XPost: comp.theory, sci.logic, sci.math
On 9/27/2021 3:52 PM, Ben Bacarisse wrote:
olcott <NoOne@NoWhere.com> writes:
This is the key basis of my refutation of the halting theorem:
The halting theorem counter-examples present infinitely nested
simulation (non-halting) behavior to every simulating halt decider.
Not a refutation of anything.
I presented this to Ben more than four years ago and he successfully
changed the subject with various dishonest dodges so that it could not
be properly evaluated until now.
Liar.
Infinitely Recursive input on HP Proofs
peteolcott Mar 11, 2017, 3:13:03 PM
https://groups.google.com/g/comp.theory/c/NcFS02hKs1U
This was a post about a different topic. You are confused even about
what you were saying back then. I've explained in anther reply. You
are now saying the same thing over and over, so I won't copy my reply
out here.
All of the "rebuttals" to the {key basis of my refutation} have taken
the form of the strawman error, here is the most common
The halting theorem does not specify a simulating halt decider.
The most common one is that false is the wrong answer for a halting computation. That's the error I see most commonly pointed out.
You were clear, even then, that your "solution" or "rebuttal" or
whatever was to redefine halting:
"This definition of halting circumvents the pathological
self-reference error for every simulating halt decider:
An input is decided to be halting only if its simulation never needs
to be stopped by any simulating halt decider anywhere in its entire
invocation chain.
On that basis:
Ĥ(<Ĥ>) ⊢* Ĥ.qn
H(<Ĥ>,<Ĥ>) ⊢* H.qn"
There you are (May 17 2017) clearly stating that you've defined H
rejecting a halting computation to be correct! I must say I'd forgotten
how long you have been flogging this dead horse.
(There is an error of logic where you think that being specific -- some special kind of decider -- gets round a proof that is about all TMs, but
you present that error only every now and then.)
As I carefully think this through again and again I continue to get
deeper insights.
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qy ∞
if the simulated ⟨Ĥ⟩ applied to ⟨Ĥ⟩ halts, and
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
if the simulated ⟨Ĥ⟩ applied to ⟨Ĥ⟩ does not halt
Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
// because the simulation of ⟨Ĥ⟩ applied to ⟨Ĥ⟩ by Ĥ.qx DOES NOT HALT
The computation of Ĥ applied to ⟨Ĥ⟩ is a distinctly different
computation than the computation of the simulation of ⟨Ĥ⟩ applied to ⟨Ĥ⟩
by Ĥ.qx.
If we want to specify a computation that is equivalent to Ĥ applied to ⟨Ĥ⟩ we must specify H applied to ⟨Ĥ⟩ ⟨Ĥ⟩. H applied to ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* H.qy
The difference is that the input to Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ invokes a copy of Ĥ.qx
whereas the input to H does not invoke a copy of H.
The pathological self-reference error that I first discovered in 2004 is
the key to finally resolved these otherwise undecidable decision problem inputs.
comp.theory
Halting Problem Final Conclusion
Peter Olcott Sep 5, 2004,
The Liar Paradox can be shown to be nothing more than
a incorrectly formed statement because of its pathological
self-reference. The Halting Problem can only exist because
of this same sort of pathological self-reference.
https://groups.google.com/g/comp.theory/c/RO9Z9eCabeE/m/Ka8-xS2rdEEJ
--
Copyright 2021 Pete Olcott
"Great spirits have always encountered violent opposition from mediocre
minds." Einstein
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