The Birth of Modern Science: Galileo and Descartes, a lecture by Ricardo Nirenberg. Fall 1996, the University at Albany, Project Renaissance.

February 2017: A translation of this lecture into the Czech language, by Barbora Lebedová, appears at

June 2017: A translation of this lecture into the Estonian language, by Karolin Lohmus, appears at

June 2017: A translation of this lecture into Russian, by Sandi Wolfe, appears at

July 2018: A translation of this lecture into German, by Philip Egger, appears at:

August 2019: A translation of this lecture into Croatian, by Milica Novak, appears at:

February 2022: A translation of this lecture into Punjabi, by Naresh Ram, appears at:



Last time I left you with a question whose answer I do not know. The question was: why do human beings search for unity? Not only is the answer unknown, but the question itself risks being badly misunderstood. What kind of unity am I talking about? The Renaissance, whose name this Project has proudly donned, was also the time, as you must have read in Ortega's book, when Spain achieved political and religious unity by expelling Jews and Muslims, people who had lived there in relative peace for many centuries. Hitler too screamed: "Ein Volk! Ein Reich!" (One nation, one state), and killed the Jews and the Gypsies. We saw in the Soviet Union, in Bosnia, in Rwanda, and in many other places the search for unity—ethnic, religious, ideological—as the prelude to, and excuse for, massacre. So you may say, "Who wants unity? What we want is diversity!" And indeed, if that's the unity I mean, you would be right. But that, of course, is not the unity I mean. What I really mean by unity and oneness will be clarified only after we talk about the beginnings of modern science and philosophy and about those two founding figures, Galileo and Descartes.

As a consequence of the horrors of this century, the word and the concept "unity" or "oneness," which used to have a supreme value for both Western and Eastern thought, have become profoundly unfashionable among Western intellectuals. But nothing is more interesting than to re-think unfashionable thoughts, to think them through yet again. In our own country, the rejection of unity was taught by a professor at Harvard, the influential philosopher William James (1842-1910). He ventured the idea that there exist worlds which are totally disconnected, meaning that an event in one world cannot influence another world: no cause-effect relation obtains between those separate worlds. He called this doctrine "pluralism," and gave, as unassailable example of disconnected worlds, the dreams of two dreamers. He didn't mean it metaphorically, as when politicians say, "the American dream," or as when Martin Luther King said, "I have a dream": those dreams are understood to be shared. No, he meant the dreams of two different people who are sleeping. Whether or not two such worlds are really disconnected, let us discuss Galileo and Descartes, who dealt with unity and disconnection in their own, and extremely influential, ways.



Galileo Galilei was born in Pisa (modern Italy) in 1564; thus he was of the same generation as Kepler (about whom we talked in the last lecture). At age eighteen Galileo had to quit his studies at the University of Pisa because his family couldn't afford the tuition and the university wouldn't give him financial aid; at age twenty-five, however, he was named professor of mathematics there. The generation of Galileo, to which Kepler and Descartes belonged among many other illustrious men, is the starting point for Ortega's meditation in his book: it was, he says, a time of crisis. Why was it a crisis? The word "crisis" comes from the Greek verb "krinein," meaning to choose, to decide between alternatives. At a time of crisis people must, as always, decide, but it is specially hard to know how to decide, which alternative to choose: even the most knowledgeable people find it difficult or impossible to decide; Galileo, for example, who certainly knew astronomy and contributed important discoveries to it—the moons of Jupiter, the phases of Venus, the sun-spots, the fact that the Milky Way is a conglomerate of stars, etc.—, thought that Kepler's new system of elliptical orbits was wrong, and before him, Tycho Brahe thought that Copernicus' heliocentric theory was wrong. One could go on with these sobering examples, but the important thing to keep in mind is that the 1600's was a time when a systematic view of the world, which is called "Scholasticism" because it was taught at schools and universities and which was based to a large extent on ancient texts—Euclid, Aristotle, Ptolemy, etc.—, was being gradually replaced by another systematic view, which we usually call "Modern Science." It is often asserted that the difference between the two views is the use of experiments (not used in the old view, used in the modern one): there is truth in this, but it is a very partial and superficial truth. Medieval people and the Scholastics were not set against experiments; but in order to carry out experiments one must know beforehand what one is trying to find, what questions one is trying to answer.

