In this article I examine five kinds of conflicting intuitions about the nature of causality. The viewpoint is that of a probabilistic theory of causality, which I think is the right general framework for examining causal questions. It is not the purpose of this article to defend the general thesis in any depth but many of the particular points I make are meant to offer new lines of defense of such a probabilistic theory. To provide a conceptual framework for the analysis, I review briefly the more systematic aspects of the sort of probabilistic theory of causality I advocate. I first define the three notions of prima facie cause, spurious cause, and genuine cause. The technical details are worked out in an earlier monograph (Suppes 1970) and are not repeated.