The cosmological revolution of the seventeenth century saw the establishment of physics and astronomy as autonomous spheres. The Ptolemaic universe was a hierarchy of dignity – sun and stars above, lowly earth at the bottom – supported by a hierarchy of disciplines that set theology and metaphysics at the apex of intellectual life. The advancing belief in heliocentrism that undid the first was paralleled by challenges to the second, starting with the humanist celebration of rhetoric and moral philosophy and carried further by Copernicus’s exaltation of astronomy, hitherto assigned the lowly place of a mere computational aid, as a source of truth. The authority of the Church was often restricted by political and cultural divisions, so that many heretical ideas could not be stamped out, and Galileo long found support from Jesuits and even the pope. As he lost it, he sought backing in a wider audience, publishing his writings in Italian rather than Latin, and in a popular style. Newton and his followers would similarly seek to substitute horizontal connections for the vertical ones around which intellectual life had long been organized, demonstrating elements of their theories to popular audiences and explicitly describing the kind of science they favored as “public.”

Hegel has commonly been ridiculed for views expressed in his 1801 dissertation, On the Orbits of the Planets, in the final pages of which he had adopted a series of numbers from Plato’s Timaeus – a cosmological text earlier taken seriously by Kepler – to account for the ratios of the distances from the sun of the then known six planets of the solar system. While defenders of Hegel have usually toned down the extent of these claims, this chapter argues that Hegel’s reference to Plato’s Pythagorean cosmology must be taken seriously – not as cosmology, however, but as instantiating the logic appropriate for empirically based science. Hegel’s allusion to Plato’s mythologically expressed “syllogism” is consistent with his idea that logic as Plato conceived it allowed its application to the empirical world but that this applicability had been compromised by Aristotle adaptation of it. With the proper grasp of logic’s utilization of the category of “singularity” in its difference to “particularity” – available to Plato but not Aristotle – we can appreciate how, while Kepler’s Laws were empirically based, Newton’s were not as they relied on abstract entities that could not be justified empirically.

Natural History and Science’ focuses on Goldsmith’s eight-volume An History of the Earth, and Animated Nature (1774), a comprehensive natural history that synthesizes the works of various naturalists, including Carl Linnaeus and Georges Louis Leclerc, Comte de Buffon. Goldsmith’s incorporation of these other writers’ observations into his scientific literature participates in the collective, collaborative mode of natural history, a science that invited amateur participation and revision in this era.

Chapter 1 looks at depictions of human perfection in sources not usually consulted within Christian ethics. The first source is church memorials, first in Westminster Abbey -- particularly the twentieth-century Memorial to the Unknown Warrior and the seventeenth-century memorial to Isaac Newton -- and then seventeenth- and eighteenth-century family memorials in three parish churches near Canterbury Cathedral. The second source is recent depictions of perfection within the arts and sport mostly gleaned from the columns of The Times. And the last source is John Bayley’s autobiographical account of a ‘perfect’ meal cooked by his future wife, the novelist and philosopher Iris Murdoch. Together they indicate that a dynamic form of ‘perfection’ was, and still is, readily attributed to human endeavours.

In this chapter, I interpret section 6.361 of Wittgenstein’s Tractatus – containing Wittgenstein’s second reference to Heinrich Hertz in the book – in the context of the nearby framing remarks concerning the ‘law of causality’. Attention to the relevant details of Hertz’s work sheds light on a number of Wittgenstein’s remarks about mechanics in the 6.3s and, in particular, explains Wittgenstein’s claim that ‘What can be described can happen too, and what the law of causality is meant to exclude cannot even be described’ (6.362). For Wittgenstein, to describe events in causal terms is to describe them via an appeal to temporal and spatial asymmetries. However, no alternative is available: a description that did not appeal to such asymmetries would not be a description of anything. According to the Tractatus, descriptions are recognized as causal when they are embedded in a unified theoretical framework, but causal powers, understood as relations of material necessity, do not exist.

Fortified as a Parliamentarian stronghold under Oliver Cromwell, Cambridge emerged from the English Civil War intact, and flourished under the Restoration of Charles II in 1660. A great age of science and architecture at Cambridge followed, inspired by Trinity fellow Isaac Newton and architect-mathematician Christopher Wren. Stephanie Boyd explains why the building of college courts, chapels and libraries boomed in this period, and classical masterpieces such as the Wren Library at Trinity sprung up. Comparison is drawn between the fine Cambridge colleges and the squalor of the town, and the impact of the Great Plague on townspeople and scholars. The contributions of individuals such as Francis Bacon and Pepys are included, along with local businessman Thomas Hobson, originator of both fresh water to the town from Nine Wells and the expression ‘Hobson’s Choice’.

Two scientists more than anyone else have contributed in defining our understanding of gravity: Newton in 1679 and Einstein in 1915. The mathematical frameworks the two have developed and proposed, however, are very different. Newton’s gravity is the one we learn at school and is normally taught at university. It provides a very natural interpretation of what we experience - the apple falls from the tree because the Earth attracts it! Einstein’s gravity is studied only in the most advanced courses at the university and provides a very counterintuitive explanation, requiring the concepts of spacetime and curvature. This chapter will provide a first description of the Einstein equations and, although it will not enter into the mathematical aspects of the equations, it will explain the basic concepts behind them. Acquiring a first qualitative understanding of Einstein equations will be useful to comprehend better the concept of spacetime curvature discussed in Chapter 4.

