XPost: comp.theory, sci.logic, sci.math   
   From: user7160@newsgrouper.org.invalid   
      
   On 1/24/26 4:52 PM, Richard Damon wrote:   
   > On 1/24/26 5:28 PM, dart200 wrote:   
   >> 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   
   >>   
   >   
   > And "Partial Recognizers" are well known and nothing new,   
      
   i suppose it's progress that we've gone from u repeatedly calling them   
   "liars" because they merge results, to "well known and nothing new"...   
   🫩🫩🫩   
      
   >   
   >> 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   
   >   
   > And the "contradiction" input just makes sure that its recognizer can't   
   > decide on it, making sure it is just a partial recognizer.   
   >   
   >>   
   >> 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   
   >   
   > And what good is this set. You don't know if it is even Turing Complete   
   > Set (which it likely isn't).   
      
   if it can be proven that no paradoxical machine is the simplest of all   
   machines functionally equivalent to that paradoxical machine ...   
      
   then just excluding paradoxical machines does not reduce the   
   completeness of the minimal turing complete subset.   
      
   yes i get that i haven't proven that to u 🙄🙄🙄   
      
   >   
   >   
   >>   
   >>>   
   >>>>   
   >>>>>   
   >>>>>>   
   >>>>>> 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   
   >>   
   >   
   > Because the machine you just tried to classify, are really no different   
   > if form than others you don't do so. Your criteria is based on   
   > uncomputable values.   
      
   i apologize, that did not clarify anything to me   
      
   --   
   arising us out of the computing dark ages,   
   please excuse my pseudo-pyscript,   
   ~ nick   
      
   --- SoupGate-Win32 v1.05   
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