Vagueness, Identity and Leibniz’s Law

Abstract

When we reflect on the individuation of objects, we soon encounter hard cases. We are presented with pairs of objects the grounds for classifying which as identical look no better and no worse than the grounds for classifying them as distinct; we have no idea how to decide the question. For instance, the diachronic identity of the ship of Theseus was already a matter of philosophical debate when Plutarch wrote, and has still not been settled:

The thirty-oared galley in which Theseus sailed with the youths and returned safely was preserved by the Athenians down to the time of Demetrius of Phalerum. At intervals, they removed the old timbers and replaced them with sound ones, so that the ship became a classic illustration for the philosophers of the disputed question of growth and change, some of them arguing that it remained the same, and others that it became a different vessel. (Plutarch, ‘Life of Theseus’ §23, Scott Kilvert (trans.) [1960])

If the name ‘S1’ is conferred by ostension at the time of Theseus on the ship then present, and the name ‘S2’ is conferred by ostension at the time of Demetrius of Phalerum on the ship present at that later time, then it seems unclear whether S1 = S2; S1 and S2 are apparently neither clearly identical nor clearly distinct. Examples of this kind abound.

Thanks to audiences at Edinburgh, St Andrews, Bergamo and Syracuse for helpful comments on earlier versions of this material, and in particular to Dorothy Edgington for her reply at Bergamo, to Brian Weatherson for his reply at Syracuse, and to Kit Fine, Richard Holton and Graham Priest for further discussion.