XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 12/14/2025 4:43 AM, Mikko wrote:   
   > On 13/12/2025 18:44, 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.   
   >   
   > Every property a Turing machine can compute is a syntactic property.   
   > A Turing machine sees only its input. It does not see any neaning of   
   > the input. Therefore it has no access to semantic properties. A   
   > semantic property can be computed only if it is equivalent to a   
   > syntactic property.   
   >   
      
   If that was true then Rice's theorem would be   
   wrong before it even got started.   
      
   In computability theory, Rice's theorem states   
   that all non-trivial semantic properties of   
   programs are undecidable. A semantic property   
   is one about the program's behavior   
   https://en.wikipedia.org/wiki/Rice%27s_theorem   
      
   --   
   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)