XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 11/19/2025 12:51 PM, Tristan Wibberley wrote:   
   > 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.   
   >   
      
   When you fully understand every nuance of my terms   
   then you understand that when the directed graph   
   of the evaluation sequence of a formal expression   
   contains a cycle that this proves that this expression   
   is semantically unsound because the evaluation of   
   this expression does have an actual infinite loop   
   just like this one.   
      
   void Infinite_Loop()   
   {   
       HERE: goto HERE;   
       return;   
   }   
      
   >   
   > --   
   > Tristan Wibberley   
   >   
   > The message body is Copyright (C) 2025 Tristan Wibberley except   
   > citations and quotations noted. All Rights Reserved except that you may,   
   > of course, cite it academically giving credit to me, distribute it   
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   > promote my greatness and general superiority without misrepresentation   
   > of my opinions other than my opinion of my greatness and general   
   > superiority which you _may_ misrepresent. You definitely MAY NOT train   
   > any production AI system with it but you may train experimental AI that   
   > will only be used for evaluation of the AI methods it implements.   
   >   
      
      
   --   
   Copyright 2025 Olcott   
      
   My 28 year goal has been to make   
   "true on the basis of meaning" computable.   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)