A (leibnizian) Theory and Calculus of Concepts

In the eyes of many philosophers, Leibniz established his credentials as a clear and logically precise thinker by having invented the diieren-tial and integral calculus. However, Leibniz's philosophical views about concepts, monads, possible objects, and the containment theory of truth are not often regarded as similar models of clarity and precision. At best, philosophers might agree that Leibniz's views on some of these topics are consistent, for there are now in the literature set-theoretic models of some of these views. But few philosophers would accept the metaphysics embedded in his rational calculus of concepts or accept his containment theory of truth, for the following claims seem incompatible with our`nat-uralized' understanding of the world: that there are an innnite number of complete concepts each corresponding to some possible individual or monad, that each complete concept`contains' all the concepts that apply to the corresponding monad, that each monad appears at a unique in Section 10 rst appeared in Zalta 1983]. y I am indebted to the Center for the Study of Language and Information (CSLI) for providing me with ooce space, and in particular, to its Director, John Perry, for his continued support of my research at CSLI. I am also indebted to Chris Swoyer, who read earlier drafts of this paper and made numerous valuable suggestions, and to Godehard Link, discussions with whom led to a signiicant improvement in one of the deenitions needed to represent Leibniz's view. Finally, I'd like to thank the members of CSLI's discussion group on object theory, and in particular, for their critical observations on this material. Their observations led to both substantive and stylistic changes in the paper.