[continued from previous message]   
      
   You will always eventually cycle back to a word you have already used.   
      
   >   
   >>  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. 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.   
      
   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.   
      
   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.   
      
   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)