, of the theory, would either not be
>>>> evident or would see contradictions.
>>>>
>>>>
>>>> So, yeah, "ZFC solution to incorrect questions: reject them",
>>>> is what's called "restriction of comprehension" and then
>>> Great !!!
>>>
>>>> what you do is get into all the various combinations of
>>>> otherwise the expansion of comprehension, then get into
>>>> why the models of the universe of the objects so related,
>>>> is a wider theory where ZFC, or ZF, set theory, is variously
>>>> considerable as either a fragment or an extension,
>>>> the universe of the objects of ZF and ZFC set theories,
>>>> in all theory in all comprehension according to what's, "true".
>>>>
>>>>
>>>> Or, you know, "not false".
>>>>
>>>>
>>>>
>>>> So of course there are names for all these things and
>>>> studies of all these things and criteria for all these
>>>> things, what basically results for "Set Theory" what's
>>>> called "Class/Set Distinction", a sort of, meta-theory,
>>> NBG set theory
>>> https://www.britannica.com/science/proper-class
>>>
>>>> about set theory, where "elt" has a sort of complement
>>>> "members" reflects "elt's sets are contained in sets"
>>>> while "members' classes contain classes", that also the
>>>> Class/Set distinction reflects objects as of the,
>>>> "Inconsistent Multiplicities", of set theory, that
>>>> one can relate to the, "Indeterminate Forms", of
>>>> mathematics, that variously kind of do or don't have
>>>> structure, "models" in the "model theory", where a
>>>> theory has a model and a model has a theory is the meta-theory,
>>>> helping explain why the wider world of theory knows that
>>>> ZFC, or ZF, set theory, is a fragment of the universe of
>>>> the objects of ZF set theory, which is its model in
>>>> the wider model theory,
>>>>
>>>> Theory of ZF, of course, doesn't actually acknowledge,
>>>> "a universe of objects of ZF, the domain of discourse"
>>>> not so much as it's axiomatic "there is no universe of
>>>> objects in ZF set theory", but that it's a theorem that's
>>>> a consequence of restriction of comprehension, "foundational
>>>> well-foundedness", which follows from otherwise a very
>>>> useful result called "uncountability", .
>>>>
>>>> Now, "Regularity" means "the Rulial", it rules or defines
>>>> a rule, so other theories otherwise about sets can have
>>>> their own sorts rulial definitions, just saying that the
>>>> theory where Well-Foundedness is rulial, just indicates
>>>> that this is moreso "ZF's axiom that establishes ZF's
>>>> main restriction of comprehension as ruliality, AoR
>>>> the Axiom of Regularity, is particular to ZF, and it's
>>>> called Well-Foundedness or Foundation, to reflect that
>>>> theories without it are called Non-Well-Founded or
>>>> sometimes Anti-Well-Founded, with regards to the regular
>>> Yes I get that and have known about it for some years.
>>>
>>>> or rulial the ruliality of what may be other theories,
>>>> of sets, which are defined by one relation, elt".
>>>>
>>>>
>>>>
>>>> So anyways, there are others.
>>>
>>> *Your knowledge of these things seem truly superb*
>>> I had forgotten many of the details that you referenced.
>>>
>>
>> Well, yeah, my mathematical curiousity brought me
>> to questions of foundations.
>>
> I love foundations because I noticed errors in the understanding
> of the notion of true_on_the_basis_of_semantic_meaning(x) back
> in 2004.
>
>> "Question" is a word, and it's kind of loaded. For
>> example, the German language has two different words
>> for "question-able", "fraglich", as, dubious, and,
>> "question-providing", "fragwuerdig", as, profound.
>>
>> I.e., the profound, opens new questions, vis-a-vis
>> the interrogable, which may or may not.
>>
>> I'm reading about this in Steiner on Heidegger as
>> of from old Roger Bacon. (I've sort of got a
>> trio of anti-Plato's in Wittgenstein, Nietzsche,
>> and Heidegger as various rejections of logical
>> positivism in the accommodation of logical positivism
> The coherent notion of true_on_the_basis_of_semantic_meaning(x)
> seems to affirm logical positivism over Gödel.
>
>> after their compensation in search of teleology
>> after the breakwater of ontology, that of course
>> they're each strong Platonists in otherwise a
>> world of mundane, subjective, inauthentic,
>> Existentialists, the adrift logical positivists.
>> Of course that's for a strong logical positivism
>> overall, with re-attaching the silver thread, or cord.)
>>
>>
>>
>> The universe of logical and mathematical objects
>> is its own, intuitively structured, thing. All
>
> Yes, hence true_on_the_basis_of_semantic_meaning(x) does
> not apply to reality only mental models of reality.
>
>> matters of relation are assumed to exist in it,
>> both the concrete as realizable mathematically,
>> and of course all suchly matters of mathematical
>> or logical consistency, and inconsistency, so effable,
>> or ineffable.
>>
> Perhaps with true_on_the_basis_of_semantic_meaning(x)
> it becomes effable.
>
>> Then, humans or objectively thinkers, or course have
>> limited or finite means, and, communication has its
>> own finite yet open means.
>>
> Yet with Montague semantics can be formalized to eliminate
> all ambiguity.
>
>>
>>
>> I thank you for your compliments, affinity,
>> then would suggest that you look to the fuller
>> complements, complementarity, as what such
>> notions of the fuller dialectic, arrive largely
>> as fundamentally from "complementary duals",
>> that not only is something filled, also filling.
>>
> I can only understand those aspects of my ideas that you
> directly referenced that I acknowledged that I understood.
> This was much more tan I expected to understand. I had
> forgotten some of the key details that you referenced.
>
>> I.e., "is there an axiom?" "Inverse".
>>
>> Or, you know, yes and no.
>>
>>
>>
>> You can find some hundred hours or readings
>> and lectures on my youtube channel as of
>> like https youtube /@rossfinlayson .
>>
>> Or, you know, the 10,000's posts to sci.math.
>

