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Re: Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn is correct and forms no contradiction. [ Ben accepts one point? ] (typo fixed )

Subject Re: Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn is correct and forms no contradiction. [ Ben accepts one point? ] (typo fixed )
Newsgroups comp.theory, comp.ai.philosophy, comp.software-eng, sci.math.symbolic
References (17 earlier) <87fsvggdxz.fsf@bsb.me.uk> <HISdnXl3NPSvnYn8nZ2dnUU7-eHNnZ2d@giganews.com> <878s17fqji.fsf@bsb.me.uk> <yuGdneaGkeN-84n8nZ2dnUU7-cnNnZ2d@giganews.com> <87bl62cu25.fsf@bsb.me.uk>
From olcott <NoOne@NoWhere.com>
Date 2021-08-12 15:36 -0500
Message-ID <qeedncFT9pmvG4j8nZ2dnUU7-RnNnZ2d@giganews.com> (permalink)

Cross-posted to 4 groups.

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On 8/12/2021 3:00 PM, Ben Bacarisse wrote:
> olcott <NoOne@NoWhere.com> writes:
> 
>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qy ∞
>> if M applied to wM halts, and
>>
>> Ĥ.q0 wM ⊢* Ĥ.qx wM wM ⊢* Ĥ.qn
>> if M applied to wM does not halt
>>
>> // M refers to the TM of the first wM parameter to Ĥ.qx
>>
>> Now that you accept that the above is true...
> 
> I don't.  It's a garbled formula arising from a silly error on your
> part.  I'd like to know where (you think) I said I accept this nonsense
> so I can correct any such impression.
> 
>> ... we can move on to the next point. My proof must proceed exactly
>> one point at a time an cannot possibly move to the next point until
>> the current point is fully accepted.
> 
> It would be simpler if we worked though the reasons you are wrong
> because there are fewer steps.
> 
> You've stated that
> 
>    Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
> 
> and you accept (at least you keep quoting) that Linz requires that this
> should be the case only if Ĥ applied to ⟨Ĥ⟩ does not halt.  QED.
> 
>> That you believe that the fact that Ĥ applied to ⟨Ĥ⟩ transitions to
>> its final state of Ĥ.qn and halts nullifies the fact that Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩
>> does correctly decide that its input never halts is the next point.
> 
> ⟨Ĥ⟩ ⟨Ĥ⟩ is a string that encodes a halting computation as shown a few
> lines above.  That Ĥ applied to ⟨Ĥ⟩ halts does not "nullify" anything,
> it's just wrong as clearly stated by Linz.
> 

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn
⟨Ĥ⟩ ⟨Ĥ⟩ is not a string that encodes a halting computation.

Ĥ is a TM that halts only because
Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ correctly decides that its input never halts.

When you examine this in its x86utm equivalent of H(P,P) there are no 
loopholes that can slip through the cracks because every detail is 
explicitly encoded in the x86 language.

When we examine this as Ĥ applied to ⟨Ĥ⟩ there are millions of pages of 
Turing machine code that cannot be explicitly specified.

None-the-less the key element of all this is the fact that if we assume 
that the simulating halt decider at Ĥ.qx is simply a UTM then it becomes 
quite obvious that we have an infinite cycle from Ĥ.qx to Ĥ.q0.

Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn

If we know that we have an infinite cycle then this knowledge all by 
itself proves that the simulating halt decider at Ĥ.qx must abort the 
simulation of its input which proves that this input never halts.


-- 
Copyright 2021 Pete Olcott

"Great spirits have always encountered violent opposition from mediocre 
minds." Einstein

