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Topic: I Bet \$25 to your \$1 (PayPal) That You Can¹t Pr
ove Naive Set Theory Inconsistent

Replies: 17   Last Post: Mar 11, 2013 5:15 PM

 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: Mar 9, 2013 8:50 PM

On Mar 10, 9:54 am, George Greene <gree...@email.unc.edu> wrote:
> YOU will have A MUCH HARDER time proving that Frege's system is not
> INCONSISTENT,
> in a way most EASILY shown by what you will ALSO have a hard time
> proving is not RUSSELL'S PARADOX.
> Since Frege and Russell themselves BOTH PROVED this, we remain unclear
> you have discovered some FLAW in THEIR reasoning, or why you ask
> ANYone here to present some!

I think if we could see a contradictory system in action proving a
false formula

e.g. 2+2=5?
NO

then we entered in RUSSELLS SET

if [ ! [ e X X ] ] [ e X rs ]
if [ e X rs ] [ ! [ e X X ] ]

2+2=5?
YES <---- FROM A CONTRADICTION YOU CAN PROVE ANYTHING

then it would be clear by actual application
that Naive Set Theory is inconsistent.

I use a variant of N.S.T. in Block Prolog

DEFINE PREDICATE NAT
nat(0)
nat(s(X)) <- nat(X).

DEFINE SET NATS
e( A , nats ) <- nat(A).

Then, we could try to fix how sets are defined or use other methods to

2+2=5 ?
NO

Herc
--

Date Subject Author
3/9/13 Graham Cooper
3/9/13 Charlie-Boo
3/9/13 george
3/10/13 Graham Cooper
3/10/13 Charlie-Boo
3/10/13 Charlie-Boo
3/10/13 Graham Cooper
3/10/13 Graham Cooper
3/10/13 Charlie-Boo
3/10/13 Charlie-Boo
3/10/13 Graham Cooper
3/11/13 Charlie-Boo
3/11/13 Graham Cooper
3/11/13 Charlie-Boo
3/11/13 William Elliot
3/11/13 Charlie-Boo