Commentary: David Lewis, Parts of Classes, Oxford: Blackwell, 1991

Abstract

David Lewis‘s Parts of Classes is a great book, in all respects. But one of its most interesting thesis, in my mind, is not its core thesis that standard set theory — ZFC — reduces to classical mereology + plural quantification + a primitive singleton-relation, but rather its sub-thesis of how to understand classical mereology, what Lewis calls the thesis of Composition as Identity: (CAI): a whole is the same portion of reality as its many parts taken together; it is them collectively, they collectively are it. CAI is needed as an assumption for the core thesis of Parts of Classes — the reduction of ZFC — on pain of it being unmotivated.1 But CAI is the most interesting in its own right. It is also as such it is presented by Lewis, and received in the literature. In what follows, I critically assess CAI as Lewis presents it in Parts of Classes. I first argue that Lewis‘s presentation of CAI has been misunderstood in the literature (section 1). I then argue that the best (if not the only) way to understand it entails a slightly revisionary semantics for a certain form of predication (section 2). I finally end by showing that this might create more trouble than it solves for Lewis (section 3).