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Thread

Re: Black box halt decider is NOT a partial decider [ H(P,P)==0 is correct ] olcott <NoOne@NoWhere.com> - 2021-07-26 09:38 -0500
  Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] olcott <NoOne@NoWhere.com> - 2021-07-28 17:08 -0500
    Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you game ? ) olcott <NoOne@NoWhere.com> - 2021-07-29 21:05 -0500
      Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you game ? ) olcott <NoOne@NoWhere.com> - 2021-07-30 09:35 -0500
        Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you game ? ) olcott <NoOne@NoWhere.com> - 2021-08-01 22:17 -0500
          Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you game ? ) olcott <NoOne@NoWhere.com> - 2021-08-02 13:16 -0500
            Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you game ? ) olcott <NoOne@NoWhere.com> - 2021-08-02 13:25 -0500
            Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you game ? ) olcott <NoOne@NoWhere.com> - 2021-08-03 08:00 -0500
              Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you game ? ) olcott <NoOne@NoWhere.com> - 2021-08-03 10:21 -0500
                Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you game ? ) olcott <NoOne@NoWhere.com> - 2021-08-03 14:26 -0500
                Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you game ? ) olcott <NoOne@NoWhere.com> - 2021-08-03 15:47 -0500
                Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you game ? ) olcott <NoOne@NoWhere.com> - 2021-08-03 16:03 -0500
                Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you game ? ) olcott <NoOne@NoWhere.com> - 2021-08-03 16:50 -0500
                Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] ( Are you game ? ) olcott <NoOne@NoWhere.com> - 2021-08-03 19:42 -0500
    Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] olcott <NoOne@NoWhere.com> - 2021-07-29 21:28 -0500
      Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] olcott <NoOne@NoWhere.com> - 2021-07-30 09:54 -0500
        Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ] olcott <NoOne@NoWhere.com> - 2021-07-30 20:16 -0500
          Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ] olcott <NoOne@NoWhere.com> - 2021-07-31 21:20 -0500
            Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ] olcott <NoOne@NoWhere.com> - 2021-08-01 09:45 -0500
            Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ][ GIGO ] olcott <NoOne@NoWhere.com> - 2021-08-01 10:02 -0500
              Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ][ GIGO ] olcott <NoOne@NoWhere.com> - 2021-08-04 10:48 -0500
                Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ][ GIGO ] olcott <NoOne@NoWhere.com> - 2021-08-04 17:31 -0500
            Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn [ succinct ] olcott <NoOne@NoWhere.com> - 2021-08-01 11:02 -0500
            Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ] olcott <NoOne@NoWhere.com> - 2021-08-01 14:45 -0500
            Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ] olcott <NoOne@NoWhere.com> - 2021-08-01 22:45 -0500
              Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ] olcott <NoOne@NoWhere.com> - 2021-08-02 15:53 -0500
                Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ] olcott <NoOne@NoWhere.com> - 2021-08-02 19:55 -0500
                Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ] olcott <NoOne@NoWhere.com> - 2021-08-02 21:11 -0500
                Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ] olcott <NoOne@NoWhere.com> - 2021-08-04 11:15 -0500
                Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ] olcott <NoOne@NoWhere.com> - 2021-08-04 17:38 -0500
                Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ] olcott <NoOne@NoWhere.com> - 2021-08-05 07:07 -0500
                Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ Only Inputs Count ] olcott <NoOne@NoWhere.com> - 2021-08-03 22:23 -0500
                Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ Only Inputs Count ]( Honest Dialogue ) olcott <NoOne@NoWhere.com> - 2021-08-04 10:11 -0500
                Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ Only Inputs Count ] olcott <NoOne@NoWhere.com> - 2021-08-04 10:14 -0500
                Re: Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn is correct and forms no contradiction. [ Is Ben a Liar or simply woefully ignorant? ] olcott <NoOne@NoWhere.com> - 2021-08-11 09:28 -0500
                Re: Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn is correct and forms no contradiction. [ Is Ben a Liar or simply woefully ignorant? ] olcott <NoOne@NoWhere.com> - 2021-08-11 09:58 -0500
                Re: Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn is correct and forms no contradiction. [ Is Ben a Liar or simply woefully ignorant? ] olcott <NoOne@NoWhere.com> - 2021-08-11 14:53 -0500
                Re: Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn is correct and forms no contradiction. [ Is Ben a Liar or simply woefully ignorant? ] olcott <NoOne@NoWhere.com> - 2021-08-11 19:26 -0500
                Re: Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn is correct and forms no contradiction. [ Halting Problem is solved for Ĥ on ⟨Ĥ⟩ ] olcott <NoOne@NoWhere.com> - 2021-08-11 21:14 -0500
                Re: Ĥ.qx ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.qn is correct and forms no contradiction. [ Ben accepts one point? ] (typo fixed ) olcott <NoOne@NoWhere.com> - 2021-08-12 15:36 -0500
            Re: Black box halt decider is NOT a partial decider [ Ĥ.qx(⟨Ĥ⟩,⟨Ĥ⟩) == Ĥ.qn ] [ succinct ] olcott <NoOne@NoWhere.com> - 2021-08-01 22:56 -0500

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