XPost: comp.theory, sci.logic, sci.math   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   On 21/11/2025 01:14, Tristan Wibberley wrote:   
   > On 17/11/2025 22:59, olcott wrote:   
   >   
   >> Ultimately it is essentially the Liar Paradox in disguise.   
   >   
   > Yes, it is, I'm pretty sure (I haven't gone through it in such detail to   
   > satisfy all audiences).   
   >   
   > It's roughly evaluation of the contradictory G (as defined by Olcott in   
   > an inconsistent suppositional axiom extension) as opposed to judgement   
   > of that defining axiom (where judgement would be evaluation in a   
   > partiality monad instead of directly or in the identity monad).   
   >   
   > Where we have the craziness of nonstrict evaluation such as in Haskell,   
   > a partiality monad can be used for judgement and then used to construct   
   > evaluation using the monad's catamorphism with a simple empty loop.   
      
   For clarity, the "disguise" is obviously that a purported universal   
   decider is constructed of many of the same elements using a partiality   
   monad for judgements and combining them to what is "the universal   
   decider with what would be uniquely identifying characteristics if it   
   exists"   
      
   I think the catamorphism is required to complete the disguise because   
   the universal halting decider would be an infinite loop inside the monad   
   and to match the liar paradox it has to be merged with the empty case on   
   application of its catamorphism.   
      
   Obviously there are so many identities among the ways of couching these   
   things that it must be that the halting problem is the liar paradox in   
   disguise. It's interesting to explore how and how far removed are they   
   (not really very far).   
      
   --   
   Tristan Wibberley   
      
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