 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 LMU in Munich. If someone asked you to summarize the place of medieval philosophy in the history of Western science in only two sentences, you could do worse than to say, In the medieval period, science was based largely on Aristotle. Early modern thinkers had to free themselves from Aristotelianism to launch the scientific revolution. On the other hand, you could also do a lot better. Of course, any two-sentence summary of a whole philosophical age is likely to be misleading. The only perfect one that comes to mind for me is, medieval philosophy is really interesting. There's this great podcast about it, which you should really check out. But it's particularly misleading to portray the medievals as backward-thinking Aristotelians. True, they did devote considerable effort to understanding Aristotle's newly available works on natural philosophy and related material from the Islamic world, but they were not backward-thinking. Some of the new ideas that emerged in early modern science have their ultimate roots in commentaries on Aristotle's physics, composed beginning around the middle of the 13th century. And some of these innovations were put forward by that shadowy, multifaceted thinker we have come not to know, but to love anyway, Anonymous. When we think about the deficiencies of the ancients' natural philosophy, the first thing to leap to mind is their false view of the cosmos. I hate to break this to any Aristotelians who may be listening, but the universe is not in fact a perfect sphere, containing nested smaller spheres that serve as seats for the planets, with the earth sitting still in the middle of the whole system. We now know that the sun does not circle the earth, but the other way around, although we continue to speak of sunrise and sunset, which is a good thing since those words are needed to put on productions of Fiddler on the Roof. But it was not just an incorrect cosmology that Aristotle bequeathed to posterity. It was also a well-entrenched theory of fundamental physical principles like motion, time, and space, or rather place. 13th century commentators on the physics are not going to challenge the earth-centered cosmology, but they are going to make productive suggestions about these principles of natural philosophy. Their suggestions were not necessarily intended as innovations. In fact, they were often put forward as explanations of what Aristotle himself meant to say. But the commentators didn't just want to get Aristotle right, they wanted to show that what he said was itself right. Better to give an implausible interpretation of his texts that credits him with a true theory, than to give a more convincing reading of his words that has him making a mistake. If all else failed, they were willing to depart from Aristotle's teachings when they couldn't account for the phenomena we see around us. Thus, the medievals bring to bear observations from the natural world in their commentaries. Consider, for instance, the difference between throwing a feather and throwing a baseball. Non-American listeners may wish to substitute a different culturally appropriate example. For instance, British audience members can imagine throwing a cricket ball, and Germans a potato dumpling. Why is it so much easier to throw the baseball than to throw the feather, so that the same amount of force will cause the baseball to fly a considerable distance, but the feather to float harmlessly to one's feet? It turns out that this is a very difficult question for Aristotle to answer. In fact, he is hard-pressed to explain the motion of projectiles at all, since he generally explains motion and change in terms of the influence of a mover on something that can move. In his jargon, the mover actualizes the movable thing's potential for motion or change. He applies this analysis not just to spatial motion, but other kinds of change, like making something hot. That would indeed be a nice example for his theory. If you put a baseball next to a fire, the heat of the fire will actualize the potential hotness of the baseball, in other words, warm it up. Likewise, if a group of people are pushing a broken down car along a road, they are actualizing its potential for motion. If the actuality is bestowed by the mover, though, why does the motion continue once the mover is no longer exerting any influence? The baseball does stop heating up as soon as it's taken away from the fire, as Aristotle's account would expect, but the car may continue to roll briefly after the people stop pushing it. And if you throw the baseball, its motion occurs almost entirely after it is no longer in contact with your hand. So what is causing it to keep moving? And what determines the distance it flies before dropping to the ground? Like a clumsy bartender, Aristotle was grasping at straws as he tried to provide an answer. He suggested that the medium through which the projectile is moving is somehow responsible for keeping it in motion. When you throw the baseball into the air, the baseball displaces the air and it is the motion of the air, rather than your throwing arm, that keeps the ball moving forward. A strike against this theory is the aforementioned fact that it is sometimes easier to throw heavy things than light things. If you displace the air with the same amount of force, shouldn't anything fly along in the same way? This point was made by Richard Rufus of Cornwall, who was thought to be the author of one of the most interesting commentaries on the physics written in the first half of the 13th century. Rufus taught at the universities in Oxford and Paris, serving first as a Master in the Arts faculty at Paris before joining the Franciscans. He wrote commentaries on Aristotle already in the 1230s, making him one of the earliest masters to engage seriously with these works. Rufus's account of projectile motion is reminiscent of one that had been proposed by the ancient Christian commentator on Aristotle, John Philoponus. Rufus thinks that when you throw the baseball, you give it what he calls an impression, which makes it move unnaturally. The baseball's natural inclination would be to simply drop to the ground, but thanks to the impression made when you throw it, the baseball can temporarily move towards home plate instead, pushing air out of the way as it does so. This also explains why it is easier to throw baseballs than feathers. The baseball is heavier, so that you have to exert more force on it when you throw, hence the impression made upon it is more powerful. Here Rufus is trying to explain how projectile motion works, and in the process departing from Aristotle in what looks to be a promising direction. But we shouldn't credit him with too much. This is not quite the later idea of impetus, since Rufus lacks the idea