Sparseness, Immanence, and Naturalness∗

In the past fteen years or so there has been a lot of attention paid to theo-ries of “sparse ” universals, particularly because of the work of D. M. Armstrong. These theories are of particular interest to those of us concerned with the dis-tinction between natural and non-natural properties, since, as David Lewis has observed, it seems possible to analyze naturalness in terms of sparse universals. Moreover, Armstrong claims that we should conceive of universals as being “immanent ” as opposed to “transcendent”, and if universals are immanent then, as we will see, there is pressure to admit they are sparse as well. But I will argue that neither of these alleged reasons to accept a sparse conception of universals succeeds: the outlook for a fully general analysis of naturalness in terms of universals is not good, and the apparent advantages of immanence over transcendence are illusory. 1. Sparse Universals and Naturalness We’ll need a specic conception of the claim that universals are abundant. It will be convenient to speak David-Lewis-style, of merely possible objects, each of which inhabits exactly one possible world. (I assume this talk must be ultimately reduced in some way; moreover, the assumption of world-bound individuals plays no role in my arguments and is made purely for convenience.) An L-property is dened as a class of possible objects, and an n-place L-relation is dened as a class of n-tuples of possible objects. Let us say that universal U and L-property (n-place L-relation) P correspond just when P is the class of (n-tuples of) U’s instances; we may then take the claim that universals are abundant to mean that every L-property or L-relation has a corresponding universal. In contrast, on a “sparse ” view of universals, only a select minority of the L-properties have corresponding universals. At the heart of Armstrong’s Universals and Scientic Realism is his rejection of the idea that there is a universal for ∗This paper is partially based on chapter 6 of my doctoral dissertation (Sider, 1993). I woul