
Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Posted:
Oct 14, 2012 9:21 PM


> LHS & (LHS > (a&b>c)) > a&b>c > > to derive models of backward chainable embedded theories that are > recursively provable back to the axioms! >
BINARY MODUS PONENS
a & b & (a&b)>c > c
This not only WORKS! It derives all proofs!
PROOF = backward chainable binary directed acylic graph
You're still stuck on the 'CLASSIC THEOREM'!
******** 10 YEARS DEBUGGING TO FIX THIS **********
> NOT(PA  P) & NOT(PA  ~P). > That is the classical theorem. Duh. > [...] > >> I don't see your point. The theorem says that PA can not decide a > >> particular formula. > > no, a particular wff (conditions apply) > When I say "formula", I mean "WFF". I have no reason to talk about > nonwellformed formulas.
That's why your proof is wrong.  [ERROR 1] By WFF you mean it has a single reduction tree in predicate calculus from sub predicates and atomic formula, giving it a unique interpretation. So you have limited the scope of your proof to boolean formula (true or false).  [ERROR 2] THEN: YOU START ADDING FORMULA AT WILL. "WE CAN CONSTRUCT ANY FORMULA AND TRY TO ADD IT TO THE THEORY" ERROR!
PA  P This is using an axiomless or inconsistent theory CONTRADICTION  ANYTHING  [VALID STEP] Because P is "true" by some rudimentary reductions (P can't be false) NOT( PA  P ) NOT( PA  ~P )  [ERROR 3] P <> NOT( PA  P ) so P is TRUE (in PA)  [ERROR 4] P is a WFF in PA AND P is TRUE in PA > P is a missing theorem of PA
You EQUATE WFF + TRUE > THEOREM  [ERROR 5] Because: (P > Q) > (P ^ AXIOM) > Q is true for 0 order terms (not formula with quantifiers) You conclude adding AXIOMS to PA could never filter out the Godel Statement and call it MONOTONIC LOGIC! 
Herc

