On a sufficient condition for hyperintensionality

Let an X/Y distinction be a distinction between kinds of properties, such as the distinctions between qualitative and non-qualitative, intrinsic and extrinsic, perfectly natural and less-than-perfectly natural or dispositional and categorical properties. An X/Y distinction is hyperintensional iff there are cointensional properties P and Q, such that P is an X-property, whereas Q is a Y-property. Many accounts of metaphysical distinctions among properties presuppose that such distinctions are non-hyperintensional. In this paper, I call this presupposition into question. I develop a sufficient condition for the hyperintensionality of X/Y distinctions and argue that this condition is satisfied by a number of standard classifications of properties. It follows that non-hyperintensional analyses of distinctions among properties are harder to defend than is often assumed