Does Vagueness Exclude Knowledge?

On two standard views of vagueness, vagueness as to whether Harry is bald entails that nobody knows whether Harry is bald—either because vagueness is a type of missing truth, and so there is nothing to know, or because vagueness is a type of ignorance, and so even though there is a truth of the matter, nobody can know what that truth is. Vagueness as to whether Harry is bald does entail that nobody clearly knows that Harry is bald and that nobody clearly knows that Harry is not bald. But it does not entail that nobody knows that Harry is bald or that nobody knows that Harry is not bald. Hence, the two standard views of vagueness are mistaken. Where exactly does your chin meet your cheek? It is vague where your chin meets your cheek. On two standard views of vagueness, it is therefore impossible for you to know where your chin meets your cheek, either because vagueness is a type of missing truth—and so there is nothing for you to know—or because vagueness is a type of ignorance— and so even though there is a truth of the matter, you cannot know what it is. More generally, proponents of vagueness-as-absence-of-truth and vagueness-as-ignorance endorse the following principle: Excluded Knowledge Vagueness as to whether p entails that nobody knows whether p. In this paper, I challenge vagueness-as-absence-of-truth and vagueness-as-ignorance by challenging Excluded Knowledge. First I make two preliminary points (§1). Then I argue that Excluded 1 On some versions of vagueness-as-ignorance, a question might be vague for one person but not for another. Proponents of these views would say that vagueness as to whether p entails that nobody “for whom it is vague whether p” knows whether p. 2 Cian Dorr (2003) and Brian Weatherson (MS) also argue against Excluded Knowledge. Dorr’s argument is based on a defense of the Law of Excluded Middle, together with intuitive considerations against an epistemic treatment of vagueness. Weatherson’s is based on the view that demonstratives can be substituted salva veritate within the scope of knowledge attributions. Crispin Wright (2001) refuses to accept Excluded Knowledge, but does not positively reject it. In 2001, I challenged Excluded Knowledge with an alleged counterexample during a talk at NYU.