  A more promising approach for the non-naturalist would be to offer a positive explanation of supervenience in explicitly non-naturalist terms.  In his systematic defence of non-naturalist moral realism, Russ Shafer-Landau takes just this strategy.  There he argues that although each moral property is distinct from any natural property or properties, still each instantiation of a moral property is fully constituted (or, as he sometimes puts it, ‘realized’) by some concatenation of natural properties (see Shafer-Landau 2003: 76–78). In effect, the idea is to distinguish types from tokens, and argue that the constitution of every token moral property by some concatenation of natural properties is consistent with the non-identity of that moral property with any natural property or combination of natural properties.  Shafer-Landau suggests that this strategy is the most plausible one for explaining supervenience without reduction in the philosophy of mind, and that this should make us optimistic about the prospects of an analogous strategy in the moral case.