XPost: comp.theory   
   From: polcott333@gmail.com   
      
   On 12/13/2025 11:18 AM, Tristan Wibberley wrote:   
   > On 13/12/2025 14:35, Richard Damon wrote:   
   >> On 12/12/25 11:36 PM, Tristan Wibberley wrote:   
   >>> On 12/12/2025 04:01, olcott wrote:   
   >>>> Principle 1: Turing machine deciders compute functions   
   >>>> from finite strings to {accept, reject} according to   
   >>>                            ^^^^^^^^^^^^^^^^   
   >>> "some binary classification"   
   >>>   
   >>> however, {accept, reject implies a specific human purpose that is not   
   >>> intrinsic to the decider, so I think it's not appropriate for a general   
   >>> statement.   
   >>>   
   >>>   
   >>   
   >> Perhaps you missed that the classic definition of a "Decider" was to   
   >> test if a string fit within a given "grammar"   
   >   
   > Yes, I did.   
   >   
   >   
   >> The decider would "accept" machines that fit, and "reject" things that   
   >> didn't.   
   >>   
   >> THe "grammar" for the halting problem was if the string was a   
   >> description of a Turing Machine/Input that would halt.   
   >   
   > Is that a classic definition of "grammar", too? We're talking about   
   > before Chomsky's hierarchy. If my memory serves, even after that there   
   > isn't a definition of "grammar" that covers halting semantics is there?   
   >   
      
   Here is an insight that LLM Kimi suggested entirely   
   on the basis of the text of my first principles.   
      
   The Universal TM's Illusion: The UTM appears   
   to "simulate another machine," but it's really just   
   interpreting a string as a lookup table for state   
   transitions. The simulation is pure string rewriting.   
      
   >   
   >> Thus, his Principle 1 is a correct statement for THAT definition of   
   >> decider. There are others, going to the point that one definition is   
   >> that it is any machine that will always halt no matter what input you   
   >> give it. That is, it computes a complete function of all possible input   
   >> to some set of output tapes/final states.   
   >   
   > I understood that "to decide" from the time was defined for propositions   
   > whereupon one classifies them true or false and that merely extends to   
   > the proposition that "string X fits grammar Y". Not the other way around.   
   >   
   >   
      
      
   --   
   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)