billh04
Posts:
7
Registered:
1/27/11


Re: This is False. 0/0 {x  x ~e x} e {x  x ~e x} A single Principle to Resolve Several Paradoxes
Posted:
Feb 4, 2013 9:32 AM


On Feb 4, 6:26 am, CharlieBoo <shymath...@gmail.com> wrote: > On Feb 3, 11:53 pm, camgi...@hush.com wrote:> On Feb 4, 2:19 pm, CharlieBoo <shymath...@gmail.com> wrote: > > > > > RELATION > > > > p(a, b, e) > > > > If wffs are built on relations then { x  x ~e x } is not a wff > > > because ~e is not a relation. > > > if e(x,y) is a predicate > > then not(e(x,y)) is a predicate > > And more importantly not(e(x,x)) is a predicate (diagonalization.) > > Yes, that is Naïve Set Theory, which is correct. But the IF fails. > > "e(x,y) is a predicate" is not correct due to diagonalization. There > is no Russell Paradox, only Russell's Diagonalization. > > If e(x,y) were a predicate then not(e(x,x)) would be a predicate but > because of diagonalization it is not. >
But, in ZFC, the statement "Ax.not x e x" is true and the statement "Ex. x e x" is false, among many other such statement. Certainly, e(x, y) and e(x, x) must be a predicate in ZFC. How can it not be?

