The triumph of mathematics during the Enlightenment can be judged by the strangely conflicting testimony of those mathematicians who helped to create it. In a famous letter of September 21, 1781, Joseph-Louis Lagrange (1736–1813) wrote to his mentor Jean d'Alembert that he feared mathematics had reached its limit. He compared mathematics to a mine whose precious minerals had been pursued deeper and deeper into the earth to the limit of human accessibility. “Unless new seams of ore are discovered, it will be necessary to abandon it sooner or later.” Bernard Fontenelle had sounded the same warning as early as 1699, and Diderot used the exhaustion of mathematics as the best argument for turning to the more descriptive sciences of natural history, anatomy, chemistry, and experimental physics. He argued that like the pyramids of Egypt, the creations of mathematicians would stand for centuries but that like the pyramids, they could have little added to them and little practical use could be made of them. D'Alembert and the Marquis de Condorcet, on the other hand, urged mathematicians to keep the faith and trust to the future, even though the future for mathematics was uncertain.

The Meaning of Analysis

One wonders why the mathematicians of the eighteenth century, who had witnessed the spectacular success of their discipline during their lifetimes and who had seen mathematics become the prime exemplar of reasoned thought and the model against which the other sciences were to be judged, were so uncertain about its future.

In Herbert Butterfield's famous book The origins of modern science (1300–1800) (New York, 1956), there is a chapter entitled “The postponed scientific revolution in chemistry.” The title refers to the fact that the new chemistry associated with the oxygen theory of Antoine Lavoisier did not emerge until the 1770s and 1780s, a century after Newton's Principia had put the capstone on the Scientific Revolution of the seventeenth century. It is also significant that Lavoisier's contemporaries were conscious of and frequently mentioned a “revolution” that was occurring in chemistry, and that Lavoisier himself stated in 1773, in a private memorandum, that he believed the experiments he was undertaking would “bring about a revolution in physics and chemistry.” Scientists at the time and historians since have concurred in identifying chemistry as a subject that enjoyed its “revolution” during the Enlightenment.

In fact, the Chemical Revolution was more the creation of a new science than a change in an existing one. Before 1750, chemistry could not be regarded as an independent discipline. It had long antecedents, but they were ancillary to other fields. Alchemy was a source for many of the recipes and much of the apparatus of chemistry, but this information was concealed in intentionally ambiguous and allegorical language. Alchemy sought to complicate nature, not to rationalize it, and the alchemists' search for the philosopher's stone that would allow them to change base metals into gold was as much a spiritual quest as it was a scientific one.

In 1774, Turgot — the same Turgot who wrote the article entitled “Expansibilité” for the Encyclopédie — became controller general of France under the new king, Louis XVI. For the first time the most important ministerial position in the kingdom was held by a friend of the philosophes. France had suffered a series of financial crises that had grown in severity throughout the century. The cause was not a general decline in prosperity but a tax system that made it impossible for the king to tax the real sources of wealth in the kingdom. The financial crisis had at its root a social crisis. The clergy, the nobility, and the parlements (traditional judicial bodies that claimed the right to approve taxes) jealously guarded their prerogatives and sought to extend their powers with little thought for the state as a whole. By 1774, France was approaching disaster. The failure of fiscal and social reform at that juncture (and Turgot did fail; he stayed in office for only twenty months) meant that special interests would prevail and that future ministers would be chosen not for their reforming skills but for their ability to borrow money. Fifteen years after Turgot began his ministry, France collapsed in a decade of revolution that eventually brought the needed reforms, but only at the expense of war within and without, and protracted political chaos.

