XPost: comp.theory, sci.logic   
   From: polcott333@gmail.com   
      
   On 8/5/2025 5:57 AM, Richard Damon wrote:   
   > On 8/4/25 10:02 PM, olcott wrote:   
   >> 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"   
   >   
   > Which means, such an H must behave exactly like a Halt Decider for our   
   > hypothesis to be possible.   
   >   
   >>   
   >> It was you that initially said:   
   >> "Ĥ isn't a halt decider, H is."   
   >   
   > And H^ isn't a Halt Decider, PERIOD.   
   >   
   > It never was given the requirements to act like one.   
   >   
   > It has a halt decider inside it, that it used, but that doesn't make it   
   > one itself.   
   >   
   > Unless you consider yourself just a piece of shit, because you have one   
   > inside you.   
      
   I am merely correctly your lack of precision.   
   I have made these same lack of precision mistakes.   
      
   You said that H is a halt decider and this is not   
   precisely correct. H is a hypothetical halt decider   
   that Linz believes he proved does not exist.   
      
   Are we on the same page on this point now?   
      
   --   
   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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