XPost: comp.theory, sci.logic   
   From: polcott333@gmail.com   
      
   On 8/4/2025 6:54 PM, Mr Flibble wrote:   
   > On Mon, 04 Aug 2025 18:41:40 -0500, olcott wrote:   
   >   
   >> On 8/4/2025 6:29 PM, Mr Flibble wrote:   
   >>> On Mon, 04 Aug 2025 18:21:13 -0500, olcott wrote:   
   >>>   
   >>>> On 8/4/2025 6:04 PM, Mr Flibble wrote:   
   >>>>> On Mon, 04 Aug 2025 17:57:30 -0500, olcott wrote:   
   >>>>>   
   >>>>>> On 8/4/2025 5:44 PM, Mr Flibble wrote:   
   >>>>>>> On Mon, 04 Aug 2025 17:42:24 -0500, olcott wrote:   
   >>>>>>>   
   >>>>>>>> On 8/4/2025 5:34 PM, Mr Flibble wrote:   
   >>>>>>>>> On Mon, 04 Aug 2025 13:29:04 -0500, olcott wrote:   
   >>>>>>>>>   
   >>>>>>>>>> Diagonalization only arises when one assumes that a Turing   
   >>>>>>>>>> machine decider must report on its own behavior instead of the   
   >>>>>>>>>> behavior specified by its machine description.   
   >>>>>>>>>>   
   >>>>>>>>>> Everyone assumes that these must always be the same.   
   >>>>>>>>>> That assumption is proven to be incorrect.   
   >>>>>>>>>>   
   >>>>>>>>>> When one assumes a halt decider based on a UTM then the   
   >>>>>>>>>> simulated input remains stuck in recursive simulation never   
   >>>>>>>>>> reaching simulated states ⟨Ĥ.∞⟩ or ⟨Ĥ.qn⟩.   
   >>>>>>>>>>   
   >>>>>>>>>> Ĥ.q0 ⟨Ĥ⟩ ⊢* Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩ ⊢* Ĥ.∞   
   Ĥ.q0 ⟨Ĥ⟩ ⊢*   
   >>>>>>>>> Ĥ.embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩   
   >>>>>>>>>> ⊢* Ĥ.qn   
   >>>>>>>>>>   
   >>>>>>>>>> (a) Ĥ copies its input ⟨Ĥ⟩   
   >>>>>>>>>> (b) Ĥ invokes embedded_H ⟨Ĥ⟩ ⟨Ĥ⟩   
   >>>>>>>>>> (c) embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩   
   >>>>>>>>>> (d) simulated ⟨Ĥ⟩ copies its input ⟨Ĥ⟩   
   >>>>>>>>>> (e) simulated ⟨Ĥ⟩ invokes simulated embedded_H ⟨Ĥ⟩   
   ⟨Ĥ⟩   
   >>>>>>>>>> (f) simulated embedded_H simulates ⟨Ĥ⟩ ⟨Ĥ⟩   
   >>>>>>>>>> on and on never reaching any simulated final state of ⟨Ĥ.qn⟩   
   >>>>>>>>>>   
   >>>>>>>>>> When embedded_H aborts its simulation and transitions to Ĥ.qn on   
   >>>>>>>>>> the basis that its simulated input cannot possibly reach its own   
   >>>>>>>>>> simulated final halt state of ⟨Ĥ.qn⟩ embedded_H is correct.   
   >>>>>>>>>>   
   >>>>>>>>>> This causes embedded_H itself to halt, thus contradicting its   
   >>>>>>>>>> result *only if a Turing machine decider can be applied to its   
   >>>>>>>>>> actual self*   
   >>>>>>>>>> and not merely its own machine description.   
   >>>>>>>>>   
   >>>>>>>>> Your Ĥ is not a halt decider as defined by the Halting Problem so   
   >>>>>>>>> has nothing to do with the Halting Problem.   
   >>>>>>>>>   
   >>>>>>>>> /Flibble   
   >>>>>>>>   
   >>>>>>>> You have this part incorrectly. Ask Richard because of what he   
   >>>>>>>> explained to you the other night he may correct you on this.   
   >>>>>>>   
   >>>>>>> No, your halt decider is a partial decider, Halting Problem   
   >>>>>>> deciders are total not partial.   
   >>>>>>>   
   >>>>>>> /Flibble   
   >>>>>>   
   >>>>>> Not exactly. The HP proofs attempt to prove that no total halt   
   >>>>>> decider exists on the basis of one self-referential input cannot be   
   >>>>>> decided by any decider including partial deciders.   
   >>>>>   
   >>>>> Wrong. Partial deciders have nothing to do with the Halting Problem.   
   >>>>>   
   >>>>>   
   >>>>>> The technical term "decider" does not mean its conventional meaning   
   >>>>>> of one who decides. It means an infallible Turing machine that   
   >>>>>> always decides correctly. Since this is too misleading for most   
   >>>>>> people I used "termination analyzer".   
   >>>>>   
   >>>>> Halting deciders and termination analyzers are different things and   
   >>>>> you do not get to redefine terms to suit your bogus argument.   
   >>>>>   
   >>>>> /Flibble   
   >>>>   
   >>>> I am using the term: "termination analyzer" that is not misleading at   
   >>>> all in place of the clumsy and confusing term "partial halt decider".   
   >>>   
   >>> Whilst the two terms are interchangeable it doesn't alter the fact that   
   >>> neither term is related to the Halting Problem which is only concerned   
   >>> with *TOTAL* HALT DECIDERS.   
   >>>   
   >>> /Flibble   
   >>   
   >> You keep missing a subtle nuance.   
   >> The HP presumes that is proves that no total halt decider exists on the   
   >> basis that it believes that it has found an input that no (total or   
   >> partial) decider can possibly analyze correctly. Try asking any of the   
   >> chatbots.   
   >   
   > I am not missing any nuance, you are.   
   >   
   > Even though no total halt decider exists (as proven by the Halting Problem   
   > proofs) it is the case that the Halting Problem is only concerned with   
   > total halt deciders NOT partial halt deciders (aka termination analyzers).   
   >   
   > /Flibble   
      
   I may be incorrect yet I no longer believe   
   that you are sincere about this.   
      
   --   
   Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius   
   hits a target no one else can see." Arthur Schopenhauer   
      
   --- SoupGate-Win32 v1.05   
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