I accept that the law of excluded middle might be false. But I draw the line by insisting that it is either true or it's false. There is, after all, no third possibility.
¬¬(A∨¬A) is intuitionistically valid (proof: assume ¬(A∨¬A). A would contradict this, so ¬A, but that also contradicts this). From P∨Q and ¬Q, should get P∨⊥ and thus P (I'm not sure if this part is intuitionistically valid, but seems like it should be).
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I think this is an instance of something much more general: if some proposition is classically provable, then its double negative translation is intuitionistically provable
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Yeah, that second sentence is exactly where I get confused as well.
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