```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.comBest thing to talk about is Frege's system.C-B
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