XPost: comp.theory, sci.math, sci.logic   
   From: polcott333@gmail.com   
      
   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.   
      
   > Note "when interpreted as a machine description" is NOT limited to the   
   > decider itself doing the interpretation, but is a general objective   
   > property of the input.   
   >   
   > Your attempt to convert objective criteria into subjective ones is a   
   > fundamental error, showing you don't understand what Truth is.   
      
      
   --   
   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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