XPost: comp.theory, comp.theory   
   From: polcott333@gmail.com   
      
   On 12/15/2025 6:33 AM, Richard Damon wrote:   
   > On 12/14/25 10:34 AM, polcott wrote:   
   >> On 12/14/2025 2:59 AM, joes wrote:   
   >>> Am Sat, 13 Dec 2025 14:19:01 -0600 schrieb olcott:   
   >>>> On 12/13/2025 1:17 PM, Richard Damon wrote:   
   >>>>> On 12/11/25 8:48 PM, olcott wrote:   
   >>>>>   
   >>>>>> Turing machine deciders compute functions from finite strings to   
   >>>>>> {accept, reject}.   
   >>>>>> The halting problem itself requires that deciders compute the   
   >>>>>> behavior   
   >>>>>> of executing machines, thus category error flat out and simple.   
   >>>>>   
   >>>>> Why do you say that?   
   >>>>>   
   >>>> All of the textbooks require halt deciders to report on the behavior of   
   >>>> machine M on input w.   
   >>>> Since no Turing machine ever takes any Machine M as an input this   
   >>>>  a   
   >>>> category error even when this make no difference.   
   >>>> We correct this error by saying that halt deciders must report on the   
   >>>> basis of the behavior specified by their input finite string.   
   >>>   
   >>> TMs don't take numbers as input either but can still do arithmetic.   
   >>>   
   >>   
   >> A syntactic versus semantic property.   
   >>   
   >> When a TM adds two numbers it adds the numbers   
   >> that its finite string inputs specify.   
   >>   
   >> When a halt decider decides halting it does   
   >> it on the basis of the behavior that its   
   >> finite string inputs specify.   
   >   
   > Just like a halt decider needs to de decide on the program that its   
   > input finite string specifies, which just needs to be detailed enough to   
   > fully define that program.   
   >   
      
   It is only the sequences of steps that THE INPUT   
   specifies. DD simulated by HHH specifies that it   
   calls HHH(DD) that must be simulated by HHH again.   
      
   >>   
   >> When the halting problem requires that a halt   
   >> decider report on the behavior of a machine it   
   >> is always wrong. To get closer to correct it   
   >> can ask for the behavior of the machine through   
   >> the proxy of its finite string input.   
   >   
   > But a given program only has one behavior, and thus if you have enough   
   > specificaiton to know the program, you have the details to get the answer.   
   >   
   > Just like your numbers.   
   >   
   >>   
   >> The key thing here is that when the closest proxy   
   >> and the machine disagree the proxy overrules the   
   >> machine.   
   >>   
   >   
   > But the proxy CAN'T disagree with the thing it is supposed to be a proxy   
   > for, or it wasn't the proxy in the first pace.   
   >   
   > All you are doing is arguing that you should be able to lie to you   
   > computer, but you still want it to give the right answer.   
   >   
   >> All Turing machines only compute the mapping   
   >> from input finite strings to some value.   
   >>   
   >   
   > Right, and need to get the right answer   
   >   
   > And you need to ask it the question you want answered, giving a wrong   
   > input is YOUR fault, not the machines.   
      
      
   --   
   Copyright 2025 Olcott

   
      
   My 28 year goal has been to make 
   
   "true on the basis of meaning expressed in language"
   
   reliably computable.

   
      
   This required establishing a new foundation
   
      
   --- SoupGate-Win32 v1.05   
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