that a moving object will continue to move unless something stops it. For that, we have to wait until the 14th century. The word impetus was indeed used in the 13th century, but with a different meaning, and by opponents of Rufus's impression theory. Not least among them was Roger Bacon. As we'll be seeing in a later episode, Bacon was an innovative thinker in his own right. But he had little time for Richard Rufus, about whom he remarked, No author was accounted more famous by the foolish multitude, but the wise considered him insane. Bacon preferred a version of Aristotle's original account, with the parts of the medium helping to carry the projectile along. So far we've been talking about the mechanics of how motion actually works. But if you think about it, motion is also pretty strange from a metaphysical point of view. This is because it seems to exist only over time, rather than at a time. When you are helping the baseball to get cozy and warm by the fire, it only ever has one given temperature. And at any instant while a thrown baseball is hurtling through the air, it only has one position. How are these temperatures and positions glued together, as it were, into a single fluid change or motion? The question was raised by Zeno of Elea, a follower of Parmenides whom we discussed a mere 218 episodes ago. Zeno argued that an arrow in flight is not moving, because it is at rest at each time during its supposed flight. This was another puzzle that engaged the attention of medieval commentators. They looked at it from a typically Aristotelian point of view by asking how motion relates to the scheme of 10 categories. But we can think about the problem from a less technical perspective by simply asking how motion or change relates to the property that will be reached by the end of the motion or change. How, for instance, does the heating of the baseball relate to the final condition of the baseball, which is to be, like a high-scoring instructor on the Rate Your Professor website, and how does the flight of a thrown baseball relate to the position it will have at the end of its flight? The Muslim commentator, Averroes, had given an answer to this question when he was discussing Aristotle's remark that there are four kinds of change. Something can alter in respect of its place, its quality, its quantity, or its very substance. Averroes took this to mean that a motion in respect of a quality, for instance, is nothing more than that quality in an incomplete state. For instance, when the baseball is being warmed up, it is on the way to being hot, so we can just think of its status at any one time as incomplete hotness, a score I'd be more than happy to settle for on Rate Your Professor. In other words, the change involved in heating is nothing more than a series of stages of heat. When the medieval commentators began studying the physics, they frequently read their Latin version of Averroes alongside it. Helpful a guide, though Averroes may have been, he was often criticized in the Latin commentaries. These have been studied by Cecilia Trifoli in a book surveying the remarks of no fewer than ten commentators who worked in Oxford in the middle of the 13th century. It's worth noting that all but two of them are anonymous. Just as in the earlier medieval period, unidentified authors continued to play a significant role in the development of philosophy. One of these anonymous commentators complains that Averroes' idea of motion as an incomplete property is itself incomplete. Each stage in the motion or change, for instance, each degree of heat in the increasingly warm baseball, is a product of change just as much as the degree of heat achieved at the end of the heating process. This means we'll need a separate motion to explain each partial change along the way. Besides, the commentator adds, some changes aren't gradual. When a substance like an animal comes to be, it does so all at once and not part by part. Despite these criticisms, a theory of motion inspired by Averroes is going to be put forward by another commentator on Aristotle in the following decades, whose name is not only known, but renowned, Albert the Great. He proposes that we can think of a change as being just the same form as the one that will exist at the end of the change, but with potentiality mixed in. Across time, the change flows towards its final result, with the form becoming progressively more actual at each moment. These metaphysical difficulties about motion have to do with the fact that it is, as the commentators put it, a successive entity. Motion or change exists bit by bit across time, rather than all at once. Considering how puzzling the commentators find this, it's no surprise that they also find time itself puzzling. And they aren't the only ones. Aristotle had raised a whole series of problems about time in his physics, and another main source of inspiration for the medieval's, Augustine, had wrestled with the topic in his Confessions. Both of them wondered whether we can even say that time is real. The doubt is similar to the one we saw concerning motion. Just as a motion unfolds across time and so is never entirely present, so does temporal duration seem to lie outside what presently exists. After all, the past is already gone, the future is yet to come, and the present moment has no duration of any magnitude but is an undivided instant. We often compare temporal duration to spatial magnitude, even talking about a long or short time the way we might talk about a long or short distance, but actually space is very different from time. The distance between pitcher's mound and home plate is all present at once, whereas the time it takes the ball to travel that distance is not. One way to solve this problem is to give up on time's real existence outside the mind. It is we who measure changes in the world by tracking their temporal duration so that time is really a phenomenon of the soul rather than the physical world. Aristotle flirted with this idea, saying that there can be no time without soul, and Augustine also made time a feature of our mental life. For the 13th century commentators, though, it was once again of Verroes who especially represented this skeptical view about time's existence. In his physics commentary, he pointed out that Aristotle's famous definition of time as a number of motion implies that time is mind-dependent. The motion is really out there, but the numbering only happens in your head. This doesn't mean that time is wholly fictitious, though. The motion in the world does have the potential to be numbered, so there is a basis in reality for the mental process of assigning a time to the motion. Like when somebody with a speed gun tells you that a fastball took exactly 0.4 seconds to reach home plate. But the commentators believe that Verroes has