XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 12/31/2025 6:28 AM, Richard Damon wrote:   
   > On 12/30/25 11:21 PM, olcott wrote:   
   >> A Turing-machine decider is a Turing machine D that   
   >> computes a total function D :  Σ∗ → {Accept,Reject},   
   >> where Σ∗ is the set of all finite strings over the   
   >> input alphabet. That is:   
   >>   
   >> 1. Totality: For every finite string input w ∈ Σ∗,   
   >> D halts and outputs either Accept or Reject.   
   >>   
   >> Is simplified to this barest essence across all models of computation   
   >> All deciders essentially: Transform finite string   
   >> inputs by finite string transformation rules into   
   >> {Accept, Reject} values.   
   >>   
   >> Anything that cannot be derived from actual finite string   
   >> inputs is not computable and outside the scope of computation.   
   >>   
   >   
   > But since the Halting status of the machine that finite string IS   
   > deriveed from that machine, by just running that machine, or giving it   
   > to the appropriate UTM, you are just showing that Halting is a valid   
   > question.   
   >   
   > It is also uncomputable, as has been proven.   
   >   
      
   There are no finite string transformations that HHH(DD)   
   can apply to its input that derive the behavior of UTM(DD).   
      
   There are finite string transformations that HHH(DD)   
   can apply to its input that derive the behavior that   
   the input to HHH(DD) specifies.   
      
   No decider is ever accountable to report on any behavior   
   other than the actual behavior that its actual finite   
   string input actually specifies. When the halting problem   
   requires more than that it requires too much.   
      
   > Your problem is you seem to not understand the requirement that a   
   > decider needs to CORRECTLY compute the function it is supposed to be   
   > computing, because you just don't understand the nature of truth, and   
   > think it can be just redefined.   
   >   
   > As a simile, your logic says a persian cat can be entered into the   
   > Westminster Dog show and win best of breed, just by saying it is a dog.   
   >   
      
      
   --   
   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)