[continued from previous message]   
      
   >>>>>> After all, General Knowledge is an inconsistent set of information   
   >>>>>>   
   >>>>>   
   >>>>> You just can't comprehend that knowledge is   
   >>>>> structured in an acyclic directed graph.   
   >>>>   
   >>>> Nope, it is cyclic,   
   >>>   
   >>> Show a concrete example of knowledge itself being cyclic.   
   >>   
   >> Try to define ANY word, and the words used to define it, and so one   
   >> till you get to a word that just is without a defintion.   
   >>   
   >> You will always eventually cycle back to a word you have already used.   
   >>   
   >   
   > A concrete example is a specific word that does this.   
   >   
   >>>   
   >>>>  as our base facts of knowledge are interrelated. The is on one root   
   >>>> fact.   
   >>>>   
   >>>   
   >>> You have a type that makes your sentence gibberish.   
   >>   
   >> Yes, I have a typ*o*, as did you   
   >>   
   >> There is no one root fact in our knowledge.   
   >   
   > {Thing} is the root of the knowledge ontology.   
   >   
   >> If every fact has other facts that it is based on, there is no root   
   >> fact, and the system, since it is finite, is cyclical.   
   >>>   
   >>>>>   
   >>>>>>>   
   >>>>>>>> It can not handle most systems with a countably infinite domain   
   >>>>>>>> of regard, so not Natural Numbers, not Finite Strings, not   
   >>>>>>>> Turing Complete Systems.   
   >>>>>>>>   
   >>>>>>>   
   >>>>>>> It can handle them at least to the same extent   
   >>>>>>> as humans minds. Algorithmic compression.   
   >>>>>>   
   >>>>>> NOPE, As if it could handle Natural Numbers, then we could create   
   >>>>>> the G for the system, and it couldn't prove it.   
   >>>>>>   
   >>>>>   
   >>>>> It is merely that diagonalization hides the semantic   
   >>>>> incoherence that reject's G.   
   >>>>   
   >>>> Nope. It seems you don't understand that G is just a statement that   
   >>>> no number statisfies a specific (complicated) Primitive Recursive   
   >>>> Relationship. A Relationship that can ALWAYS, for ANY number, be   
   >>>> evaluated in finite time.   
   >>>>   
   >>>   
   >>> "that no number satisfies a specific (complicated) Primitive   
   >>> Recursive Relationship" How is this shown?   
   >>   
   >> In the meta-theory that undrstands the added meaning to the numbers.   
   >>   
   >   
   > Is a separate thing thus not:   
   >   
   > 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))   
      
   But such a thing is not.   
      
   Because ANY logic that has "symbols" of any form, might have the ability   
   for those symbols to be given meaning by a meta-theory.   
      
   After all, how many diffferent ways can you encode some meaning onto the   
   numbers?   
      
      
   >   
   >> In the base theory, the numbers do not have that meaning, but, since   
   >> this meta-theory developes a method to express as a single number ANY   
   >> statement/collection of statements that can be expressed in the   
   >> theory, and, because of the structure of these numbers, can check if a   
   >> given the given statement is a proof for another statement. And the   
   >> PRR is an embodeyment of such an algorithm to check if a statement is   
   >> a proof of the statement G.   
   >>   
   >   
   > You merely ignored my specified requirements. (see above).   
   > It is possible to defined f-cked up systems that are incomplete   
   > That is not the same thing as all systems are necessarily incomplete.   
      
   Right, any system small enough to not be able to express the Natural   
   numbers might be complete (but not necessarily).   
      
   Such systems are inherently less interesting than systems that can   
   express the Natural Numbers.   
      
   >   
   >> THus *ANY* proof of G, will create a number which will satisfy that   
   >> PRR, thus making G false.   
   >>   
   >> Since it is impossible for there to be a correct proof of a false   
   >> statement, there can not be a number that satisfies the PRR of G, as   
   >> that would lead to the contradiction.   
   >>   
   >> This means that no number can staisfy that PRR, and thus G must be true.   
   >>   
   >> This proof can only be done in the meta-system that has the knowledge   
   >> of the meaning of all the numbers, and there are an infinite number of   
   >> possible systems assigning meaning, so we can't just search them all.   
   >>   
   >> The key is that the meta-system was specifically constructed so that   
   >> statements, like that G, and its PRR, that do not reference the   
   >> additional "facts" the create the meaning, will have the same truth   
   >> values in the two systems.   
   >>   
   >> Thus, since G and the PRR meet that requirement, our knowledge in the   
   >> Meta-System transfers to the base system, but the proof, that uses   
   >> that knowledge does not.   
   >>   
   >>>   
   >>>> There is no "diagonalization" in G. You are confusing different proof.   
   >>>>   
   >>>> The question of G is a pure mathematical question, either a number   
   >>>> does or does not satisfy it.   
   >>>>   
   >>>> In other words, your "logic" says some questions with factual   
   >>>> answers are just wrong.   
   >>>>   
   >>>> In other words, your logic is proven to be self-inconsistant, as   
   >>>> statements provably true are considered to be illogical.   
   >>>>   
   >>>   
   >>> You know that the Liar Paradox: "This sentence is not true"   
   >>> is not a truth bearer. None-the-less when we add one level   
   >>> of indirect reference   
   >>> This sentence is not true: "This sentence is not true"   
   >>> it becomes true.   
   >>>   
   >>   
   >> Yes. So?   
   >>   
   >> The statement G has a truth value, because no number does satisfy the   
   >> PRR, and thus it is true.   
   >>   
   >> It can not be proven in the base system, as the only verification   
   >> would require testing EVERY finite value, of which there are an   
   >> infinite number of them, so it doesn't form a proof, but does   
   >> establish its truth.   
   >>   
   >> This is not true of the Liar's paradox. It just can not have a truth   
   >> value.   
   >>   
   >   
   > It does not have a truth value in the theory:   
   > "This sentence is not true"   
   > because of pathological self-reference   
   >   
   > It does have a truth value in the meta-theory:   
   > This sentence is not true: "This sentence is not true"   
   > because of pathological self-reference has been eliminated.   
      
   In other words, you don't understand what a sentence is or a meta-theory.   
      
   You don't "add" a level of indirect to a statement. Forming a   
   meta-theory may allow you to make ANOTHER statement that has more   
   indirection, but it doesn't change the original statement itself.   
      
   >   
   >> This comes from the fundamental difference between the statements of   
   >> "I am not True" and "I am not Provable".   
   >>   
   >> The first can not have a truth value, as either value creates a   
   >> contradiction.   
   >>   
   >> This is not true of the second. It can not be false, as if it is   
   >> false, then it is provable, so it must be true (as we can only prove   
   >> true statements in a non-contradictory system),   
   >>   
   >> It CAN be True, as there is no actual requirement of True statments   
   >> being provable, as Truth can come out of an infinite number of steps   
   >> of implication.   
   >>   
   >> It also can be a non-truth-bearer if there isn't anything that makes   
   >> it true.   
   >>   
   >> The key to the proof is that the statement isn't just a statement of   
   >> that form, but a statement that must have a truth value as it is a   
   >> statement is about something which follows the law of the excluded   
   >> middle, that only derives that meaning when we add additional   
   >> information from the meta-system.   
   >   
   >   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)