XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 12/12/2025 2:20 AM, Mikko wrote:   
   > olcott kirjoitti 11.12.2025 klo 18.05:   
   >> On 12/11/2025 3:09 AM, Mikko wrote:   
   >>> olcott kirjoitti 11.12.2025 klo 4.00:   
   >>>> *It has take me 21 years to boil it down to this*   
   >>>>   
   >>>> When the halting problem requires a halt decider   
   >>>> to report on the behavior of a Turing machine this   
   >>>> is always a category error.   
   >>>   
   >>> No, that is not a category error. If the question to be answered   
   >>> is something other than "does this computation halt" then there   
   >>> is not point to call the decider a "halting decider".   
   >>>   
   >>>> The corrected halting problem requires a Turing   
   >>>> machine decider to report in the behavior that   
   >>>> its finite string input specifies.   
   >>>   
   >>> The usual defintion does the same. But usually the requirement is   
   >>> that the solution to the problem includes encoding rules that   
   >>> specify what the input shall be in order to specify the behaviour   
   >>> asked about.   
   >>   
   >> No this has always been the error of conflating the   
   >> behavior of the machine with the behavior specified   
   >> by the input finite string. In every case besides   
   >> pathological self-reference this makes no difference.   
   >   
   > As I said the usual formulation of the halting problem asks about   
   > the behaviour of the machine. It is left to the solver of the   
   > problem to crate encoding rules   
      
   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.   
      
   It is incorrect to require a halt decider to report on   
   a sequence of steps that are not already directly encoded   
   in its finite string input.   
      
   > to ensure that the behavour   
   > specified by the input to the halting decider is the same as the   
   > behaviour asked about.   
   >   
      
   int sum(int x, int y){ return x + y; }   
      
   That is the same as saying that it is up to the   
   implementer to determine how to make sum(3,4)   
   produce the required sum of 5 + 6 instead of   
   producing the sum that is directly encoded in   
   the input.   
      
   > If you don't like it that way you must post a pointer to the   
   > formulation you think is better for your purposes.   
   >   
      
      
   --   
   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)