XPost: comp.theory, sci.math, sci.logic   
   From: polcott333@gmail.com   
      
   On 10/13/2025 12:36 PM, dbush wrote:   
   > On 10/13/2025 1:22 PM, olcott wrote:   
   >> On 10/13/2025 11:43 AM, dbush wrote:   
   >>> On 10/13/2025 12:30 PM, olcott wrote:   
   >>>> On 10/13/2025 11:18 AM, dbush wrote:   
   >>>>> On 10/13/2025 12:14 PM, olcott wrote:   
   >>>>>> On 10/13/2025 9:24 AM, dbush wrote:   
   >>>>>>> On 10/13/2025 10:15 AM, olcott wrote:   
   >>>>>>>> The directly executed DD() is outside of the   
   >>>>>>>> domain of the function computed by HHH(DD)   
   >>>>>>>> because it is not a finite string thus does   
   >>>>>>>> not contradict that HHH(DD) correctly rejects   
   >>>>>>>> its input as non-halting.   
   >>>>>>>>   
   >>>>>>>   
   >>>>>>> Actual numbers are outside the domain of Turing machines because   
   >>>>>>> they are not finite strings, therefore Turning machines cannot do   
   >>>>>>> arithmetic.   
   >>>>>>>   
   >>>>>>> Agreed?   
   >>>>>>   
   >>>>>> Should I start simply ignoring everything that you say again?   
   >>>>>> Prove that you want an honest dialogue or be ignored.   
   >>>>>>   
   >>>>>   
   >>>>> You stated that Turing machines can't operate on directly executed   
   >>>>> Turing machine because they only take finite strings as input and   
   >>>>> not actual Turing machines.   
   >>>>>   
   >>>>   
   >>>> Now ChatGPT also agrees that DD() is outside of the domain   
   >>>> of the function computed by HHH(DD) and HHH(DD) is correct   
   >>>> to reject its input on the basis of the function that it   
   >>>> does compute.   
   >>>>   
   >>>> https://chatgpt.com/share/68ec6e96-7eb8-8011-90c7-86248034d475   
   >>>>   
   >>>>   
   >>>   
   >>>   
   >>> And if you remind it what a finite string description is:   
   >>>   
   >>   
   >> No, no, no, this is where you and the halting problem   
   >> definition screw up. It never was a mere finite string   
   >> machine description.   
   >>   
   >> It was always the behavior that its input finite string   
   >> machine description specifies. This expressly excludes   
   >> the behavior of the directly executed DD() because the   
   >> directly executed DD() is not an input in the domain of HHH.   
   >>   
   >   
   > Nope, see below.   
   >   
   >>> ---   
   >>> But since a Turing machine description encodes all information about   
   >>> a Turing machine, Turing machines are within the domain of other   
   >>> Turing machines via their description. Therefore the definition of a   
   >>> halt decider, a Turing machine that determines whether any arbitrary   
   >>> Turing machine X with input Y will halt when executed directly, is   
   >>> correct and valid.   
   >>> ---   
   >>>   
      
   Why the three levels of quotes instead of   
   just plain text that was cut-and-pasted   
   like this cut-and-pasted quoted text?   
      
      Theorem (Domain Invalidity of the Halting Predicate   
      in Reflective Models): In any computational model   
      where programs can call the universal interpreter,   
      the halting predicate HALT(p) is undefined for some   
      syntactically valid p. Hence, the classical definition   
      of the halting problem as a total decision problem   
      over all program texts is semantically incorrect in   
      that model.   
      
   https://chatgpt.com/share/68ec6e96-7eb8-8011-90c7-86248034d475   
      
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   Copyright 2025 Olcott "Talent hits a target no one else can hit; Genius   
   hits a target no one else can see." Arthur Schopenhauer   
      
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