XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 12/8/2025 12:51 AM, Tristan Wibberley wrote:   
   > On 08/12/2025 03:14, olcott wrote:   
   >> Turing machine deciders only compute a mapping from   
   >> their [finite string] inputs to an accept or reject   
   >> state on the basis that this [finite string] input   
   >> specifies or fails to specify a semantic or syntactic   
   >> property.   
   >   
   > replace 'a' with 'some' or with 'a particular'   
   >   
   >   
      
   That last one is an improvement.   
      
   Turing machine deciders only compute the mapping from   
   their [finite string] inputs to an accept or reject   
   state on the basis that this [finite string] input   
   specifies or fails to specify a particular semantic   
   or syntactic property.   
      
   That one paragraph is the basis for refuting the   
   Halting problem itself as a category error.   
      
   When a halt decider H is based on a UTM that simulates   
   its input D until the behavior of this input correctly   
   matches a correct non-halting behavior pattern then   
   it is necessarily correct to abort its simulation of   
   D and reject its input D as non-halting.   
      
   This causes the the directly executed D to have different   
   behavior than the behavior that the input to H(D) specifies.   
      
   The halting problem requires H to report on this different   
   behavior than the behavior that its actual input actually   
   specifies, thus forming the category error.   
      
      
   --   
   Copyright 2025 Olcott

   
      
   My 28 year goal has been to make 
   
   "true on the basis of meaning" computable.

   
      
   This required establishing a new foundation
   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)