I still don't really understand what contextuality means in reference to quantum mechanics. If someone could give a clear definition that would be great. It sounds like it means you can't always relate the state of a system to its wavefunction or something? That confuses me since it seems to violate quantum mechanics. So a clear explanation would be great.
The question is then, does any interpretation of quantum mechanics require us to accept contextuality? This paper seems to claim yes, but I don't know enough to evaluate it, so would appreciate a professional's eye: http://arxiv.com/abs/1006.0500
(This is a follow up on a previous question: What combinations of realism, non-locality, and contextuality are ruled out in quantum theory? )