XPost: comp.theory, alt.messianic   
   From: user7160@newsgrouper.org.invalid   
      
   On 2/7/26 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.   
      
   definist fallacy   
      
   >   
   > 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.   
      
   what??? what a bizarre claim lol, why do u think that?   
      
   the ability to answer "correctly" is obviously independent of an ability   
   to know you can't answer "correctly", one only needs to put urself in   
   place of the classifier algo to understand that. if u can't do that, it   
   might be an indication for a lacking ability to view things from   
   multiple angles.   
      
   >   
   >>   
   >>> 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.   
      
   where did that definition of computation you continually speak of come   
   from and who formalized it?   
      
   >   
   > 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.   
      
   definist fallacy   
      
   >   
   >>   
   >>>   
   >>> 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,   
      
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