Philosophical arguments must be understood in relation to the historical contexts in which they were produced. This yields the recognition that the distinction between early modern “philosophy” and “science” is an anachronistic imposition—the philosophical foundation of modernity and the Scientific Revolution are facets of the same transformations. However, the “contextualist turn” presents methodological difficulties arising from the opposition of philosophical analysis and historical narrative. This introduction presents two strategies for resolving these tensions in the study of the period. First, examination of how authors identified with peers and opposed themselves to foes generates a fine-grained understanding of early modern disciplines, without anachronistic impositions. Second, shifts in disciplinary boundaries can be used as entry points into the networks of influences that ramified across the intellectual landscape, yielding narratives that are sensitive to a wide range of textual and contextual factors. Together, awareness of disciplinary boundaries and their “inflection points” offers an updated methodology for the investigation of the early modern period. Anachronistic grand narratives of early modern philosophy and of the Scientific Revolution will be superseded by more modest but much more sophisticated accounts of the multiplication and reorganization of intellectual disciplines.

Just as a debate about the fundamental nature of physical entities arose after Descartes, a similar issue arose after Newton. Like Descartes, but of course with very different epistemological and methodological considerations, Newton held that the most fundamental conserved quantity was “quantity of motion” or momentum. Leibniz opposed this, arguing instead for vis viva or “living force.” This controversy introduced two kinds of problems: 1) whether and how empirical proofs could be generated for metaphysical conceptions, and consequently 2) how to understand the relationship between metaphysics and experimental philosophy. These concerns were handled quite differently by two important philosophers: Gravesande and Du Châtelet. Their moves partly resolved older debates, but also partly reconfigured them into new questions we are still attempting to answer.

The Scientific Revolution completely transfigured the European intellectual landscape. Old divisions disappeared, while new fault lines emerged. Ancient philosophical sects had been replaced by new schools, featuring novel masters, disciples, and methodological commitments. However, the new schools still engaged in antagonistic discourse, attacking one another along new fronts—e.g., Cartesians against Gassendists, Newtonians against Leibnizians. This chapter presents the diverse philosophical camps that arose in the later stages of the Scientific Revolution by noting a shift in the use of the term ‘sect’. While it still signified something like an Ancient philosophical school for some, it could also take on a more negative polemical meaning, intended to disparage one’s opponents. Moreover, the individuals associated with the “sects” did not all faithfully subscribe to explicit, coherent, and systematic programs. On the contrary, declaring membership of a sect was as often a signal of opposition as of allegiance to a methodology or theory. Despite calls for conciliatory research programs, sectarian attitudes did not disappear by 1750, but delineated new battle lines between the Cartesians, the Leibnizians, and the Newtonians.

Natural philosophy was often seen as a means of reading the “Book of Nature” written by God’s creative act, and therefore must be seen against the background of religion. Older commentary has examined how post-Reformation confessional divides affected the moral and spiritual project of “Physico-Theology.” Some intellectual historians have suggested that there was something that could be described as the confessionalization of early modern physics. Other intellectual historians have argued that the homogenizing pressure of confessionalization was much less successful, both in popular culture and in natural philosophy. This chapter aims to advance these controversies by contrasting general confessionalization claims with case studies that examine whether and how particular contents of natural philosophy were shaped by theological concerns specific to different Christian denominations. These case studies analyze the influence theories of special providence had on cosmology, the problems that doctrines of the Eucharist raised for matter theories, the persistence of moral interpretations of natural particulars in natural histories, and the methodological foundations of eclectic natural philosophies. The upshot of these considerations is that confessionalization led to a much lower degree of homogeneity in natural philosophy than has been supposed.

