XPost: comp.theory, sci.logic, sci.math   
   From: polcott333@gmail.com   
      
   On 12/29/2025 10:05 AM, Richard Damon wrote:   
   > On 12/29/25 10:48 AM, olcott wrote:   
   >> 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.   
   >   
   > Then you could express a root node that needs no other knowledge to be   
   > expressed.   
   >   
      
   Now you are proving they you do not understand type   
   hierarchies.   
      
   > Your failure shows you don't know what you are talking about and thus   
   > are admitting you are just a liar.   
   >   
   > You  are not allowed to just assume such a thing,   
   >   
   >>   
   >>> 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.   
   >>>>>>>>>>>>   
   >>>>>>>>>>>>   
   >>>>>>>>>>>   
      
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