In 1939 Abraham Wolf published his History of science, technology and philosophy in the eighteenth century. Since that time much has changed in the history of science, but no new general study of eighteenth-century science has appeared. The present book is intended to fill the gap — or perhaps a slightly different gap. Wolf's book emphasized technology and instrumentation, whereas mine emphasizes science and ideas. It is impossible to include within the compass of one small volume all of the detail that appeared in Wolf's two large ones. Instead I have outlined the major events in the development of eighteenth-century science, with an eye toward indicating the directions that modern scholarship has taken. In particular, I have attempted to trace the emergence of modern scientific fields. The treatment is not technical, although in some cases (as in the chapter on chemistry), it has been necessary to give an account of actual experiments in order to make the modern interpretations clear.

The history of eighteenth-century science appears in this book as part of the Enlightenment, which means that the viewpoint tends to be French, some might say unremittingly French. My only excuse is that because France was the center of the Enlightenment, my account seemed to flow most naturally from that source, although I would be the first to admit that other viewpoints could be found that would be equally valid.

In 1759 the French mathematician Jean Lerond d'Alembert (1717—83) described a revolution that he saw taking place in natural philosophy:

This revolution came to be called the Scientific Revolution, a cultural event associated with great names like those of Galileo Galilei (1564–1642), Johannes Kepler (1571–1630), René Descartes (1596–1650), and Isaac Newton (1642–1727). D'Alembert obviously believed that it was a revolution still in progress in 1759 and one that was continually accelerating. Natural philosophy could never be put back in its former course. As d'Alembert observed, “Once the foundations of a revolution have been laid down it is almost always the succeeding generation which completes that revolution.” The seventeenth century had begun the revolution; the eighteenth century would complete it.

The expression “Scientific Revolution” had been coined by mathematicians like d'Alembert, and it was mathematics that appeared to them as the greatest revolutionizing force. In 1700, Bernard le Bovier de Fontenelle (1657–1757), “perpetual secretary” of the Paris Academy of Sciences, first talked about an”almost complete revolution in geometry” that had begun with the analytic geometry of Descartes.

By the end of the Enlightenment, experimental physics had come to mean the use of a quantitative, experimental method to discover the laws governing the inorganic world. The original meaning of the term physics, however, had been quite different; and as a result the word continued to be used ambiguously throughout the eighteenth century. The discipline of physics had originally been created by Aristotle, and it had nothing to do with experiment or quantitative measure, nor was it limited to the inorganic world. Aristotle's Physics treated form, substance, cause, accident, place, time, necessity, and motion through a priori arguments that could then be used to explain the phenomena of the world, both organic and inorganic. In fact Aristotle was more successful in his description of the animal world (also part of physics) than he was in his writings on cosmology or terrestrial motion.

Experiment was almost unknown in antiquity. An experimental tradition did begin in Western Europe during the Renaissance, but it was called “natural magic,” not physics. There was also a tradition of applied mathematics, but it was not physics either. It was called “mixed mathematics.” During the seventeenth century, physics, as part of speculative philosophy, continued to be taught in the schools in Latin, whereas mathematics, a practical subject with mostly military applications, was taught in the vernacular. Descartes, for example, graduated from college with the impression that mathematics was useful only in the mechanical arts.

This chapter is about the world of living things. It could be called a chapter on biology, except for the fact that biology, as a word and as a discipline, did not appear until the very end of the eighteenth century. To see the world the way the men and women of the Enlightment saw it, we have to see it through the eyes of natural history. “Natural history” means an inquiry or investigation into nature; and “nature,” in the Aristotelian sense, means that part of the physical world that is formed and that functions without the artifice of man. A growing tree and a falling rock are both part of “nature” because they move and grow without human direction. Natural history, then, covers the entire range of observable forms from minerals to man, excluding only those objects crafted by human hands and intelligence. Its method is descriptive, and its scope is encyclopedic. Francis Bacon called it the “great root and mother” of all the sciences and made it the indispensable prelude to his experimental philosophy.

In spite of its enormous scope, natural history did not treat all questions about living things. The purpose of natural history was to describe and classify the forms of nature; it did not include a search for causes. Both plant and animal physiology — that is, the investigation of plant and animal functions as opposed to their forms — were still part of physics.