Untyped Pluralism

In the semantic debate about plurals, pluralism is the view that a plural term denotes some things in the domain of quantification and a plural predicate denotes a plural property, that is, a property that can be instantiated by many things jointly. According to a particular version of this view, untyped pluralism, there is no type distinction between objects and properties. In this article, I argue against untyped pluralism by showing that it is subject to a variant of a Russell-style argument put forth by Timothy Williamson and that it clashes with a plural version of Cantor's theorem. I conclude that pluralists should postulate a type distinction between objects and properties.