XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 12/13/2025 1:14 PM, Richard Damon wrote:   
   > On 12/13/25 11:44 AM, olcott wrote:   
   >> At the most fundamental level:   
   >> All Turing machines only compute the mapping   
   >> from input finite strings to some value.   
   >>   
   >> Turing machine Deciders are a subset of this   
   >> where the value indicates accept or reject a   
   >> finite string by some criterion measure.   
   >>   
   >> A further elaboration of this comes from the   
   >> notion of computable functions and Rice's   
   >> Theorem:   
   >>   
   >> Turing machine deciders compute functions from   
   >> *finite string inputs* to {accept, reject} values   
   >> 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*   
   >>   
   >   
   > So, if the function isn't "Computable", it is still a Function, but no   
   > Turing Machine (or equivalent) can compute it.   
   >   
      
   There seems to be no such thing as uncomputable   
   functions when Turing machines are construed   
   entirely in terms of finite string rewrite rules.   
      
   --   
   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)