XPost: comp.theory   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   On 26/10/2025 14:46, olcott wrote:   
      
   > The philosophical point: A Turing machine decider should only be   
   > expected to report on properties determinable from its input. When the   
   > halting problem construction makes the "actual behavior" dependent on   
   > the decider's output, it's asking the decider to report on something   
   > outside its input - hence, a category error.   
      
   When a copy of HHH is embedded in the input then the copy is part of the   
   input, yet, to be a universal decider every copy of HHH must be able to   
   decide on all inputs that have another copy of HHH embedded in it. Since   
   a subject program may copy itself and the HHH that's embedded in it, the   
   subject can always (on a TM, simulated or otherwise) create another   
   identical input with all of its original (or some reduced/partially   
   interpreted) form, including a new copy of HHH.   
      
   Your text looks like it shows you have assumed that cannot be done.   
      
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   Tristan Wibberley   
      
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    * Origin: you cannot sedate... all the things you hate (1:229/2)