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AntonioLao · 04-27-2005, 02:33 PM

as an alternate idea to Russell's paradox, see Godel's theorem at
http://mathworld.wolfram.com/Goedels...ssTheorem.html

A statement sometimes known as Gödel's second incompleteness theorem states that if number theory is consistent, then a proof of this fact does not exist using the methods of first-order predicate calculus. Stated more colloquially, any formal system that is interesting enough to formulate its own consistency can prove its own consistency iff it is inconsistent.

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AntonioLao Raider of the lost time Status: Offline Posts: 5,613 Thanks Given: 790 Thanked 180x in 174 Posts Join Date: Nov 2003 Rep Power: 80	04-27-2005, 02:33 PM as an alternate idea to Russell's paradox, see Godel's theorem at http://mathworld.wolfram.com/Goedels...ssTheorem.html A statement sometimes known as Gödel's second incompleteness theorem states that if number theory is consistent, then a proof of this fact does not exist using the methods of first-order predicate calculus. Stated more colloquially, any formal system that is interesting enough to formulate its own consistency can prove its own consistency iff it is inconsistent.