Abstract

Leibniz's metaphysics is distinctively idealist. To see why, we need to understand his critical engagement with Descartes's conception of matter. Leibniz employs several different types of argument against this Cartesian conception. Some are based on considerations from physics while others raise deeper, more fundamental questions about the nature of the reality that underlies the world of bodies and their motions. The most important and difficult of these are arguments that focus on the notion of extension itself and challenge the coherence of the very idea that extension could constitute the essence of a something real. ;Starting early in his career, Leibniz argued that shape and the other Cartesian modes of extension contain something imaginary and relative to our perception. I interpret his arguments for this claim, especially with respect to shape, aiming to bring out both his reasons for charging Descartes with confusion and his grounds for thinking that the objects of physics must ultimately be immaterial. ;I argue first that by "imaginary" Leibniz means much the same thing that he means when he says that a color is imaginary. In the case of both color and shape, his claim is that having an idea of such properties involves cognizing qualities that would disappear upon analysis and that do not have a mind-independent existence. ;Leibniz offers two subtly different arguments for the claim that shape is imaginary. The central premise of the first argument is that no shape could be infinitely complex. The second argument does not, I claim, depend on this premise. After analyzing and criticizing the first argument, I offer a novel interpretation of the second. The key to this interpretation is seeing that in an infinitely divided plenum any supposed shape of a body will be imaginary in much the same way that sensory qualities are. A perceived shape will disappear at some level of analysis in the same way that the green disappears once I am perceiving the blue and yellow that constitute it. This is the sense, according to Leibniz, in which shapes are imaginary. While this conclusion is not by itself sufficient to establish immaterialism, it does, I argue, play an essential role in a larger argument for immaterialism. ;After examining the implications of the second argument, I then go on to consider two potential criticisms of my interpretation. The first says that Leibniz is claiming only that shapes as defined by traditional geometry are imaginary. The second objection is that Leibniz's metaphysics in the period during which he gave the shape arguments was not yet idealist but rather countenanced genuinely extended, quasi-Aristotelian corporeal substances. I argue that if the first objection is correct, it renders the shape arguments too weak to have any force against the Cartesian view. The second objection, I argue, is based on a reading of various texts that presupposes the very sort of interpretation the texts are intended to support