XPost: comp.theory, sci.math, comp.ai.philosophy   
   From: polcott333@gmail.com   
      
   On 12/29/2025 7:37 AM, Richard Damon wrote:   
   > On 12/28/25 11:59 PM, olcott wrote:   
   >> On 12/28/2025 9:31 PM, Richard Damon wrote:   
   >>> On 12/28/25 7:42 PM, olcott wrote:   
   >>>> On 12/28/2025 11:15 AM, Richard Damon wrote:   
   >>>>> On 12/28/25 8:49 AM, olcott wrote:   
   >>>>>> On 12/27/2025 7:12 PM, Richard Damon wrote:   
   >>>>>>> On 12/27/25 7:54 PM, olcott wrote:   
   >>>>>>>> A system such all semantic meaning of the formal   
   >>>>>>>> system is directly encoded in the syntax of the   
   >>>>>>>> formal language of the formal system making   
   >>>>>>>> ∀x ∈ L (Provable(L,x) ≡ True(L,x))   
   >>>>>>>   
   >>>>>>> Which is IMPOSSIBLE, as for any sufficiently expressive system,   
   >>>>>>> as it has been shown that for a system that can express the   
   >>>>>>> Natural Numbers, we can build a measure of meaning into the   
   >>>>>>> elements that they did not originally have.   
   >>>>>>>   
   >>>>>>   
   >>>>>> In other words artificially contriving a fake meaning.   
   >>>>>   
   >>>>> But it can be a real meaning.   
   >>>>>   
   >>>>>>   
   >>>>>> ...We are therefore confronted with a proposition which   
   >>>>>> asserts its own unprovability. 15 … (Gödel 1931:40-41)   
   >>>>>   
   >>>>> Right, because in the language created, and "understood" by the   
   >>>>> meta- system, that is what that number means.   
   >>>>>   
   >>>>>>   
   >>>>>> According to Gödel this last line sums up his whole proof.   
   >>>>>> Thus the essence of his G is correctly encoded below:   
   >>>>>   
   >>>>> But, only in the meta-system, which ins't where the system is   
   >>>>> allowed to create its proof.   
   >>>>>   
   >>>>> Your problem is you just don't understand "Formal Logic Systems",   
   >>>>> because they have RULES which you just can't understand   
   >>>>>   
   >>>>>>   
   >>>>>> ?- G = not(provable(F, G)).   
   >>>>>   
   >>>>> But there is no "provable" predicate, so your statement is just   
   >>>>> nonsense.   
   >>>>>   
   >>>>>> G = not(provable(F, G)).   
   >>>>>> ?- unify_with_occurs_check(G, not(provable(F, G))).   
   >>>>>> false.   
   >>>>>   
   >>>>> In part because it doesn't know what provable is, and just can't   
   >>>>> handle the logic.   
   >>>>>   
   >>>>   
   >>>> This is merely your own utterly profound ignorance   
   >>>> of this specific topic.   
   >>>>   
   >>>> ?- LP = not(true(LP)).   
   >>>> LP = not(true(LP)).   
   >>>> ?- unify_with_occurs_check(LP, not(true(LP))).   
   >>>> false.   
   >>>   
   >>> Which shows that you think logic is limited to the simple logic of   
   >>> Prolog.   
   >>>   
   >>   
   >> Do you even know what a cycle in the directed graph   
   >> of an evaluation sequence is?   
   >   
   > Sure. Do you?   
   >   
   > Can you show a finite directed graph with no root node that doesn't have   
   > a cycle?   
   >   
      
   That you do not even understand what a directed acyclic   
   graph is seems to be why you can't fully understand the   
   effect of a cycle in the directed graph of an evaluation   
   sequence. The term "evaluation sequence" may also be   
   difficult for you.   
      
   > Do you understand that your precious Prolog ADMITS that it is limited in   
   > the form of logic it performs.   
   >   
   > It can't even reach a full first-order logic.   
   >   
   > You keep on diverting to simple things that just don't prove what you   
   > claim, when something too tough is brought up.   
   >   
   > That is just admitting that you see yourself as wrong, but can't admit   
   > it openly.   
   >   
   > Your "Prolog" statement about G just isn't actually Prolog, as Prolog   
   > has no "provable" predicate.   
   >   
   >>   
   >>> You seemed to have just diverted from the fact you LIED about Prolog   
   >>> having a "provable" operator, which just shows your stupidity.   
   >>>   
   >>>>   
   >>>> This is the final and complete total resolution   
   >>>> of the Liar Paradox conclusively proving that it   
   >>>> was never grounded in any notion of truth.   
   >>>   
   >>> But that hasn't actually been a problem. It has been known to be a   
   >>> non- truth-bearer for a long time, at least in Formal Logic.   
   >>>   
   >>> They know-nothing philosophers might have been arguing about it, but   
   >>> thas is because there field can't actually resolve anything.   
   >>>   
   >>>>   
   >>>>>>   
   >>>>>> Gödel, Kurt 1931.   
   >>>>>> On Formally Undecidable Propositions of Principia   
   >>>>>> Mathematica And Related Systems   
   >>>>>>   
   >>>>>> The last part is what unify_with_occurs_check() actually means.   
   >>>>>> So far everyone here has been flat out stupid about that.   
   >>>>>   
   >>>>> Nope, as Prolog can't handle the logic of the system Godel talks   
   >>>>> about.,   
   >>>>>   
   >>>>> Your problem is YOU can't handle that logic system either, because   
   >>>>> you are just to stupid.   
   >>>>>   
   >>>>> Try to give Prolog the ACTUAL definition of G, I'm not sure it even   
   >>>>> has the ability to represent that G asserts there isn't a natural   
   >>>>> number g that meets some predicate, like x * x = -1   
   >>>>>   
   >>>>> If you can't express that part, how do you expect it to understand   
   >>>>> the full definition.   
   >>>>>   
   >>>>> Your problem is you are just to stupid to understand your logic's   
   >>>>> restrictions.   
   >>>>>>   
   >>>>>>>>   
   >>>>>>>> "true on the basis of meaning expressed in language"   
   >>>>>>>> is reliably computable by the above formalism.   
   >>>>>>>   
   >>>>>>> But it can only apply to limited systems, namely the systems   
   >>>>>>> smaller than the proof of incompleteness specified.   
   >>>>>>>   
   >>>>>>>>   
   >>>>>>>> I have thought this through for 30,000 hours over   
   >>>>>>>> 28 years.   
   >>>>>>>>   
   >>>>>>>>   
   >>>>>>>   
   >>>>>>> And you should have figured out its problems a lot earlier.   
   >>>>>>   
   >>>>>>   
   >>>>>   
   >>>>   
   >>>>   
   >>>   
   >>   
   >>   
   >   
      
      
   --   
   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-DOS v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)