XPost: comp.theory, sci.math, sci.logic   
   From: polcott333@gmail.com   
      
   On 12/23/2025 11:48 AM, Richard Damon wrote:   
   > On 12/23/25 12:20 PM, olcott wrote:   
   >> 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.   
   >>   
   >   
   > I wasn't "paraphrasing", I was showing a necessary consequence of it.   
   >   
   > I guess you are just too stupid to understand LOGIC.   
   >   
   > If you can't point out how that doesn't follow, You are just admitting   
   > your whole basis is a LIE.   
   >   
   > How can H not be "responsible" of the behavior of the machine the input   
   > encodes, when that is explicitly one of the things it IS responsible for.   
      
      
   (b) Semantic property: This only applies to the   
   subset of finite strings that are valid machine   
   descriptions a property of the sequence of   
   computational steps explicitly encoded by the   
   input string, i.e., the behavior that the input   
   itself specifies.   
      
   If you don't apply your bias of certainty that I   
   am incorrect you will see that the above paragraph   
   derives that H(P)==0.   
      
   computational steps explicitly encoded by the string   
   IS NOT THE SAME AS   
   computational steps explicitly encoded by the *input* string   
      
   Three different LLMs are able to see that this   
   subtle little difference CHANGES EVERYTHING.   
      
   --   
   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)