XPost: comp.theory, sci.math, sci.logic   
   From: polcott333@gmail.com   
      
   On 12/23/2025 10:59 AM, Richard Damon wrote:   
   > On 12/23/25 11:32 AM, olcott wrote:   
   >> On 12/23/2025 9:59 AM, Richard Damon wrote:   
   >>> On 12/23/25 10:34 AM, 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.   
   >>>>   
   >>>> 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.   
   >>>>   
   >>>   
   >>> Ok, do you understand what this means?   
   >>>   
   >>> In particular your 2(b) means that whether the MACHINE that the input   
   >>> is an encoding of will halt when run is a valid property.   
   >>>   
   >>   
   >> You seem to have a reading comprehension problem.   
   >   
   > So, what is wrong with my reading of it?   
   >   
      
   You derived an incorrect paraphrase on   
   the basis of ignoring most of the words.   
      
   --   
   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   
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