XPost: comp.theory, sci.logic   
   From: polcott333@gmail.com   
      
   On 8/4/2025 8:55 PM, Richard Damon wrote:   
   > On 8/4/25 9:41 PM, olcott wrote:   
   >> 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.   
   >>   
   >   
   > No, H is a hypothetical Halt Decider, or a claimed halt decider,   
   > depending on which method of proof you are using.   
   >   
      
   If you pay close attention you will notice   
   that is what I said in my first line above:   
   "More precisely H is hypothesized to be a halt decider"   
      
   It was you that initially said:   
   "Ĥ isn't a halt decider, H is."   
   --   
   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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