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Topic:
I Bet $25 to your $1 (PayPal) That You Can¹t Pr ove Naive Set Theory Inconsistent
Replies:
4
Last Post:
Mar 8, 2013 4:44 PM




Re: I Bet $25 to your $1 (PayPal) That You Can¹t Pr ove Naive Set Theory Inconsistent
Posted:
Mar 8, 2013 4:44 PM


On Feb 27, 9:04 pm, Graham Cooper <grahamcoop...@gmail.com> wrote: > On Feb 28, 9:10 am, CharlieBoo <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. > > > CB > > 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= {xp(x)} > IFF > provable( ALL(X) ALL(p(X)) > E(S) S= {xp(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.
CB



