XPost: comp.theory, sci.math, comp.ai.philosophy   
   From: user7160@newsgrouper.org.invalid   
      
   On 1/24/26 9:24 AM, Richard Damon wrote:   
   > On 1/24/26 11:49 AM, dart200 wrote:   
   >> 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?   
   >   
   > "Redundent" isn't really defined in Computation Theory.   
      
   that's because i'm exploring it in ways that previous have gone unexplored   
      
   >   
   > ALL machines that compute the same answers are considered to be   
   > semantically equivalent.   
      
   and anything more than the first one which produces a particular result   
   is redundant in terms of a minimal turing complete subset of machines.   
      
   >   
   > Part of your problem is you don't understand that trying to base you   
   > idea on an uncomputable filter won't help you.   
      
   from the reference point of a partial recognizer for functional   
   equivalence, two machines can be one of three semantic classifications:   
      
   - decidable non-equivalent   
   - decidable equivalent   
   - undecidable   
      
   since a partial recognizer only has two output: true/false, we merge one   
   of the decidable results with undecidable for the false output, and we   
   are left with a partial recognizer for the other decidable result   
      
   there's no way to produce a contradiction with such a machine. from the   
   reference of any given classifier an input can either be decidedly   
   decidable or not decidable. if it's decidedly decidable the we can   
   output the classification, if it's not decidable then we cannot. there's   
   no middle ground here to exploit for a contradiction   
      
   as we iterate down the full enumeration of machines to build a minimal   
   turing complete subset, we can test each one for functional   
   non-equivalence against all previous found to be in that subset, with a   
   non-equivalence partial recognizer that outputs true iff decidedly   
   non-equivalent, or false iff decidedly equivalent OR not decidable. only   
   if a machine returns true when tested against all previous machines in   
   the subset is it then added to the minimal turing complete subset. both   
   machines with any decidable equivalence or undecidability with respect   
   to machines already in the subset are therefore not put in the subset   
      
   >   
   >>   
   >>>   
   >>>>   
   >>>> 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   
   >>   
   >   
   > Then you consider truth to be a paradox, and paradox to be an   
   > uncomputeable property.   
      
   no idea why u said that   
      
   --   
   arising us out of the computing dark ages,   
   please excuse my pseudo-pyscript,   
   ~ nick   
      
   --- SoupGate-Win32 v1.05   
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