Necessarily, no two situations can differ normatively without differing in some of their descriptive or non-normative properties. Properly understood, this so-called “supervenience” thesis is extremely plausible, perhaps even a priori true. A longstanding challenge for so-called “non-naturalist” theories of the meanings of normative predicates is to explain supervenience. Non-naturalist theories hold that normative predicates refer to irreducible non-natural normative properties. The worry is that non-naturalism threatens to make supervenience mysterious. For why should one set of properties (the normative ones), which are utterly irreducible to some other set of properties (the descriptive and non-normative ones), necessarily supervene in this way?

In this paper, I begin by sharpening this challenge. In particular, I suggest that the problem is not so much explaining why supervenience is true, but explaining how there could be any non-natural normative properties, given supervenience. I explore this challenge in the context of Ralph Wedgwood’s recent and sophisticated defense of his own novel form of non-naturalism. Although Wedgwood engages more directly with this challenge, and with more acuity and sophistication than most non-naturalists to date, I argue that his approach ultimately is implausible. Non-naturalists still cannot plausibly explain supervenience.