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RAA is actually viewed with some skepticism in some branches of logic (not so much because it is invalid but because it can be more easily misused in arguments where the underlying assumptions are not apparent). RAA is kind of analogous to the Axiom of Choice if you like — some logicians go out of their way to avoid it.

Not disagreeing with you, just raising a point.



Here's a relevant link:

http://en.wikipedia.org/wiki/Intuitionistic_logic

Incidentally (a further parallel to the Axiom of Choice) Intuitionist Logic is also referred to as Constructive Logic.

http://en.wikipedia.org/wiki/Constructivist_mathematics

One branch of constructivist mathematics eschews the axiom of choice, and all do not allow proof of existence by RAA on non-existence.




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