The true difference between the old view and the new one is metaphysical. To understand what is at stake here, we must first define what is meant by metaphysics. Originally, the word meant simply those works of Aristotle which came after (in Greek meta) his works on Physics, in the received, traditional arrangement of his works. Aristotle himself called his "Metaphysics" by a different name: "First (or Basic) Philosophy." The word, however, came to signify something quite different. Here's a brief definition of what metaphysics came to mean: methaphysics is the study and the doctrine of internal, active principles in things. Metaphysics assumes that there are such internal, inner, or intrinsic principles or virtues (a Latin word which means, more or less, "force") in things; in other words, by its very being, each thing in the universe exercises an activity which is intrinsic to it. For the Scholastics, for example, heavy things possess an intrinsic quality: they tend to move toward the center of the earth. Souls, on the other hand, are not heavy, and, unless weighed down by bodily desires, they tend toward God. Fire is not heavy either, and it tends toward the upper spheres of the stars. Thus, we already see that in the concept "activity" the concept of motion, or rather, of motion-toward, is involved. And this, in turn, allows us to understand why the new physics of Galileo and the other modern scientists, which had to do primarily with the concept of motion, had to clash with metaphysical doctrines. But motion and activity are not the only concepts involved in our definition of metaphysics: there are others—the concepts of principle, the concept of inner or intrinsic, the concept of individual thing, and finally, the very concept of being. Any serious analysis of metaphysics must take up all these particularly difficult concepts. Remember from our lecture on language: analysis means to untie or loosen the bindings which hold our concepts together.

Now, there was one idea that was common to all the founders of modern science: to ignore, or to dispense with, what they called "occult virtues or qualities of things": these had been thoroughly abused by the Scholastics, and much fun was poked at them in the 1600's and later; writers of comedies had ridiculous doctors solemnly proclaim that opium made one sleep because of its "dormitive virtue," as if that explained anything. What was understood by "occult" did vary, though, with different thinkers. In any case, the Scholastic system had come to a point were explanations became too complicated and, above all, they lacked unity. Unity is lost when each phenomenon requires an explanation ad-hoc, without connection to all other explanations—but, as I've said at the beginning, human beings yearn for unity. To take another example, if contemporary physics should require, say, 300 different kinds of forces obeying laws having nothing to do with each other, that would be the end of physics. This was the root cause of the 1600 crisis, yet it is not a characterization of it: to characterize the early modern crisis we must show what were the options which opened up to thinkers at that time. I have chosen to speak of Galileo and Descartes on the same day because they exemplify superbly the two roads that opened up to thought at the beginning of our modern era, precisely in regard to metaphysics.

Galileo, as you've heard from Dr. Hagelberg, was the founder of modern kinematics: this means the description of motion. He showed by experiment that the velocity of a freely falling body is directly proportional to the time elapsed, regardless of the weight of the body (contrary to what Aristotle had taught); as an application of this he showed that the period of a pendulum is independent of the amplitude of the oscillations (provided they are not too large) and of the mass of the bob: it only depends on the length of the rod. He showed, too, that the trajectory of any heavy projectile is a parabola, another of the conic sections studied by the Greeks (together with the ellipse and the hyperbola), which now found a surprising application. Most importantly, Galileo established a principle that was later to be called Galilean relativity (to distinguish it from Einstein's relativity): all motion is relative, and this means that it does not makes sense to speak of the motion of an individual thing, it only makes sense to speak of the motion of one thing A with respect to another thing B; moreover, if A moves with respect to B with uniform velocity, we cannot tell whether A or B is moving, a phenomenon with which you are familiar: when you travel on a train, it is only your memories and common sense which convince you that the train is moving, and not the landscape in the opposite direction. Galileo's principle defies metaphysics, in the sense that motion turns out not to be an intrinsic quality of things. The consequence of this was enormous, once scientists and thinkers started reducing all phenomena in nature to the one phenomenon of motion: the consequence was that physics didn't care for metaphysics. But when metaphysics is expelled, it will come back through the back door: one asks, what is it that moves? Answer: planets, particles, atoms, etc. Why does a planet (say) move? Because it has mass and an initial impulse (as Newton would state some years later). And what is mass? An inner, active principle in things. So there we go again, as Ronald Reagan used to say. Next semester we'll see how Newton, Leibniz, and other great scientists and philosophers, dealt with the problem.

