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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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Graham Cooper

Posts: 4,280
Registered: 5/20/10
Re: I Bet $25 to your $1 (PayPal) That You Can¹t Pr
ove Naive Set Theory Inconsistent

Posted: Feb 28, 2013 2:00 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply


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

----PROVABLE SET THEORY------

A(X) A(P)

E(S) [XeS  <-> P(X)]
<->
~(~E(S) [XeS <-> P(X)]  )


------------------------------------------


My P.S.T. Axiom is actually a Tautology!

A(x) A(p) formula <-> ~~formula


-------------------------------------------

N.S.T the L.H.S. of P.S.T

A(X) A(P)
E(S) [XeS  <-> P(X)]


stipulates what qualifies for a set to exist.

------------------------------------------

P.S.T. is a RESTRICTION that eliminates ASSUMPTION OF RUSSELL'S SET!

A(X) A(P)
E(S) [XeS  <-> P(X)]
<->
~(~E(S) [XeS <-> P(X)]  )

-->

E(RS) [XeRS <-> P(X)]
<->
~(~E(S) [XeS <-> P(X)] )

-->
E(RS) [XeRS <-> P(X)]
<->
~(TRUE)

--> ~EXIST(RS)

***************************

Most other sets like N (as in ZFC)
can safely be assumed in P.S.T.

Herc
--
http://tinyurl.com/BLUEPRINTS-MATHEMATICS




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