Date: Mar 8, 2013 4:44 PM
Author: Charlie-Boo
Subject: Re: I Bet $25 to your $1 (PayPal) That You Can¹t Pr<br> ove Naive Set Theory Inconsistent
On Feb 27, 9:04 pm, Graham Cooper <grahamcoop...@gmail.com> wrote:

> On Feb 28, 9:10 am, Charlie-Boo <shymath...@gmail.com> wrote:

>

> > On Feb 27, 5:24 pm, Rupert <rupertmccal...@yahoo.com> wrote:

> > > For every formula with exactly one free variable phi(x), NST proves

> > {x:phi(x)} exists. It doesn't mean anything to ask whether NST proves

> > the existence of a set not defined by a formula, there is no way to

> > express that in the language of NST.

>

> > No way to express exactly what and how do you know?

>

> > The question is whether you can prove it yourself and that is the

> > subject of the wager. If you cannot, then you don't know if phi(x)

> > exists or not due to possible inconsistency in your definitions, just

> > as there is inconsistency in defining a set to be expressed by x~ex.

>

> > C-B

>

> Possible inconsistency in your definitions??

>

> OK Charlie Boo wins!

>

> No known system has that capability.

>

> Of course, NO PROOF of ANYTHING exists in Charlie's framed world.

>

> Charlie, would you accept the AXIOMS OF PROVABLE_SET_THEORY?

>

> ALL(X) ALL(p(X))

> E(S) S= {x|p(x)}

> IFF

> provable( ALL(X) ALL(p(X))

> E(S) S= {x|p(x)} )

>

> ALL(thm)

> ( not(thm) IFF not(provable(thm) )

>

> ---------------------------

>

> i.e. a Set Exists only if that set not existing is not true

>

> A(X) ALL(P)

>

> E(S) [XeS <-> P(X)]

> <->

> ~(~E(S) [XeS <-> P(X)] )

>

> Since: ~E(RS) [XeRS <-> X~eX]

> The RHS of <-> is FALSE

> so the LHS : EXIST(RS) is also false

>

> Herc

> --www.BLoCKPROLOG.com

Best thing to talk about is Frege's system.

C-B