XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   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*   
      
   --   
   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)