
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 9:58 AM


On Feb 4, 9:32 am, billh04 <bill...@gmail.com> wrote: > 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?
In this case, because primitives of logical expressions must be relations and ~e is not a relation. It depends on how you define wff, including substitution for (aka interpreting) symbols for these primitives. How do you define it?
CB

