XPost: comp.theory   
   From: acm@muc.de   
      
   [ Followup-To: set ]   
      
   In comp.theory Tristan Wibberley   
    wrote:   
   > On 11/02/2026 21:53, Alan Mackenzie wrote:   
   >> Mathematicians have proven that many decision problems can not be   
   >> answered, all the nonsense about "idiosyncrasies of self-referential   
   >> logic" notwithstanding.   
      
   > It's not at all clear to me that those unanswerables are properly   
   > classified as "decision problem" unless one uses an auto-explication (my   
   > term for when a term is both an explicatum and explicandum of an   
   > explication). Carnap's definition of explication excludes such an act   
   > (though I don't know if he'd picked up the bad habit of using "decision   
   > problem" as an explicatum).   
      
   My understanding of a "decision problem" is one whose solution is a   
   machine which, in finite time, can correctly classify any machine into   
   one of two categories.   
      
   In this sense there is no solution to the halting problem.   
      
   > I think Carnap would have admitted "L-decision problem" as an explicatum   
   > of the explicandum "decision problem". The nonsense act of calling   
   > pathologically self-referential problems ....   
      
   What would these be?  We haven't encountered any such problem in this   
   newsgroup.  The halting problem, for example, is a simple yes/no   
   question without any references, self- or otherwise.   
      
   > .... as "L-decision problems" would be obvious because one does not   
   > have a problem of choosing between only classifications "true" and   
   > "false" when one has merely been fooled into thinking those are   
   > candidates without a whole heap of others beside.   
      
   Those are the possibilities made possible by the definition of a   
   "decision problem".  If there are more possibilities, we have a   
   different animal.  Who's fooling whom here?   
      
   > I hereby indulge myself with some old-timey assertive logistic   
   > philosophy, you might call it a strawman, something to ponder and burn down:   
      
   > We can understand the fallacy by making explicit the implicit false   
   > assumption: "the sentence after the conjunctive connector following can   
   > be assigned no valuation but 'true' or 'false' AND blah-blah". That is   
   > the cultural synergy covertly induced in the ponderer by a poetic form   
   > of expression ("proposition" the explicatum, not the explicandum, it's   
   > another auto-explication) but it's not /well/ formalised in that it's a   
   > mess of massive description and wonderment. I think usage of AND gives   
   > us falsity for pathologically self-referential 'blah-blah' if we have   
   > the right type-system but other connectives give us other, non-truth,   
   > classifications. A connective that means the implication of neither   
   > truth nor falsity is also available. Of course, the ponderer has the   
   > inducement in the form of a volition to be disobedient and choose to   
   > react in a variety of unassertive ways.   
      
   Sorry, you've completely lost me with that paragraph - too many long   
   words and long sentences, too abstract.   
      
   >> A proof is a proof.   
      
   > Tautology.   
      
   Context, please!  There are posters here who seem to think that a proof   
   is merely somebody's opinion.  That sentence was to encourage them to   
   revise their false notions.   
      
   > --   
   > Tristan Wibberley   
      
   --   
   Alan Mackenzie (Nuremberg, Germany).   
      
   --- SoupGate-Win32 v1.05   
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