On Leibniz: Expanded Edition

3. Leibniz on Intermonadic Relations

68  3 Leibniz on Intermonadic Relations 1. Introduction His theory of relations represents a crucial component of Leibniz’s philosophy . It is one of those many points of fertile concurrence where logic and metaphysics come together in fruitful symbiosis. But the theory confronts many problems. One of the gravest of these is the question, Are intermonadic relations real, or are they matters of mere seeming? It is sometimes said that for Leibniz, relations are mere creatures of the mind: That they are “our own creation” and “not in nature,” and so forth. This is indeed the doctrine of Spinoza,1 and is approximated by such nominalist and materialist thinkers as Gassendi2 and Hobbes.3 But it is by no means the theory of Leibniz. Nothing could be further from the truth than Bertrand Russell’s contention that on Leibniz’s theory a relation is merely an “ideal thing” and that If he were pushed as to [the nature of] this “ideal thing,” I am afraid he would declare it to be an accident of the mind which contemplates [it].4 The aim of this discussion is to examine and clarify Leibniz’s position on this pivotal issue of the reality and the nature of intermonadic relations. 2. The Crucial Role of Relations in Incompossibility His view of intermonadic relations is crucially likened to Leibniz’s theory of possible worlds. Since the complete individual concept of a Leibnizian substance embraces the specification of literally every facet of its career,5 it Leibniz on Intermonadic Relations 69 involves all details of the relation of this substance to others.6 But now suppose that (1) Possible substance #1 has the property P and also has the feature that there is no substance having property Q to which it (#1) stands in the relationship R. (2) Possible substance #2 has the property Q and also has the feature that every substance having the property P stands in the relationship R to it (#2). These two substances are patently incompatible (on logical grounds). God might realize #1 or He might realize #2, but He cannot possibly realize both of them. (It is a fundamental tenet of Leibniz’s philosophy that even omnipotence cannot accomplish the impossible.) Substances that clash in this way are characterized by Leibniz as incompossible. All of the substances comprising any possible world must, of course, be mutually compossible in the correlative sense: otherwise they could not possibly coexist within one shared world environment. The purely logical fact that different possibilities can be mutually incompatible —that not all possibilities will be compossible in admitting of concurrent realization—plays a crucial role in Leibniz’s metaphysics. It yields the reason why God must unavoidably choose between alternative schemes of things, between different possible worlds. The need for such a choice is crucial to God’s status as a moral agent. As Leibniz wrote the day after his meeting with Spinoza in 1676: If all possibles existed, no reason for existence would be needed and possibility alone would suffice. Therefore there would be no God save insofar as He is possible. But such a God as the pious believe in would not be possible if the opinion of those is true who hold that all possibles exist.7 The prospect of incompossible worlds is thus a logical circumstance that has profound philosophical and theological implications. And the crucial role of relations in Leibniz’s system emerges against this background. For it transpires that if substances were not mutually interrelated there would be no prospect of their incompossibility. Leibniz’s clear insistence that substances have relational properties—as with “Adam is the father of Cain”—is motivated by the consideration that in this way alone can substances be incom­ 70 Leibniz on Intermonadic Relations possible, as the actual Adam is incompossible with a Noah characterized as (inter alia) “the father of Cain.” It is clear now how one must proceed in endeavoring to answer, on Leibniz ’s behalf, the question, How can the complete individual notions of two individually possible substances a and b be so constituted as to render them mutually incompossible? One begins with two crucial observations: (1) “being related by R to b [i.e., to any substance answering to b’s description ]” is one of the relational properties of a, i.e., a has (lx)xRb. and further (2) “not standing in the relation R to a...