Armstrong on Quantities and Resemblance

Abstract

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.

Two Conceptions of Similarity

“…First, some authors maintain that as well as resemblances between particulars, there are also resemblance between the (sparse) properties themselves -red, for example, is supposed to resemble orange more than blue (Armstrong, 1978b, 101-15). The topic of similarity between properties raises many questions which are closely related to the questions raised in this paper (see, for example, Eddon, 2006). Nevertheless, this paper is exclusively concerned with similarity between particulars.…”

The Partial Identity Account of Partial Similarity Revisited

“…Consider our two apples: according to the high-order properties account, the similarity between them with respect to colour is partial because their two instances of green have all the same higher-order characteristics except for the fact that one has the property of being a determinate of Greenness with intensity x (or, at any rate, some property determining its being the specific determinate that it is) and the other the property of being a determinate of Greenness with intensity y (or, at any rate, some property determining the specific determinate that it is). Against this view, it is usually pointed out (e.g., in Pautz (1997;109) and Eddon (2007;386)) that the higher order account of partial similarity was discarded by the foremost contemporary defender of universals, David Armstrong, on the basis that it is ontologically inflationary and, since it assumes that certain properties are instantiated necessarily by first-order universals, it conflicts with the combinatorial view of possibility that Armstrong endorses. 1 As a matter of fact, though, the problems for the high-order properties account of partial similarity are even worse: for, if universals (or, perhaps better, their instances) necessarily instantiate certain higher-order universals determining their exact 'qualitative content', one may wonder what qualitative content (if any) the universal has in itself.…”

“…Structural universals, instead, involve monadic universals standing in certain relations, and result from a process of mereological composition of material parts. That is, what Eddon (2007;387) calls the 'constituency principle' holds, according to which a universal x is a constituent of universal y if and only if every object in every possible world that instantiates y has some proper part that instantiates x. This means that the complexity of structural universals directly mirrors that of the objects exemplifying them.…”

A Companion to Philosophy in Australia and New Zealand (Second Edition)

“…Mass universals, for example, resemble each other. armstrong (1978: 120-7, 1989a: 105-6) accounts for this resemblance in terms of mass universals sharing constituents: however, as Pautz (1997) and Eddon (2007) have argued, this account has serious problems. as an alternative, bigelow (1988) and bigelow and Pargetter (1989) have defended a relational account of quantities (cf.…”