Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle

Replies: 53   Last Post: Feb 13, 2013 3:53 PM

 Messages: [ Previous | Next ]
 Graham Cooper Posts: 4,495 Registered: 5/20/10
Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle

Posted: Feb 3, 2013 4:03 PM

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

>
> > 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

Date Subject Author
2/1/13 Graham Cooper
2/3/13 Charlie-Boo
2/3/13 Graham Cooper
2/3/13 Charlie-Boo
2/3/13 Graham Cooper
2/3/13 Graham Cooper
2/3/13 Charlie-Boo
2/3/13 Graham Cooper
2/3/13 Charlie-Boo
2/3/13 camgirls@hush.com
2/4/13 Charlie-Boo
2/4/13 billh04
2/4/13 Charlie-Boo
2/4/13 William Hale
2/4/13 Lord Androcles, Zeroth Earl of Medway
2/9/13 Graham Cooper
2/5/13 Charlie-Boo
2/4/13 Graham Cooper
2/5/13 Charlie-Boo
2/5/13 Graham Cooper
2/5/13 Brian Q. Hutchings
2/6/13 Graham Cooper
2/6/13 Charlie-Boo
2/4/13 fom
2/4/13 Charlie-Boo
2/4/13 fom
2/5/13 Charlie-Boo
2/7/13 fom
2/9/13 Charlie-Boo
2/9/13 Graham Cooper
2/11/13 Charlie-Boo
2/10/13 fom
2/10/13 Graham Cooper
2/10/13 fom
2/10/13 Graham Cooper
2/11/13 Charlie-Boo
2/11/13 Charlie-Boo
2/11/13 Charlie-Boo
2/11/13 Graham Cooper
2/13/13 Charlie-Boo
2/11/13 Charlie-Boo
2/11/13 fom
2/5/13 Charlie-Boo
2/5/13 fom
2/6/13 fom
2/11/13 Charlie-Boo
2/11/13 fom
2/13/13 Charlie-Boo
2/13/13 fom
2/4/13 Graham Cooper
2/4/13 Charlie-Boo
2/5/13 Charlie-Boo