‘Science seems to be either all good or all bad. For some, science is a crusading knight beset by simple-minded mystics while more sinister figures wait to found a new fascism on the victory of ignorance. For others it is science which is the enemy; our gentle planet, our slowly and painfully nurtured sense of right and wrong, our feel for the poetic and the beautiful, are assailed by a technological bureaucracy – the antithesis of culture – controlled by capitalists with no concern but profit. For some, science gives us agricultural self-sufficiency, cures for the crippled, a global network of friends and acquaintances; for others it gives us weapons of war, a school teacher's fiery death as the space shuttle falls from grace, and the silent, deceiving, bone-poisoning, Chernobyl.

Both of these ideas of science are wrong and dangerous. The personality of science is neither that of a chivalrous knight nor pitiless juggernaut. What, then, is science? Science is a golem.

A golem is a creature of Jewish mythology. It is a humanoid made by man from clay and water, with incantations and spells. It is powerful. It grows a little more powerful every day. It will follow orders, do your work, and protect you from the ever threatening enemy. But it is clumsy and dangerous. Without control a golem may destroy its masters with its flailing vigour; it is a lumbering fool who knows neither his own strength nor the extent of his clumsiness and ignorance.

We always remember where we were when we first heard about a momentous event. Those over forty-five years old know what they were doing when they heard that John F. Kennedy had been assassinated. Similarly, anyone who was watching television remembers where they were at 11:38 a.m. Eastern Standard Time on 28 January, 1986 when the Space Shuttle Challenger exploded. The billowing cloud of white smoke laced with twirling loops made by the careering Solid Rocket Boosters proclaimed the death of seven astronauts and the end of the space programmme's ‘can do’ infallibility.

Unlike the inconclusive Warren Commission that inquired into Kennedy's death, the Presidential Commission chaired by William Rogers soon distributed blame. There was no ambivalence in their report. The cause of the accident was a circular seal made of rubber known as an O-ring. The Challenger's Solid Rocket Boosters were made in segments, and the O-rings sealed the gap between them. A seal failed and the escaping exhaust gas became a blow torch which burned through a strut and started a sequence of events which led to the disaster.

The Commission also revealed that the shuttle had been launched at unprecedentedly low temperatures at the Cape. Richard Feynman the brilliant, homespun American physicist is often credited with the proof. At a press conference he used a piece of rubber O-ring and a glass of iced water to show the effect of cold on rubber.

Shortly after the Second World War, an engineer from New Zealand, ‘Bill’ Phillips, working at the London School of Economics, built a model of the economy. The marvellous thing about this model was that it ran on water. Phillips's model was a set of tanks, valves, pumps, pipes, baffles and cisterns. If, say, the flow into some cistern increased while the cross section of the output remained the same, the water in the cistern would rise. The new level might increase the flow of water into another cistern, raising its level, or it might be enough to trigger a valve and restrict the flow somewhere else. The whole thing, which stood about seven feet high, weighed a good part of a ton, and was prone to leakage and corrosion, was meant to represent the flows of income around a national economy. Changes of levels were linked by indicators to scales which represented measures of economic performance such as price indices, stocks of money, or Gross National Product. It was even possible to link one of these gurgling monsters to another, thus representing the interaction of two national economies, or the interaction of one economy with the rest of the world. Phillips's hydraulic model of the economy has been restored recently and can be seen at the Science Museum in London.

Nowadays no one would dream of building a model of the economy that ran on water.

These words were uttered in 1984 by the late Sir Walter Marshall, chairman of Britain's then Central Electricity Generating Board (CEGB). The CEBG used the rail system to transport spent nuclear waste from its generating plants to its reprocessing plants. In spite of the fact that the fuel was contained in strong containers, or flasks, the public was not happy. The CEGB therefore arranged for a diesel train, travelling at a hundred miles per hour, to crash head-on into one of their flasks to show its integrity. Sir Walter's words were spoken to the cameras immediately following the spectacular crash, witnessed by millions of viewers either on live television or on the nation's televized news bulletins. Sir Walter was claiming that the test had shown that nuclear fuel flasks were safe. (The source from which Sir Walter's quotation was taken and of the basic details of the train crash is a video film produced by the CEGB Department of Information and Public Affairs entitled ‘Operation Smash Hit’.)

