Composition as General Identity

Abstract

Here are three main challenges defenders of composition as identity: the syntactic challenge, the semantic challenge, and the discernibility challenge . In this chapter, the author claims all three challenges can be met. The first — van Inwagen’s — is that the view cannot be expressed grammatically in English. The author responds by appealing to free relatives as operators that shift syntactic number while leaving semantic number fixed. The second — Lewis’s — is that no generalization of standard notions of identity can be put in service of composition as identity. The author responds by giving full set-theoretic models of a generalized identity relation that preserves standard singular and plural identity. The author also derives a generalization of the parthood relation that preserves classical extensional mereology, and shows that standard features of plural logic are preserved. The third — Lewis’s — is that one cannot account for apparent failures of Leibniz’s Law. This challenge is met by utilizing two different cover-based semantics for predication in plural logic involving no restrictions on Leibniz’s Law for general identity.

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