The meaning of definite descriptions (like ‘the King of France’, ‘the girl’, etc.) has been a central topic in philosophy and linguistics for the past century. Indefinites (‘Something is on the floor’, ‘A child sat down’, etc.) have been relatively neglected in philosophy, under the assumption that they can be unproblematically treated as existential quantifiers. However, an important tradition in linguistic semantics, drawing from Stoic logic, draws out patterns which suggest that indefinites are not well treated simply as existential quantifiers.
There are two broad classes of response to puzzles like this, e-type and dynamic. These approaches raise deep foundational questions. Inter alia, both require revisionary notions of sentential content and non-classical treatments of the connectives. The proper treatment of (in)definites is thus of crucial importance to philosophical questions about the nature of content, the meaning of (in)definites, and the logic of natural language.
In this paper I develop a new approach to (in)definites. On my theory, contents are static, and indefinites have the truth-conditions of existential quantifiers. But they also have a secondary role: they have a witness presupposition which requires that, if the indefinite’s truth is witnessed by any individual, then some such individual is assigned to their variable. This means that indefinites license subsequent anaphora to their witnesses. Crucially, the connectives in this system are classical. This shows that we can account for the behavior of (in)definites with resources that are much more conservative than those deployed by e-type or dynamic theories—and in particular, with a classical notion of content and connectives.