XPost: comp.theory, sci.logic, sci.math   
   From: tristan.wibberley+netnews2@alumni.manchester.ac.uk   
      
   On 19/11/2025 01:36, olcott wrote:   
   > On 11/18/2025 7:03 PM, Tristan Wibberley wrote:   
   >> On 17/11/2025 22:59, olcott wrote:   
   >>> On 11/17/2025 4:45 PM, Tristan Wibberley wrote:   
   >>>> On 17/11/2025 22:15, Alan Mackenzie wrote:   
   >>>>   
   >>>>> There is no proper academic conversation to be had over 2 + 2 = 4.   
   >>>>> It is   
   >>>>> firm, unassailable knowledge, unchallengeable.  The Halting Theorem   
   >>>>> is of   
   >>>>> the same status, proven using the same methodology from the same   
   >>>>> fundamentals.   
   >>>>   
   >>>>   
   >>>> It's a completely different league from 2 + 2 = 4.   
   >>>> It's closer to x = 1/2 + x/2 but it's still conceptually /much/ harder   
   >>>> than that.   
   >>>> It's more like the problem of whether a fixed point exists or not, but   
   >>>> it's for the fixed point of a limit of a particular, conceptually   
   >>>> weird,   
   >>>> sequence of functions.   
   >>>>   
   >>>> It really is quite peculiar.   
   >>>>   
   >>>   
   >>> Ultimately it is essentially the Liar Paradox in disguise.   
   >>>   
   >>> The Liar Paradox formalized in the Prolog Programming language   
   >>>   
   >>> This sentence is not true.   
   >>> It is not true about what?   
   >>> It is not true about being not true.   
   >>> It is not true about being not true about what?   
   >>> It is not true about being not true about being not true.   
   >>> Oh I see you are stuck in a loop!   
   >>>   
   >>> This is formalized in the Prolog programming language below.   
   >>>   
   >>> ?- LP = not(true(LP)).   
   >>> LP = not(true(LP)).   
   >>> ?- unify_with_occurs_check(LP, not(true(LP))).   
   >>> false.   
   >>   
   >> true/0   
   >> use \+/1 rather than not/1   
   >>   
   >>   
   >>> Failing an occurs check seems to mean that the   
   >>> resolution of an expression remains stuck in an   
   >>    ^^^^^^^^^^   
   >>> infinite loop.   
   >>   
   >> You mean "judgement" ?   
   >   
   > I mean like this thingy:   
   >   
   > void Infinite_Loop()   
   > {   
   >   HERE: goto HERE;   
   >   return;   
   > }   
      
   Ah the terminological problem of what to call something like a   
   "normalisation" process when it might be that no normal form exists.   
      
   In the pure functional world your C characterisation is typically called   
   "a computation" but I'm not sure where the boundary lies or whether you   
   really mean "judgement" or "evaluation". In the C world "evaluation" of   
   "Infinite_Loop()" is a real thing that exists, even if the expression   
   has no value or any normal form in any conventionally reasonable   
   formalisation and the mapping of your original terms to Infinite_Loop is   
   just one choice for how to judge.   
      
      
   --   
   Tristan Wibberley   
      
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