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Re: I Bet $25 to your $1 (PayPal) That You Can¹t Pr
ove Naive Set Theory Inconsistent
Posted:
Mar 9, 2013 8:50 PM
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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
> about why you think
> 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
http://blockprolog.com/EX-CONTRADICTIONE-SEQUITUR-QUODLIBET.png
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
remove Ex-Contradiction-Sequitur-Quodlibet.
2+2=5 ?
NO
Herc
--
http://blockprolog.com/EX-CONTRADICTIONE-SEQUITUR-QUODLIBET.png
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