XPost: comp.theory   
   From: user7160@newsgrouper.org.invalid   
      
   On 11/20/25 12:53 PM, Mike Terry wrote:   
   >> a) you can construct halting paradoxes that contradicts multiple and   
   >> possibly even infinite deciders. certainly any finite set, after which   
   >> it becomes cat and mouse: if you define a new decider, i can add to my   
   >> growing multi-paradox that includes it.   
   >>   
   >> homework assignment for the group: write a multi-decider paradox that   
   >> confounds both H1 and H0   
   >   
   > I'm not clear what you mean by "writing a paradox".  The HP is not a   
   > paradox, in my view, and I would guess in most computer scientists /   
   > mathematicians views (but that's just a guess).   
      
   it's a paradox in how the liar's paradox is a paradox   
      
   >   
   > It sounds as though you're challenging posters to write some kind of /   
   > program/ ?, so maybe just replace your use of "paradox" with "program"   
   > or at leas some more descriptive term.  I think there's  a risk that   
   > people seeing you talking about HP paradoxes could dismiss you as a   
   > crank.  (I'm not suggesting you are a crank, just that your terminology   
   > may result in people disengaging from your work...)   
   >   
   > Clearly every TM halts or does not halt, so this "program" must be some   
   > kind of program that neither halts nor doesn't halt?  Ummm....  Well, I   
   > guess you want people to write one of your context-sensitive programs?   
   > Perhaps they simply don't have any concept of halting?   
   >   
   > But is it really the case that cs_TMs don't have a halting status?  That   
   > sounds wrong, but for sure we might need to work on setting a new   
   > appropriate definition of halting, applicable for cs-TMs?  As soon as we   
   > do that, my previous argument will work with appropriate adjustments.   
   >   
   > [Basically, what I said holds as long as there are only a small number   
   > of halting statuses that apply to cs-TMs.  In fact, I imagine we will   
   > still have just "halts" or "neverhalts", so my H0, H1 will suffice as   
   > they are - regardless of whether your program "confounds" them!.)   
   >   
   > So I don't think (a) disagrees with my previous post.   
   >   
   >>   
   >> b) turing's original semantic paradox ("satisfactory" circle-free vs   
   >> circular computable number) cannot be solved by a secondary decider on   
   >> the matter. the halting problem is fundamentally a simple form of   
   >> semantic paradox than the "satisfactory" problem.   
   >   
   > I think you're just saying that HP cannot be solved by having two   
   > deciders e.g. my H0/H1, such that given any input M, one of H0/H1   
   > decides M correctly.  That's true, as the HP asks for /one/ TM decider,   
   > not two, and crucially we don't have a way to combine H0/H1 into a   
   > single decider that satisfies HP.   
      
   i'm saying that for the "satisfactory" paradox written about by turing   
   having two partial deciders is utterly meaningless on the matter,   
      
   it's not even a "partial" solution it's just another total failure to   
   resolve the paradox involved in a literal diagonal computation across   
   *all* computable numbers   
      
   --   
   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)