Cosmology, Time's Arrow, and That Old Double Standard

It is widely accepted that temporal asymmetry is largely a cosmological problem; the task of explaining temporal asymmetry reduces in the main to that of explaining an aspect of the condition of the early universe. However, cosmologists who discuss these issues often make mistakes similar to those that plagued nineteenth century discussions of the statistical foundations of thermodynamics. In particular, they are often guilty of applying temporal "double standards" of various kinds---e.g., in failing to recognise that certain statistical arguments apply with equal force in either temporal direction. This paper aims to clarify the issue as to what would count as adequate explanation of cosmological time asymmetry. A particular concern is the question whether it is possible to explain why entropy is low near the Big Bang without showing that it must also be low near a Big Crunch, in the event that the universe recollapses. I criticise some of the objections raised to this possibility, showing that these too often depend on a temporal double standard. I also discuss briefly some issues that arise if we take the view seriously. (Could we observe a time- reversing future, for example?)