If time necessarily has a direction it will not be possible to think coherently of a world of which it would not be appropriate to use a directed order relation in giving the temporal order of things in that world. The incompatibility of judgments of temporal order suggested by memory impressions with well-entrenched causal regularities would also provide such grounds. The upshot of this is that there is some non-contingent link between temporal order and memory impressions. Consequently, the task is to explicate some notion of temporal order that can be appealed to in vindicating claims of causal connection. The ability of conscious beings in the fantasy situation to impute an undirected order of events would depend on their ignorance of things at a temporal distance in either direction from the present. A theory providing a physical correlate for the before relation might involve the claim that in the absence of directed time, consciousness could not arise.