The concepts of inductive and deductive inference are introduced and contrasted. An artificial example is used to emphasize the logical structure of the problem of induction. To see how the problem of induction relates (and also does not relate) to a real episode of experimental inquiry, this chapter considers the case of Isaac Newton’s optical experiments using prisms to investigate the refraction of light. Although Newton did not concern himself with the problem of induction as philosophers now understand it, he used experimental strategies designed to address possible errors in the conclusions about light that he drew from his observations.

Deterministic and probabilistic mathematical theories have in common that they construct mathematical representations of real-world phenomena. On a basic level this can be regarded as a type of explicit problem-solving. This involves presenting the problem in ‘abstract form’ in symbols (often numbers, letters, or geometrical elements). These symbols are then manipulated in accordance with precise rules: Strings of symbols in sets of equations come to represent ideas. The construction of mathematical theories involves testing whether experimental observations fit the postulated ‘mathematical rules.’ If they do not fit then the ‘mathematical rules’ may be refined, extended, or new ones may be formulated. Newly mathematically formalized ideas are validated by testing whether they align with observations but also by examining whether they are consistent with other, previously established, mathematical rules.

This chapter explores the impact of science and technology’s objectifying gaze on society, Culture, and politics throughout history. It discusses how this gaze has turned the world into an object and humans into observers, diminishing moral, psychological, and political aspects. The chapter analyzes the duality of objectification, which renders man-made objects external despite embodying human values and actions. It examines the Industrial Revolution as a pivotal historical context where technology was seen as a mark of progress and an embodiment of objective Nature. Eventually, the human choices and interests behind technology were exposed, leading to the reconsideration of technologies from ethical, economic, political, and aesthetic viewpoints. The chapter also points to the ambivalence surrounding technology, including both fear and admiration, and how the disillusionment with technology has impacted the democratic epistemological framework. Additionally, it discusses the influence of philosophers-scientists like Descartes and Newton on modern dualistic cosmology, highlighting how science and technology have shaped various socio-political fields such as law, medicine, economics, and political science.

This chapter discusses the sections of finite and absolute mechanics of Hegel’s Philosophy of Nature which are predicated upon his theory of space and time. It starts with the emergent notions of matter and movement before giving the details of the mechanical analysis in a close reading. Giving a foundation for Kepler’s laws is not only a touchstone of Hegel’s theory but is an integral rung in a system of steps building natural science from space and time. The chapter exposes three main strands of argument: dimensional realization of time and space in movement of matter, striving towards inner and outer centers of extended bodies, and the realization of a system of bodies in motion which materializes a complexity paralleling not only of the tripartite system general-particular-individual of his logic but additionally includes two particulars – as necessary in Hegel’s account of nature. Lastly, the chapter comments briefly on the relationship to Kant, Newton, and classical mechanics, as well as on modern aspects. As it demonstrates, Hegel’s treatment of mechanics is not an idiosyncratic way of presenting celestial mechanics but contains radical, quite modern metaphysical concepts which are not only interesting in their own right but furnish a key to the understanding of his system.

Chapter 23 sets Goethe’s Farbenlehre (Theory of Colours) in context. Colour had been the subject of intensive study, both aesthetic and scientific, in the eighteenth century, and the chapter reconstructs the many influences on Goethe and his contemporaries, from the recent discoveries of Herschel and Ritter, to earlier figures, above all Newton, but even Aristotle and Hippocrates. The chapter also presents the central tenets of Goethe’s Farbenlehre, with a particular focus on the theoretical first part, which offers a physiological theory of colours and deals with the physical nature of light.

This chapter focuses on the figure of the Cyclops and the use of ‘the animal’ in thinking human difference. It presents the animalizing of certain humans (the attribution of animal features to them) as a potent strategy to dehumanize and thus marginalize certain ways of being human. In the ethnographic imagination of Homer’s Odyssey, the margins of the known world are shown to coincide with the margins of the human. The chapter further illustrates that this spatial concept of the human did not remain restricted to the ancient world but carries on into the modern: The figure of the Cyclops, whose problematic humanity is in sharp contrast to the enlightened, educated, and cunning Odysseus, in many ways anticipates that of ‘the savage’ as the quintessential ‘other’ in the modern Western ethnographic literature. And yet the question arises as to whether the ancient story does not already expose the kind of hubris at play when we normalize certain ways of being human while dismissing others.

