If categorical properties are physical under the object conception but not under the theory conception, the two conceptions pick out different classes of properties.
Do these conceptions characterize the same class of properties? There are a number of different possibilities here, but one that has received some attention in the literature is that physical theory only tells us about the dispositional properties of physical objects, and so does not tell us about the categorical properties, if any, that they have — a thesis of this sort has been defended by a number of philosophers, among them Russell (1927), Armstrong (1968), Blackburn (1992) and Chalmers (199