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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

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Charlie-Boo

Posts: 1,588
Registered: 2/27/06
Re: I Bet $25 to your $1 (PayPal) That You Can¹t Pr
ove Naive Set Theory Inconsistent

Posted: Mar 8, 2013 4:44 PM
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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



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