XPost: comp.theory, alt.messianic   
   From: punditster@gmail.com   
      
   On 2/7/2026 6:34 AM, Richard Damon wrote:   
   > On 2/7/26 1:06 AM, dart200 wrote:   
   >> On 2/6/26 7:55 PM, Richard Damon wrote:   
   >>> On 2/6/26 9:36 PM, dart200 wrote:   
   >>>> my proposal starts with the reminder that *no* machine computes a   
   >>>> unique function. for every function that is computed, there is a   
   >>>> whole (infinite) class of machines that are functionally equivalent   
   >>>> (same input -> same output behavior).   
   >>>   
   >>> Fine   
   >>>   
   >>>>   
   >>>> we should then consider a working thesis: no paradoxical machine is   
   >>>> the simplest of their class of functionally equivalent machines.   
   >>>   
   >>> Something you would need to PROVE.   
   >>>   
   >>> And, something of not particular value since determining the   
   >>> equivalence class of a given machine is non-computable.   
   >>>   
   >>>>   
   >>>> why? the paradox structures do not actually contribute to the output   
   >>>> (since deciders themselves do not create output for the “calling”   
   >>>> machine), they are just sort of junk computation that selects a   
   >>>> particular execution branch (or blocks entirely), a result which can   
   >>>> exist without that paradox fluff being involved.   
   >>>   
   >>> Not really a proof, but a presumption.   
   >>>   
   >>> And remember, the "output" of the "paradoxical" machine includes its   
   >>> possible deciding to not halt.   
   >>>   
   >>> And again, it doesn't help you answer the actual question.   
   >>>   
   >>>>   
   >>>> consider the basic paradox form:   
   >>>>   
   >>>>    deciderP(input) - decides if input has property P or !P   
   >>>>    machineP()      - machine that has property P   
   >>>>    machine!P()     - machine that has property !P   
   >>>>   
   >>>>    // undecidable by deciderP for property P   
   >>>>    undP = () -> {   
   >>>>      if ( deciderP(undP) == TRUE )   
   >>>>        machine!P()   
   >>>>      else   
   >>>>        machineP()   
   >>>>    }   
   >>>>   
   >>>> huh, i guess i kinda get why this wasn’t really spotted before. as   
   >>>> far as i can tell, classical computing theory normally recognizes   
   >>>> three kinds of classifiers:   
   >>>>   
   >>>>   
   >>>>    classical decider:   
   >>>>      TRUE iff input has P   
   >>>>      FALSE iff input has !P (always DECIDABLE)   
   >>>>      impossible interface   
   >>>>   
   >>>>    classical recognizer:   
   >>>>      TRUE iff input has P (always DECIDABLE)   
   >>>>      FALSE iff input has !P (block if UNDECIDABLE)   
   >>>   
   >>> Not "UNDECIDABLE", but *I* Couldn't decide.   
   >>   
   >> yes, i'm aware that undecidability is *always* in respect to   
   >> particular inputs for particular interfaces, as for any true   
   >> classifier one can construct input that it can decide on   
   >   
   > No, "Undeciable" is an attribute of a PROBLEM, that says that any   
   > attemped full decider will always fail for some input. That input does   
   > not need to be the same for every decider.   
   >   
   > "Inputs" are not "DECIDABLE" as the domain of deciablity is PROBLEMS not   
   > INPUTS.   
   >   
   > Thus, you definition is just a categorical ERROR.   
   >   
   > Your "awareness" is just an error.   
   >   
   >>   
   >>>   
   >>>>   
   >>>>    partial decider:   
   >>>>      TRUE iff input has P   
   >>>>      FALSE iff input has !P   
   >>>>      (block if either UNDECIDABLE)   
   >>>   
   >>> Again, not "UNDECIDABLE", but *I* couldn't decide.   
   >>   
   >> yes that's what the return value means, the input was UNDECIDABLE in   
   >> respect to the classifier being asked the question   
   >   
   > And if you could tell that you were going to be wrong, you could correct   
   > yourself and not be wrong in the first place.   
   >   
   >>   
   >>> Also, not iff, just if I was able to decide it had.   
   >>   
   >> lol, that is like the ONE useful comment in ur entire post here. i   
   >> honestly went back and made that more precise for whereever i post   
   >> this next. i guess that's worth digging thru ur endless gishgallop  👌   
   >> 😂🔫👌   
   >>   
   >>>   
   >>> As, for a proper question, all inputs either have P or !P   
   >>>   
   >>> (Like all machines Halt or do not halt, there is no other possibility)   
   >>>   
   >>>>   
   >>>> ... so the paradoxes (involving either a classical recognizer or   
   >>>> partial decider) always result in a blocking, non-returning program   
   >>>> making this thesis still valid, but less interesting/compelling.   
   >>>   
   >>> Right, PARTIAL halt deciders are know to be able to be made, so not   
   >>> even "less-interesting" but not interesting unless you can show that   
   >>> you can answer a comparative reasonable amount of answers.   
   >>>   
   >>> Just another method, without comparing to the existing, just isn't   
   >>> interesting at all.   
   >>>   
   >>>>   
   >>>> i have instead been working on the logical interface for alternative   
   >>>> classifiers. one example are the context-aware classifiers i’ve been   
   >>>> previously posting quite a bit on, but let’s consider a less general   
   >>>> classifier that might exist on TMs alone, what i’m calling a partial   
   >>>> recognizer:   
   >>>   
   >>> But the problem is that such things end up not being "Computation"   
   >>> and thus outside of the field.   
   >>   
   >> begging the ct-thesis again   
   >   
   > But the proof of it being non-computable isn't based on CT, but on the   
   > definition of a computation.   
   >   
   > It seems you don't understand that abstraction, because you just don't   
   > understand what you are talking about.   
   >   
   >   
   >>   
   >>>   
   >>>>   
   >>>>    partial recognizer   
   >>>>      TRUE iff input has P AND is DECIDABLE   
   >>>>      FALSE iff input has !P OR is UNDECIDABLE   
   >>>   
   >>> Again, All inputs will either have P or !P, and your criteria isn't   
   >>> "is it decidable", but can I determine the answer.   
   >>   
   >> yes, whether the particular input is DECIDABLE by the particular   
   >> classifier returning the answer   
   >   
   > But DECIDABILITY isn't about the input.   
   >   
   > Your problem is you are just showing you don't know the language you are   
   > trying to talk.   
   >   
   >>   
   >>>   
   >>> The problem is that "Decidablity" isn't really a property of a specific   
   >>   
   >> see, it's weird that you acknowledge earlier that it's that particular   
   >> inputs that cause UNDECIDABLE returns for particular interfaces...   
   >>   
   >> but here u revert to this red herring of also being able to talk about   
   >> undecidability in terms of whole problems as if that "refutes" anything   
   >   
   > I guess you don't understand logic and proofs.   
   >   
   > Since we can show that we can make an specific input for ANY decider,   
   > thaty it will get wrong, we can thus prove that there does not exist a   
   > decider that gets every input right.   
   >   
   > I guess that property of Qualifiers, since it needs using real logic, is   
   > beyond you.   
   >   
   > That the decider gets a particular input wrong isn't about   
   > "Decidability" but about "Correctness". (But since correctness seems out   
   > of you understand, that is an understandable confusion).   
   >   
   >   
   >   
   >>   
   >>> input, but of the problem as a whole. HALTING, as a problem, is   
      
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