Two parallel trends prepared scholars for the investigation of the mind–body relationship so that a model of psychological inquiry could evolve. The first trend was methodological, characterized by the triumph of empiricism. Scientific innovations by Francis Bacon and Newton were firmly based on careful observations and quantification of observables. Using inductive methods, moving from observed particulars to cautious generalization, empiricism stood in contrast to the deductive methods of the Scholastic philosophers. The second trend occurred in the attempt to develop conceptions on the nature of humanity and was more a philosophical enterprise. Spinoza taught that mind and body are manifestations of the same unity of the person. Human activity, although unique because of humanity’s higher intellectual powers, is determined by the laws of nature. Descartes stated that the first principle of life is self-awareness of the idea, and all else that we know proceeds from self-reflection. His dualism of the interaction between mind and body distinguishes psychology from physiology. Descartes’ views were developed in the French and British philosophical traditions; Spinoza influenced the German efforts to develop a model of psychology.

This chapter defends Peirce’s conception of science against a pair of current, mutually antagonistic ideas of the difference of modern science from classical and medieval philosophy. The one party celebrates the difference, the other deplores it, but they agree that modern science rejects the classical ideal of theory as knowledge good for itself. Peirce saw that difference more subtly as one in which the classical ideal of knowing is transformed rather than abandoned. This revolution in cognitive aim did not occur arbitrarily. Well-established facts about the defeat of the Aristotelian world-view are cited to support the novel thesis that it depended on an empirical yet normative discovery, that restless, unending, specialist inquiry is more satisfying intellectually than is the dialectic of systems. The history of science reviewed in this chapter provides evidence for the argument of Chapter 9, that there is normative knowledge and that it is empirical.

Chapter 1 examines the relationship between Old and New Mechanism and uses it to illuminate the relations between metaphysical and methodological conceptions of mechanism. This historical examination will directly motivate our new deflationary account of mechanism developed in the subsequent chapters. We start by focusing on the role of mechanistic explanation in seventeenth-century scientific practice, by discussing the views of René Descartes, Christiaan Huygens, Gottfried Wilhelm Leibniz and Robert Boyle, and the attempted mechanical explanations of gravity by Descartes and Ηuygens. We thereby illustrate how the metaphysics of Old Mechanism constrained scientific explanation. We then turn our attention to Isaac Newton’s critique of mechanism. The key point is that Newton introduced a new methodology that freed scientific explanation from the metaphysical constraints of the older mechanical philosophy. Last, we draw analogies between Newton’s critique of Old Mechanism and our critique of New Mechanism. The main point is that causal explanation in the sciences is legitimate even if we bracket the issue of the metaphysics of mechanisms.

Chapter 10 briefly comments the influence of Euclid’s theory of magnitude and the Eudoxian theory of proportions on Kant’s thought in light of advances in mathematics from the early seventeenth century to the late eighteenth century. Despite these advances, mathematics was still often viewed as a science of magnitudes and their measure. The chapter also indicates further work to be done to understand Kant’s philosophy of geometry, arithmetic, algebra, and analysis.

Can we 'see' photons, black holes, curved spacetime, quantum jumps, the expansion of the universe, or quanta of space? Physics challenges appearances, showing convincingly that our everyday vision of reality is limited, approximate and badly incomplete. Established theories such as quantum theory and general relativity and investigations like loop quantum gravity have a reputation of obscurity. Many suggest that science is forcing us into a counterintuitive and purely mathematical understanding of reality. I disagree. I think that there is a visionary core at the root of the best science. Where 'visionary' truly means formed by visual images. Our mind, even when dealing with abstract and difficult notions, relies on images, metaphors and, ultimately, vision. Contrary to what is sometimes claimed, science is not just about making predictions: it is about understanding, and, for this, developing new eyes to see. I shall illustrate this point with some concrete cases, including the birth of quantum theory in Einstein’s intuition, curved spacetimes and quanta of space.

