XPost: comp.theory, sci.logic, sci.math   
   From: user7160@newsgrouper.org.invalid   
      
   On 1/24/26 4:24 AM, Richard Damon wrote:   
   > On 1/24/26 4:21 AM, 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).   
   >   
   > In other words, you disagree with you own claim.   
      
   may argument is that paradoxes are redundant, mikko did not add such a   
   claim. so ur suggesting he was agreeing with my rational that they are   
   redundant?   
      
   >   
   >>   
   >> paradoxical machines are still produce computations ... just not   
   >> computations that are unique in their functional result compared to   
   >> non- paradoxical ones.   
   >>   
   >   
   > The problem is no machine is generically a "paradox". In the proof, it   
   > is only a paradox to a particular machine that it refutes.   
   >   
   > The construction template (which isn't a machine, but a formula to build   
   > a machine) is paradoxical to the Halt Decider API (which again isn't a   
   > machine but a definition of the mapping for a machine to generate).   
   >   
   > You (like Peter) just confuse classes of machines with machines   
   > themselves, which is just an error.   
      
   any machine in that class is a paradox   
      
   --   
   arising us out of the computing dark ages,   
   please excuse my pseudo-pyscript,   
   ~ nick   
      
   --- SoupGate-Win32 v1.05   
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