 Hi, I'm Peter Adamson, and you're listening to the History of Philosophy podcast, brought to you with the support of the philosophy department at King's College London and the University of London. Over the last couple of episodes, I've been trying to place two great astronomers of the 16th century within the context of that time. But rather ironically, it's only now that we come to a third great astronomer, who lived well into the 17th century, that the intellectual currents of the Renaissance become impossible to ignore. Johannes Kepler was born in 15 71 and died only in 1630, meaning that his life overlapped with that of figures like René Descartes and Thomas Hobbes, but then Hobbes lived to be 91 years old, so overlapping with him was easy to do. Certainly some aspects of Kepler's thought seem at home in the 17th century. His repeated comparison of the cosmos to a clock fits with the mechanistic conception of nature we find in Descartes and other Enlightenment philosophers. But in most respects, Kepler comes across as a figure of the Renaissance and Reformation period. Like Lipsius, his career was shaped by conflict between Protestants and Catholics. Like Melanchthon, he was himself a deeply pious Lutheran who saw astronomy and astrology as the ideal route to the knowledge of God. And speaking of ideal, he was, like Nicholas of Cusa and Marsilio Ficino, a Platonist. In one of his most important works, On the Harmony of the World, Kepler credits Plato with the idea that God, the actual fount of geometry, practices eternal geometry and does not stray from his own archetype. You could hardly do better as a statement of Kepler's own intellectual project. We can begin his story by picking up where we left off last time. At the end of his life, having lost favor with the Danish court, Tycho Brahe had moved to live near Prague. Here he took on the young Kepler as an assistant. Kepler had already been shaped by his studies in Tübingen, where Melanchthon's ideas shaped the curriculum. Despite curricular and religious reform, Aristotle was still a fundamental author there, and Kepler was very familiar with his works. He had sufficiently strong ancient Greek to second-guess translations of Aristotle's metaphysics, and when he came to defend Copernican heliocentrism, he referred to Aristotle for evidence that this view had been anticipated by the Pythagoreans. As this shows, Kepler was shaped by the humanistic values of Tübingen, which included the study of mathematics as a classical science that needed to be revived or restored. Remember that this rhetoric was also used by Brahe. The most significant influence on him was probably that of his mathematics professor Michael Mestlin. As we saw, Mestlin defended a realist version of the new Copernican astronomy. He passed this conviction on to Kepler, along with the theological rationale for research on such topics. As Kepler put it in a 1595 letter to Mestlin, Even in astronomy, my work worships God. Another thing Kepler took away from his student years was an enthusiasm for astrology. The intellectual culture created by Melanchthon obviously stands behind Kepler's remark, I am a Lutheran astrologer throwing away the nonsense and keeping the kernel. He was, like Melanchthon and Brahe, dubious about the possibility of using astrological methods like horoscopes to predict the fate of individual people. Kepler gave himself as an example. While the stars may have influenced his natural dispositions in some ways, he had assets like relative wealth, an advantageous male gender, and good schooling that were not given to others born under the same configuration of stars. But when it comes to larger scale phenomena, like the weather, it does make sense to seek explanation at the level of heavenly influence. He saw comets and the new stars, that is the two supernovas, that became visible in 1572 and 1604 as portents sent by God. Whenever something new and extraordinary appears in the heavens, he wrote, sublunar nature trembles in some way. For him, such manifestations were part of a providentially ordered system of the world, a conviction he illustrated with an anecdote about him and his wife. At dinner, Kepler joked that if lettuce, oil, vinegar, and sliced eggs flew around in the air for long enough, they would come together to make a salad like the one she had just served him. Yes, she said, but not so well arranged. During her lead, Kepler gave a severe dressing down to proponents of the Epicurean notion that the world comes together as a result of random interactions. The new star of 1604 was, he argued, no chance appearance of celestial matter, but a divine sign of momentous events and a puzzle sent by God to test our powers of ingenuity. Whatever momentous event this supernova signified, it was not the meeting of Kepler and Brahe, because that pivotal event in the history of science had already occurred. By chance, or maybe not, it came almost exactly at the dawn of the 17th century, early in the year 1600. The two men wanted different things out of their collaboration. Kepler wanted to make use of Brahe's meticulous and extensive record of celestial observations, which thanks to his instrumentation and careful methods were as much as 50 times more accurate than the values used by Copernicus. To give you some idea of the potential of this information, Kepler was able on this basis to predict a transit of Mercury across the face of the Sun in 1631. It happened as he predicted, though he did not live to see it. As for Tycho, what he wanted was to settle a score. He prevailed upon Kepler to write a refutation of Nicholas Reimer, known in Latin as Ursus. He was an imperial mathematician and a royal pain in Brahe's backside. To make a long story short, Ursus and Brahe were involved in a dispute over priority for invention of the Tychonic system. As discussed last time, this set of hypotheses has the five planets orbiting the Sun and the Sun and Moon orbiting an unmoving Earth. The fact that we