XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 12/29/2025 9:11 AM, Richard Damon wrote:   
   > On 12/29/25 9:55 AM, olcott wrote:   
   >> 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 an acyclic graph   
   >> is seems to be why you can't understand an acyclic   
   >> evaluation sequence.   
   >>   
   >   
   > No, I understand what an acyclical graph is, but you just can't call   
   > something an acyclical graph if it has cycles.   
   >   
   > It seems TRUTH isn't a concept you understand.   
   >   
      
   The entire body of general knowledge is inherently   
   structured within a directed acyclic graph.   
      
   > You can't just assume that something exists or can be done.   
   >   
   >>> 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-Win32 v1.05   
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