Click here to read the complete article

Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --new focus--

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From: mikko.le...@iki.fi (Mikko)
Newsgroups: comp.theory
Subject: Re: ZFC solution to incorrect questions: reject them
Date: Tue, 12 Mar 2024 11:00:11 -0700
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by: Mikko - Wed, 13 Mar 2024 16:45 UTC

On 2024-03-12 15:31:58 +0000, olcott said:

> On 3/12/2024 5:06 AM, Mikko wrote:
>> On 2024-03-12 03:37:53 +0000, olcott said:
>>
>>> On 3/11/2024 10:31 PM, Richard Damon wrote:
>>>> On 3/11/24 7:52 PM, olcott wrote:
>>>>> On 3/11/2024 9:32 PM, immibis wrote:
>>>>>> On 12/03/24 03:24, olcott wrote:
>>>> \
>>>>>>> Troll detected.
>>>>>>>
>>>>>>
>>>>>> Once we understand that either YES or NO is the right answer
>>>>>
>>>>> Not for this decider/input question: Ĥ.H / ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>> For that decider/input question both YES and NO are the wrong answer.
>>>>
>>>> The problem that you keeep on missing is that by the point we can ask
>>>> this question, H and H^ are FULLY CODED, and thus we know their
>>>> behavirs.
>>>
>>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy // Ĥ applied to ⟨Ĥ⟩ halts
>>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>
>>> Since you know that is false why lie?
>>> ⊢* specifies an infinite set of encodings.
>>
>> No, it does not. The notation is defined by Linz to denote
>> a finite sequence of configurations.
>>
>
> If it is required to report on a single finite sequence of
> configurations then that only proves that there exists some
> halt decider that decides some input incorrectly.
>
> If it is reporting on every finite sequence of configurations
> then that proves that there does not exist a halt decider that
> decides every input correctly.
>
> *Formalized*
> ∀ H ∈ Turing_Machine_Deciders
> ∃ TMD ∈ Turing_Machine_Descriptions |
> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)

Yes, this is one way to state Linz' conclusion.

> There is some input TMD to every H such that
> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)

Yes, this is another way to state Linz' conclusion.

--
Mikko

Re: H ⟨Ĥ⟩ ⟨Ĥ⟩ is correct when reports on the actual behavior that it sees

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by: Mikko - Wed, 13 Mar 2024 16:54 UTC

On 2024-03-12 15:39:06 +0000, olcott said:

> On 3/12/2024 5:10 AM, Mikko wrote:
>> On 2024-03-11 15:31:37 +0000, olcott said:
>>
>>> On 3/11/2024 10:06 AM, Mikko wrote:
>>>> On 2024-03-11 14:58:55 +0000, olcott said:
>>>>
>>>>> On 3/11/2024 5:49 AM, Mikko wrote:
>>>>>> On 2024-03-11 05:05:19 +0000, olcott said:
>>>>>>
>>>>>>> Does your input halt on its input?
>>>>>>> is an incorrect question for each Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>
>>>>>> It is incorrect in sthe sense that it is not the question
>>>>>> asked in the halting problem. Otherwise it can be a reasonable
>>>>>> question.
>>>>>>
>>>>>
>>>>> *MIT Professor Michael Sipser agreed this verbatim paragraph is correct*
>>>>> (He has neither reviewed nor agreed to anything else in this paper)
>>>>> (a) If simulating halt decider H correctly simulates its input D until
>>>>> H correctly determines that its simulated D would never stop running
>>>>> unless aborted then
>>>>> (b) H can abort its simulation of D and correctly report that D
>>>>> specifies a non-halting sequence of configurations.
>>>>>
>>>>> When simulating termination analyzer H ⟨Ĥ⟩ ⟨Ĥ⟩ computes
>>>>> the mapping from its input to its own final state on
>>>>> the basis of the behavior that it actually sees then
>>>>> halting is always computable.
>>>>>
>>>>> Expecting it to compute the mapping from its input on
>>>>> the basis of behavior that it does not see is incorrect.
>>>>
>>>> None of that says anything about correctness of questions.
>>>>
>>>
>>> int sum(int x, int y){ return x + y; }
>>> It is the same as requiring sum(3,4) to report on the sum of 5 + 6.
>>
>> Just read the specification of sum carefully and code accordingly.
>> What you think it should specify is irrelevant.
>>
>
> The specification of the halting problem requires H ⟨Ĥ⟩ ⟨Ĥ⟩ to
> report on Ĥ ⟨Ĥ⟩ that (because of pathological self-reference)
> has different behavior than the behavior that H ⟨Ĥ⟩ ⟨Ĥ⟩ actually sees.

Yes, that too. But Linz' Ĥ ⟨Ĥ⟩ rejects if and only if H ⟨Ĥ⟩ ⟨Ĥ⟩ rejects,
which is the only relevant aspect of its behaviour.

