Is the likeness of red apples an additional entity to apples?

Abstract

My aim in this paper is to survey some replies to the challenge raised by Bertrand Russell to resemblance nominalism. The challenge consists in the claim that resemblance nominalism can’t explain the relationship of resemblance between particulars without postulating one universal of resemblance, and if you insist in avoiding postulate such additional entity, then you will fall into a vicious infinite regress. The attempts to deal with the challenge are, on the one hand, to hold that infinite regress isn’t is not vicious and, on the other hand, to hold that there is not an infinite regress at all – thus, the resemblance nominalist would continue justified in not postulating one additional entity beyond particulars. However, these two answers to the challenge, namely in the versions of Armstrong (1989) and Rodriguez-Pereyra (2002), do not seem sound to me, and, to that extent, I’m intuitively willing to accept Russell’s arguments, except what concerns the step in which he argues that if we accept one universal of resemblance, then we would not have any justifications for not accepting the other universals. I think that we have reasons to stay only with one universal of resemblance (mainly by reasons of ontological economy). But before presenting Russell’s challenge and surveying the answers, it is relevant to begin with a contextualization of the problem of the universals.