Space, Monads, and Incompossibility

This chapter offers a novel account of how to understand Leibniz’s views on compossibility when applied to infinite worlds constituted by unextended, immaterial substances or ‘monads’. The first section sets the stage by taking up some essential questions about the relationship between monads and space. The second section argues that—with a better understanding of that relationship—it is possible to see how the so-called ‘packing strategy’ can be applied quite directly, even intuitively, to monadic worlds and substances. The third section argues that thinking through the application of the packing strategy to monadic worlds highlights an important, neglected Leibnizian commitment and reveals surprising affinities between the packing strategy and recent cosmological interpretations.

Leibniz’s Imaginary Bridge

This chapter discusses the analogy between bare possibles and imaginary numbers, developed by Leibniz during his Paris years. In this period, he came to realize that imaginary quantities are not impossible in themselves, but they cannot be geometrically represented, for they cannot be ordered within the number line. Similarly, he regarded actual things as belonging to a single ‘series of things’, where each member is connected to every other by relations of position and succession. Bare possibles, on the contrary, can be placed nowhere in the series and, therefore, must be regarded as fictions (though reference to them is in a sense unavoidable, like the use of imaginary quantities in algebra). The young Leibniz does not extend the model of a ‘series of things’ to possibles, thus in this period he seems to reject the very idea of a plurality of possible worlds.

Locke, God, and Materialism

This chapter investigates Locke’s views about materialism, by looking at the discussion in Essay IV.x. There Locke—after giving a cosmological argument for the existence of God—argues that God could not be material, and that matter alone could never produce thought. In discussing the chapter, I pay particular attention to some comparisons between Locke’s position and those of two other seventeenth-century philosophers, René Descartes and Ralph Cudworth. Making use of those comparisons, I argue for two main claims. The first is that the important argument of Essay IV.x.10 is fundamentally an argument about the causation of perfections. Indeed, Locke gives multiple such arguments in the chapter. My second main claim is that my proposed reading of IV.x is not merely consistent with what Locke says elsewhere about superaddition, but also provides reasons to favor a particular understanding of what superaddition is.

Knowledge and Sensory Knowledge in Hume’s Treatise

I argue that the Hume of the Treatise maintains an account of knowledge according to which (i) every instance of knowledge must be an immediately present perception (i.e., an impression or an idea); (ii) an object of this perception must be a token of a knowable relation; (iii) this token knowable relation must have parts of the instance of knowledge as relata (i.e., the same perception that has it as an object); and any perception that satisfies (i)–(iii) is an instance of knowledge. I then apply this account to the case of sense perception. I argue that Hume holds that relations of impressions can be intuited, are knowable, and are necessary. For Hume, these relations constitute sensory knowledge. While Hume is rightly labeled an empiricist for many reasons, a close inspection of his account of knowledge reveals yet another way in which he deserves the label.

Thomas White on Location and the Ontological Status of Accidents

The work of Thomas White represents a systematic attempt to combine the best of the new science of the seventeenth century with the best of Aristotelianism. This attempt earned him the criticism of Hobbes and the praise of Leibniz, but today, most of his attempts to navigate between traditions remain to be explored in detail. This chapter does this for his ontology of accidents. It argues that his criticism of accidents in the category of location as entities over and above substances was likely aimed at Francisco Suárez, and shows how White’s worries about the analysis of location were linked with his broader cosmological views. White rejects real qualities, but holds that the quantity of a substance is in some way distinct from its bearer. This reveals a common ground with some of his scholastic interlocutors, but lays bare his disagreement with thinkers like Descartes on the nature of matter.

The Univocity of Real Essence in Locke

I argue that Locke’s various descriptions of real essence pick out one and the same thing, namely a nature that can be ascribed to many things, and in terms of which we can get matters of classification right or wrong. On my reading, Locke does not attack real essences of the sort that are the essences of real species, but rather the presumption that a sorting according to our species concepts and their names is a sorting of things according to their real essences. And the lesson of Locke’s empirical argument against that presumption, I argue, is that our species concepts often function more like higher taxa, grouping together things that knowledge of their real essences would distinguish into distinct lowest species.

The Metaphysics of Natural Right in Spinoza

In the Theological-Political Treatise (TTP), Spinoza argues that an individual’s natural right extends as far as their power. Subsequently, in the Political Treatise (TP), he offers a revised argument for the same conclusion. This chapter offers an account of the reasons for the revision. In both arguments, an individual’s natural right derives from God’s natural right. However, the TTP argument hinges on the claim that each individual is part of the whole of nature (totius naturae) and for this reason inherits part of the natural right of that whole. Using several analogous cases from the Ethics, it is shown that this form of argument from division is not compatible with Spinoza’s considered metaphysical views. The revised argument, by contrast, avoids the pitfalls of his earlier efforts. It also better reveals the deep roots by which the monistic metaphysics of the Ethics feeds into Spinoza’s conception of natural right.