We defend Jaegwon Kim’s ‘causal inheritance’ principle from an objection raised by Jurgen Schröder. The objection is that the principle is inconsistent with a view about mental properties assumed by Kim, namely, that they are second-order properties. We argue that Schröder misconstrues the notion of second-order property. We distinguish three notions of second-order property and highlight their problems and virtues. Finally, we examine the consequence of Kim’s principle and discuss the issue of whether Kim’s ‘supervenience argument’ generalizes to all special (...) sciences or not. (shrink)