The positive view adopted later in this book defends a conception of parthood and composition which carries genuine ontological commitment: contrary to the Lewisian Composition-as-Identity model, wholes according to this alternative conception are in no way to be identified with their parts; rather, a commitment to wholes is a commitment to entities that are numerically distinct from their parts. A crucial piece of apparatus which supports this ontologically loaded conception of parthood and composition is a certain style of argument which reasons from Leibniz's Law to the numerical distinctness of wholes and their parts: according to this style of argument, wholes and their parts are numerically distinct by Leibniz's Law, because they do not share all of their properties. This present chapter defends this style of argument for the numerical distinctness of wholes and their parts.
Keywords: composition, parthood, identity, Leibniz's Law, contingent identity, temporary identity, indeterminate identity, relative identity, non-existent objects, coincidence,