XPost: comp.theory, sci.math, comp.ai.philosophy   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   On 13/12/2025 16:44, 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.   
      
   I continue to reject the use of "accept" and "reject" here. And I also   
   reject the use of "indicates" wrt to them.   
      
   There's no good reason to suppose this is about grammars and strings   
   rather than propositions about programs. To the extent that they might   
   be isomorphic you need to introduce the notion of grammars and string   
   acceptance by them to give "accept" and "reject" and "indicates" the   
   correct meaning.   
      
      
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   Tristan Wibberley   
      
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