XPost: comp.theory, sci.logic, sci.math   
   From: mikko.levanto@iki.fi   
      
   On 24/01/2026 11:21, dart200 wrote:   
   > On 1/24/26 12:42 AM, Mikko wrote:   
   >> On 23/01/2026 07:21, dart200 wrote:   
   >>> On 1/22/26 3:58 PM, olcott wrote:   
   >>>> It is self-evident that a subset of Turing machines   
   >>>> can be Turing complete entirely on the basis of the   
   >>>> meaning of the words.   
   >>>>   
   >>>> Every machine that performs the same set of   
   >>>> finite string transformations on the same inputs   
   >>>> and produces the same finite string outputs from   
   >>>> these inputs is equivalent by definition and thus   
   >>>> redundant in the set of Turing complete computations.   
   >>>>   
   >>>> Can we change the subject now?   
   >>>   
   >>> no because perhaps isolating out non-paradoxical machine may prove a   
   >>> turing-complete subset of machines with no decision paradoxes,   
   >>> removing a core pillar in the undecidability arguments.   
   >>   
   >> The set of non-paradoxical Turing machines is indeed Truing complete   
   >> because there are no paradoxical Turing machines. Of course any Turing   
   >> machine can be mentioned in a paradox.   
   >>   
   >   
   > i don't see how the lack of paradoxes ensures all possible computations   
   > are represented (therefore being turing complete).   
   >   
   > paradoxical machines are still produce computations ... just not   
   > computations that are unique in their functional result compared to non-   
   > paradoxical ones.   
      
   I doesn't. The set, unlike some other sets, is complete in the sense   
   that every computable function is computed by some machine in the set.   
      
   --   
   Mikko   
      
   --- SoupGate-DOS v1.05   
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