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Re: If ZFC is a FORMAL THEORY ... then what is THEOREM 1 ?
Posted:
Oct 9, 2012 6:01 PM
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[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 ZERO-AXIOM logic systems.
If NST is inconsistent, what rules in Predicate Calculus
are you using to ensure ZFC does not inherit NST inconsistency?
Herc
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