XPost: comp.theory, sci.logic, sci.math   
   From: user7160@newsgrouper.org.invalid   
      
   On 1/25/26 10:20 AM, Richard Damon wrote:   
   > On 1/24/26 10:03 PM, dart200 wrote:   
   >> 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"...   
   >> 🫩🫩🫩   
   >   
   > Well, people calling the "Deciders" and ignoring the partial are liars.   
   >   
   >   
   >>   
   >>>   
   >>>> 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 🙄🙄🙄   
   >   
   > The problem is the results of the "paradoxical" machine was never the   
   > problem, it was that the decider gave the wrong answer to it.   
   >   
   > You seem to think there is something problematical about these   
   > "paradoxical" machines in general.   
      
   philosophical errors are inherently limiting in ways we can't even truly   
   imagine, so why bother trying to explain fully?   
      
   >   
   > It is just that it make one particular machine wrong, and that one   
   > exists for every decider.   
      
   if my thesis is correct: a minimal turing complete subset of turing   
   machines cannot be shown to have a halting problem, removing a core   
   pillar of undecidability proofs.   
      
   i get that u have basically no creativity or wonder left in ur soul, but   
   that potential excites me with the theoretical progress it might induce.   
      
   >   
   >   
   >>   
   >>>   
   >>>   
   >>>>   
   >>>>>   
   >>>>>>   
   >>>>>>>   
   >>>>>>>>   
   >>>>>>>> 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   
   >>>>>>   
   >>>>>   
      
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