XPost: comp.theory, sci.logic, sci.math   
   From: user7160@newsgrouper.org.invalid   
      
   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   
      
   --   
   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)