Isaac Newton's Observations upon the Prophecies of Daniel, and the Apocalypse of St. John, prepared for the press from his manuscripts by his nephew Benjamin Smith, was published in two editions in London and Dublin in 1733. According to Richard S. Westfall, Newton's finest twentieth-century biographer, the author “had cleansed his Observations”and his heirs “could publish the manuscript without concern.” Yet one might be permitted to wonder whether either the actual or the intended reception of Newton's posthumous work was as uncontroversial as it has seemed to late twentienth-century eyes. The book was dedicated to Peter King, baron of Ockham, the lord chancellor, who had defended Newton's sometime disciple, William Whiston, during his trial for heresy in July 1713. Although Whiston later fell out with King, he nevertheless continued to maintain that King's youthful writings on the primitive Church supported the Arian position for which he had himself been condemned. King was also the dedicatee of other works of dubious theological orthodoxy, such as Daniel Mace's attempted revision of the New Testament.

The opposition between analytical and synthetic proof methods has an intriguing and complex role in the history of Western mathematics. In Antiquity analytical method (in brief, analysis) was conceived of as a method of discovery, or problem solving: it starts from what is sought as if it had already been achieved, and, working step by step backwards, it eventually arrives at what is known. This and similar rather vague definitions were aimed at describing in a general way a whole apparatus of geometric problem solving procedures developed by the Greeks. Synthesis goes the other way round: it starts from what is known and, working through the consequences, it arrives at what is sought. The axiomatic and deductive structure of Euclid's Elements was the model of the synthetic method of proof. Analysis (or resolutio) was often thought of as a method of discovery preliminary to the synthesis (or compositio), which, reversing the steps of the analytical procedure, achieves the true scientific demonstration. Analysis was thus the working tool of the geometer, but it was with synthesis that one could demonstrate things in an indisputable way. In the Middle Ages this pattern of definitions became bound up with the philosophical and logical tradition. A question which was often raised concerned the relationship between the mathematical proof methods and other accepted forms of deductive proof, typically those codified in Aristotle's Organon.

INTRODUCTION

The first edition of Isaac Newton's Principia was published in 1687, followed by a second edition in 1713 and a third in 1726, the year before he died. The Principia is universally held to have been a major turning point in natural philosophy in the seventeenth century. That turning point is clearly reflected in the comparison of the title of Descartes's 1644 Principles of Philosophy with the title of Newton's Mathematical Principles of Natural Philosophy. Even though both men were noted mathematicians, Newton's book is distinguished from that of Descartes by virtue of being a mathematical description of nature. In the General Scholium of the second edition Newton sets out the difference quite clearly: “But hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses . . . And to us it is enough, that gravity does exist, and acts according to the [mathematical] laws which we have explained.” Although Newton was strongly influenced by the Cartesian mechanical philosophy during the first two decades of his scholarly work, he nevertheless expressed himself analytically from the very beginning of his work in 1664. By 1684, however, he had rejected Cartesian mechanical explanations for gravity, and in the Principia he emphasized the analytical expression of the inversesquare law for gravity. The final impetus for that rejection came from Newton's correspondence in 1679 with Robert Hooke, which led Newton to derive Kepler's area law as a geometrical measure of time to employ in analyzing orbital motion. That same correspondence has shown that Newton's later work is an extension, not a revision, of his earlier work.

VARIETIES OF FORCE IN THE PRINCIPIA

Newton's physics is based on two fundamental concepts: mass and force. In the Principia Newton explores the properties of several types of force. The most important of these are the forces that produce accelerations or changes in the state of motion or of rest in bodies. In Definition 4 of the Principia, Newton separates these into three principal categories: impact or percussion, pressure, and centripetal force. In the Principia, Newton mentions other types of forces, including (in Book 2) the forces with which fluids resist motions through them. Of a different sort is Newton's “force of inertia,” which is neither an accelerative force nor a static force and is not, properly speaking in the context of dynamics, a force at all.

The structure of Newton’s Principia follows a classical pattern: definitions and axioms, followed by the statement of propositions and their demonstrations. Newton’s treatise differs, however, from classical (or Greek) geometry in two respects. First, there is a constant appeal to the method of limits – Newton’s “first and ultimate ratios,” as set forth in Book 1, Section 1. Second, the validity of propositions is tied to evidence of experiment and critical observation.

In the demonstrations in the Principia, Newton generally proceeds by establishing a series of proportions from a geometric configuration. He then allows one or more of the parameters to be diminished without limit, thereby obtaining a limiting (“ultimate”) value of the geometric ratio. It is in the limit that Newton’s proofs are valid.