--
Mikko

Re: H ⟨Ĥ⟩ ⟨Ĥ⟩ is correct when reports on the actual behavior that it sees

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by: olcott - Wed, 13 Mar 2024 17:00 UTC

On 3/13/2024 11:54 AM, Mikko wrote:
> On 2024-03-12 15:39:06 +0000, olcott said:
>
>> On 3/12/2024 5:10 AM, Mikko wrote:
>>> On 2024-03-11 15:31:37 +0000, olcott said:
>>>
>>>> On 3/11/2024 10:06 AM, Mikko wrote:
>>>>> On 2024-03-11 14:58:55 +0000, olcott said:
>>>>>
>>>>>> On 3/11/2024 5:49 AM, Mikko wrote:
>>>>>>> On 2024-03-11 05:05:19 +0000, olcott said:
>>>>>>>
>>>>>>>> Does your input halt on its input?
>>>>>>>> is an incorrect question for each Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>
>>>>>>> It is incorrect in sthe sense that it is not the question
>>>>>>> asked in the halting problem. Otherwise it can be a reasonable
>>>>>>> question.
>>>>>>>
>>>>>>
>>>>>> *MIT Professor Michael Sipser agreed this verbatim paragraph is
>>>>>> correct*
>>>>>> (He has neither reviewed nor agreed to anything else in this paper)
>>>>>> (a) If simulating halt decider H correctly simulates its input D
>>>>>> until H correctly determines that its simulated D would never stop
>>>>>> running unless aborted then
>>>>>> (b) H can abort its simulation of D and correctly report that D
>>>>>> specifies a non-halting sequence of configurations.
>>>>>>
>>>>>> When simulating termination analyzer H ⟨Ĥ⟩ ⟨Ĥ⟩ computes
>>>>>> the mapping from its input to its own final state on
>>>>>> the basis of the behavior that it actually sees then
>>>>>> halting is always computable.
>>>>>>
>>>>>> Expecting it to compute the mapping from its input on
>>>>>> the basis of behavior that it does not see is incorrect.
>>>>>
>>>>> None of that says anything about correctness of questions.
>>>>>
>>>>
>>>> int sum(int x, int y){ return x + y; }
>>>> It is the same as requiring sum(3,4) to report on the sum of 5 + 6.
>>>
>>> Just read the specification of sum carefully and code accordingly.
>>> What you think it should specify is irrelevant.
>>>
>>
>> The specification of the halting problem requires H ⟨Ĥ⟩ ⟨Ĥ⟩ to
>> report on Ĥ ⟨Ĥ⟩ that (because of pathological self-reference)
>> has different behavior than the behavior that H ⟨Ĥ⟩ ⟨Ĥ⟩ actually sees.
>
> Yes, that too. But Linz' Ĥ ⟨Ĥ⟩ rejects if and only if H ⟨Ĥ⟩ ⟨Ĥ⟩ rejects,
> which is the only relevant aspect of its behaviour.
>

Date 10/13/2022 11:29:23 AM
*MIT Professor Michael Sipser agreed this verbatim paragraph is correct*
(He has neither reviewed nor agreed to anything else in this paper)
(a) If simulating halt decider H correctly simulates its input D until H
correctly determines that its simulated D would never stop running
unless aborted then
(b) H can abort its simulation of D and correctly report that D
specifies a non-halting sequence of configurations.

*When we apply this criteria* (elaborated above)
Will you halt if you never abort your simulation?
*Then the halting problem is conquered*

*Yet they both get the correct answer to the above criteria*

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

Re: ZFC solution to incorrect questions: reject them

<ussm6q$11via$1@dont-email.me>

copy mid

https://www.novabbs.com/devel/article-flat.php?id=55007&group=comp.theory#55007

copy link Newsgroups: comp.theory

by: Mikko - Wed, 13 Mar 2024 17:02 UTC

On 2024-03-12 15:52:10 +0000, olcott said:

