Abstract

In this article we investigate putative counterexamples to Leibniz’s principle of the Identity of Indiscernibles. In particular, we look at the status of spacetime points: although these all possess exactly the same properties in symmetrical spacetimes and thus seem indiscernible, there are certainly more than one of them. However, we shall defend Leibniz’s principle, even for such highly symmetrical cases. Part of our strategy will be to invoke the notion of “weak discernibility”, as proposed in the recent literature. Weakly discernible objects share all their properties but stand in irreflexive relations to one another—this irreflexivity makes it possible to show that Leibniz's principle implies their numerical diversity. However, we shall argue that this notion of weak discernibility only serves its purpose if it is supplemented by a criterion of physical meaningfulness of the relations and relata in question; and that in the final analysis weak discernibility only helps out when it can be seen as a degenerate case of strong, absolute discernibility. The case of spacetime points is an example of such a situation.