Throughout the early modern period, the vast majority of natural philosophers remained deeply invested in exploring the meaning of ancient philosophical texts—there was no anti-humanist turn initiated by Descartes. Discussion of ancient philosophy was used, above all, in a genealogical manner, to shed light on the historical origins of doctrinal or methodological error. Accordingly, calls for a “return” to the philosophy of the presocratics, of Hippocrates, etc., should not be understood as simplistic recourse to authority, but rather as historico-methodological arguments about the disciplinary identity of natural philosophy. Indeed, natural-philosophical innovators were often more sure of what they stood against than what exactly they stood for. Seen from this perspective, the “philosophy of the Scientific Revolution” was an anti-philosophy, driven primarily by the colonization of the discipline by physicians on the one hand and mixed mathematicians on the other; the two groups eventually coming to work in tandem to squeeze out anything that looked like metaphysical physics.

During the Scientific Revolution, philosophers wondered how best to understand space. Many debates revolved around the account advanced in Descartes’s Principles of Philosophy (1644), and this chapter treats it as a focal point. Descartes argued for a return to the Aristotelian view that there is no difference in reality between space and matter, entailing that empty space—space empty of matter—is impossible. Over the next century, all kinds of philosophers attacked this position, and this chapter takes their rejections of Cartesian space as a starting point for exploring alternative views. A varied selection of philosophers who reject Cartesian space are discussed, in chronological order: Henry More, Samuel Clarke, Isaac Newton, Catharine Cockburn, and Gottfried Wilhelm Leibniz. The sheer breadth of alternative theories of space they advance demonstrates the metaphysical richness of this era. Nonetheless, there is a deep agreement among their alternatives: all the accounts agree on the features of space. This base agreement set the scene for Kant’s theory of space, advanced after the Scientific Revolution ended.

Characteristic of the early modern period was the idea of a new start for philosophy and the sciences. In the period, those who advocated for such a program were collectively called the novatores or “innovators.” This chapter traces the emergence and the complex posterity of this term. Though now considered positive, it was much contested in the period, and the novatores were involved in numerous polemical disputes. Tracing the origins, history, and use of the term gives us precious insights into the dynamics of the great transformation of philosophy usually designated by another polemical label—the Scientific Revolution.

It has long been recognized that astronomy was a catalyst of the Scientific Revolution, spurring on deeply consequential speculation about the nature of the cosmos and its physical principles. Yet the history of celestial physics is far richer than was thought a generation ago, and there is much to be learned about the origins of the field, particularly in the sixteenth century, when humanist activity brought forth a dazzling array of philosophical possibility—from reconsiderations of Aristotle and Islamicate commentary to the revival of Platonic, Epicurean, and Stoic worldviews. Celestial physics offered some of the most heated arguments for or against the Aristotelian cosmos, with controversial attempts to account for astronomical observation by integrating various causal innovations. This chapter will focus on a number of themes that mark celestial physics and cosmological speculation in the sixteenth and early seventeenth centuries: the order of the celestial bodies and their nature, the relationship between celestial and terrestrial things, the question of celestial animism or vitalism, and the status of the divine in celestial nature.

This chapter looks at the mathematization of the study of nature by focusing on how practical mathematicians from the sixteenth century onward understood mathematics as primarily devoted to solving problems through mathematical construction. This constructive understanding of the nature of mathematics is then related to the double movement of physicalizing mathematics (giving physical interpretations to mathematical constructions) and mathematizing physics (understanding physics as basically involving the solution of problems). The work of seventeenth-century thinkers like Galileo, Descartes, and Mersenne is used to further illustrate these ideas, which led to the establishment of mathematical physics as characterized by its problem-solving nature.

During the seventeenth century, the advent of what were known as the “common” and “new” analyses fundamentally changed the landscape of European mathematics. The widely accepted narrative is that these analyses, analytic geometry and calculus (mostly due to Descartes and Leibniz, respectively), occasioned a transition from geometrical to symbolic methods. In dealing with the science of motion, mathematicians abandoned the language of proportion theory, as found in the works of Galileo, Huygens, and Newton, and began employing the Newtonian and Leibnizian calculi when differential and fluxional equations first appeared in the 1690s. This was the advent of a more abstract way of practicing mathematics, which culminated with the algebraic approach to calculus and mechanics promoted by Euler and Lagrange in the eighteenth century. In this chapter, it is shown that geometrical interpretations and mechanical constructions still played a crucial role in the methods of Descartes, Leibniz, and their immediate followers. This is revealed by the manner in which they handled equations and how they sought their solutions. The passage from proportions to equations did not occur in a single step; it was a process that took a century to reach completion.

