XPost: comp.theory, sci.logic, sci.math   
   From: user7160@newsgrouper.org.invalid   
      
   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   
      
   this isn't hard, it's just adding half a line of code to the original   
   paradox   
      
   --   
   a burnt out swe investigating into why our tooling doesn't involve   
   basic semantic proofs like halting analysis   
      
   please excuse my pseudo-pyscript,   
      
   ~ nick   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)