  This paper relates both to the metaphysics of probability and to the physics
of time asymmetry. Using the formalism of decoherent histories, it investigates
whether intuitions about intrinsic time directedness that are often associated
with probability can be justified in the context of no-collapse approaches to
quantum mechanics. The standard (two-vector) approach to time symmetry in the
decoherent histories literature is criticised, and an alternative approach is
proposed, based on two decoherence conditions ('forwards' and 'backwards')
within the one-vector formalism. In turn, considerations of forwards and
backwards decoherence and of decoherence and recoherence suggest that a
time-directed interpretation of probabilities, if adopted, should be both
contingent and perspectival.
