In recent years, philosophers bent on defending physicalism have been attracted to the notion that apparently nonphysical features of our world supervene on its physical features. Mental and moral properties, for instance, though not perhaps identifiable with or reducible to physical properties, are thought nevertheless to depend on, and to be determined by, physical properties. More generally, supervenience claims are taken to range over collections or “families” of supervenient properties (A-properties) regarded as depending on distinct families of subvenient B-properties. I shall designate claims of this sort “A/B-supervenience” claims. Sometimes the supervenience relation is distilled into a pair of slogans: “No A-difference without a B-difference”; “Two objects identical with respect to their B-properties must be identical with respect to their A-properties.”

According to Richard Miller, appeals to supervenience on behalf of physicalism are empty; it is “trivially” true that “the nonphysical supervenes on the physical.” Worse,

Miller advances a pair of interesting and important claims. First, the supervenience of the nonphysical on the physical is “trivial.” Second, the supervenience relation is invariably symmetrical: when As supervene on Bs, the supervenience of Bs on As is “all but guaranteed.”