XPost: comp.theory, comp.theory   
   From: polcott333@gmail.com   
      
   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.   
      
   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.   
      
   The key thing here is that when the closest proxy   
   and the machine disagree the proxy overrules the   
   machine.   
      
   All Turing machines only compute the mapping   
   from input finite strings to some value.   
      
      
   --   
   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   
   for correct reasoning.   
      
   --- SoupGate-Win32 v1.05   
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