In recent years Jaegwon Kim has offered an argument – the ‘supervenience argument’ – to show that supervenient mental properties, construed as second- order properties distinct from their first-order realizers, do not have causal powers of their own. In response, several philosophers have argued that if Kim’s argument is sound, it generalizes in such a way as to condemn to causal impotency all properties above the level of basic physics. This paper discusses Kim’s supervenience argument in the context of his (...) reply to this so-called ‘generalization argument’. In particular, the paper focuses on the level/order distinction, to which Kim appeals in his reply to the generalization argument, and on the relation between this distinction and two varieties of functionalism, ‘realizer’ vs. ‘role’ functionalism. The author argues that a proper analysis of the notions of levels and orders undermines Kim’s response to the generalization argument, and suggests that Kim’s reductionist strategy for vindicating the causal powers of mental properties is better served if mental properties are construed as first-order properties, as realizer-functionalism recommends. (shrink)