Samuel Elgin

ABSTRACT Purity is the principle that fundamental facts only have fundamental constituents. In recent years, it has played a significant (if sometimes implicit) role in metaphysical theorizing. A philosopher will argue that a fact [p]$[p]$ contains a derivative entity and cite Purity as a reason to deny that [p]$[p]$ is fundamental. I argue that recent developments in higher order logic reveal a subtle ambiguity regarding the interpretation of Purity; there are stronger and weaker versions of that principle. Justifications for Purity support only the weaker interpretation, but arguments that rely upon it only succeed if the stronger interpretation holds. Consequently, nearly every metaphysician who has invoked Purity has made a mistake, in that their inferences are not justified by their arguments.

It is often said that there are two varieties of identity theory. Type-identity theorists interpret physicalism as the claim that every property is identical to a physical property, while token-identity theorists interpret it as the claim that every particular is identical to a physical particular. The aim of this paper is to undermine the distinction between the two. Drawing on recent work connecting generalized identity to truth-maker semantics, I demonstrate that these interpretations are logically equivalent. I then argue that each has the resources to resolve problems facing the other.