XPost: comp.theory, sci.math, comp.theory   
   From: polcott333@gmail.com   
      
   On 12/14/2025 7:56 PM, Richard Damon wrote:   
   > On 12/14/25 8:17 PM, olcott wrote:   
   >> On 12/14/2025 7:00 PM, Richard Damon wrote:   
   >>> On 12/14/25 7:31 PM, olcott wrote:   
   >>>> Whenever any textbook says that a halt decider   
   >>>> must compute halting for machine M on input w   
   >>>> is it wrong. At best it only computes the halting   
   >>>> of M/w through the proxy of finite strings ⟨M⟩/w.   
   >>>   
   >>> Nope, you are just wrong because you are too stupid to understand   
   >>> representations.   
   >>>   
   >>   
   >> You already agreed to this, you didn't bother   
   >> to pay close enough attention to the paraphrase   
   >> of what you already agreed to.   
   >>   
   >> Halt deciders report on the behavior of   
   >> Turing machines only through the proxy   
   >> of finite string machine descriptions.   
   >>   
   >> Whenever textbooks do not say it exactly that   
   >> way they are being less than completely accurate.   
   >   
   > Nope, and thus you show you don't understand how language works.   
   >   
   > The fact that the text you read weren't explicit enough   
      
   Proves that they are not as precise as they could be.   
   That lack of precision leads to universal misconception.   
      
   >  for you just   
   > shows that likely you don't have the needed background for them, and   
   > that fact was presumed already known by the student.   
   >   
   > Just like a calculus book won't explicitly warn you that division by 0   
   > is just undefined, or that multiplication by 1 is a no operation.   
   >   
   >>   
   >>>>   
   >>>> Turing machine deciders compute the mapping from   
   >>>> input finite strings to an accept or reject value   
   >>>> by some criterion measure.   
   >>>   
   >>> Right, and for a Halt Decider, that criteria is the behavior of the   
   >>> machine the input string represents.   
   >>>   
   >>   
   >> There is a key semantic difference between   
   >> finite string x has a syntactic property   
   >> and finite string x specifies a semantic property   
   >   
   > yes, and that is part of the problem. Finite machine deciders can only   
   > compute syntactic operations.   
   >   
      
   Then Rice's theorem is tossed out the window?   
      
   In computability theory, Rice's theorem states   
   that all non-trivial semantic properties of   
   programs are undecidable. A semantic property   
   is one about the program's behavior   
      
   https://en.wikipedia.org/wiki/Rice%27s_theorem   
      
   > Questions can be about semantics.   
   >   
   > To make a decider, you need to find the algorithmic bridge between the   
   > two of them.   
   >   
   > For instance, Proof VERIFICATION, which is a semantic operation, can be   
   > reduced to syntactic steps, and thus we can build a Machine to see if a   
   > given input it a proper proof, and said machine can work for all input   
   > string.   
   >   
      
   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.   
      
   > But, what cant' be done is to write a machine that takes a proposition   
   > and tells you if it is provable, as that can not be converted into a   
   > syntactic operation.   
   >   
   >   
      
      
   --   
   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)