XPost: comp.theory, sci.logic, sci.math   
   From: user7160@newsgrouper.org.invalid   
      
   On 11/20/25 11:55 AM, Kaz Kylheku wrote:   
   > 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?   
   >   
      
   assume the premise exist and show a contradiction for both deciders   
   within one machine   
      
   --   
   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   
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