But Galileo didn't deal with it, nor did he care for it. If at the beginning of his career he had tried, in some letters, to deal with religious problems, that had caused him only troubles. All he cared for was motion (which was, needless to say, a lot). So, Galileo's decision, his way out of the crisis, was this: he sharply separated physics from metaphysics—had he used today's academic jargon he would have said: "They are two separate, untranslatable discourses, and I talk only physics." This makes him the first professional scientist. I'm using the word "professional" in a very definite way: it means, precisely, this attitude, this ability to sharply separate spheres of thought, feeling and activity and make them disconnected, and to be able to say, "I deal with this one only—that's my job." It is, in other words, the quality of detachment, by which the human yearning for unity is suppressed. In connection with professionalism I must mention the famous trial of Galileo. A rather choleric man who did not suffer fools and who wielded a sharp and sarcastic pen, he had made some powerful enemies, especially among the Jesuits. The Catholic Church ostensibly objected to Galileo's adoption of the Copernican heliocentric model as a true description of reality because it was contrary to Scripture, but the Church had another, better reason to condemn the physicist: his unconcern for metaphysics. For many centuries, ever since Christianity wedded philosophy, metaphysics was the rational ground for believing in God. It is not hard to see how: God was defined as the supreme individual, whose inner principle is perfection (there's metaphysics for you!). At least since the 11th century (St. Anselm), the argument went as follows: if such an individual did not exist, it would lack the attribute of existence and therefore it wouldn't be perfect: but it was assumed that it was perfect, therefore it must exist. This is called "the ontological argument for the existence of God." Thus, without metaphysics, a rational proof of the existence of God cannot work, and I should remind you that, even today, the possibility of such a proof is a dogma of the Catholic Church. And there was another Catholic dogma, of particular relevance during the Reformation and Counter-Reformation, whose truth was threatened by the new Galilean physics: I mean the Eucharist, the doctrine that the body of Christ becomes present in the consecrated wafer. This doctrine was rationally justified by the Aristotelian distinction between "substance" and "qualities" or "attributes." The qualities of the wafer were still the same (e.g. it was white) but its substance was changed, it became God, so the argument went. Galilean physics, by conflating both substance and qualities under the general idea of atoms in motion, tended to obliterate the distinction, and justify all kinds of heresies.

Anyway, Galileo was condemned. But the Roman Inquisition, which had burnt Giordano Bruno a few decades before, in 1600, for (among other things) professing Copernican doctrines, did not kill Galileo. This was because he did not consider it necessary to die; instead, he publicly recanted his own teachings and beliefs. Compare his behavior with Socrates': condemned by the Athenians to death for his teachings and "for corrupting the city's youth," far from recanting and asking for mercy, Socrates defied the court, affirmed his beliefs and perished (read Plato's Apology, Crito and Phaedo). It would be silly to conclude that Socrates was brave and Galileo a coward, or that Socrates had developed a taste for self-sacrifice and Galileo had not. No, Socrates had to die, and Galileo didn't have to: the truth of Socrates' moral teachings were an integral part of his life, of his identity, a vital organ like his brain or his heart—not only that, those moral teachings were exemplified by his conduct. Instead, Galileo's astronomy and physics, fundamental as they are, were separate from the rest of his self, didn't have anything to do with his conduct, and could be amputated—remember: detachment is the defining virtue of the professional. Self-sacrifice results out of an attachment to some truth that's stronger than one's natural attachment to life. Therefore, self-sacrifice is unprofessional.



Having described Galileo's separation of physics from metaphysics and his unconcern for the latter, we come now to Descartes, who was a great admirer of Galileo but followed a different path. René Descartes was born in a small village in central France, in 1596, and was educated by the Jesuits; by 1616 he had got a degree in Law. In the years 1618-1619 he joined an army, traveled in Germany, and there, on November 10, 1619, he had a vision and three dreams, in which a new and marvelous science was revealed. What was this "marvelous science" that was revealed to the young soldier in his dreams? The education he had gotten at the Jesuit college was superb (Jesuits were Galileo's enemies, but they were and are superb teachers—I still remember the one who taught me Latin in high school), but Descartes, who professed admiration for his teachers, concluded that he had learned nothing that wasn't subject to crippling doubts. Except, that is, for what he had learned in mathematics. Math was the exemplary science, and any knowledge which aspired to truth had to partake of the certainty and clarity of mathematical theorems; in Descartes' own words, knowledge had to be "clear and distinct," else it was not genuine knowledge. It had to impose itself on all sober minds, regardless of their customs or culture. Being a brilliant mathematician, he could have, like Galileo, restricted himself to the exact and mathematical sciences, but Descartes was no detached professional: he had a burning desire for cognitive unity, and so, when he came to write his Regulae (Rules) (1628) and then his famous Discourse on Method (1637), his purpose was not simply to set down rules for solving math or physics problems, but rules and a method for reaching the truth about anything whatsoever. Here's the gist of Descartes' rules for discovering truth:

  1. To accept nothing in one's judgments beyond what presents itself so clearly and distinctly to one's mind that one cannot doubt it.
  2. Divide each difficulty into as many parts as possible and solve them one by one.
  3. Start from the simplest objects and advance toward knowledge of the more complex.
  4. Make careful enumerations and reviews so that nothing is left out.

