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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 ]
 Charlie-Boo Posts: 1,618 Registered: 2/27/06
Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle

Posted: Feb 4, 2013 9:58 AM

On Feb 4, 9:32 am, billh04 <bill...@gmail.com> wrote:
> On Feb 4, 6:26 am, Charlie-Boo <shymath...@gmail.com> wrote:
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> > On Feb 3, 11:53 pm, camgi...@hush.com wrote:> On Feb 4, 2:19 pm, Charlie-Boo <shymath...@gmail.com> wrote:
>
> > > > > RELATION
> > > > > p(a, b, e)

>
> > > > If wffs are built on relations then { x | x ~e x } is not a wff
> > > > because ~e is not a relation.

>
> >  >  if  e(x,y) is a predicate
> >  >  then  not(e(x,y)) is a predicate

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> > And more importantly not(e(x,x)) is a predicate (diagonalization.)
>
> > Yes, that is Naïve Set Theory, which is correct.  But the IF fails.
>
> > "e(x,y) is a predicate" is not correct due to diagonalization.  There
> > is no Russell Paradox, only Russell's Diagonalization.

>
> > If e(x,y) were a predicate then not(e(x,x)) would be a predicate but
> > because of diagonalization it is not.

>
> But, in ZFC, the statement "Ax.not x e x" is true and the statement
> "Ex. x e x" is false, among many other such statement. Certainly, e(x,
> y) and e(x, x) must be a predicate in ZFC. How can it not be?

In this case, because primitives of logical expressions must be
relations and ~e is not a relation. It depends on how you define wff,
including substitution for (aka interpreting) symbols for these
primitives. How do you define it?

C-B

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