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 ]
 Lord Androcles, Zeroth Earl of Medway Posts: 11 Registered: 1/1/13
Re: This is False. 0/0 {x | x ~e x} e {x | x ~e x} A single Principle to Resolve Several Paradoxes
Posted: Feb 4, 2013 2:43 PM

"William Hale" wrote in message
news:billh04-154C6A.13334504022013@news.eternal-september.org...

In article
Charlie-Boo <shymathguy@gmail.com> wrote:

> On Feb 4, 9:32 am, billh04 <bill...@gmail.com> wrote:
> > On Feb 4, 6:26 am, Charlie-Boo <shymath...@gmail.com> wrote:
> >
> >
> >
> >
> >
> >
> >
> >
> >

> > > 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

> >
> > > 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.

I (1) don't make the assumption that primitives of logical expressions must
be relations. I (2) assume you mean the relation "~e" to be the set of
ordered pairs (x, y) such that x ~e y.

Since I (3) don't take logical expressions to be sets, I (4) certainly don't
take logical expressions to be relations. I (5) would prefer to say that a
logical expression may sometimes determine a set. But sometimes a
logical expression won't determine a set (e.g., the logical expression
"x ~e x" wont' determine a set.)

Thus, I (6) say that "x ~e x" is a wff, but "x ~e x" cannot be used to
define a relation that corresponds to it.

> It depends on how you define wff,
> including substitution for (aka interpreting) symbols for these
> primitives.

I (7) don't include the substitution for symbols in my consideration of
whether a statement or expression is a wff. For me (8), whether something is
a wff is a syntactical question.

> How do you define it?

Do you want to know or do you want to see if I (9) know? If you want to see
if I (10) know, I (11) will concede that I (12) am not an expert on wffs. I
(13) suspect
that you want to show that it cannot be explained even though people
claim that a wff can be defined.
==============================================================
Thirteen references to yourself.
You really are an opinionated fuckwit, aren't you?
*plonk*

-- This message is brought to you from the keyboard of
Lord Androcles, Zeroth Earl of Medway.
When the fools chicken farmer Wilson and Van de faggot present an argument I
cannot laugh at I'll retire from usenet.

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