Geoffrey Gorham

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.

This chapter identifies three main sources of the Stoic elements in Hobbes's philosophy: the early Christian‐Stoic Tertullian, the modern “Neo‐Stoic” school of Justus Lipsius, and the natural philosophers of the Cavendish Circle he frequented. Perhaps the most direct Stoical impact on Hobbes was the second/third century Church Father Tertullian. Hobbes and Cavendish are at bottom kindred Stoic spirits, though their systems diverge on the precise nature of material activity. The chapter explores the Stoic character of Hobbesian space, time, causality, and God, especially as these notions are employed in his natural philosophy. Hobbes's quasi‐realism about imaginary space is highly reminiscent of the Stoics' conception of pure space as one of the problematic “incorporeals.” The chapter shows that Hobbes's metaphysical views, though quite unorthodox in his day, served to buttress his overall materialist, empiricist, and mechanist program in natural philosophy.

Richard Popkin opened an early paper with the observation "No figure in the history of European philosophy has had a more direct and enduring influence on American thought than George Berkeley."2 Popkin's case for Berkeley's "enduring" influence well into classical pragmatism is compelling.3 But in what follows I will be concerned with his more "direct" influence on the Connecticut philosopher and theologian Samuel Johnson —not to be confused with the English stone-kicking confuter of Berkeley—during Berkeley's brief, abortive Rhode Island sojourn of 1729–31. Johnson studied classics and history at the nascent Yale College, until, "accidentally lighting on Lord Bacon's Instauratio Magna or Advancement of...

The Scottish philosopher Norman Kemp Smith (1872–1958) is best known for his 1929 English translation of Kant’s Critique of Pure Reason, and for his incisive commentaries on Descartes, Hume, and Kant. These achievements have overshadowed his original philosophical work in several areas, including the experience of time. A realist with idealist sympathies, Kemp Smith developed a non-transcendental version of Kant’s conception of time as a ‘pure intuition’ (though he insisted that temporal perception involved ‘categories’). He employed this conception to solve a problem that was widely discussed in early twentieth-century European and American philosophy, which William James dubbed the ‘specious present’: how can we perceive an extended duration, like a full golf swing, or the cadence of a brief tune, if we only perceive the present? A closely related problem: if we only ever perceive the present, how can we distinguish among the future, present, and past? In this paper, I explain Kemp Smith’s proposed solution, and compare it with two of his contemporary influences: Samuel Alexander and George F. Stout. Finally, I suggest that these problems are still with us, and are likely to be for some time, especially if we ignore the insights offered by earlier discussions.

Locke is famed for his caution in speculative matters: “Men, extending their enquiries beyond their capacities and letting their thoughts wander into those depths where they can find no sure footing; ‘tis no wonder that they raise questions and multiply disputes”. And he is skeptical about the pretensions of natural philosophy, which he says is “not capable of being made a science”. And yet Locke is confident that “Our reason leads us to the knowledge of this certain and evident truth, that there is an eternal, most powerful and most knowing being; which whether anyone will please to call God it matters not”. His certainty about the existence and attributes of God, I will argue, led him to surprisingly strong convictions about a deep and disputed problem at the intersection of seventeenth century metaphysics and natural philosophy: the absolute reality of space and time. Specifically, he based his absolutist conceptions of space and time on God’s literal omnipresence and eternity. Leibniz probably had Locke in mind when he inveighed in 1716 against “real absolute space, the idol of some modern Englishmen”. And Leibniz was right a decade earlier to voice through his mouthpiece Theophilus the suspicion that, despite Locke’s claim to know nothing about the substance of void space, “there are grounds for thinking you know more about it than you say or believe that you do. Some people have thought that God is the place of objects”.

It is well-known that Isaac Newton’s conception of space and time as absolute -- “without reference to anything external” (Principia, 408) -- was anticipated, and probably influenced, by a number of figures among the earlier generation of seventeenth century natural philosophers, including Pierre Gassendi, Henry More, and Newton’s own teacher Isaac Barrow. The absolutism of Newton’s contemporary and friend, John Locke, has received much less attention, which is unfortunate for several reasons. First, Locke’s views of space and time undergo a dramatic evolution that mirrors the overall absolutist trend of the era. Second, there are good reasons to suppose that Locke was influenced late in this evolution by Newton’s Principia, which he read and reviewed shortly after its 1687 publication. It is even possible that Locke read or knew of the earlier and unpublished, though now famous, Newtonian tract De Gravitatione. Third, despite the influence of Newton, Locke’s retains a skeptical attitude concerning our empirical knowledge of absolute space and time. He is especially cautious about absolute time, bucking a widespread tendency to treat time as strongly analogous to space. Their disagreement about the measure of absolute time, we will suggest, reflects a deeper disagreement in the philosophy of science. While Locke counts as scientific knowledge only ideas and demonstrations derivable from immediate experience, Newton endorses a more theory-driven brand of empiricism, which holds that our best explanations of the phenomena provide genuine knowledge that goes beyond what we can directly observe.

