Intrinsicality and the classification of uninstantiable properties

It is often held that identity properties like the property of being identical to Paris are intrinsic. It is also often held that, while some logically uninstantiable properties are intrinsic (such as the property of being a non-cubical cube), some logically uninstantiable properties are non-intrinsic (such as the property of being next to a non-cubical cube). The combination of these views, however, raises a problem, since virtually every existing account of intrinsicality fails to analyse a notion of intrinsicality on which both these views are true.In this paper, I argue that, given the orthodox theory of counterlogicals (on which all counterlogicals have the same truth-value), there is no notion of intrinsicality on which both these views are true. If this argument is sucessful, then, at least given orthodoxy about counterlogicals, we face no challenge in analysing a notion of intrinsicality on which both these views are true, since there is no such notion. In addition, if we are also convinced that there is a notion of intrinsicality on which one of these views is true and a notion of intrinsicality on which the other of these views is true, we should hold that there is more than one notion of intrinsicality.