We consider the so-called problem of the many, formulated by Peter Unger. It arises because ordinary material things do not have precise boundaries: it is always possible to find borderline parts of which it is not true to say either that they are parts or that they are not. Unger's conclusion is that there are no ordinary things at all. We describe the solutions of Peter van Inwagen and David Lewis, and make some critical comments upon them. After that we present our own suggestion which is based on ideas developed by Leibniz in connection with problems of unity and plurality. We suggest that what the problem of the many teaches us is that in order to understand what ordinary things are, we have to take seriously the Leibnizian-Kantian distinction between phenomena and things-in-themselves.