Composition as identity, Leibniz’s Law, and slice-sensitive emergent properties

Abstract

Moderate composition as identity holds that there is a generalized identity relation, “being the same portion of reality,” of which composition and numerical identity are distinct species. Composition is a genuine kind of identity; but unlike numerical identity, it fails to satisfy Leibniz’s Law. A composite whole and its parts differ with respect to their numerical properties: the whole is one; the parts (collectively) are many. Moderate composition as identity faces the challenge: how, in the absence of Leibniz’s Law, can one characterize what counts as a genuine kind of identity? This paper explores a promising answer: a genuine kind of identity must satisfy a version of Leibniz’s Law restricted to properties that ascribe qualitative character. Strong composition as identity holds that there is only one identity relation, that it satisfies Leibniz’s Law, and that the parts are identical with the whole that they compose. Strong composition as identity faces the challenge of showing that numerical properties do not provide counterexamples to Leibniz’s Law, and doing so in a way that is compatible with the framework of plural logic that is needed to formulate the theory. The most promising way to do this is to hold that plural logic is fundamental at the level of our representations, but not fundamental at the level of being. At the level of being, portions of reality cannot be characterized as either singular or plural. It turns out that the proposed moderate theory and the proposed strong theory are one and the same. In spite of its many attractions, I reject it. The main issue has to do with whether slice-sensitive emergent properties are possible. I argue that they are, making use both of specific examples and general principles of modal plenitude. I do not claim that my arguments are irresistible. But they cannot be evaded as easily as a related argument against strong composition as identity given by Kris McDaniel. I critically examine McDaniel’s argument to pave the way for my own.