To the question, Does time have an arrow?, it seems that physics alone can give no unequivocal answer at the present. In this situation, and especially if we believe that time should not be reified, it is useful to consider what bearing the facts of consciousness may have on the issue. Perception and cognition, it is pointed out, are irreversible in an absolute sense. Also the criterion of before and after which is offered by consciousness has a logical primacy over any criterion arising from science. These points give support to the view that time should be regarded as anisotropic. They indicate further that it is reasonable to speak of the direction of time. These considerations, it is suggested, should not lightly be set aside for the sake of symmetry in physics. To attribute any degree of reality to a reverse time direction which would make us "unobservers", rather than "observers", would create endless paradox and absurdity.