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Mind–body dualism in the classic Cartesian style envisages two non-overlapping domains of particulars (‘‘substances’’) that are, by and large, equal in ontological standing. Mental items are thought to share a certain defining property (‘‘thinking’’or ‘‘consciousness,’’according to Descartes) that excludes the defining property shared by the items on the physical side (‘‘extension,’’according to Descartes). And associated with each domain is a distinct family of properties, mental properties for one and physical properties for the other, in terms of which the particulars within that domain can be exhaustively characterized. We are thus presented with a bifurcated picture of reality: the world consists of two metaphysically independent spheres existing side by side.

But not everyone who accepts a picture like this thinks that the two domains are entirely unrelated; although there are notable exceptions, such as Leibniz and …