XPost: comp.theory, comp.lang.prolog, sci.math   
   From: polcott333@gmail.com   
      
   On 12/22/2025 1:32 PM, Richard Damon wrote:   
   > On 12/22/25 2:05 PM, olcott wrote:   
   >> On 12/22/2025 12:57 PM, Richard Damon wrote:   
   >>> On 12/22/25 1:35 PM, olcott wrote:   
   >>>> On 12/22/2025 12:29 PM, Richard Damon wrote:   
   >>>>> On 12/22/25 1:09 PM, olcott wrote:   
   >>>>>> On 12/22/2025 12:07 PM, Richard Damon wrote:   
   >>>>>>> On 12/22/25 12:59 PM, olcott wrote:   
   >>>>>>>> On 12/22/2025 11:41 AM, Richard Damon wrote:   
   >>>>>>>>> On 12/22/25 12:30 PM, olcott wrote:   
   >>>>>>>>>> On 12/22/2025 11:23 AM, Richard Damon wrote:   
   >>>>>>>>>>> On 12/22/25 12:19 PM, olcott wrote:   
   >>>>>>>>>>>> On 12/22/2025 11:11 AM, Mikko wrote:   
   >>>>>>>>>>>>> On 22/12/2025 18:39, olcott wrote:   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>>> % This sentence is not true.   
   >>>>>>>>>>>>>>   ?- LP = not(true(LP)).   
   >>>>>>>>>>>>>> LP = not(true(LP)).   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>> The Prolog implementation's opinion is that it is true.   
   >>>>>>>>>>>>>   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> % This sentence is not true.   
   >>>>>>>>>>>>   ?- LP = not(true(LP)).   
   >>>>>>>>>>>> LP = not(true(LP)).   
   >>>>>>>>>>>> ?- unify_with_occurs_check(LP, not(true(LP))).   
   >>>>>>>>>>>> false.   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> By erasing the last line you seem to be dishonest   
   >>>>>>>>>>>> was that your intention?   
   >>>>>>>>>>>>   
   >>>>>>>>>>>> Also you do not seem to understand exactly   
   >>>>>>>>>>>> what unify_with_occurs_check() means even   
   >>>>>>>>>>>> when I quoted Clocksin & Mellish on this.   
   >>>>>>>>>>>>   
   >>>>>>>>>>>   
   >>>>>>>>>>> It means that the input sentence didn't obey Prologs non-   
   >>>>>>>>>>> recursvie nature.   
   >>>>>>>>>>>   
   >>>>>>>>>>   
   >>>>>>>>>> No that is not what it means.   
   >>>>>>>>>> It means that the evaluation of LP is stuck   
   >>>>>>>>>> in infinite recursion. LLMs are smart enough   
   >>>>>>>>>> to immediately see this.   
   >>>>>>>>>   
   >>>>>>>>> BECAUSE Prolog, and the simplistic logic it uses, can't handle   
   >>>>>>>>> that statement.   
   >>>>>>>>   
   >>>>>>>> Counter-factual.   
   >>>>>>>>   
   >>>>>>>> Prolog (and Olcott's Minimal Type Theory) detects   
   >>>>>>>> cycles in the directed graph of the evaluation   
   >>>>>>>> sequence of an expression.   
   >>>>>>>   
   >>>>>>> But Cycles are not inherently a problem.   
   >>>>>>>   
   >>>>>>   
   >>>>>> The same thing as stuck in an infinite loop.   
   >>>>>>   
   >>>>>   
   >>>>> But only because it uses a bad algorithm.   
   >>>>>   
   >>>>   
   >>>> 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!   
   >>>>   
   >>>>   
   >>>   
   >>> Again with to going off topic as a disraction.   
   >>>   
   >>   
   >> It proves that the Liar Paradox does specify   
   >> infinite recursion in a way that cannot be   
   >> correctly denied.   
   >   
   > No, it only specifies infinite recursion in logic system that can't   
   > actually handle recursive definitions.   
   >   
   > Since that is the only type of logic you understand, the problem is on you.   
   >   
   >>   
   >>> My sentence was L = true(L) or x or not(x).   
   >>>   
   >>> want to try again?   
   >>>   
   >>> it seems you really don't know how logic works becuase you refused to   
   >>> learn it so you brainwashed yourself to avoid it.   
   >>   
   >> It has never been that I do not know how logic   
   >> works. It has always been the my understanding   
   >> of the philosophy of logic is better than most.   
   >   
   > Nope. You can't even do induction, as you have tried but couldn't even   
   > come up with the basics.   
   >   
   > You have shown you don't understand the meaning of a "proof"   
   >   
   >>   
   >> Everyone here accepts foundations as inherently   
   >> infallible when indeed they are not.   
   >>   
   >   
   > Which shows your fundamental error,   
   > as in Formal Logic, the foundations   
   > ARE "infallible" in the logic system.   
   >   
      
   Even in the at least hypothetical case where   
   its own definitions contradict each others.   
      
   > You can possible show a given system is internally inconsistant, but   
   > then you have to use just things defined in that system, and not try to   
   > introduce new concepts as then the inconsistance can be cause by your   
   > concepts not the system.   
   >   
      
   Undecidability is incoherent within computation.   
   When requirements exceed fundamental capabilities   
   then it is the requirements that are incorrect.   
      
   > But then, you don't understand such rules, because you don't understand   
   > rules, but only the ruleless general philosophy area.   
      
   It has taken me 22 years to derive succinct foundations   
   from my mere intuitions. It certainly has never been   
   that I did not understand the conventional view.   
      
   I always understood that the halting problem is   
   the liar paradox in disguise.   
      
   My first post on the halting problem.   
   https://groups.google.com/g/sci.logic/c/V7wzVvx8IMw/m/ggPE6a-60cUJ   
      
      
      
   --   
   Copyright 2025 Olcott

   
      
   My 28 year goal has been to make 
   
   "true on the basis of meaning expressed in language"
   
   reliably computable.

   
      
   This required establishing a new foundation
   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)