> On 3/12/2024 5:20 AM, Mikko wrote:
>> On 2024-03-11 16:02:28 +0000, olcott said:
>>
>>> On 3/11/2024 10:12 AM, Mikko wrote:
>>>> On 2024-03-11 14:54:34 +0000, olcott said:
>>>>
>>>>> On 3/11/2024 5:45 AM, Mikko wrote:
>>>>>> On 2024-03-11 04:38:40 +0000, olcott said:
>>>>>>
>>>>>>> On 3/10/2024 11:10 PM, Richard Damon wrote:
>>>>>>>> On 3/10/24 8:33 PM, olcott wrote:
>>>>>>>>> On 3/10/2024 9:13 PM, Richard Damon wrote:
>>>>>>>>>> On 3/10/24 7:05 PM, olcott wrote:
>>>>>>>>>>> On 3/10/2024 8:52 PM, Richard Damon wrote:
>>>>>>>>>>>> On 3/10/24 6:00 PM, olcott wrote:
>>>>>>>>>>>>> On 3/10/2024 2:23 PM, Richard Damon wrote:
>>>>>>>>>>>>>> On 3/10/24 11:23 AM, olcott wrote:
>>>>>>>>>>>>>>> On 3/10/2024 12:55 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>> On 3/10/24 10:17 AM, olcott wrote:
>>>>>>>>>>>>>>>>> On 3/10/2024 12:08 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>> On 3/10/24 9:52 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>> On 3/10/2024 10:50 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>> On 3/10/24 7:28 AM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>> On 3/10/2024 12:16 AM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>> On 3/9/24 9:49 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>> On 3/9/2024 11:36 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>> On 3/9/24 9:14 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>> On 3/9/2024 10:55 PM, Richard Damon wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/9/24 8:30 PM, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/9/2024 7:40 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 10/03/24 02:37, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/9/2024 7:32 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 10/03/24 02:29, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/9/2024 7:24 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 10/03/24 01:30, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/9/2024 6:24 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 10/03/24 01:22, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/9/2024 5:57 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 10/03/24 00:26, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/9/2024 5:10 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 9/03/24 23:22, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 3/9/2024 3:50 PM, immibis wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> On 9/03/24 22:34, olcott wrote:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> What criteria would you use so that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ knows what
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> wrong answer to provide?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ is stipulated to use the exact same objective criteria that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H ⟨Ĥ⟩ uses.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Simulating halt deciders must make sure that they themselves
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> do not get stuck in infinite execution. This means that they
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> must abort every simulation that cannot possibly otherwise halt.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> This requires Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ to abort its simulation and does not
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> require H ⟨Ĥ⟩ ⟨Ĥ⟩ to abort its simulation when Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ aborts
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> its simulation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ does simulate itself in recursive simulation H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> does not simulate itself in recursive simulation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ is stipulated to use the exact same objective criteria that
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H ⟨Ĥ⟩ uses.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> *Only because Ĥ.H is embedded within Ĥ and H is not*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ can possibly get stuck in recursive simulation and
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> H ⟨Ĥ⟩ ⟨Ĥ⟩ cannot possibly get stuck in recursive simulation.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> You dishonestly ignored that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ is stipulated to use the exact
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> same OBJECTIVE criteria that H ⟨Ĥ⟩ uses.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> The above is true no matter what criteria that is used
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> as long as H is a simulating halt decider.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Objective criteria cannot vary based on who the subject is. They are
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> objective. The answer to different people is the same answer if the
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> criteria are objective.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is objectively true that Ĥ.H can get stuck in recursive
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> simulation because Ĥ copies its input thus never runs
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> out of params.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> It is objectively true that Ĥ cannot possibly get stuck
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> in recursive because H does not copy its input thus runs
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> out of params.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Wrong. Dead wrong. Stupidly wrong. So wrong that a dead monkey could do
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> better. Write the Olcott machine (not x86utm) code for Ĥ and I would
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> show you.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> *In other words you are denying these verified facts*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> *In other words you are denying these verified facts*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> *In other words you are denying these verified facts*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn   // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> That's not a verified fact, that's just something you want to be true.
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> ∞ means infinite loop. Infinite loop doesn't halt. You see how stupid
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> it is, to say that an infinite loop halts?
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Execution trace of Ĥ applied to ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (a) Ĥ.q0 The input ⟨Ĥ⟩ is copied then transitions to Ĥ.H
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (b) Ĥ.H applied ⟨Ĥ⟩ ⟨Ĥ⟩ (input and copy) simulates ⟨Ĥ⟩ applied to ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> (c) which begins at its own simulated ⟨Ĥ.q0⟩ to repeat the process
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> Execution trace of H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ BECAUSE IT IS PRECISELY
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> IDENTICAL TO STEPS B AND C:
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> > (b) Ĥ.H applied ⟨Ĥ⟩ ⟨Ĥ⟩ (input and copy) simulates ⟨Ĥ⟩ applied to ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>> > (c) which begins at Ĥ's own simulated ⟨Ĥ.q0⟩ to repeat the process
