Provocatively, David Armstrong's properties are supposed to be both universals and spatio-temporal. What does this amount to? I consider four of Armstrong's views, in order of ascending plausibility: (1) the exemplification account, on which universals are exemplified by space-times; (2) the location account, on which universals are located at space-times; (3) the first constituent account, on which spatio-temporal relations are elements of what I call the form of time; and, the true view, (4) the second constituent account, on which universals (...) are spatio-temporal only 'derivatively' by being constituents of states of affairs which are so 'primarily'. The first two accounts are rejected because they entail that space-times must be substantival. In making plausible the second constituent account, I distinguish primitive and derivative spatio-temporality. Something is primitively spatio-temporal when it is at a space-time, or stands in spatio-temporal relations. Something is derivatively spatio-temporal when it is a constituent of something primitively spatio-temporal. (shrink)

Peter Geach proposed a substitutional construal of quantification over thirty years ago. It is not standardly substitutional since it is not tied to those substitution instances currently available to us; rather, it is pegged to possible substitution instances. We argue that (i) quantification over the real numbers can be construed substitutionally following Geach's idea; (ii) a price to be paid, if it is that, is intuitionism; (iii) quantification, thus conceived, does not in itself relieve us of ontological commitment to real (...) numbers. (shrink)

I show that Armstrong’s view of laws as second-order contingent relations of ‘necessitation’ among categorical properties faces a dilemma. The necessitation relation confers a relation of extensional inclusion (‘constant conjunction’) on its relata. It does so either necessarily or contingently. If necessarily, it is not a categorical relation (in the relevant sense). If contingently, then an explanation is required of how it confers extensional inclusion. That explanation will need to appeal to a third-order relation between necessitation and extensional inclusion. The (...) same dilemma reappears at this level. Either Armstrong must concede that some properties are not categorical but have essential powers – or he is faced with a regress. (shrink)

Is the relation between properties and the causal powers they confer necessary, or contingent? Necessary, says Sydney Shoemaker, on pain of skepticism about the properties. Contingent, says David Lewis, swallowing the skeptical conclusion. I shall argue that Lewis is right about the metaphysics, but that Shoemaker and Lewis are wrong about the epistemology. Properties have intrinsic natures (quiddities), which we can know.

Scientific essentialism aims to account for the natural laws' special capacity to support counterfactuals. I argue that scientific essentialism can do so only by resorting to devices that are just as ad hoc as those that essentialists accuse Humean regularity theories of employing. I conclude by offering an account of the laws' distinctive relation to counterfactuals that portrays laws as contingent but nevertheless distinct from accidents by virtue of possessing a genuine variety of necessity.