  It is widely accepted that a Born probability of 1 is sufficient for the
existence of a corresponding element of reality. Recently Vaidman has extended
this idea to the ABL probabilities of the time-symmetrized version of quantum
mechanics originated by Aharonov, Bergmann, and Lebowitz. Several authors have
objected to Vaidman's time-symmetrized elements of reality without casting
doubt on the widely accepted sufficiency condition for `ordinary' elements of
reality. In this paper I show that while the proper truth condition for a
quantum counterfactual is an ABL probability of 1, neither a Born probability
of 1 nor an ABL probability of 1 is sufficient for the existence of an element
of reality. The reason this is so is that the contingent properties of
quantum-mechanical systems are extrinsic. To obtain this result, I need to
discuss objective probabilities, retroactive causality, and the objectivity or
otherwise of the psychological arrow of time. One consequence of the extrinsic
nature of quantum-mechanical properties is that quantum mechanics presupposes
property-defining actual events (or states of affairs) and therefore cannot be
called upon to account for their occurrence (existence). Neither these events
nor the correlations between them are capable of explanation, the former
because they are causal primaries, the latter because they are fundamental:
there are no underlying causal processes. Causal connections are something we
project onto the statistical correlations, and this works only to the extent
that statistical variations can be ignored. There are nevertheless important
conclusions to be drawn from the quantum-mechanical correlations, such as the
spatial nonseparability of the world.