In two rarely discussed passages – from unpublished notes on the Principles of Philosophy and a 1647 letter to Chanut – Descartes argues that the question of the infinite extension of space is importantly different from the infinity of time. In both passages, he is anxious to block the application of his well-known argument for the indefinite extension of space to time, in order to avoid the theologically problematic implication that the world has no beginning. Descartes concedes that we always imagine an earlier time in which God might have created the world if he had wanted, but insists that this imaginary earlier existence of the world is not connected to its actual duration in the way that the indefinite extension of space is connected to the actual extension of the world. This paper considers whether Descartes’s metaphysics can sustain this asymmetrical attitude towards infinite space vs. time. I first consider Descartes’s relation to the ‘imaginary’ space/time tradition that extended from the late scholastics through Gassendi and More. I next examine carefully Descartes’s main argument for the indefinite extension of space and explain why it does not apply to time. Most crucially, since duration is merely conceptually distinct from enduring substance, the end or beginning of the world entails the end or beginning of real time. In contrast, extension does not depend on any enduring substance besides itself.

I develop a new theory of theoretical progress or 'truthlikeness'. Unlike previous theories, my approach focuses on the sets of models of scientific theories, rather than their linguistic formulations. Such an approach, I argue, avoids several long-standing problems in the philosophy of theoretical progress. I find in Chapter One that the most prominent schools of twentieth century philosophy of science have all failed to account for theoretical progress. I further argue that such an account is an essential element of the best argument for the doctrine of scientific realism. Chapter Two offers a taxonomy of recent theories of verisimilitude. A four-part classification is proposed according to where the theories stand on each of two basic meta-theoretical dichotomies: the structure of scientific theories, the measure of theoretical progress. My own approach is based on a semantic view of theories and a similarity-based measure of progress. I argue in Chapter Three that such an approach avoids the problems of language-dependence and incommensurability; it also explains the relation between truth and truthlikeness. In Chapter Four, I develop my own theory in detail. I propose that one scientific theory is closer to the truth than another just in case its family of models is more structurally similar to the actual world. Chapter Five is an historical illustration of my theory: the theory of atomic structure, 1867-1913.

The pantheon of seventeenth-century European philosophy includes some remarkably heterodox deities, perhaps most famously Spinoza’s deus-sive-natura. As in ethics and natural philosophy, early modern philosophical theology drew inspiration from classical sources outside the mainstream of Christianized Aristotelianism, such as the highly immanentist, naturalistic theology of Greek and Roman Stoicism. While the Stoic background to Spinoza’s pantheist God has been more thoroughly explored, I maintain that Hobbes’s corporeal God is the true modern heir to the Stoic theology. The Stoic and Hobbesian gods are necessitarian, entirely corporeal, and thoroughly intermixed with ordinary bodies, while also supremely intelligent, providential, and good. And both gods serve as the ultimate source of diversity and change in a material world divested of Aristotelian forms and causes. Unfortunately, scholars on both sides of the long debate about the sincerity of Hobbes’s theism have not taken very seriously his late articulation of a corporeal theology. One probable reason for this dismissive attitude is a lack of thorough investigation of the historical precedents for such an unusual godhead available to Hobbes. The first part of this article attempts to establish a close congruence between the Stoic and Hobbesian gods. The second part traces the likely sources for Hobbes’s Stoic theology in his intellectual context

In his recent survey of the “dialectic of creation” in seventeenth-century philosophy, Thomas Lennon has suggested that Descartes’s assumptions about causality encourage a kind of “pantheistic emanationism”. Lennon notes that Descartes regularly invokes the principle that there is nothing in the effect which was not previously present, either formally or eminently, in the cause. Descartes also believes that God is the continuous, total, and efficient cause of everything. From these assumptions it should follow that everything that exists in the created world is previously present in God. Indeed, Descartes embraces the emanationist doctrine explicitly when, at the end of his replies to the Second Set of Objections, he arranges the arguments of the Meditations in “geometrical fashion.” The demonstration of Proposition III includes a sub-proof of the proposition that “he who preserves me has within himself, either formally or eminently, whatever is in me”. Since God preserves the entire universe, it follows that everything is in him, either formally or eminently. While far from the radical Spinozistic view that God and the world are identical, the notion that everything in creation is also in God would seem to have its own unwelcome theological consequences, at least from a Cartesian point of view. In particular, it implies that extension, and hence divisibility, are in God. But, as Descartes himself cautions, “being divisible is an imperfection” and so completely foreign to God.

The employment by seventeenth-century natural philosophers of stock theological notions like creation, immensity, and eternity in the articulation and justification of emerging physical programs disrupted a delicate but longstanding balance between transcendent and immanent conceptions of God. By playing a prominent (if not always leading) role in many of the major scientific developments of the period, God became more intimately involved with natural processes than at any time since antiquity. In this discussion, I am particularly concerned with the causal and spatio-temporal relations between God and nature in the seventeenth century as recent scholarship has revealed how dramatically traditional conceptions of these relations were transformed by philosophers and scientists like Descartes, Malebranche, More, and Newton.