In his book Personal Agency, E. J. Lowe has argued that a dualist theory of mental causation is consistent with “a fairly strong principle of physical causal closure” and, moreover, that it “has the potential to strengthen our causal explanations of certain physical events.” If Lowe’s reasoning were sound, it would undermine the most common arguments for reductive physicalism or epiphenomenalism of the mental. For it would show not only that a dualist theory of mental causation is consistent with a widely held scientific principle, but also that there is some positive reason for accepting the theory. However, I argue that Lowe’s reasoning is unsound, for it requires that causation both is, and is not, transitive: a contradiction. I conclude that if Lowe succeeds in proving that a dualist theory is consistent with physical causal closure, he fails to show that it serves an explanatory purpose.