Resemblances obtain not only between objects but between properties. Resemblances of the latter sort -in particular, resemblances between quantitative properties -prove to be the downfall of David Armstrong's well-known theory of universals. This paper examines Armstrong's efforts to account for such resemblances, and explores several ways one might extend the theory in order to account for quantity. I argue that none succeed.A theory of universals takes at face value the idea that things share properties. Such a theory holds that universals can be instantiated by numerically distinct objects. One of the natural applications of this theory is to explain how two things resemble one another, and thus to offer an answer to the so-called Problem of Resemblance: two things intrinsically resemble one another if and only if they share some of their universals. 1 David Armstrong claims that universals provide the only tenable account of resemblance, because they provide the only reductive account (see Armstrong). 2 But whether universals provide an attractive analysis of resemblance hinges on a crucial question: can a theory of universals account for resemblance relations among properties as well as resemblance relations among objects? Armstrong believes so. He offers an account according to which the more parts two properties share, the more similar they are. 3 This strategy is fatally flawed. As a result, I argue, a theory of universals cannot count an analysis of resemblance among its virtues. Since one of its alleged strengths is an elegant and reductive analysis of resemblance, the failure to produce such an account is a mark against the theory. (I will not be weighing other costs and benefits here.)In this paper I will look at how Armstrong's theory deals with quantitative properties, particularly those of classical mechanics. I do this for three reasons. First, Armstrong himself claims that universals are in a unique position to accommodate quantitative properties. 4 Second, a world where the laws of classical mechanics hold is metaphysically possible, and Armstrong should be able to 1 In this paper I am interested only in intrinsic resemblance, not extrinsic resemblance. For instance, I do not address cases where there is some sense in which two things resemble (perhaps each has the property of being five feet from a poodle), but where this resemblance does not arise from the intrinsic properties of each object alone.

The standard counterexamples to David Lewis’s account of intrinsicality involve two sorts of properties: identity properties and necessary properties. Proponents of the account have attempted to deflect these counterexamples in a number of ways. This paper argues that none of these moves are legitimate. Furthermore, this paper argues that no account along the lines of Lewis’s can succeed, for an adequate account of intrinsicality must be sensitive to hyperintensional distinctions among properties.

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Two grams mass, three coulombs charge, five inches long – these are examples of quantitative properties. Quantitative properties have certain structural features that other sorts of properties lack. What are the metaphysical underpinnings of quantitative structure? This paper considers several accounts of quantity and assesses the merits of each.

Several variants of Lewis's Best System Account of Lawhood have been proposed that avoid its commitment to perfectly natural properties. There has been little discussion of the relative merits of these proposals, and little discussion of how one might extend this strategy to provide natural property-free variants of Lewis's other accounts, such as his accounts of duplication, intrinsicality, causation, counterfactuals, and reference. We undertake these projects in this paper. We begin by providing a framework for classifying and assessing the variants of the Best System Account. We then evaluate these proposals, and identify the most promising candidates. We go on to develop a proposal for systematically modifying Lewis's other accounts so that they, too, avoid commitment to perfectly natural properties. We conclude by briefly considering a different route one might take to developing natural property-free versions of Lewis's other accounts, drawing on recent work by Williams (this volume).