XPost: comp.theory, sci.logic   
   From: polcott333@gmail.com   
      
   On 12/12/2025 10:31 AM, Richard Damon wrote:   
   > On 12/12/25 10:04 AM, olcott wrote:   
   >> On 12/12/2025 8:35 AM, Richard Damon wrote:   
   >>> On 12/12/25 9:29 AM, olcott wrote:   
   >>>> On 12/12/2025 8:12 AM, Richard Damon wrote:   
   >>>>> On 12/11/25 11:01 PM, olcott wrote:   
   >>>>>> Principle 1: Turing machine deciders compute functions   
   >>>>>> from finite strings to {accept, reject} according to   
   >>>>>> whether the input has a syntactic property or specifies   
   >>>>>> a semantic property.   
   >>>>>>   
   >>>>>> The halting problem requires that a halt decider   
   >>>>>> report on the direct execution of a Turing machine,   
   >>>>>> thus category error.   
   >>>>>>   
   >>>>>   
   >>>>> Which is a semantic property of the string, assuming it is a   
   >>>>> representation of the machine in question,   
   >>>>   
   >>>> Principle 1: Turing machine deciders compute functions   
   >>>> from finite strings to {accept, reject} according to   
   >>>> whether the input has a syntactic property or specifies   
   >>>> a semantic property.   
   >>>>   
   >>>> Turing machine deciders only report on the behavior   
   >>>> of Turing machines indirectly through the proxy of   
   >>>> finite strings. *This key detail has been ignored*   
   >>>   
   >>> But, you seem to forget, that said finite string can fully contain   
   >>> the information needed to recreate that execution behavior, and thus   
   >>> that behavior is a valid target for a question to it.   
   >>>   
   >>>>   
   >>>> Principle 2: We measure the semantic property that   
   >>>> the finite string specifies by a UTM-based halt   
   >>>> decider that simulates its input finite string   
   >>>> step-by-step and watches the execution trace of   
   >>>> this behavior.   
   >>>>   
   >>>>   
   >>>   
   >>> No, it is measured by the results created by an ACTUAL UTM.   
   >>>   
   >>   
   >> Principle 1: Turing machine deciders compute functions   
   >> from *finite string inputs* to {accept, reject} according   
   >> to whether the input has a syntactic property or specifies   
   >> a semantic property.   
   >>   
   >> Turing machine deciders only report on the behavior   
   >> of Turing machines indirectly through the proxy of   
   >> finite string inputs. *This key detail has been ignored*   
   >>   
   >   
   > But the finite string is a representation of the Turing Machine,   
      
   "representation" has always been way too vague of a term.   
      
   It is the actual sequence of steps specified by the input.   
      
   It is ONLY the actual sequence of steps encoded by the   
   finite string AS AN INPUT not in any other context.   
      
   When the halting problem requires more than this it is   
   a category error.   
      
   --   
   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   
   for correct reasoning.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)