do indeed call this the Tychonic system shows that Brahe has gone down as the winner in history's books. But a book put out by Ursus in 1597 on astronomical hypotheses portrayed Brahe as a total loser. Alongside accusations of mathematical incompetence and scientific malfeasance, Ursus descended to the level of sexual innuendo aimed at Brahe's common-law wife. Kepler had innocently strayed into this dispute by writing an admiring letter to Ursus adopting the tone of a respectful younger scholar. Ursus cynically exploited the letter by quoting it in his own book so as to insinuate that Kepler was on his side. Now, Brahe wanted Kepler to repudiate Ursus' publicly and Kepler, keen to establish a good working relationship with Brahe, was willing to oblige, though evidently not eager given how long he took over the project. By the time the resulting work was done, Tycho was already dead and it was not published in print. As sordid as the whole situation was and Kepler's reluctance notwithstanding, the treatise is well worth the attention of historians of philosophy and science. For one thing, the very fact that Ursus and Brahe were so concerned over issues of scientific priority was, like a comet or supernova, a sign of the times. You might recall that in the middle of the 16th century, Girolamo Cardano was involved in a controversy over who could take credit for a certain mathematical discovery. I mentioned this in episode 363. We're seeing similar issues arise here, and interestingly, claims for priority were made on the basis of private correspondence and not only publication in print. For another thing, the work that Kepler produced in response to Ursus turns out to be something of a philosophical tour de force. He took the opportunity to defend a realist approach to astronomy against the instrumentalism adopted by Oseander and proponents of the Wittenberg interpretation. Actually, it was really Ursus who raised the issue in his own treatise. There, he characterized astronomical hypotheses as convenient falsehoods or fabrications to be used only for purposes of calculation. He portrayed the introduction of physical hypotheses, like the postulation of perfect transparent celestial spheres as seats for the visible planets, as a corruption of the most ancient science. In his telling, this unwise departure from purely mathematical constructions began around the time of Plato and Aristotle. Kepler was thus drawn into a dispute over the history of astronomy as well as its proper method. As he wrote to his professor, Maeslin, in the treatise against Ursus, the principal concern is with antiquity and with the explication of the opinions of the ancients. So the treatise is to be hardly mathematical, but rather philological. Fortunately, Kepler's humanist training prepared him very well for that task, and he was able to cast doubt on Ursus's reading of Aristotle, the Pythagoreans, and the ancient astronomer Eudoxus. He is especially caustic when it comes to Apollonius of Perga, who Ursus ridiculously claimed had already set forth the tachonic system in antiquity, so that Brahe's supposed discovery had actually been anticipated about 2,000 years earlier. No, argues Kepler, Tycho Brahe really was the originator of his system, and this system is more than just a rearrangement of Copernicus's. For instance, Brahe realized what Copernicus did not, namely that there are no solid orbs in the heavens, since this was disproven by the appearance of those comets. Now, Kepler did not agree with the tachonic system, being himself a convinced Copernican. But in this context, there was a more central point than the correctness of one system or another, namely that the scientific goal was a description of the real physical arrangement of the cosmos. In order to rebut Ursus's instrumentalism, Kepler offers a sophisticated discussion of the nature of scientific hypotheses. A hypothesis does begin as a mere assumption, but it is then confirmed as being true, really true, not just instrumentally useful, when its implications are found to match with our observations. The objection to this had always been that the same set of observations could be compatible with several inconsistent hypotheses. Kepler was obviously aware of this, and in fact would later give a nice analogy for the mathematical equivalence of the tachonic and Copernican systems. It's like the fact that you can draw the same circle by moving a pen in a circle on a piece of paper, or by holding the pen still and moving the paper under it. However, we can still be realists about whatever is shared by all the assumptions that yield the correct results. In this case, even if we are not sure about which heavenly body is orbiting which other body, we can assert as a physical fact that a certain relative distance separates the two bodies at any given time. Instrumentalists like Ursus and Oseander were effectively extrapolating from some undecidable cases to suggest that all of astronomy is undecidable, but this is clearly wrong, as we can see in cases where there is no dispute, like the measurements of the diameters of celestial bodies. Kepler thought he could go further though and establish once and for all how the cosmos is arranged. Admittedly, mere observations, even the painstaking ones made by Brahe, were only going to allow for calculation of relative distances, but other considerations would settle the issue between one set of hypotheses and another. For Kepler, these considerations would come from a rather surprising direction, Platonist metaphysics. In an early work from 1596 called the Mysterium Cosmographicum, or Cosmographic Secret, Kepler set out to explain why there are exactly as many planets as there are, or were then thought to be. In answer, he unveiled what he took to be the hidden divine arrangement of the heavens. He had discovered that if, with Copernicus, we assume that the Earth and other planets are going around the Sun, then the orbits of those planets can be fitted within