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Armstrong on Quantities and Resemblance Philosophical Studies

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. 2 See Armstrong (1978) and (1989a). 3 See Armstrong (1988) and (1989a, pg. 101-105). 4 See Armstrong (1989a, pg. 101).