XPost: comp.theory, sci.logic, sci.math   
   From: mikko.levanto@iki.fi   
      
   On 15/12/2025 01:46, olcott wrote:   
   > 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.   
      
   No, the Rice's theorem does not imply that the Rice's theorem be wrong.   
      
   > 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   
      
   Where non-trivial means 'not equivalent to a syntactic property'.   
      
   --   
   Mikko   
      
   --- SoupGate-Win32 v1.05   
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