spheres that contain the shapes of all five platonic solids. These are the cube, the pyramid, or tetrahedron, the octahedron, the icosahedron, and the dodecahedron. They had been used in Plato's Timaeus as an explanation for the construction of the elements and the heavens. Now, Kepler pointed out that if you arrange the platonic solids in the right order and inscribe them within circles, you will get, more or less, exactly the ratios of the orbits of the planets that were then known. The Earth will be right in the middle, further from the Sun than Mercury and Venus, closer than Saturn and Jupiter. When Kepler discovered this, he wept tears of joy, for he felt that he had finally made good on the ambition of his predecessors to discern God's cosmic plan. As a bonus, he could now explain the empty spaces between the planetary orbits in the Copernican system. They need to be that far apart for the sake of mathematical proportion. Furthermore, he thought that this discovery could banish all talk of equivalent hypotheses and instrumentalism. The number and arrangement of platonic solids has a mathematical rationale behind it. Even without ever looking into the night sky, we could expect that God, Plato's eternal geometer, might construct the universe with just this perfect structure. Then, lo and behold, observations confirm that this is indeed the structure he has chosen. Now, this line of thought might evoke our skepticism. In a book on the Platonism Underlying Kepler's Science, Rhonda Martens admits, where Kepler speaks as though he derived the archetypal theory by a priori reasoning and then tested for fit against empirical data, it's more accurate to say that he first had the empirical pattern and then tried to fit it to an archetypal account. But Kepler was convinced that mathematics gives us independent insight, not based on observation, into the causes of the heavenly arrangement. Remember that in this period, an a priori scientific account is one that uses causes to explain effects rather than vice versa, so he took himself to have provided the a priori rationale, confirming the hypothetical proposal of Copernicus. Using the same method, he believed he could rule out even theories embraced by fellow Copernicans. Around the same time, Giordano Bruno was arguing that the universe is infinite and contains other worlds that we cannot observe. But Kepler believed that the universe is limited in size. Having made ordered proportion quite literally central to his cosmology, he could hardly admit that the universe is unbounded and in fact has no center. Though he did admit, as a hypothesis that could not yet be decided by observation, that some of these so-called fixed stars might be closer to us than others. Kepler felt vindicated rather than undermined when the invention of the telescope facilitated the sighting of previously invisible stars. If the universe were infinite and full of stars in all directions, he argued, we should see a dome of solid brilliance above us at night rather than scattered penpricks of light. This problem, now called Olber's paradox or the dark night sky paradox, was first posed by the English Copernican Thomas Digues. Since the basis of Kepler's case was his philosophy of mathematics, we should say a bit more about it. He makes a number of illuminating remarks on the topic in On the Harmony of the World, which came out in 1619, more than 20 years after the Mysterium Cosmographicum. By this time he had made his famous discovery that the orbits of the planets around the Sun will match Brahe's exacting measurements if they are moving elliptically, not in perfect circles. But he remained convinced that geometrical perfection is the key to understanding astronomy as a discipline that fuses mathematics with physics. The arrangement in terms of Platonic solids has the force of necessity, he says, because the Platonic solids and their order are relations that partake of divine archetypes. Plato was right to say in his dialogue, the Meno, that the soul recollects the truths of mathematics, that is, discovers them as knowledge that lies hidden within the soul. Here, Kepler was influenced by the late ancient Platonist Proclus, whose commentary on Euclid is quoted at length in Kepler's treatise. As both Plato and Proclus taught, when we undertake mathematical inquiry, we begin by studying harmonies that can be grasped by sensation, and then understand them by discovering those same harmonies as innately present within our own souls. While the observable motions of the heavens are one case of a harmony that is available to the senses, a more obvious case, and one that is nearer to hand, is music. Thus Kepler devotes on the harmony of the world to the Pythagorean theory of harmony, which can be applied to both astrology and astronomy. He even includes musical notation, where individual notes written on a staff are labeled with the names of the planets, and says that different singing voices correlate to different heavenly bodies. If you are a tenor, for instance, then you have a Martian singing voice, since its place on the harmonic scale is like that of Mars relative to the other planets. Fans of the old Bugs Bunny cartoons can now enjoy a moment of revelation, as they finally understand what Marvin the Martians' Eludium PU36 explosive space modulator was supposed to modulate. Since Kepler was born before the advent of Warner Brothers, he thinks of a different cultural reference, the Pythagorean idea of the music of the spheres. Kepler does not think there is literally audible sound in the heavens, but there doesn't need to be. God has composed a cosmos that is musical in the deeper sense of possessing a perfect harmony, which is entirely rational and entirely natural, as he puts it. Given that Kepler is nowadays most famous for having proposed elliptical orbits, it's downright astonishing to see how little is said about this in his magnum opus on harmony. He does mention it briefly, and talks at somewhat greater