This chapter focuses on the intellectual activities of Aristotelian philosophers within the late-Renaissance and early modern university context. It shows that Scholastic Aristotelianism constituted a varied, dynamic, and long-lasting philosophical tradition rooted in, but not limited to, problems arising from Aristotle’s texts. Late Scholastic solutions did not always pose obstacles to new sciences and matter theories, but also anticipated them. The chapter examines key variants of Aristotelianism in the context of their institutional settings and curricula. This provides an opportunity to re-assess radical Aristotelianism (e.g., Averroism), the late-Scholastic revival (e.g., the Jesuit Ratio Studiorum and Suárez) and Protestant Scholasticism. Developing Charles Schmitt’s thesis that there were many different, even conflicting, Aristotelianisms, the chapter argues that some so-called “anti-Aristotelians,” whom the moderns conscripted as allies to their cause, are better understood as working within a broader Aristotelian framework. Identifying the shared Aristotelian problem space of both more orthodox and controversial philosophers of the period affords a better understanding of both the conflicts themselves and the extensive debts that later developments bore to this tradition.

Sidereus Nuncius was a seminal text of the Scientific Revolution. It reported celestial observations whose implications upended the geocentric cosmology few had ever doubted. But Galileo’s treatise also combined topics and methodologies that traditionally had been assigned separately to mixed mathematics and natural philosophy. Whereas the bounds between these disciplines had been weakened by earlier controversies, particularly about the regressus method and about the certainty of mathematics (i.e., the Quaestio de Certitudine), Sidereus Nuncius broke them down altogether, to the delight and dismay of readers. Galileo’s application of mathematical methods—empiricism and quantification—to natural philosophy framed the ensuing discussions, such that even those who disagreed with his conclusions responded on those grounds. Thus, the book was pivotal in the process of disciplinary admixture that reorganized the study of nature into modern science.

In the Scientific Revolution the concept of body evolved along several divergent lines, from conceptions that rely exclusively on extension and motion to more elaborate accounts that include attributes such as solidity and force. A host of complications were disputed, such as atomism versus the infinite divisibility of bodies, the distinction between primary and secondary properties, and the possibility of a vacuum. This chapter explores these and other issues, but with an emphasis on the relationship between body and spatial extension. Descartes's three-part distinction—i.e., whether the relationship between body and extension is conceptually, modally, or really distinct—serves as a framework for investigating the development of early modern theories of material body, a process that laid the basis for the ontology and epistemology of modern science.

Newton’s remarkable achievements in planetary theory and dynamics were followed by a century of equally remarkable advances in the generalized science of forces acting on bodies in motion. Far from merelyformalizing the Newtonian framework, these advances aimed at solving deep problems left in Newton’s wake. First, Newtonian theory focused on centripetal forces, which are not characteristic of motion under arbitrary constraints or bodily deformation due to pressure and stress. Second, Newton’s attempts at fluid mechanics made clear that media could not be adequately analyzed using strategies developed for point-particles. Both considerations suggested that different forms of body required different analytical and conceptual tools. They required the formulation of generalized principles flexible enough to treat heterogeneous material configurations, but stringent enough to preserve the unity of mechanics as a study of matter and motion. Ultimately, Newton’s successors established a new discipline, analytical mechanics. Its primary object of investigation was the functional representation of the invariant relations behind dynamic phenomena, not the geometric representation of trajectories. The philosophical suppositions behind the new mechanics constituted a new mechanical philosophy, but one that hearkened back to, and completed the project of, the mechanical philosophy of the mid-seventeenth century.