 Perhaps non-cognitivists (or “quasi-realists,” in Blackburn’s favored terminology; see Blackburn 1984) and error theorists reap the greatest dialectical dividends from reflection on how we might explain supervenience. The standard view is that the non-cognitivist’s explanatory task differs from the explanatory task facing both naturalist and non-naturalist forms of cognitivism. Whereas the naturalist and non-naturalist must explain a metaphysical relationship between two potentially distinct sets of properties the non-cognitivist instead needs only to explain the sensibility of a practice of moralizing governed by a supervenience constraint. Since one of the main points of moral discourse is to recommend options on the basis of their natural properties it is easy enough to see why such a constraint is sensible. To abandon that constraint would be to abandon the project of moralizing so understood. For if our practice of moralizing were not to include such a constraint then you could evaluate options differently even if they were identical in all their natural properties and this would make it hard to see in what sense options were being recommended on the basis of their natural properties. Since for the non-cognitivist there are no moral properties (from the perspective of serious metaphysics, anyway; but we can still “speak with the vulgar” as if there were such properties) we can in the same way derive that our moralizing must not allow that two items identical in their non-moral properties might still differ morally. For the point of moralizing is to recommend options on the basis of their natural properties and all the natural properties are non-moral according to the non-cognitivist.  One worry about this line of argument is that quasi-realist expressivism, if successful, allows us to make all of the original and seemingly metaphysically problematic claims about moral reality in the only sense in which those claims can be understood.  In that case, it is not entirely obvious why the quasi-realist does not, at the end of the day, face exactly the same explanatory burden as the non-naturalist realist (see Street 2011).  Perhaps quasi-realists can avoid this specific worry about self-defeat by holding that moral properties are, after all, natural properties on their view.  The view can remain expressivist so long as it also maintains that taking a view about just which natural property is identical to a given moral property is constituted by adopting suitable non-cognitive attitudes.