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> *Yes and the key step of copying its input is left out so*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>> *H ⟨Ĥ⟩ ⟨Ĥ⟩ runs out of params and Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ never runs out of params*
>>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>>> that isn't how any of this works. Do you even know what words mean?
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> (b) and (c) are not the same as (1) and (2)
>>>>>>>>>>>>>>>>>>>>>>>>>>> Execution trace of H applied to ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>> (1) H applied ⟨Ĥ⟩ ⟨Ĥ⟩ simulates ⟨Ĥ⟩ applied to ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>> (2) which begins at simulated ⟨Ĥ.q0⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>> (a) Ĥ.q0 The input ⟨Ĥ⟩ is copied then transitions to Ĥ.H
>>>>>>>>>>>>>>>>>>>>>>>>>>> (b) Ĥ.H applied ⟨Ĥ⟩ ⟨Ĥ⟩ (input and copy) simulates ⟨Ĥ⟩ applied to ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>>>>>>>>>> (c) which begins at its own simulated ⟨Ĥ.q0⟩ to repeat the process
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>> This means that Turing machine H ⟨Ĥ⟩ ⟨Ĥ⟩ can see one more execution
>>>>>>>>>>>>>>>>>>>>>>>>>>> trace of Ĥ ⟨Ĥ⟩ than its simulated Turing machine Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ can see.
>>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> Nope, your just being stuupid, perhaps intentionally.
>>>>>>>>>>>>>>>>>>>>>>>>>> (c) just moves around to its simulation of a
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> (a) H^.q0 (H^)
>>>>>>>>>>>>>>>>>>>>>>>>>> H^ then makes a copy of its inp
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> (b) H^.H (H^) (H^) == (1) H (H^) (H^)
>>>>>>>>>>>>>>>>>>>>>>>>>> The algorithm of H begins a simulation of its input, watching the
>>>>>>>>>>>>>>>>>>>>>>>>>> behaior of H^ (H^)
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> (c) = (2)
>>>>>>>>>>>>>>>>>>>>>>>>>> Which begins at the simulation of H^.q0 (H^)
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> (d = sim a) = (sim a)
>>>>>>>>>>>>>>>>>>>>>>>>>> Ths Simulated H^.q0 (H^) makes a copy of its input
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> (e = sim b) = (sim b)
>>>>>>>>>>>>>>>>>>>>>>>>>> The Simulated H^.H (H^) (H^) has is H begin the simulation of its input ...
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> and so on.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> Both machine see EXACTLY the same level of details.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> Yes, the top level H is farther along at any given time then its
>>>>>>>>>>>>>>>>>>>>>>>>>> simulated machine, and that is H's problem, it has to act before it
>>>>>>>>>>>>>>>>>>>>>>>>>> sees how its simulation will respond to its copy of its actions.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> Thus, if it stops, it needs to make its decision "blind" and not with
>>>>>>>>>>>>>>>>>>>>>>>>>> an idea of how the machine it is simulating will perform.
>>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>>> If it doesn't stop, the level of recursion just keeps growing and no
>>>>>>>>>>>>>>>>>>>>>>>>>> answer ever comes out.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>> The earliest point that H ⟨Ĥ⟩ ⟨Ĥ⟩ can possibly see to abort
>>>>>>>>>>>>>>>>>>>>>>>>> its simulation is immediately before Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ would begin
>>>>>>>>>>>>>>>>>>>>>>>>> its simulation. Right before its cycle repeats the first time.
>>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> So?
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> If it DOES abort there, then so will H^.H when it gets to that point in
>>>>>>>>>>>>>>>>>>>>>>>> its simulation, which will be AFTER The point that H has stopped
>>>>>>>>>>>>>>>>>>>>>>>> simulating it, so H doesn't know what H^ will do.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>>> Thus, if H DOES abort there, we presume from your previous answer it
>>>>>>>>>>>>>>>>>>>>>>>> will think the input will not halt and answer qn.
>>>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
>>>>>>>>>>>>>>>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn   // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>>>>>>>>>>>>>>>>>>>>> H ⟨Ĥ⟩ ⟨Ĥ⟩ aborts right after Ĥ.Hq0 before it simulates ⟨Ĥ⟩ ⟨Ĥ⟩.
>>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>> And if it does, as I said below, so will H^.H when it is run.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Yes.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> And thus, H^.H will give the same answer as H,
>>>>>>>>>>>>>>>>>>>> so H^ will act contrary to what H says,
>>>>>>>>>>>>>>>>>>>> so H will give the wrong answer.
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Unlike anything else that anyone else has ever done both H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>>>>>>>>> and Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ correctly determine that they must abort their own
>>>>>>>>>>>>>>>>>>> simulation to prevent their own infinite execution.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> NOPE.
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> If no source can be cited then the Olcott thesis
>>>>>>>>>>>>>>>>> "that no one did this before" remains unrefuted.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Since, BY THE DEFINITIONS of what H MUST do to be correct, and what H^
>>>>>>>>>>>>>>>> WILL do by its design, as shown in the Linz Proof.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> If no source can be cited that shows a simulating halt decider can
>>>>>>>>>>>>>>> correctly determine that it must abort its simulation of the Halting
>>>>>>>>>>>>>>> Problem's pathological input to prevent its own non-termination, then
>>>>>>>>>>>>>>> innovation remains attributable to me.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> <snip>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Of course it can abort its simulation.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> It just needs some way to get the right answer.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> *I have always been using this long before I read about it*
>>>>>>>>>>>>> blind variation and selective retention (BVSR)...
>>>>>>>>>>>>> Two common phenomena characterize BVSR thinking: superfluity and
>>>>>>>>>>>>> backtracking. Superfluity means that the creator generates a variety of
>>>>>>>>>>>>> ideas, one or more of which turn out to be useless.
>>>>>>>>>>>>
>>>>>>>>>>>> But if you have mo idea how things actually works, this seems to just
>>>>>>>>>>>> generate random noise.
>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> Backtracking signifies that the creator must often return to an earlier
>>>>>>>>>>>>> approach after blindly going off in the wrong direction.
>>>>>>>>>>>>> https://www.scientificamerican.com/article/the-science-of-genius/
>>>>>>>>>>>>>
>>>>>>>>>>>>> *I am aware of no one else that had the idea to apply a simulating*
>>>>>>>>>>>>> *termination analyzer to the halting problem counter-example input*
>>>>>>>>>>>>> Professor Hehner had a seed of this idea before I did.
>>>>>>>>>>>>
>>>>>>>>>>>> Nope, I remember talk of that when I was in college, and they showed
>>>>>>>>>>>> why it can't work.
>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> From a programmer's point of view, if we apply an interpreter to a
>>>>>>>>>>>>> program text that includes a call to that same interpreter with that
>>>>>>>>>>>>> same text as argument, then we have an infinite loop. A halting program
>>>>>>>>>>>>> has some of the same character as an interpreter: it applies to texts
