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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
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On Feb 4, 3:01 am, Charlie-Boo <shymath...@gmail.com> wrote:
> On Feb 1, 3:35 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:
>
> > On Feb 2, 4:09 am, Charlie-Boo <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.
>
> C-B
>
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
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