XPost: comp.theory, sci.logic   
   From: polcott333@gmail.com   
      
   On 8/4/2025 8:36 PM, Richard Damon wrote:   
   > On 8/4/25 9:25 PM, olcott wrote:   
   >> On 8/4/2025 8:18 PM, Richard Damon wrote:   
   >>> On 8/4/25 6:42 PM, 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.   
   >>>>   
   >>>   
   >>> Ĥ isn't a halt decider, H is.   
   >>   
   >> That is quite a bit less than perfectly   
   >> accurate see if you can do better.   
   >> H is a what?   
   >>   
   >>   
   >   
   > H is supposed to be a Halt Decider.   
   >   
      
   More precisely H is hypothesized to be a halt decider.   
   If H actually was an actual halt decider   
   (as you initially stated) then the Halting Problem   
   proof would be over before it began.   
      
   --   
   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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