One of the keys to achieving a better understanding of the world was the development of better ways of obtaining knowledge. Two important thinkers, Francis Bacon (1561–1626) and René Descartes (day-KAHRT) (1596–1650), were influential in describing and advocating for improved scientific methods based, respectively, on experimentation and mathematical reasoning.

The English politician and writer Francis Bacon was the greatest early propagandist for the experimental method. Rejecting the Aristotelian and medieval method of using speculative reasoning to build general theories, Bacon argued that new knowledge had to be pursued through empirical research. The researcher who wants to learn more about leaves or rocks, for example, should not speculate about the subject but should rather collect a multitude of specimens and then compare and analyze them to derive general principles. Bacon’s contribution was to formalize the empirical method, which had already been used by Brahe and Galileo, into the general theory of inductive reasoning known as empiricism.

On the continent more speculative methods retained support. In 1619, as a twenty-three-year-old soldier serving in the Thirty Years’ War (1618–1648), the French philosopher René Descartes experienced a life-changing intellectual vision. Descartes saw that there was a perfect correspondence between geometry and algebra and that geometrical spatial figures could be expressed as algebraic equations and vice versa. A major step forward in mathematics, Descartes’s discovery of analytic geometry provided scientists with an important new tool.

Descartes used mathematics to elaborate a highly influential vision of the workings of the cosmos. Drawing on ancient Greek atomist philosophies, Descartes developed the idea that matter was made up of identical “corpuscules” (tiny particles) that collided together in an endless series of motions, akin to the working of a machine. All occurrences in nature could be analyzed as matter in motion, and, according to Descartes, the total “quantity of motion” in the universe was constant. Descartes’s mechanistic philosophy of the universe depended on the idea that a vacuum was impossible, which meant that every action had an equal reaction, continuing in an eternal chain reaction. Although Descartes’s hypothesis about the vacuum proved wrong, his notion of a mechanistic universe intelligible through the physics of motion spread widely.

Descartes’s greatest achievement was to develop his initial vision into a whole philosophy of knowledge and science. The Aristotelian cosmos was appealing in part because it corresponded with the evidence of the human senses. When experiments proved that sensory impressions could be wrong, Descartes decided it was necessary to doubt them and everything that could reasonably be doubted, and then, as in geometry, to use deductive reasoning from self-evident truths, which he called “first principles,” to ascertain scientific laws. Descartes’s reasoning ultimately reduced all substances to “matter” and “mind” — that is, to the physical and the spiritual. The devout Descartes believed that God had endowed man with reason for a purpose and that rational speculation could provide a path to the truths of creation. His view of the world as consisting of two fundamental entities is known as Cartesian dualism. Descartes’s thought was particularly influential in France and the Netherlands but less so in England, where experimental philosophy won the day.

Both Bacon’s inductive experimentalism and Descartes’s deductive mathematical reasoning had flaws. Bacon’s inability to appreciate the importance of mathematics and his obsession with practical results illustrated the limitations of antitheoretical empiricism. Likewise, some of Descartes’s positions demonstrated the inadequacy of rigid, dogmatic rationalism. He believed, for example, that it was possible to deduce the whole science of medicine from first principles. Although insufficient on their own, Bacon’s and Descartes’s extreme approaches are combined in the modern scientific method, which began to crystallize in the late seventeenth century.