In 1644, the French philosopher, scientist, and mathematician René Descartes formulated several “laws of nature,” which helped lay the groundwork for classical physics and the Scientific Revolution. Descartes’ laws, published in his Principles of Philosophy, included progenitors of both the concept of inertia (Isaac Newton’s famous first law of motion) and the conservation of momentum — another key principle of classical mechanics.

Descartes’ conservation law refers to “motion” rather than “momentum” and holds for what physicists today would call “speed,” rather than “velocity” (speed plus direction). Later scientists, including Newton, would overcome these deficiencies and articulate the modern concept of momentum. But Descartes’ formulation nevertheless marked an important step in the development of modern physics.

How did Descartes hit upon this conservation law? Not simply by observing nature. “In fact,” he points out, “it often happens that experience may appear to conflict with the rules I have just explained.” Descartes believed that the methodology of physics resembles mathematics more than the “scientific method” we learn in school — beginning not with observations and experience but with certain “clear and distinct” principles, from which conclusions may be derived with logical rigor. It is not that observation and experience were irrelevant to Descartes; rather, his idea was that truths about the natural world should hold with the same degree of certainty as those of mathematics.

One such principle to which Descartes appeals in his “proof” of the conservation of motion is “the immutability of the workings of God.” From this, he argues, it follows that “the motion which [God] preserves is not something permanently fixed in given pieces of matter, but something which is mutually transferred when collisions occur.” It is the finite motion that God imparts to the material world which gets conserved in physical interactions. Inversely, then, “the very fact that creation is in a continual state of change is…evidence of the immutability of God.”

This reasoning should shock the modern reader. It is, first of all, explicitly un-empirical; even more scandalously, it makes explicit appeal to God! How could Descartes — a key figure in the development of modern science — invoke a theological principle at a crucial point in his derivation of a physical law?

Descartes is often remembered today for criticizing the Aristotelian physics associated with Medieval scholasticism and formulating an alternative — modern — account of nature. But he clearly did not adhere to our own “modern” assumptions about science and religion. For Descartes, science is hardly incompatible with revealed religion, as today’s “metaphysical naturalists argue — he thought the existence of God could be demonstrated rationally. Nor, apparently, did he think that scientific reasoning is radically distinct from theological reasoning — as “methodical naturalists” maintain. In this, Descartes, the so-called father of modern philosophy, appears rather un-modern.

Today’s readers might dismiss Descartes’ theological musings as irrelevant to the justification of the conservation of momentum. Descartes may have (somehow) hit on the right physical principle — or, at least, a forerunner of it — but his explanation is nevertheless scientifically deficient, this argument would go. But it’s hard to ignore the historical fact that theological ideas played a role in Descartes’ discovery. However unscientific his theological beliefs may seem to us today, they nevertheless bore fruit in the advancement of science. As contemporary historians have observed, such instances are surprisingly common in the history of modern science — challenging the assumption that religion is inherently inimical to scientific progress.

Descartes’ appeal to theology will seem less surprising when you consider that he rejected an idea often invoked today when distinguishing science from religion: that all scientific knowledge — if not all knowledge — is “empirically verifiable.” We are taught in school that science advances by formulating hypotheses based on observations and then testing them against experience. If we understand science in this way, theological claims may, indeed, appear un-scientific or even — if we take all knowledge to be empirical in this way — a matter of mere opinion, rather than knowledge. But Descartes rejected this “inductive” approach to science in favor of his own, “deductive” one.

The inductive method begins with empirical experience, from which the scientist makes probabilistic generalizations. The deductive method is almost the opposite, beginning with general principles and deriving from them necessary conclusions about experience. If, as Descartes thought, science is not entirely reducible to what is observable — resting instead on general principles and sound reasoning — then it starts to look a lot more like mathematics or philosophy than what we usually think of science. It might even resemble traditional theology, which reasons about unobservable things.

Descartes’ rejection of inductivism is not as antiquated as it sounds. In fact, most philosophers of science today reject the crude inductivism attributed (rightly or wrongly) to Newton and other pivotal players of the Scientific Revolution, such as Francis Bacon. They point out that scientific reasoning depends upon empirical observations as well as extra-empirical assumptions — such as the uniformity of nature and thus the validity of induction itself — which are, by definition, not empirically verifiable. Many contemporary historians of science, beginning especially with the pioneering work of Alexandre Koyré, have gone so far as to argue that early modern scientists such as Galileo — and even Newton himself — did not really practice the inductive empiricism they preached. Thus the stark distinction between Cartesian “rationalism” and Newtonian “empiricism” — familiar to all philosophy 101 students — begins to blur.