This chapter begins with a survey of the young Newton’s early exposure to experimental philosophy and then turns to the emergence of experimental pedagogy in the last years of the seventeenth century and its rapid expansion in the early decades of the century that followed. The proliferation of courses in experimental philosophy, both public and university-based, in Oxford, Cambridge, London, and St Andrews, is testimony to its success and legitimacy. So much so, we argue, that when his commitment to universal gravity came under attack by Continental detractors, Newton openly and very strategically aligned himself with experimental philosophy, in part because of the credibility that this approach to natural philosophy already possessed. This is not to claim that every Newtonian was partial to experimental philosophy, and in this chapter we examine the views of one opponent, the Oxford natural philosopher John Keill. We document the process by which Newton publicly declared himself to be an experimental philosopher in the second edition of the Principia of 1713, and then go on to examine his role in the eclipse of Baconian natural history.

In the years after the publication of the second edition of the Principia, Newton further elaborated his vision of the genealogy of knowledge, and his subsequent conception of the limits of ‘legitimate’ knowledge. Metaphysics now emerged for him as the unifying force that explained all the evils of intellectual life, above all pagan idolatry; the hubristic rationalism in theology that gave birth to odium theologicum and persecution; and the unwarranted search for speculative, causal explanations in natural philosophy. In a set of elaborate writings, ranging from the ecclesiastical-historical ‘Of the Church’ (in which we see the influence of Bayle’s close friend Jacques Basnage) to further polemical writings against various followers of Leibniz and Malebranche, he developed his mature vision of a Kingdom of Darkness at the centre of which lay speculative, metaphysical philosophy. The manuscript ‘Tempus et Locus’ should be dated to this period, rather than to the 1690s. Finally, it is shown that Newton’s earliest followers understood perfectly the broad methodological message which he was trying to advance, and continued to disseminate it aggressively in their writings. The earliest decades of the eighteenth century were devastating for the practice of ‘philosophy’ as it had been conducted for much of Western history.

This chapter explores the development of Newton’s methodological thought up to c.1700, as well as that of his first followers. Newton’s caution in not antagonising Huygens in particular is highlighted. It was only in this decade that Newton started to emphasise the natural-theological significance of his natural philosophy, especially in manuscripts related to the Classical Scholia. But there was no metaphysical component; rather, Newton insisted on the analogical predication of the divine. Even more important was his reconsideration of the Hypotheses of the first edition, which eventually became the Rules of Philosophising of the second. It is shown that these were not abstract methodological principles, but rather a set of dialectical arguments designed to negate the possibility of weightless matter. Nonetheless, they shaped Newton methodological agenda and language for the rest of his life. His position was understood perfectly by his earliest follows: David Gregory and John Keill, both of whom were teaching in Oxford.

This chapter introduces Newton’s intellectual biography before the publication of the Principia, and provides a new account of his methods as a natural philosopher. From the 1660s onwards, Newton – in line with his mentor Isaac Barrow and with other mixed mathematicians discussed in I.1 – sought a phenomenological science of properties, actively disdaining conjecture concerning the underlying causes of phenomena. The famous ‘De gravitatione’ manuscript is shown to stem from hydrostatical lectures delivered in 1671; contrary to most of the literature, it contains no elaborate metaphysics of divine omnipresence. Newton’s interest in revealed theology developed when he had to perform disputations in 1677; he did not become an antitrinitarian until the late-1680s, and there is no evidence that his theological views influenced the Principia. For all its mathematical sophistication, that work was very much the product of a methodology not much different from that which mixed mathematicians had been advocating for the previous century. In particular, Newton’s ideas at this time bear a strong conceptual resemblance to those developed by other English mixed mathematicians, such as John Wallis. The very first ‘Newtonians’ recognised the anti-metaphysical thrust of his ideas.

In 1713 Newton finally published the second edition of the Principia. Its changes included not only the new Rules of Philosophising discussed in III.1, but also the very famous General Scholium. This chapter provides the fullest ever contextualisation and interpretation of that text. It charts in detail how Newton’s dispute with Leibniz led him to double-down on his anti-metaphysical stance, and to declare many questions – not least concerning causation – to be beyond the boundaries of legitimate natural philosophy (now described as ‘experimental’). Second, it shows that Newton’s talk of the ‘God of Dominion’ was derived from Samuel Clarke’s recent writings – in line with Clarke’s position, Newton had now moved away from his earlier neo-Arianism into a position of trinitarian nescience in which all speculation on the subject, with consubstantialist or Arian, was dismissed as ‘metaphysical’. The role played by the ‘God of Dominion’ was simply the standard refrain of Newtonian natural theology: that the true conception of the divine that could be predicated from nature was not of an impersonal metaphysical first principle, but of a living God. Finally, Newton’s talk of God’s ‘substantial’ omnipresence was again not a concession to metaphysical thinking, but a residue of yet another polemic devised by his friend Samuel Clarke, this time against the freethinker Anthony Collins.

This chapter focusses on the famous queries appended to the Latin Optice, in which Newton made some notorious – but also very ambiguous – statements about space being akin to the divine sensorium. Many commentators have speculated about how this implied a metaphysics of divine omnipresence. It is shown that this was not the case – rather, Newton was developing the anti-metaphysical analogical natural theology he had first conceived in the 1690s. But now, his argument took on a new, polemically anti-Cartesian dimension. This was the result of the influence on him of some of his followers, above all Samuel Clare, the translator of the English Opticks. Indeed, there is very strong circumstantial evidence that Clarke was actively involved in the composition of the new material in the Optice queries, or at least their natural-theological material. That material also owed a debt to another early Newtonian, the Scottish physician George Cheyne.

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.

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.

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.

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.