
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 4:18 PM


On Feb 3, 4:03 pm, Graham Cooper <grahamcoop...@gmail.com> wrote: > 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.
The problem isn't with the connectives. What can X be for starters  the most primitive wffs from which we build others?
CB
> 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