After his first optical publications in 1672 Newton was identified by his contemporaries and later generations as a supporter of the corpuscular or emission theory of light, in which light is assumed to consist of corpuscles, or atoms, emitted from a luminous source such as the Sun. While it is true that Newton believed in a corpuscular theory, utilized it in developing many of his optical experiments and theories, and argued vigorously against the wave theory of light, he never believed that it was a demonstrated scientific truth and considered it to be only a probable hypothesis. This distinction explains why, for example, he never set forth a synthetic account of the emission theory and eschewed it in his public accounts of his scientific theories. In order to understand Newton's advocacy and use of atomism in his optics it is necessary to understand his views on hypotheses and certainty in science.

HYPOTHESES IN NEWTON’S SCIENCE

From the beginning of his scientific career Newton was concerned with establishing a new, more certain science to replace contemporary science, which he felt was rife with “conjectures and probabilities.” He believed that he could establish a more certain science both by developing mathematical theories and by basing his theories on experimentally discovered properties. To establish a more certain science, Newton insisted that one must “not mingle conjectures with certainties.”

THE INTELLECTUAL BACKGROUND OF A NATURAL PHILOSOPHER OF THE SEVENTEENTH CENTURY

Newton's theological manuscripts are concerned principally with two subjects: the interpretation of the prophecies of the Apocalypse and Daniel, and the history of the early Church. These two subjects are linked, but it was as a consequence of his interpretation of the Apocalypse that Newton undertook his study of the history of the Church. The study of prophetic literature was firmly rooted in Cambridge, where this subject was taught by Joseph Mede, author of a Clavis Apocalyptica (or Key to the Apocalypse), a work much used by Newton.

Newton’s interest in the prophecies is already documented in the “Quaestiones” of the Trinity Notebook (1664–5). In “Of Earth” (c. 1664) Newton made deductions about physics, “in rerum natura,” directly from the Scriptures: the final conflagration of the earth, and the probable succession of worlds. This last affirmation was supported by a passage of the Book of Revelation which referred to days and nights after the Last Judgment, which would have made no sense had the world finished for ever. In “Of the Creation” (c. 1664) Newton made use of a passage from Genesis to prove that God had created time. From these entries it is evident that Newton used biblical texts to determine the truth of a philosophical proposition. Strange or ingenuous as this approach of Newton’s might seem, given that the trial and condemnation of Galileo had shown the difficulty of reconciling philosophy and religion, it was one he maintained in subsequent years.

INTRODUCTION: PHILOSOPHICAL CONTROVERSY OVER NEWTON’S IDEAS OF SPACE, TIME, AND MOTION

Newton's concepts of “absolute space,”“absolute time,” and “absolute motion” met with serious objections from such philosophical contemporaries as Huygens, Leibniz, and Berkeley. Among philosophers of the early twentieth century, after the advent of Special and General Relativity, the objections bordered on scorn: Newton's concepts were not only lately outmoded, but they were also epistemologically inherently defective, empirically unfounded - concepts not scientific at all, but “metaphysical,” in so far as science is concerned precisely with “sensible measures” rather than obscure notions of what is “absolute.”The prevailing idea was that Einstein had established not only a new theory of space and time, but a deeper philosophical viewpoint on space and time in general. From this viewpoint, space, time, and motion are essentially relative, and to call them absolute was an elementary philosophical error. As Einstein put it, General Relativity had taken from space and time “the last remnant of physical objectivity.”

The philosophical motivation for this viewpoint seems obvious. Space cannot be observed; all that we can observe is the relative displacement of observable things. Therefore, if we observe two bodies in relative motion, to say that one of them is “really” moving, or that it is moving “relative to absolute space,” is to pass beyond the bounds of empirical science. If we wish to decide which bodies are moving, we have to construct a frame of reference – that is, we must designate some reference-points to be fixed, and compare the motions of other bodies to these.

The aspect of Newton's Principia that has provoked the most controversy within the philosophy of science, other than his invocation of absolute space, time, and motion, has been his claim to have “deduced” the law of universal gravity from phenomena of orbital motion. In particular, a tradition that began with Pierre Duhem and continued with Karl Popper and then Imre Lakatos has argued that this claim is at best misleading (Duhem) and at worst a subterfuge (Lakatos). Among other reasons they have advanced against any such deduction is the objection that no deduction from consistent premises can yield a conclusion that entails one or more of these premises is false; yet one consequence of the law of universal gravity is that all the orbital phenomena from which Newton proceeds in his supposed deduction are, strictly, false. Duhem, Popper, and Lakatos insist, to the contrary, that only a hypothetico-deductive construal of Newton's evidence for universal gravity makes sense, Newton's outspoken objections to hypothetico-deductive evidence notwithstanding. More recently, Clark Glymour has offered a “bootstrapping” construal of Newton's evidence, proposing that it captures the logical force of the reasoning for universal gravitation in the Principia better than a straight-forward hypothetico-deductive construal can. Glymour too, however, sees no way around concluding that some of what Newton seems to think he is doing cannot be correct.

