The attempt to reconcile the counterintuitive features of quantum mechanics with the hypothesis that it is in principle a complete description of the physical world, even at the level of everyday objects. A paradox arises because, at the atomic level where the quantum formalism has been directly tested, the most natural interpretation implies that where two or more different outcomes are possible it is not necessarily true that one or the other is actually realized, whereas at the everyday level such a state of affairs seems to conflict with direct experience.