This introductory chapter gives a brief survey of some of the phenomena for which classical general relativity is important, primarily at the largest scales, in astrophysics and cosmology. The origins of general relativity can be traced to the conceptual revolution that followed Einstein’s introduction of special relativity in 1905. Newton’s centuries-old gravitational force law is inconsistent with special relativity. Einstein’s quest for a relativistic theory of gravity resulted not in a new force law or a new theory of a relativistic gravitational field, but in a profound conceptual revolution in our views of space and time. Four facts explain a great deal about the role gravity plays in physical phenomena. Gravity is a universal interaction, in Newtonian theory, between all mass, and, in relativistic gravity, between all forms of energy. Gravity is always attractive. Gravity is a long-range interaction, with no scale length. Gravity is the weakest of the four fundamental interactions acting between individual elementary particles at accessible energy scales.

Historians consider the “Scientific Revolution” of the sixteenth and seventeenth centuries the period in which the foundations of modern scientific practice and methodology first took shape. Francis Bacon (1561-1626), sometimes known today as the creator of the scientific method, inspired the formation of the first scientific societies, including the Royal Society of London and the French Académie Royale des Sciences, and their members made experiment and empiricism central to the study of nature. More recently, however, historians have had to wrestle with an interesting conundrum: some of those long hailed as pioneers of scientific experimentalism, such as Robert Boyle (1627-1691) and Isaac Newton (1643-1727), were also committed alchemists. Their dedication to this mysterious and misunderstood art led some modern biographers to deny or even suppress evidence of their alchemical pursuits. Yet, alchemical ideas were central to how Boyle, Newton, and others understood nature. In fact, Newton’s groundbreaking scientific achievements owe a particular debt to alchemical theories, without which his revolutionary vision of the cosmos would not have existed.

The chapter presents concepts of space as developed by Hobbes and Leibniz respectively. It highlights commonalities and differences in their respective concepts of space. For Hobbes, the concept of space is articulated through ideas of imaginary and real space. Hobbesian space emerges as determined by the measurment of bodies, material and thus controllable. This view of space strongly resonates with the uses of space is contemporary spatial justice studies. For Leibniz, space is a logical grounding against which the materiality of the world unfolds but also the outcome of the activity of monads as simple substances. For Leibniz, space as an order of relationships is not controllable but knowable.

This chapter argues that William Cowper aligned various faiths against atheism and the moral degeneration that, in his mind, atheism necessarily produced. Examining poems from all phases of Cowper’s career – including his 1782 moral satires, the Olney Hymns (1779), The Task (1785), and “The Castaway” (1799; 1803) – I elucidate his belief that, unlike insensible atheists, Christians should extend their sympathy to all parts of God’s creation: to the Indians oppressed by British colonialism, to the poor inhabitants of the British countryside, even to the hares Cowper kept as pets in Olney. The only figure unworthy of such sympathy in Cowper’s thinking was the atheist. Thus, for Cowper, non-Christians from abroad were excusable, and even respectable, as long as they believed in a deity and did their best with the portion of divine light they had been granted. Cowper rejected all faiths but evangelical Christianity as false, yet he aspired to a form of sociability that was available to all theists. Although there were clear limits to Cowper’s ecumenical impulses, they reveal the imaginative multifaith alliances eighteenth-century atheism was capable of engendering.

Newton codified the laws of motion and gravity, their primitive forms being enunciated in 1665-66. Using Kepler's laws, he discovered the inverse square law of gravity and went on to show that gravity is the same force which holds the planets in their orbits, as well as that which causes apples to fall to the ground. Newton was a brilliant experimentalist who invented the Newtonian, reflecting telescope which eliminated the aberrations of refracting telescopes such as those built by Galileo. Newton's researches culminated in the publication of his revolutionary Principia Mathematica of 1687. He devoted as much effort to chemical (or alchemical) analyses and to the interpretation of ancient texts and the scriptures. He was also the inventor of differential and integral calculus.