```Date: Feb 27, 2013 9:04 PM
Author: Graham Cooper
Subject: Re: I Bet \$25 to your \$1 (PayPal) That You Can¹t Pr<br>	ove Naive Set Theory Inconsistent

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)}   IFFprovable( 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 trueA(X) ALL(P)E(S) [XeS  <-> P(X)]<->~(~E(S) [XeS <-> P(X)]  )Since:   ~E(RS) [XeRS <-> X~eX]The RHS of <-> is FALSEso the LHS : EXIST(RS) is also falseHerc--www.BLoCKPROLOG.com
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