Andrew M. Cavallo

Monads are simple substances, where “simple” means “no parts.” It is therefore more accurate to say that monads are spatially simple and thus indivisible. Moreover, Leibniz's theory of spacetime as a property of monadic perception implies that monads are logical antecedents of spacetime rather than existing therein.

However, it does not follow that, because monads lack spatial properties, they necessarily lack all properties. After all, only nonexistent objects have no properties—not even the property of nonexistence. Therefore, if monads exist, they must have properties, though they undoubtedly have no spatial properties. What properties do they have, then? I shall discuss this matter in the section on monadic perception.

Leibniz writes:

“For it shows that there are of necessity substances which are simple and without extension, scattered throughout all Nature; that these substances must subsist independently of every other except God...”¹

Why does Leibniz say that monads must exist? A common mistake is to interpret Leibniz through the lens of atomism. Given that Leibniz sometimes employs analogies with atoms, this mistake is, perhaps, understandable. But Leibniz is emphatically not an atomist.

In fact, Leibniz insists explicitly that matter is infinitely divisible; that is, there are no material atoms. But Leibniz is not an atomist even in some incorporeal sense, as each monad, though indivisible, reflects the entire universe. Moreover, monads of the highest order—spirits—reflect the divine as well.

Leibniz's argument for the existence of monads is rather more interesting than the “building blocks” argument of the atomist. The argument is essentially as follows: the existence of systems implies the existence of monads because only true unities—monads—can unite.

This observation is closely related to my 2012 paper on the topological problem of system boundary,² wherein I describe how a system often shares a boundary with its environment that permits the local entanglement of elements of the system with elements of the environment without thereby collapsing the environment and the system into one unit.

But the existence of such a boundary is not enough to secure the identity of a system; that is, it is not enough to warrant talking of this system as opposed to that system. A system is only a unit insofar as it has a unifier. Moreover, only a true unity—a monad—can be a unifier. Therefore, each system must have a governing monad.

I shall discuss more fully how monadology resolves the problem of how an individual can possess an identity or essence when we come to Leibniz's doctrine of the complete individual concept.

Since natural death occurs part by part, monads are not subject to it. But God can instantaneously annihilate them.

Since natural formation and evolution occur part by part, monads are not subject to them. But God can instantaneously create monads from nothing.

Given two monads, x and y, x ≠ y. The assumption that x = y contradicts the Principle of Sufficient Reason.

This last statement marks a point of agreement between Aquinas and Leibniz. Leibniz writes:

“There follow from these considerations several noticeable paradoxes; among others, that it is not true that two substances may be exactly alike and differ only numerically, solo numero; and that what St. Thomas says on this point regarding angels and intelligences (quod ibi omne individuum sit species infima) is true of all substances.”³

Notes

1. Gottfried Wilhelm Leibniz, “The New System of the Nature and Communication of Substances, as well as the Union That Exists Between the Soul and the Body,” in The Philosophical Works of Leibnitz, trans. George Martin Duncan (New Haven: Tuttle, Morehouse & Taylor, 1890), available through Project Gutenberg . ↩
2. Andrew M. Cavallo, “On Mario Bunge's Definition of System and System Boundary,” Science & Education 21, no. 10 (2012): 1595–1599, https://doi.org/10.1007/s11191-011-9365-0 . ↩
3. Gottfried Wilhelm Leibniz, Discourse on Metaphysics, Correspondence with Arnauld, and Monadology , trans. George R. Montgomery (Chicago: Open Court, 1908), §9. ↩