once again swung and missed. Richard Rufus, followed by anonymous authors, argued that Verroes was confusing number with counting. The 0.4 seconds that it takes for the ball to reach home plate really is the number of the motion, whether or not anyone counts it. That number is already an actuality, and the only sense in which it is potential is that the number may or may not be measured or counted, for instance by the guy with the speed gun. This is not the only context in which our commentators tackle the problem of number. It also arises when they are discussing the treatment of infinity in Aristotle's physics. The standard Aristotelian view here is that nothing can be actually infinite, but there can be potential infinities. For instance, you cannot have an infinitely big body, but you could have a body that is increasing indefinitely in size while always remaining finitely large. Of course, the ban on thinking about actual infinities is one of the things that will have to be abandoned if we are to get to developments in modern science and especially mathematics. So it's noteworthy that our medieval commentators begin to argue for the possibility of actual infinities in physics. They still don't want to say that there could be an infinitely large body, but there is a kind of infinity even in a body of limited size. As Aristotle himself had said, any body can at least in principle be divided and subdivided without limit. The ancient atomists were wrong to think that you would ever reach a smallest body that can no longer be cut. The question, then, is what we should say about the divisions that can be made in a given body. Let's imagine slicing a baseball in half, then in a quarter, then an eighth, and so on, like taking apart an orange with an indefinitely large number of segments. Maybe this is what they have in mind when they talk about juicing a baseball. On the face of it, this sounds like a standard case of potential infinity. There are indefinitely many segments you can get out of the ball if you have a sharp enough knife. But think about the case of time, which we just considered. We decided that the number of time is actual in the world. What is potential is the counting of that time. So couldn't we say that even if the divisions of the ball are potential, the number of potential divisions is actual? According to this view, which was defended by some of the commentators, infinity would be a real feature of number outside the soul. Other commentators disagreed, and said that the number of divisions becomes actual only when you do some dividing, whether it is with a knife, or by imagining divisions in your mind. At the bottom of this dispute is an ambiguity in the concept of infinity. Is infinity an unlimited magnitude, or is it just the idea that something is indefinite, as when you can at each stage make an even smaller division than the last division you made? We've now considered medieval discussions about motion, time, and infinity, three of the four principles of natural philosophy discussed by Aristotle. The last of them was place, and in this case too Aristotle's account raised serious problems. His canonical definition tells us that the place of a thing is the inner surface of whatever contains that thing. Suppose, for instance, that I were to plunge a baseball into a pitcher of water. After all, what good is a baseball without a pitcher? In this case, the place of the baseball would be the surface of the water that surrounds it, while the place of the water would be the pitcher, or rather the inner surface of the pitcher where it touches the water. Aristotle considered and dismissed a rival theory, which is that the place of each thing is the three-dimensional extension occupied by that thing. So on this view, the place of the baseball in the water is a spatial region exactly the size of the baseball itself. This region was previously occupied by water, but when the baseball was plunged into the pitcher it displaced some of the water and quite literally took its place. Even though Aristotle explicitly rejected this idea of place as extension, commentators found it attractive, because it could help resolve tensions within Aristotle's physics. For example, he thought that there are natural places for the four elements. Earth is trying to get to its proper place at the center of the cosmos and fire to the outer edge of the realm below the celestial spheres, which is why Earth falls and fire rises. Pretty clearly, these natural places are not containing boundaries, they sound more like regions of space. Then there was the problem of the place of the universe itself. For Aristotle, there is nothing outside the spherical cosmos, not even empty space, so there is no further body containing the cosmos to provide it with a place. Absurdly, it would seem that the universe is nowhere at all. Yet again, the commentators turned their ingenuity to solving these problems. Regarding the place of the cosmos, they engaged with an ingenious solution suggested by Averroes. Since nothing contains the outermost sphere of the cosmos, we can in this exceptional case say that its place is provided by the center point of the whole universe around which the sphere is rotating. Strike three for Averroes, according to some of our commentators. His solution would make the Earth prior to the heavens an explanation, which is inconsistent with the heavens' superior role in Aristotelian natural philosophy. They devised substitute accounts, for instance that the place of the outermost heaven could be its own outer surface. As for the place of more everyday objects, like baseballs, they suggest that we might be able to find a compromise between Aristotle's definition and the idea that place is extension. After all, the containing boundary of a body defines a three-dimensional region within itself, which is exactly the extension occupied by the body. By the middle of the 13th century then, considerable progress was being made in natural philosophy, concerning topics we still associate with physics, cosmology, motion, time, infinity, and space, or at least place. But for Aristotle and his medieval followers, natural philosophy included much more than this. They took physics to include the study of plants, animals, and human nature itself. Such living beings all have a principle that gives them life, which is what Aristotle meant by soul. On this topic too, 13th century philosophers wrestled with the ideas they were finding in Aristotle and in works of the Islamic world. This time, the situation was like post-season baseball because there was much more to play for. The religious implications of Aristotelian ideas about the soul were deeply troubling. My pitch to you is that you should join me next time to find out why, here on The History of Philosophy Without Any Gaps.