
Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Posted:
Oct 9, 2012 6:01 PM


[1] > a proof that Er[ xer <> ~xex ]. IF THAT HAPPENS, THEN YOUR THEORY > IS INCONSISTENT and SOME part of it MUST be abandoned.
So the AXIOMS are a *CONSTRAINT* what formula are allowed.
[2] > (P>Q)>((P^R)>Q) IS A TAUTOLOGY  and there are MANY SIMPLE > "algorithms" that PROVE THAT THAT IS A TAUTOLOGY!
only in FOL.
Axioms (R here) are 2OL or 3OL (Regularity)
so they range over all expressions within their own theory (including P and Q) and LIMIT the usage/range of certain symbols.
[3] >You need ZFC to tell you what sets DO exist!  This validity ONLY >tells you that a certain kind of set canNOT exist!
ALL(set) mem e set IFF p(mem,set) AND EXIST(anotherset) mem e anotherset
This is what ZFC does, limits the relation 'e'.
[4] > The way this paradox can thwart your set theory > IS IF your set theory, in proving that many sets exist, > HAPPENS TO STUMBLE ACROSS > a proof that Er[ xer <> ~xex ]. > IF THAT HAPPENS, THEN YOUR THEORY IS > INCONSISTENT and SOME part of it MUST be abandoned. > In naive set theory, THIS DOES happen > (this set r MUST exist), so naive set > theory is inconsistent (and therefore worthless).
What's the difference between Predicate Calculus and Naive Set Theory.
They are both ZEROAXIOM logic systems.
If NST is inconsistent, what rules in Predicate Calculus are you using to ensure ZFC does not inherit NST inconsistency?
Herc