If Descartes was apparently premodern in his blending of theological and scientific reasoning, he was quintessentially modern in another sense. Indeed, the method for which Descartes is perhaps most famous is not deductive, but skeptical — the two are interconnected. For Descartes, the paragon of rationality is to question everything — including the testimony of the senses and that of tradition — leaving only those principles which are so clear and distinct as to be beyond all doubt, thereby serving as the foundation of knowledge. Rational inquiry thus always starts afresh, doubting everything in order to discover self-evident truths from which all other may be deduced.

Descartes’ epistemological foundationalism is still hotly contested by philosophers. But his skeptical posture toward all knowledge not derived from unassailable foundations remains a common trope in discussions of science today. Thus “questioning authority” and “thinking for oneself” are associated with the scientific outlook — and most famously with Galileo — while dogmatism, superstition, and even authoritarianism go with religious belief. Here is the symbolic importance of the much-referenced but little-understood Galileo affair — where Galileo is seen as defying the dogmatic authority of the Church on the basis of unassailable experience. The irony, of course, is that Cartesian skepticism was directed not only at tradition but also sensory experience — which today’s new atheists accept uncritically.

Be that as it may, the rejection of tradition — and the corresponding idea that knowledge must always begin de novo — remains crucial to the self-understanding of modern science. It is, moreover, a purported feature that has long served to distinguish science from religion, the latter taking tradition and the testimony of scripture as authoritative. Scientific findings, by contrast, are understood as resting not on the authority of past figures — Galileo, Newton, or Einstein — much less religious texts, but on the sound reasoning and observations of present-day practitioners. This is why students of science are sent into the laboratory to perform experiments, not the library to interpret ancient manuscripts.

Interestingly, historians of science since the middle of the last century have questioned the Cartesian assumption that science is foundationalist. They emphasize how science is itself a historical discipline — a tradition — with its own authoritative texts and ideas, which helps explains how and why scientific ideas change over time.

Thomas Kuhn famously argued that scientific knowledge advances through changing “paradigms” of thought. What is a paradigm? Kuhn sometimes explained it as an exemplary scientific discovery, one that provides the methods and practices to be learned and imitated by students of science. It is when those methods and practices no longer appear adequate to address new phenomena that a “paradigm shift” occurs. Whence the origin of a scientific revolutions.

On what basis do students accept these paradigms? Not experience, says Kuhn, but, rather, the authority of their teachers. Consider how students of Physics 101 are required to reproduce Galileo’s “inclined plane” experiment. This procedure is hardly undertaken without preconceived notions; on the contrary, the students are instructed to produce Galileo’s conclusion — that the weight of an object is independent of its rate of fall — and to treat any results that contradict it as deviations. There is an illustration of “confirmation bias” if ever there was one.

It is not as if scientists only ever confirm preconceived ideas or that scientific reasoning is circular and therefore deficient. Once they strike out on their own, students are expected to design and conduct their own experiments and thereby make new discoveries. Kuhn’s point is that students learn first by imitation and practice and — assuming they receive a good education — once they strike out on their own, they will have been successfully inculcated into a particular scientific tradition. They will thus be prepared to recognize, pose, and solve scientific problems.

If we take tradition to be antithetical to scientific rationality, Kuhn’s conclusions will appear disquieting. And, indeed, Kuhn’s critics rejected his arguments as “irrationalist.” But if, on the contrary, we take tradition to be essential to rationality, then Kuhn’s conclusions will not only be acceptable, but also unsurprising. According to the moral philosopher Alasdair MacIntyre, before we can begin to reason at all, we must first acquire the habits necessary to recognize and, ultimately, replicate rational behavior. To do so, there must first be exemplars that we take to be authoritative — in the moral domain these will be exceptionally virtuous people, in the scientific domain, exceptionally good scientists. To become rational, in other words, one must be educated within a tradition of inquiry.

Science, on this view, is not Cartesian — at least as far as epistemological foundationalism is concerned — even if it remains eminently rational.

Where does this leave us? If, with Descartes, we reject “inductivism,” and, against him, reject epistemological foundationalism, the fact that religious beliefs are not entirely reducible to empirical experience and partly depend upon tradition doesn’t make them irrational or even anti-scientific. Thus a popular way of opposing science and religion starts to look untenable. This hardly means the two become indistinguishable. But it does suggest that science and religion could be conceived of as distinct — but possibly harmonious, even sometimes mutually beneficial — traditions of rational inquiry.