The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Graham Cooper

Posts: 4,495
Registered: 5/20/10
Re: I Bet $25 to your $1 (PayPal) That You Can¹t Pr
ove Naive Set Theory Inconsistent

Posted: Feb 27, 2013 9:04 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Feb 28, 9:10 am, Charlie-Boo <> wrote:
> On Feb 27, 5:24 pm, Rupert <> 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)}
provable( ALL(X) ALL(p(X))
E(S) S= {x|p(x)} )

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


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


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


Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.