XPost: comp.theory, comp.ai.philosophy, sci.math   
   From: 643-408-1753@kylheku.com   
      
   On 2025-11-20, dart200  wrote:   
   > On 11/19/25 6:58 PM, Kaz Kylheku wrote:   
   >> On 2025-11-20, dart200  wrote:   
   >>> On 11/19/25 6:29 PM, Kaz Kylheku wrote:   
   >>>> On 2025-11-20, dart200  wrote:   
   >>>>> a) you can construct halting paradoxes that contradicts multiple and   
   >>>>> possibly even infinite deciders. certainly any finite set, after which   
   >>>>   
   >>>> This is not possible in general. The diagonal test case must make   
   >>>> exactly one decision and then behave in a contradictory way: halt or   
   >>>> not. If it interrogates as few as two deciders, it becomes intractable   
   >>>> if their decisions differ: to contradict one is to agree with the other.   
   >>>>   
   >>>> If the deciders are H0(P) { return 0; } and H1(P) { return 1; } you can   
   >>>> see that between the two of them, they cover the entire space: there   
   >>>> cannot be a signal case whch both of these don't get right. One   
   >>>> correctly decides all nonterminating cases; the other correctly decies   
   >>>> all terminating cases, and every case is one or the other.   
   >>>   
   >>> common man those deciders do not provide an /effectively computable/   
   >>> interface and you know it   
   >>>   
   >>> try again, it's quite simple to produce a paradox that confounds two   
   >>> legitimate deciders that genuinely never give a wrong answer   
   >>   
   >> But we have a proof that deciders which never give a wrong answer do not   
   >> exist.   
   >>   
   >> If halting algorithms existed   
   >>   
   >> - they would all agree with each other and thus look the same from the   
   >>    ouside and so wouldn't constitute a multi-decider aggregate.   
   >>   
   >> - it would not be /possible/ to contradict them: they never give   
   >>    a wrong answer!   
   >>   
   >> So if we want to develop diagonal cases whch contradict deciders,   
   >> we have to accept that we are targeting imperfect, partial deciders   
   >> (by doing so, showing them to be that way).   
   >   
   > for the sake of proof/example assume they are honest until you produce   
   > the paradox   
      
   By "until", are you referring to some temporal concept? There is a time   
   variable in the system such that a decider can be introduced, and then   
   for at time, there exists no diagonal (or other) case until someone   
   writes it?   
      
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