In "Supervenience, Necessary Coextension, and Reducibility" (Philosophical Studies 49, 1986, 163-176), among other results, I showed that weak or ordinary supervenience is equivalent to Jaegwon Kim's strong supervenience, given certain assumptions: S4 modality, the usual modal conception of properties as class-concepts, and diagonal closure or resplicing of the set of base properties. This last means that any mapping of possible worlds into extensions of base properties counts itself as a base property. James Van Cleve attacks the modal conception of (...) property and diagonal closure. To me it seems desperate to reject diagonal closure merely in order to save supervenience-materialism. But I concede that it may be unacceptable in the context of a sparser theory of properties. (shrink)

This paper provides an account of the closure conditions that apply to sets of subvening and supervening properties, showing that the criterion that determines under which property-forming operations a particular family of properties is closed is applicable both to the finitary and to the infinitary case. In particular, it will be established that, contra Glanzberg, infinitary operations do not give rise to any additional difficulties beyond those that arise in the finitary case.