
Re: This is False. 0/0 {x  x ~e x} e {x  x ~e x} A single Principle to Resolve Several Paradoxes
Posted:
Feb 3, 2013 12:01 PM


On Feb 1, 3:35 pm, Graham Cooper <grahamcoop...@gmail.com> wrote: > On Feb 2, 4:09 am, CharlieBoo <shymath...@gmail.com> wrote: > > > > > > > > > > > There is a peculiar parallel between Semantic Paradoxes, Set Theory > > Paradoxes and ordinary formal Arithmetic. > > > Consider the following 3 pairs of expressions in English, Set Theory > > and Mathematics: > > > A > > This is false. > > This is true. > > > B > > 1/0 > > 0/0 > > > C > > {x  x ~e x} e {x  x ~e x} > > {x  x e x} e {x  x ~e x} > > {x  x ~e x} e {x  x e x} > > {x  x e x} e {x  x e x} > > > A is the Liar Paradox, B is simple Arithmetic, and C is Russell?s > > Paradox. > > This is Russells Paradox > > {x  x ~e x} e {x  x ~e x} > <> > {x  x ~e x} ~e {x  x ~e x} > > To make a consistent set theory the formula { x  x ~e x } > must be flagged somehow.
How do you define a wff  precisely? That is the problem. Frege was right, Russell was wrong, and all you need is an exact (formal) definition of wff.
CB
> e.g.in ZFC > > { x  x e y } IFF E(z) y C z > > Axiom of Specification. > > there is no z such that RS C z > so RS is impossible to define in ZFC. > > I'm working on an automated Proof By Contradiction of RS. > > You need to forward chain MODUS PONENS > which is new to PROLOG LOGIC since it requires > depth limiting. (which is simple enough and we've > got DL working on backward chaining MP already) > > Herc > www.BLoCKPROLOG.com

