XPost: comp.theory, sci.math, comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   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.   
      
   2. Decision basis: Each input string is evaluated   
   according to one of two types of properties:   
      
      (a) Syntactic property: a property of the input   
      string itself, such as containing a particular   
      substring or satisfying a structural pattern.   
      
      (b) Semantic property: a property of the sequence of   
      computational steps explicitly encoded by the input   
      string, i.e., the behavior that the input itself   
      specifies when interpreted as a machine description.   
      
   The decider outputs Accept if the corresponding property   
   holds for the input and Reject otherwise.   
      
   --   
   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)