Abstract: Leibniz often uses a mirror analogy to explain his monads. Referring to a monad as a simple substance, he writes in one representative passage: "each simple substance is a perceptual, living mirror of the universe" (M 56). Leibniz's mirror analogy has received much attention from Leibniz scholars. For example, some interpreters have drawn out the striking similarities between mirrors and fundamental features of monads such as their points of view (Nachtomy 2019), while other commentators have placed Leibniz's mirror analogy in a wider historical context to highlight the sorts of mirrors that were, in fact, available in Leibniz's day (Phemister 2017).

Despite these commentaries, Leibniz's mirror analogy continues to be puzzling. We typically suppose, for example, that mirrors reflect bodies that exist prior to and independently of the mirrors. It is also natural to think that the perspective according to which the mirror reflects things presupposes a space wherein the mirror is placed. But this intuitive gloss on Leibniz's mirror analogy is hard to square with his monadic metaphysics. For one animating thought of Leibniz's monadic metaphysics is the idea that facts about the world must be explained by facts about monads. Leibniz would thus have us believe that bodies presuppose monads, rather than the other way around. Likewise, he would argue that space presupposes the points of view of monads, not versa. Leibniz's mirror analogy thus seems to raise more questions than it answers.

Nevertheless, I argue that Leibniz's mirror analogy can shed light on his monadic metaphysics. For as I read Leibniz's mirror analogy, it successfully brings out a sense in which bodies and space depend on mirrors and, by extension, monads. Just as we might think that the blueprint for a building exists prior to and independently of the building and its space, Leibniz maintains that the mirrors in his analogy exist prior to and independently of bodies and space. To develop and defend my reading, I draw on Leibniz's technical writings on perspective. For it is now clear from the work of Debuiche (2023; 2013) that Leibniz had expertise in a branch of mathematics concerned with perspective drawings or perspectiva and that his mirror analogy is based on his work on perspectiva. Leibniz's mirror analogy should therefore make sense when seen in that light.

The talk is divided into three sections. In section one, I outline a critical fact that Leibniz learned from perspectiva, which is that any point on a body can be projected onto a drawing in such a way so as to preserve its spatial relations to other points on the body. The second section argues that Leibniz saw a valuable opportunity in this fact because it suggests that there is a kind of equivalence between a body and its perspectival representations. This equivalence, in turn, indicates that we can think of a body as an aggregate of its perspectival representations. The final section sketches how Leibniz can exploit this equivalence to develop his thesis that a body is an aggregate of monads.