It has been often pointed out that these rules are too general and not of much help in specific cases. Descartes agreed, so he didn't just offer a set of rules, but gave several examples of how to apply them to solve difficult problems. In his Discourse on Method he dealt with optics and gave the law for the refraction of light (also called Snell's law): if you have two media (air and water, for example) separated by a surface, a ray of light will hit and go through the surface in such a way that the incoming and outcoming rays and the perpendicular to the surface at the hitting point will be on the same plane, and the angles the ray forms with the perpendicular on both sides of the surface are related thus: the ratio of their sines is a constant (refraction index) which depends on the two media. Further, Descartes dealt with meteorological phenomena such as the rainbow: using his refraction law, he computed how the rays of light from the sun hit a spherical water drop, and showed that those rays come out of the drop showing a marked preference for one angle, corresponding to the main rainbow, and two subsidiary angles, corresponding to two fainter rainbows (next time you see a rainbow, try to detect the other two!) And most importantly, he dealt with geometry, and solved one of the hardest problems left by the ancient Greek geometer Pappus. I won't go into what that problem was, although it's not too hard, and the reason it's not too hard for us is that we know something called Analytic Geometry, which is what Descartes came up with in order to solve it.

Analytic geometry is an extremely powerful tool: it reduces geometric problems to algebraic ones, that is, to solving algebraic equations. This is achieved as follows: each point on a straight line is thought of as a "real number"—not just the fractions but "irrationals" such as square root of 2, or 3, etc. as well. Then we take two such lines, say perpendicular to each other. Once we do that, each point in the plane is located by giving two real numbers called its Cartesian coordinates (in honor of Descartes). If we call these two numbers the abscissa x and the ordinate y of a point, then for different values of x and y we have all the points in the plane. If, on the other hand, we establish a relation between x and y containing the equal sign (an equation), we get a one-dimensional curve. For example, the equation 3x+2y = 5 represents a straight line in the plane; the equation x2+y2 = 9 represents a circle centered at (0,0) and having radius 3; the equation 2x2+6y2 = 10 represents an ellipse; and so on with more complex curves. Once Descartes was able to do this, he proceeded to solve old problems as well as new ones. The importance of Analytic Geometry on the development of science has been enormous: it made possible the invention of Calculus (of which we'll talk in the second semester), and thereby the development of modern physics and the other sciences, and of modern technology in general.

It had enormous consequences, too, for our notions of space and time. Space was mathematized, made homogenous: the essence of space became number, in the best Pythagorean tradition; as for qualities like color, texture, sacredness, etc., all those became "secondary qualities," accidents which for the time being were considered "obscure," not at all clear and distinct as math was. Galileo too had considered motion and shape as primary and color, smell, etc. as secondary. From then on, science became truly abstract, but promised that eventually those secondary qualities, too, would be, in due time, be explained in terms of math. In due time means in some future time: once everything is explained clearly in terms of math, Utopia will arrive. The birth of modern science coincides with the birth of Utopian thought. Time too was mathematized, made into a real number line. When we study Descartes' notions of space and time, they seem strange to us, because we are heirs to the later tradition which starts with Newton; still, given Descartes' premises, those notions are perfectly logical. The one crucial premise was this: Descartes, like Galileo, was determined to keep metaphysics out of the picture when considering space and motion. As we will see shortly, Descartes put metaphysics to a different use, but he insisted that no "occult virtues" were to be accepted when speaking of physical phenomena. Therefore, Descartes rejected outright the notion of empty space. All space had to be filled, if not with air or such, then with a subtle substance which later physicists were to call "aether." And why? Because motion could not possibly be transmitted across empty space; Descartes would have rejected Newtonian gravitational forces as another instance of occult virtues and scholastic hocus-pocus; motion had to be transmitted directly from object to object, from particle to particle, like when billiard balls hit one another—no "action-at-a-distance"!

When it comes to time, here's Descartes himself, in his Third Meditation on First Philosophy: "It is quite clear to anyone who attentively considers the nature of time that the same power and action are needed to preserve anything at each individual moment of its duration as would be required to create that thing anew if it were not yet in existence." This is astounding to us. Part of what Descartes is doing here is going against the received Aristotelian notion that a God was required to give things the initial push, but that from then on things can go on on their own. Yet the main thrust of his astounding pronouncement is the total rejection of occult virtues and metaphysical essences. In effect, what happens when an object moves? In our own Galilean and Newtonian physics, it is accepted that for the object to start moving we need some action, in other words, a force; but one of the main principles of this physics is that once the object is moving, it will keep on moving in a straight line with the same velocity: this is called the principle of inertia. If you ask, what is this "inertia," the answer is that it is an intrinsic property or quality of massive objects, of mass. So, with inertia, we are back into the realm of intrinsic properties or qualities, we are back into metaphysics, something Descartes insisted on doing without. So, how did he solve the problem? Well, there's always God. God keeps the whole thing going, from moment to moment. God doesn't rest for a single instant. This, for Descartes, was another proof of the existence of God, alongside the other proofs, such as the ontological one mentioned before.

