XPost: comp.theory, comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   On 12/13/2025 3:32 PM, olcott wrote:   
   > All of the textbooks require halt deciders to   
   > report on the behavior of machine M on input w.   
   > This may be easy to understand yet not precisely   
   > accurate.   
   >   
   > Since no Turing machine ever takes any Machine   
   > M as an input this  a category error even   
   > when this makes no functional difference.   
   >   
   > They simply glossed over this key detail because   
   > they thought that it made no difference.   
   >   
   > *Defining a halt decider with perfect accuracy*   
   > Turing machine halt deciders compute the mapping   
   > from input finite strings to an {accept, reject}   
   > value on the basis of the behavior that this   
   > input finite string specifies.   
   >   
      
   By simply adding more detail we can make the   
   original definition more precise:   
      
   A Turing machine based halt decider reports on the   
   behavior of machine M on input w thorough the   
   proxy of the finite string machine description of   
   ⟨M⟩ on input w.   
      
   The above seems to be more precisely accurate   
   than any published proof. It includes a key   
   detail that all of them seem to leave out.   
      
   If you know of any published proof that directly   
   refers to the idea of a proxy, please let me know.   
      
   --   
   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   
    * Origin: you cannot sedate... all the things you hate (1:229/2)