>>>>>>>>>>>>> through abstract interpretation. Unsurprisingly, if we apply a halting
>>>>>>>>>>>>> program to a program text that includes a call to that same halting
>>>>>>>>>>>>> program with that same text as argument, then we have an infinite loop.
>>>>>>>>>>>>> https://www.cs.toronto.edu/~hehner/PHP.pdf
>>>>>>>>>>>>
>>>>>>>>>>>> You THINK so, but if the interpreter is a CONDITIONAL interpreter, that
>>>>>>>>>>>> doesn't hold.
>>>>>>>>>>>>
>>>>>>>>>>>> You seem to miss that fact.
>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> *Turing Machine and Olcott machine implementations seem to be dead*
>>>>>>>>>>>>> *This the (possibly augmented) RASP machine equivalent of x86*
>>>>>>>>>>>>> Every machine must be able to get its own machine address.
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> And the reason it is a dead end is they make it too hard for you to cheat.
>>>>>>>>>>>>
>>>>>>>>>>>> You need to hide that your H is trying to get in some extra information
>>>>>>>>>>>> to hide that the embedded version of H doesn't give the same answer,
>>>>>>>>>>>> which just shows that your H^ is built wrong.
>>>>>>>>>>>
>>>>>>>>>>> My C code proves these two have different behavior:
>>>>>>>>>>> (a) H1(D,D) + H1_machine_address
>>>>>>>>>>> (b) H(D,D) + H_machine_address
>>>>>>>>>>> H1(D,D) does correctly determine the halt status of D(D) because
>>>>>>>>>>> H(D,D) does NOT correctly determine the halt status of D(D).
>>>>>>>>>>>
>>>>>>>>>>> I say:
>>>>>>>>>>> H1(D,D) is isomorphic to H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>> H(D,D) is isomorphic to Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>>>>>>>
>>>>>>>>>>> immibis disagrees.
>>>>>>>>>>> Correct reasoning will show who is correct.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> Yes, and since H1 is a different computation than H, it getting the
>>>>>>>>>> right answer doesn't keep H from being broken.
>>>>>>>>>>
>>>>>>>>>> We can then make a D1 to break H1.
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> I think that immibis already said that and I did not notice
>>>>>>>>> the significance of it at the time.
>>>>>>>>>
>>>>>>>>
>>>>>>>> Of course.
>>>>>>>>
>>>>>>>>> Then we are back to undecidability being incorrectly construed
>>>>>>>>> as an actual limit to computation.
>>>>>>>>
>>>>>>>> Strange definition of not an actual limit if not being able to do
>>>>>>>> something isn't a limit.
>>>>>>>>
>>>>>>>>>
>>>>>>>>> Professor's Hehner and Stoddart have only construed this as
>>>>>>>>> applying to the Halting Problem's pathological input.
>>>>>>>>>
>>>>>>>>> We three perfectly agree on this as it pertains to the
>>>>>>>>> Halting Problem.
>>>>>>>>>
>>>>>>>>> That two full PhD professors of computer science and I all
>>>>>>>>> agree on this shows that I am not a crackpot/crank on this.
>>>>>>>>> I think that all of the other options may now be exhausted.
>>>>>>>>>
>>>>>>>>> I am very happy that I quit tolerating the [change the subject]
>>>>>>>>> form of rebuttal that wasted 15 years with Ben Bacarisse.
>>>>>>>>>
>>>>>>>>> *The focus now must be on finding the best words that prove*
>>>>>>>>> *this original position of mine (thus the concurring positions*
>>>>>>>>> *of professors Hehner and Stoddart) is correct*
>>>>>>>>
>>>>>>>> Go knock yourself out on that.
>>>>>>>>
>>>>>>>>>
>>>>>>>>> Alan Turing's Halting Problem is incorrectly formed (PART-TWO) sci.logic
>>>>>>>>> On 6/20/2004 11:31 AM, Peter Olcott wrote:
>>>>>>>>> > PREMISES:
>>>>>>>>> > (1) The Halting Problem was specified in such a way that a solution
>>>>>>>>> > was defined to be impossible.
>>>>>>>>
>>>>>>>> Nope.
>>>>>>>>
>>>>>>>> The PROBLEM is the question if a machine can compute the Halting Function.
>>>>>>>>
>>>>>>>> The answer to that, has turned out to be NO.
>>>>>>>>
>>>>>>>> When the problem was first being posed, it was hoped the answer woudl
>>>>>>>> be yes, so it couldn't have bee made specifically to make it impossible.
>>>>>>>>
>>>>>>>>
>>>>>>>> The Halting QUESTION, has an answer for every input that it the
>>>>>>>> description of an actual algorithm applied to an actual data input.
>>>>>>>>
>>>>>>>> Note, Not a "Template" that gets appled to the decider, that IS an
>>>>>>>> invalid question, and impossible to build a description of a Turing
>>>>>>>> Machine to ask that.
>>>>>>>>
>>>>>>>> Thus, when you admitted that your input wasn't actually a description
>>>>>>>> of a program, but just a template, you were admitting that you were
>>>>>>>> lying about working on the Halting Problem, as your input isn't of the
>>>>>>>> right type.
>>>>>>>>
>>>>>>>> Yes, asking about a template IS an invalid question.
>>>>>>>>
>>>>>>>>> >
>>>>>>>>> > (2) The set of questions that are defined to not have any possible
>>>>>>>>> > correct answer(s) forms a proper subset of all possible questions.
>>>>>>>>> > …
>>>>>>>>
>>>>>>>> And, when you are asking the actual Halting Question, about a specific
>>>>>>>> machine and input, like a SPECIFIC H^, built to foil a SPECIIFIC H,
>>>>>>>> then that input has a specific and definate behavior and there is a
>>>>>>>> specific and definate answer (That depends on the H that you chose to
>>>>>>>> build it on, but not the decider you are asking the question to).
>>>>>>>>
>>>>>>>>> > CONCLUSION:
>>>>>>>>> > Therefore the Halting Problem is an ill-formed question.
>>>>>>>>> >
>>>>>>>>
>>>>>>>> Nope, as explained above. You are just showing that you never
>>>>>>>> understood the actual question or what any of the theory actually
>>>>>>>> means, and have just wasted the last decades of your life on a stupid
>>>>>>>> misconception of your own.
>>>>>>>>
>>>>>>>>> USENET Message-ID:
>>>>>>>>> <kZiBc.103407$Gx4.18142@bgtnsc04-news.ops.worldnet.att.net>
>>>>>>>>>
>>>>>>>>> *Direct Link to original message*
>>>>>>>>> http://al.howardknight.net/?STYPE=msgid&MSGI=%3CkZiBc.103407%24Gx4.18142%40bgtnsc04-news.ops.worldnet.att.net%3E+
>>>>>>>>>
>>>>>>>
>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn   // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>>>>>
>>>>>>> That YES and NO are the wrong answer for each implementation of
>>>>>>> Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ specified by the second ⊢* state transition proves that the
>>>>>>> questions asked of these machine/inputs pairs are incorrect questions.
>>>>>>
>>>>>> An incorrect answer does not mean that the question is incorrect.
>>>>>>
>>>>>
>>>>> When every element of the infinite set of every possible
>>>>> implementation of Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ gets the wrong answer then
>>>>> there is something wrong with the question.
>>>>
>>>> According to the definition by Linz there is only one Ĥ for each H.
>>>> Anyway, a wrong answer, even if given in large quentities, does
>>>> not make the question worng.
>>>
>>> None-the-less the infinite set of every implementation of
>>> H/Ĥ.H cannot possibly get an answer that is consistent with
>>> the behavior of of Ĥ ⟨Ĥ⟩.
>>
>> The infinite set is not expected to answer. And the set is
>> infinite only if you include defective imiplementations.
>>
>> Anyway, no memeber of the set of implementations can get
>> an answer that is consistent with the corresponding counter
>> example.
>>
>
> ∀ H ∈ Turing_Machine_Deciders
> ∃ TMD ∈ Turing_Machine_Descriptions |
> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>
> There is some input TMD to every H such that
> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>
> When we disallow decider/input pairs that are incorrect
> questions where both YES and NO are the wrong answer
> (the same way the ZFC disallowed self-referential sets) then
> pathological inputs are not allowed to come into existence.

