
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 4:03 PM


On Feb 4, 3:01 am, CharlieBoo <shymath...@gmail.com> wrote: > 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 >
in the usual manner by Syntactic construction.
IF X is a WFF THEN ALL(Y) X is a WFF
and so on.
However, the mistake in Godel's proof is to assume all WFF constructed_to_have_a_true_or_false_value HAVE a true or false value.
With Sets, it's easy to spot a naive construction, with formula, people take the term WELL FORMED for granted.
A 2nd parse is required.
Herc  www.BLoCKPROLOG.com

