Does Bradley's regress support nominalism?

Abstract

One of the standard arguments against realism about universals is based on Bradley’s regress. According to this argument, realism about universals is committed to a vicious regress of instantiation relations. If realism is false and nominalism the only alternative, then, so the argument concludes, nominalism is correct. The strength of this argumentation depends on three things: (1) that commitment to Bradley’s regress makes a position untenable; (2) that nominalism as the only alternative to realism is not committed to the regress; and, most importantly, (3) that realism is committed to the regress.I have three aims in this paper. My proximate aim is to show that if (3) is correct then (2) is incorrect: if the realist is committed to Bradley’s regress then so is at least one version of nominalism, namely, trope theory. The demonstration that neither theory is committed to the regress (and hence that (3) is false) is my second aim, attained by the proof that these positions have no commitment to a condition which is generally (and rightly!) held to be necessary for Bradley’s regress. As I move along, I shall also claim that there is a widely ignored second condition necessary for the regress, to which – again – neither nominalism nor realism has any commitment. The upshot is this: Bradley’s regress problem is independent of the problem of universals. I conclude with an attempt to explain why many philosophers have been misled into thinking otherwise.