length about the physical theory that accounts for the form of the orbits. Kepler's own explosive space modulation was his proposal that each of the planets, including the Earth, moves along an elliptical path with the Sun at one of the two focal points of the path. That is his first law of planetary motion. His second law is that the planet will move proportionately faster as it comes closer to the Sun and slow down when further away. Mathematically speaking, this means that a line drawn from the Sun to the planet will sweep over equal areas at equal times. You get a fatter wedge of the area of the ellipse when the planet is near the Sun, so that this line is shorter, a slimmer but longer wedge when the planet is further away. Good news, since this proves that it is in principle possible to share out equal pieces of an elliptical birthday cake. Now an obvious question arises, apart from the question of why anyone would bake an elliptical birthday cake, what is causing the planets to accelerate upon approaching the Sun? The answer, of course, is gravity, and Kepler didn't know that, but he made a startlingly similar suggestion. He was aware of something we'll be discussing later on, namely William Gilbert's research into magnetism over in England. Kepler thought that this could be the explanation, or at least analogous to the explanation, for heavenly motion. This is the context for one of his mechanical descriptions of the celestial realm. My goal, he wrote in a letter of 1605, is to show that the heavenly machine is not a kind of divine living being, but similar to a clockwork, insofar as almost all the manifold motions are taken care of by one single absolutely simple magnetic bodily force, as in a clockwork all motion is taken care of by a simple weight. Yet he certainly did not leave behind earlier ideas about cosmic bodies as being akin to organisms as opposed to unliving machines. Like the ancient Platonists, who so inspired him, he believed that there is a soul in the earth which interacts with the heavens so as to produce phenomena like the tides and weather patterns. This accounts for something I mentioned earlier, namely the possibility of using astrology to predict the weather. By offering such arguments, Kepler suggests that the earthly realm of our everyday experience operates according to the same rules as the astronomical realm. That's something that was excluded in Aristotelian science, which as I've mentioned in previous episodes, envisioned two interacting physical systems, our lower world of elements that move straight up and down, and the higher world of perfect circular motion. But between the appearance of comets and novas further away from us than the moon, the abolition of celestial orbs and elliptical orbits instead of circles, this division of nature into two realms was increasingly embattled. Kepler's idea that magnetism could explain celestial attraction was a further attempt to apply earthly physics to heavenly things, and this was no tacit implication or unconsidered assumption on Kepler's part. To the contrary, he explicitly said that there is a much closer relation between the heavens and earth than had been admitted by Aristotle. Indeed, according to the Copernican system, the earth is in the heavens just as much as any other planet is. In a related move, Kepler blurred the strict dividing line the Aristotelians drew to separate physics from pure mathematics. Where there is matter, he said, there is geometry, justifying his idea that one can use mathematical analysis to establish the nature of physical reality. This is not to say that he fused them into a single science, though. In fact, he can be found criticizing other authors, including Aristotle himself, for failing to observe the distinction between the methods of mathematical astronomy and natural philosophy. Rather, his idea was that the structures and proportions studied by the mathematician are then discovered by empirical investigation, and in various physical contexts. Just as the attractive power of a magnet is stronger in proportion to its proximity to a chunk of metal, so the Sun's attractive power is stronger when the planet it is affecting is closer, which is why the planet speeds up. This is not a coincidence, of course, but the result of one and the same archetype being used by God to create different phenomena as he providentially designs an orderly universe. Kepler's awareness of the difference between math and physics, and of the fact that the two can work together, is summed up early in his treatise On the Harmony of the World, when he says, I am now playing the role not of a geometer in philosophy, but of a philosopher in this part of geometry. One subplot in the story we've been following over the past episodes is the way that genuinely new observations changed the course of science. Without the fortuitous appearance of those comets and novas, astronomers might have been slower to challenge some aspects of Aristotelian cosmology. Instruments like the telescope also afforded a view of previously unseen things, like stars too distant to see with a naked eye, or the craters on the moon that Galileo was the first to see. The Renaissance differs from earlier periods, in part because people had to try to understand such novelties. Sometimes their reactions were lamentably counterproductive. Later on in this series, we'll be talking about the fact that misfortunes were sometimes blamed on witches, which is not irrelevant to Kepler, who had to rush to defend his own mother from such charges. On other occasions, though, exceptions played a productive role in science. This is the general phenomenon we'll be talking about next time, as a genuinely extraordinary guest joins me for a wide-ranging discussion of Renaissance science and the way it dealt with so-called wonders, like comets, and for that matter, armadillos. So join me for a discussion with the wonderful Lorraine Dastan, here on The History of Philosophy, Without Any Gaps.