Talk:Axiom independence

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Unless I'm misunderstanding what they're saying, the second section of this article is just plain wrong. For all theorems of logic Q, if P then Q is true, and if -P then Q is also true. There is no contradiction involved because the antecedent of a conditional is not necessarily true; all the truth of both conditionals would appear to prove is that Q is a theorem of logic. The method to show independence is usually, as I understand it, to find an interpretation of the axioms that renders the axiom in question false, but the rest true. I'm putting up a dubious flag. Am I mistaken? --M.C. ArZeCh (talk) 12:52, 15 November 2009 (UTC)[reply]

I agree that this articel is/seems wrong. One way to prove independence is to show that there is a model in which P and Q hold and there is another model in which P and (not Q) hold. Hence Q does not necessarily hold when P holds. Remember that if P is true then (not P) => "anything" is also true. Independence means that from P (or not P) you can't prove either Q or (not Q). Odonovanr (talk) 08:33, 11 December 2009 (UTC)[reply]

The section is indeed just plain wrong, and has been for half of a year. I've taken a stab at rewriting the section. TotientDragooned (talk) 20:23, 29 June 2010 (UTC)[reply]