Ofra Magidor

In Physics VI.9 Aristotle addresses Zeno's four paradoxes of motion and amongst them the arrow paradox. In his brief remarks on the paradox, Aristotle suggests what he takes to be a solution to the paradox.In two famous papers, both called 'A note on Zeno's arrow', Gregory Vlastos and Jonathan Lear each suggest an interpretation of Aristotle's proposed solution to the arrow paradox. In this paper, I argue that these two interpretations are unsatisfactory, and suggest an alternative interpretation. In particular, I claim that what seems on the face of it to be Aristotle's solution to the paradox raises two puzzles to which my interpretation, as opposed to Lear's and Vlastos's, provides an adequate response.

This paper consists of two parts. The first concerns the logic of vagueness. The second concerns a prominent debate in metaphysics. One of the most widely accepted principles governing the ‘definitely’ operator is the principle of Distribution: if ‘p’ and ‘if p then q’ are both definite, then so is ‘q’. I argue however, that epistemicists about vagueness should reject this principle. The discussion also helps to shed light on the elusive question of what, on this framework, it takes for a sentence to be borderline or definite. In the second part of the paper, I apply this result to a prominent debate in metaphysics. One of the most influential arguments in favour of Universalism about composition is the Lewis-Sider argument from vagueness. An interesting question, however, is whether epistemicists have any particular reasons to resist the argument. I show that there is no obvious reason why epistemicists should resist the argument but there is a non-obvious one: the rejection of Distribution argued for in the first part of the paper provides epistemicists with a unique way of resisting the argument from vagueness.

The paper challenges Williamson’s safety based explanation for why we cannot know the cut-off point of vague expressions. We assume throughout (most of) the paper that Williamson is correct in saying that vague expressions have sharp cut-off points, but we argue that Williamson’s explanation for why we do not and cannot know these cut-off points is unsatisfactory. In sect 2 we present Williamson's position in some detail. In particular, we note that Williamson's explanation relies on taking a particular safety principle ('Meta-linguistic belief safety' or 'MBS') as a necessary condition on knowledge. In section 3, we show that even if MBS were a necessary condition on knowledge, that would not be sufficient to show that we cannot know the cut-off points of vague expressions. In section 4, we present our main case against Williamson's explanation: we argue that MBS is not a necessary condition on knowledge, by presenting a series of cases where one's belief violates MBS but nevertheless constitutes knowledge. In section 5, we present and respond to an objection to our view. And in section 6, we briefly discuss the possible directions a theory of vagueness can take, if our objection to Williamson's theory is taken on board.