Unstructured Purity

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 contains a derivative entity and cite Purity as a reason to deny that 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.