I. Introduction

Leibniz’s doctrine of individual accidents asserts that an accident cannot inhere in more than one substance. As discussed in chapter one, adherence to this doctrine leads Leibniz to reject relations simpliciter as accidents. A fundamental tenet of my account of Leibniz’s views on relations is that though Leibniz does not permit relations simpliciter to serve as accidents, he does believe relational accidents are genuine accidents. Cover and Hawthorne have articulated a novel objection to this view. They claim (or at least they seem to claim) that the allowance of relational accidents would violate the doctrine of individual accidents just as much as the allowance of relations simpliciter as accidents would. The primary goal of this chapter is to rebut this charge. In section II, I attempt to clarify what their objection is. Crucial to their argument is the assumption that individuals are constituents of relational accidents. For example, the relational accident “lover of Helen” contains the individual Helen as one of its constituents. Cover and Hawthorne provide no explanation of what it means for Helen to be a constituent of “lover of Helen,” and thus it is difficult to evaluate their assumption that she is. To remedy this, I move the discussion from the realm of relational accidents into the realm of their conceptual counterparts—the realm of extrinsic denominations. I demonstrate that complete individual concepts are not included in extrinsic denominations, and thus there is no reason to believe that Leibniz would regard individuals as constituents of relational accidents. The showing that individual concepts are not included in extrinsic denominations requires a brief foray into Leibniz’s logic of concepts and concept-inclusion, and this foray occupies much of section III. However, that individual concepts are not included in extrinsic denominations brings to light a puzzle concerning the conceptual structure of extrinsic denominations and Leibniz’s logic of concepts. In the last section, then, I consider the conceptual structure of extrinsic denominations (as well as certain types of intrinsic denominations) and show that they are not expressible in Leibniz’s logic of concepts. This result is not in any way a consequence of maintaining that extrinsic denominations are properties (or that relational accidents are genuine accidents); rather it reflects a general inadequacy of Leibniz’s logic of concepts.