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Re: ZFC solution to incorrect questions: reject them

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by: Mikko - Wed, 13 Mar 2024 17:04 UTC

On 2024-03-12 18:00:11 +0000, Richard Damon said:

> There is no problem with making a H^ from an H, it is built from
> totally legal steps.

Another way to say the same is that if H^ cannot be built
the H does not exist.

--
Mikko

Re: H ⟨Ĥ⟩ ⟨Ĥ⟩ is correct when reports on the actual behavior that it sees

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by: Mikko - Wed, 13 Mar 2024 17:07 UTC

On 2024-03-12 15:03:05 +0000, olcott said:

> On 3/12/2024 4:27 AM, Mikko wrote:
>> On 2024-03-11 15:17:42 +0000, olcott said:
>>
>>> On 3/11/2024 6:05 AM, Mikko wrote:
>>>> On 2024-03-11 02:38:30 +0000, olcott said:
>>>>
>>>>> On 3/10/2024 9:04 PM, Richard Damon wrote:
>>>>>> On 3/10/24 6:24 PM, olcott wrote:
>>>>>>> On 3/10/2024 7:40 PM, immibis wrote:
>>>>>>>> On 10/03/24 20:16, olcott wrote:
>>>>>>>>> On 3/10/2024 2:09 PM, immibis wrote:
>>>>>>>>>> On 10/03/24 19:32, olcott wrote:
>>>>>>>>>>> On 3/10/2024 1:08 PM, immibis wrote:
>>>>>>>>>>>> On 10/03/24 18:17, olcott wrote:
>>>>>>>>>>>>> ZFC simply tossed out the Russell's Paradox question as unsound.
>>>>>>>>>>>>
>>>>>>>>>>>> So you are saying that some Turing machines are not sound?
>>>>>>>>>>>>
>>>>>>>>>>>>>>> Both H ⟨Ĥ⟩ ⟨Ĥ⟩ and Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ correctly decide that:
>>>>>>>>>>>>>>> (a) Their input halts H.qy
>>>>>>>>>>>>>>> (b) Their input fails to halt or has a pathological
>>>>>>>>>>>>>>> relationship to itself H.qn.
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> But the "Pathological Relationship" is ALLOWED.
>>>>>>>>>>>>>>
>>>>>>>>>>>>> ZFC simply tossed out the Russell's Paradox question as unsound
>>>>>>>>>>>>> expressly disallowing the "Pathological Relationship".
>>>>>>>>>>>>
>>>>>>>>>>>> So you are saying that some Turing machines are not real Turing machines?
>>>>>>>>>>>>
>>>>>>>>>>>>> I am only claiming that both H and Ĥ.H correctly say YES
>>>>>>>>>>>>> when their input halts and correctly say NOT YES otherwise.
>>>>>>>>>>>>
>>>>>>>>>>>> well the halting problem requires them to correctly say NO, so you
>>>>>>>>>>>> haven't solved it
>>>>>>>>>>>
>>>>>>>>>>> All decision problem instances of program/input such that both
>>>>>>>>>>> yes and no are the wrong answer toss out the input as invalid.
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>> all decision problems are defined so that all instances are valid or
>>>>>>>>>> else they are not defined properly
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Not in the case of Russell's Paradox.
>>>>>>>>
>>>>>>>> And now we are back to: Every Turing machine and input pair defines an
>>>>>>>> execution sequence. Every sequence is either finite or infinite.
>>>>>>>> Therefore it is well-defined and there is no paradox.
>>>>>>>>
>>>>>>>> Can you show me a Turing machine that specifies a sequence of
>>>>>>>> configurations that is not finite or infinite?
>>>>>>>
>>>>>>> When we construe every yes/no question that cannot possibly
>>>>>>> have a correct yes/no answer as an incorrect question
>>>>>>>
>>>>>>> then we must correspondingly construe every decider/input
>>>>>>> pair that has no correct yes/no answer as invalid input.
>>>>>>>
>>>>>>
>>>>>> And when you remember that when we posse that ACTUAL question, the
>>>>>> input is a FIXED machine, (not a template that changes by the decide
>>>>>> that it trying to decide it) then there are a LOT of machines that get
>>>>>> the right answer. The key is we know that there is ONE that doesn't,
>>>>>> the one that particular decider was built to foil. Thus, the problem
>>>>>> isn't an invalid question.
>>>>>
>>>>>
>>>>> In computability theory and computational complexity theory,
>>>>> an undecidable problem is a decision problem for which it is
>>>>> proved to be impossible to construct an algorithm that always
>>>>> leads to a correct yes-or-no answer.
>>>>> https://en.wikipedia.org/wiki/Undecidable_problem
>>>>>
>>>>> If the only reason that a machine does not get a correct yes/no answer
>>>>> for this machine/input pair is that both yes and no are the wrong answer
>>>>> for this machine/input pair then this machine/input pair is a yes/no
>>>>> question that has no correct yes/no answer for this machine/input pair.
>>>>>
>>>>> The exact same word-for-word question:
>>>>> Are you a little girl?
>>>>> Has a different meaning depending on who is asked.
>>>>
>>>> It is semantically different question as the meaning of "you" varies.
>>> Exactly my point.
>>>
>>>> Teh interpretations of "little" and "girl" may vary, too.
>>>>
>>>>> The exact same word-for-word question:
>>>>> Does your input halt on its input?
>>>>> Has a different meaning depending on who is asked.
>>>>
>>>> Likewise, because of "you".
>>> Exactly my point.
>>>
>>>> Also depens on when it is asked
>>>> if the input is replaced. And can be an incorrect question
>>>> if the input or the input of the input does not exist or
>>>> the input is something that cannot be said to "halt" (e.g.,
>>>> a number).
>>>>
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqy ∞ // Ĥ applied to ⟨Ĥ⟩ halts
>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.Hq0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.Hqn // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>>>
>>>>> When every Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ is asked this question:
>>>>> Does your input halt on its input?
>>>>> It is an incorrect question.
>>>>
>>>> Yes, so no need say anything about it. A correct question
>>>> is "Does Ĥ ⟨Ĥ⟩ halt?".
>>>>
>>>
>>> Is a subjective specification because the behavior depends on
>>> the agent that performs it.
>>
>> The specified behaviour of halting decider does not.
>>
>
> Because the specification of a the halting problem allows pathological
> inputs this proves that this specification is subjective[Hehner].