This brings us to the other aspect of Cartesian thought: his metaphysics. For, contrary to Galileo, Descartes did think hard about metaphysics, so much so that he is considered the father of modern philosophy. But his metaphysics was kept strictly separate from his physics. How did he achieve this? By postulating that there are two entirely different substances, two different kinds of existing things: the mind, and the physical objects (such as our own body). The mind, he says, is the thinking substance, the thing whose activity is to think, and here, when we deal with mind, metaphysics (or First Philosophy, as he called it following Aristotle) is the right science. But when it comes to physical (that is, spatiotemporal) objects, their essence is extension in space, and the right science to deal with those is math and mathematical physics, leaving metaphysics aside. This theory of two essentially different substances is called Dualism. But we must keep in mind that when he dealt with the mind Descartes kept insisting on the same clarity and distinctiveness as when he dealt with math and physics. His method started with what he called "universal doubt": everything was to be put on hold, nothing was to be accepted as true unless it hit us with the same irrefutable evidence as 2+2 = 3+1. He assumed, too, that the mind is capable of examining itself, of finding the truth about itself. The first question the doubting mind puts to itself is this: Do I exist? And the answer is: I doubt of my own existence (as a mind), now doubting is a kind of thinking, which shows that I think, therefore, since the essence of my mind is thinking, this shows that I (or my mind) exist. In concise Latin: "Cogito ergo sum". This does not show that my body exists, only that my mind does. Then Descartes goes on to prove that not only does my mind exist, but that it is not dreaming, and that in believing in the existence of my body and an external world it is not being deceived by a deceiving god. This, I think, is not so clear and indubitable as the first conclusion, but let the matter stand thus, for here we cannot follow Descartes in his metaphysical thought.

To sum up, with Galileo and Descartes we encounter two different rational ways of thinking about the world: Professionalism and Dualism. Not much later, in the 18th century, we will encounter still a third way: Materialism. Actually, Materialism is quite old, going at least as far back as Epicurus, of whom Prof. Isser has talked; its basic tenet is that everything, including the mind, is reducible to matter and its properties and changes. Those three ways of thinking, Materialism, Dualism, and Professionalism, are very much with us. I'm not saying that they are the only ways of thinking about the world, merely that they are the dominant ones in our culture; besides, we often encounter them not in their pure form but in some mixture or combination. Most contemporary scientists (by no means all) adopt a mixture of materialism and professionalism. Official Christianity, on the other hand, professes some form of Dualism; recently, the Catholic Church rehabilitated Galileo, and some months ago it even rehabilitated Darwin and evolutionary biology, with one exception though: our mortal bodies (said the Pope) can be studied in accordance with Darwinian evolution, but not our immortal souls—they are two different substances. Finally, Professionalism, which started as a detachment of Physics from Metaphysics and a renouncement of cognitive unity, has become, by a curious and ironic twist, the dominating non-religious moral code in contemporary society, a phenomenon that has yet to be studied.

What can we conclude, then, in regard to our starting theme of unity and diversity? Modern science achieved unity in the laws that govern the universe, making our earth and the most distant stars parts of the same cosmos. A practical result, however, has been the specialization and fragmentation of our knowledge, and the abandonment of all attempts at cognitive unity within any one human mind. We will have more to say about this paradoxical situation — next semester.

Required Reading:

Optional Readings:

Of Galileo's works, the most important are: Il Saggiatore (The Assayer), Dialogue of the Two Chief World Systems, and Dialogue on Two New Sciences. On Galileo, you may consult Pietro Redondi, Galileo Heretic, Princeton, 1987.

Of Descartes' works, the most important are: Discourse on Method and Metaphysical Meditations (Meditations on First Philosophy). On Descartes, you may consult: Bernard Williams, Descartes, Penguin, 1990.

On the virtues of separation and detachment as characteristic of professional scientists, see New York Review of Books, October 3 1996, pp. 54 ff., exchange of letters from various professors and the views of physicist Steven Weinberg (especially his mentioning of Galileo!).

On professionalism in general, see Ricardo L. Nirenberg, "Against Professionalism," in Exquisite Corpse, no. 50, 1994/95. This is available in


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