 Is supervenience a form of entailment? The two relations are logically similar in certain ways. The entailment relation is reflexive, transitive, and non-symmetric, and so is supervenience. Supervenience is reflexive: for any set of properties A, there cannot be an A-difference without an A-difference (see, e.g., Kim 1984). It is also transitive: if A-properties supervene on B-properties, and B-properties supervene on C-properties, then A-properties supervene on C-properties. However, supervenience is neither symmetric nor asymmetric; it is non-symmetric. Sometimes it holds symmetrically. Every reflexive case of supervenience is trivially a symmetric case; consider also the case of the volume and surface area of perfect spheres mentioned in  Section 3.1.  And sometimes it holds asymmetrically. For example, while the mental may supervene on the physical, the physical does not supervene on the mental. There can be physical differences without mental differences. One uncontroversial way to see this is to note that radically physically different things—a washing machine and a paper bag, say—can be mentally just alike in virtue of lacking mental properties altogether. Thus supervenience, like entailment, is reflexive, transitive, and non-symmetric.