Many historical and philosophical studies treat infinity as an exclusively quantitative notion, whose proper domain of application is mathematics and physics. The main aim of this paper is to disentangle, by critically examining, three notions of infinity in the early modern period, and to argue that one—but only one—of them is quantitative. One of these non-quantitative notions concerns being or reality, while the other concerns a particular iterative property of an aggregate. These three notions will emerge through examination of three (...) central figures in the period: Locke, Descartes, and Leibniz. (shrink)

the meditations on first philosophy presents us with an alleged proof for the existence of God that proceeds from the existence of an idea of an infinite being in the human mind—an idea of God—to the existence of God himself. Insofar as we have an idea of an infinite being, an idea with “infinite objective reality,” we can legitimately ask whence it came to us. The only possible cause of this idea, claims Descartes, is an infinite being, namely, God. The (...) occurrence of just this idea in the proof is essential. In fact, Descartes maintains that any such causal proof for God’s existence crucially relies on this idea: “it seems to me that all these proofs based on his effects are reducible to a single one; and also .. (shrink)

My aim in this chapter is to survey some of the most important developments in thinking about essence in the early modern period, highlighting ways in which thinkers in the period gradually depart from the medieval Aristotelian tradition. In this tradition, essence is thought of as selective, explanatory, and kind-determining. Whereas in the beginning of the early modern period some figures (such as René Descartes, Thomas Hobbes, Margaret Cavendish, and Anne Conway) still adhere to this traditional view, later figures (including (...) Benedict de Spinoza, G.W. Leibniz, and John Locke) reject it. (shrink)

Descartes notoriously characterizes substance in two ways: first, as an ultimate subject of properties ; second, as an independent entity. The characterizations have appeared to many to diverge on the definition as well as the scope of the notion of substance. For it is often thought that the ultimate subject of properties need not—and, in some cases, cannot—be independent. Drawing on a suite of historical, textual, and philosophical considerations, this essay argues for an interpretation that reconciles Descartes's two characterizations. It (...) proposes that both characterizations invoke a type of independence that obtains just in case there is no relation to another entity that holds by the nature of the entity in question. Even though the ultimate subject of properties is sometimes not independent in other respects, it satisfies this independence-by-nature condition. (shrink)

This essay defends two theses regarding the explanation, or ground, of modality in the early modern period. First, for philosophers in the period, essences ground a range of important modal facts. Second, as the period progresses, we witness increased skepticism about certain modal facts, due to a growing skepticism about the scope or existence of essences. These theses are supported by examination of three case studies: Descartes’ treatment of substance and mode (which forms the core of his ontology); Malebranche’s treatment (...) of causation (which bears on his defense of occasionalism); and Locke’s treatment of necessary connections among properties (which is related to his accounts of individuals and kinds). It is shown that in each case, claims about necessity and possibility take center stage, and that in each case, the status of these claims hinges on the status of claims about essences. (shrink)

Descartes’s metaphysics posits a sharp distinction between two types of non-finitude, or unlimitedness: whereas God alone is infinite, numbers, space, and time are indefinite. The distinction has proven difficult to interpret in a way that abides by the textual evidence and conserves the theoretical roles that the distinction plays in Descartes’s philosophy—in particular, the important role it plays in the causal proof for God’s existence in the Meditations. After formulating the interpretive task, I criticize extant interpretations of the distinction. I (...) then propose an alternative at whose core is the idea that whereas the indefinite is a structural, iterative notion, designating the absence of an upper bound, the infinite is an ontic notion, signifying being in general, or what is, without qualification. (shrink)

There is a familiar story about Spinoza on which his substance monism arises straightforwardly from Descartes’ own conception of substance, which the latter combines—not entirely consistently—with substance pluralism. I argue that this story is mistaken: substance pluralism is fully consistent with Descartes’ conception of substance; it is also consistent with his claim that the term ‘substance’ is non-univocal. In defense of these claims, I argue that Descartes denies, whereas Spinoza accepts, that causation precludes the kind of independence that is characteristic (...) of substance; further, I show how Descartes’ denial is based on his view that causal relations do not belong to the natures of their relata, whereas Spinoza’s acceptance follows from his commitment to an intimate link between causation and conception, which Descartes also rejects. (shrink)

This volume contains essays that examine infinity in early modern philosophy. The essays not only consider the ways that key figures viewed the concept. They also detail how these different beliefs about infinity influenced major philosophical systems throughout the era. These domains include mathematics, metaphysics, epistemology, ethics, science, and theology. Coverage begins with an introduction that outlines the overall importance of infinity to early modern philosophy. It then moves from a general background of infinity up through Kant. Readers will learn (...) about the place of infinity in the writings of key early modern thinkers. The contributors profile the work of Descartes, Spinoza, Leibniz, and Kant. Debates over infinity significantly influenced philosophical discussion regarding the human condition and the extent and limits of human knowledge. Questions about the infinity of space, for instance, helped lead to the introduction of a heliocentric solar system as well as the discovery of calculus. This volume offers readers an insightful look into all this and more. It provides a broad perspective that will help advance the present state of knowledge on this important but often overlooked topic. (shrink)

John Locke’s treatment of quantity in the Essay Concerning Human Understanding is not nearly as extensive or as well-known as his treatment of quality and his distinction between primary and secondary qualities. Yet I contend that a close examination of Locke’s comments on quantity in the Essay reveals that he endorses a general theory of quantity that not only distinguishes quantities from qualities, but also plays several other important roles in his overall philosophy—particularly in his treatments of infinity and demonstrative (...) knowledge. Moreover, I argue that this theory does not appear out of thin air, but is in certain respects one and the same as the approach to quantity found in Aristotle and developed by medieval Aristotelian thinkers. Identifying the core tenets of this approach in the texts of Aristotle and medieval Aristotelians, and formulating them clearly enough to shed light on Locke’s theory of quantity in the Essay, is the principal task of this paper. (shrink)