One issue this raises is understanding the reasoning Newton offers in arriving at the law of universal gravity and describes as a “deduction” from phenomena. Another is the extent to which such reasoning is cogent and illuminates scientific method. The simplest way to respond to these questions is to proceed step-by-step through Newton’s reasoning.

In the Preface to the first edition (1687) Newton informs the reader straight off that he intends the Principia to illustrate a new way of doing what we now call empirical science:

Surprisingly, however, the main body of the first edition contains only two further comments about methodology: (1) a cryptic remark at the end of the opening discussion of space and time, announcing that the purpose of the work is to explain “how to determine the true motions from their causes, effects, and apparent differences, and, conversely, how to determine from motions, whether true or apparent, their causes and effects”; and (2) a scholium buried at the end of Book 1, Section 11 in which Newton proposes that his distinctive approach will make it possible to argue more securely in natural philosophy.

In the course of a long life Isaac Newton made many enemies: Francis Linus (or Hall), Robert Hooke, John Flamsteed, Gottfried Wilhelm Leibniz, Johann I Bernoulli. Of these Leibniz was by far the greatest intellect and above all an outstanding mathematician and philosopher. Newton defeated them all and outlived them all except the last, twenty-five years his junior.

It was a sad chronology that brought two such inventive mathematicians as Newton and Leibniz to live in the same age; never were temperaments and intellectual characters more at odds. Almost the only feature that they had in common was Protestant piety, yet even in appealing to God the Creator they could not agree. In mathematics and its applications to celestial mechanics, and more particularly in the development of the calculus, though the methods promulgated by the two men were equivalent, they had been reached and were justified by wholly distinct arguments. Newton was by choice a geometer, Leibniz an algebraist; the difference does not of course imply that they could not tackle the same problems. J. E. Hofmann has written that Leibniz’s “first major [mathematical] discovery in Paris [in 1673] originated in thoughts strongly influenced by considerations of logic and philosophy – and as so often with Leibniz, was not fully established but came as the fruit of a particular insight observed in simple examples and generalised by a stroke of genius.”

Isaac Newton deserves to be included in a series of companions to major philosophers even though he was not a philosopher in the sense in which Descartes, Locke, and Kant were philosophers. That is, Newton made no direct contributions to epistemology or metaphysics that would warrant his inclusion in the standard list of major philosophers of the seventeenth and eighteenth centuries - Descartes, Spinoza, Locke, Leibniz, Berkeley, Hume, and Kant - or even in a list of other significant philosophers of the era - Bacon, Hobbes, Arnauld, Malebranche, Wolff, and Reid. The contributions to knowledge that made Newton a dominant figure of the last millennium were to science, not to philosophy. By contrast, Galileo, the other legendary scientific figure of the era, not only published the most compelling critique of Aristotelian scholasticism in his Dialogues on the Two Chief World Systems, but in the process turned the issue of the epistemic authority of theology versus the epistemic authority of empirical science into a hallmark of modern times. Although Newton clearly sympathized with Galileo, he wrote virtually nothing critical of the Aristotelian tradition in philosophy, and the immense effort he devoted to theology was aimed not at challenging its epistemic authority, but largely at putting it on a firmer footing. Newton made no direct contributions to philosophy of a similar magnitude. Indeed, from his extant writings alone Newton has more claim to being a major theologian than a major philosopher.

Among the notable eighteenth-century expositions of Newton's achievements were Henry Pemberton's A View of Sir Isaac Newton's Philosophy (1728), Willem Jacob 's Gravesande's Mathematical Elements of Natural Philosophy confirm'd by experiments: or, an introduction to Sir Isaac Newton's Philosophy (6th edn, 1747), and Colin Maclaurin's posthumous An Account of Sir Isaac Newton's Philosophical Discoveries (1748). To the modern eye, there is something puzzling about these titles. We note the terms “philosophy,” “natural philosophy,” and “philosophical,”and we wonder what they mean in this setting. Take Maclaurin's Account, the best of the genre, and written by one of the leading Newtonians of the day. Newton made great scientific discoveries, and we can learn what most of them are from reading An Account, but what philosophical discoveries did he make? Maclaurin describes Newton's work in mechanics, rational and celestial, and in physics, theoretical and experimental (though not optics). But Newton the philosopher? To answer these questions requires a preliminary disentanglement of the disciplinary classifications that clustered around the business of “philosophy” in the seventeenth and eighteenth centuries.