Perhaps according to Hehner's definition of "subjective" but
not acccording to your definition.

--
Mikko

Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --new focus--

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by: olcott - Wed, 13 Mar 2024 17:07 UTC

On 3/13/2024 11:45 AM, Mikko wrote:
> On 2024-03-12 15:31:58 +0000, olcott said:
>
>> On 3/12/2024 5:06 AM, Mikko wrote:
>>> On 2024-03-12 03:37:53 +0000, olcott said:
>>>
>>>> On 3/11/2024 10:31 PM, Richard Damon wrote:
>>>>> On 3/11/24 7:52 PM, olcott wrote:
>>>>>> On 3/11/2024 9:32 PM, immibis wrote:
>>>>>>> On 12/03/24 03:24, olcott wrote:
>>>>> \
>>>>>>>> Troll detected.
>>>>>>>>
>>>>>>>
>>>>>>> Once we understand that either YES or NO is the right answer
>>>>>>
>>>>>> Not for this decider/input question: Ĥ.H / ⟨Ĥ⟩ ⟨Ĥ⟩
>>>>>> For that decider/input question both YES and NO are the wrong answer.
>>>>>
>>>>> The problem that you keeep on missing is that by the point we can
>>>>> ask this question, H and H^ are FULLY CODED, and thus we know their
>>>>> behavirs.
>>>>
>>>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy // Ĥ applied to ⟨Ĥ⟩ halts
>>>> H.q0 ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qn // Ĥ applied to ⟨Ĥ⟩ does not halt
>>>>
>>>> Since you know that is false why lie?
>>>> ⊢* specifies an infinite set of encodings.
>>>
>>> No, it does not. The notation is defined by Linz to denote
>>> a finite sequence of configurations.
>>>
>>
>> If it is required to report on a single finite sequence of
>> configurations then that only proves that there exists some
>> halt decider that decides some input incorrectly.
>>
>> If it is reporting on every finite sequence of configurations
>> then that proves that there does not exist a halt decider that
>> decides every input correctly.
>>
>> *Formalized*
>> ∀ H ∈ Turing_Machine_Deciders
>> ∃ TMD ∈ Turing_Machine_Descriptions |
>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>
> Yes, this is one way to state Linz' conclusion.
>
>> There is some input TMD to every H such that
>> Predicted_Behavior(H, TMD) != Actual_Behavior(TMD)
>
> Yes, this is another way to state Linz' conclusion.
>

Since it is a logical impossibility to determine the truth
value of a self-contradictory expression the requirement
for H to do this is bogus.

--
Copyright 2024 Olcott "Talent hits a target no one else can hit; Genius
hits a target no one else can see." Arthur Schopenhauer

devel / comp.theory / Re: Verified fact that Ĥ.H ⟨Ĥ⟩ ⟨Ĥ⟩ and H ⟨Ĥ⟩ ⟨Ĥ⟩ have different behavior ZFC --logically impossible--

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