 Hi, I'm Peter Adamson and you're listening to the History of Philosophy Podcast, brought to you with the support of King's College London and the LMU in Munich. Online at www.historyoffilosophy.net. Today's episode, Neither the Time Nor the Place – Hasdai Kreskus If you want to build something new, you sometimes need to destroy something old. It's true in the construction business, when you might need to dynamite an abandoned building to build a new one, in the agriculture business, when you need to clear a field to plant your crops, and of course in the philosophy business too. I'm sure many of you have spent this tour of philosophy looking forward to the rise of modern physics. We're not there yet, but in this episode we're going to look at a figure who helped clear the ground on which modern physics would be built. His name was Hasdai Kreskus. The writings of Maimonides and Gersonides provoked Kreskus into a stunning assault on the assumptions underlying Aristotelian physics. His criticisms were not wholly new. Some of his ideas are prefigured in the ancient Christian critic of Aristotle, John Philoponus, and the more Aristotle-friendly Andalusian Muslim thinker Ibn Bajja. But Kreskus went further than them, both in the daring of his arguments and in his historical reach. This aspect of his writings caused little excitement among Jews in the following generations, but he would be cited by Renaissance philosophers like Pico della Mirandola, and later by Smirnoff and Noza. It would be going too far to say that without Kreskus there would have been no modern science, but it would not be going far enough if we didn't credit Kreskus with some part in the gradual demise of Aristotelian science. As scientific revolutionaries go, Kreskus cut a somewhat unlikely figure. For one thing, his intentions concerning natural philosophy were mostly destructive. He was more demolition man than architect. Yet in arguing that Maimonides and Aristotle had failed to rule out such things as void and actual infinity, he was indirectly led to contemplate possibilities that had been almost universally rejected since antiquity. For another thing, Kreskus led a life dominated more by the discontents of his people than the contents of Aristotle's physics. He hailed from Barcelona, where he rose as a scholar at the city's yeshiva. This was in the mid to late 14th century, so we're talking here about Spain under the rule of Christians after the Reconquest. Christian rule was, during this period, rather favorable to Jews in general and to Kreskus in particular. He moved to Zaragoza, capital of Aragon, and the king and queen appointed him as the highest legal authority for Jews in their realm. Then, in the year 1391, disaster struck. It came in the form of pogroms against the Jews in many Spanish cities, with the Christian authorities incapable of checking the violence. The Jewish community of Kreskus's former home in Barcelona was destroyed, and Kreskus's own son was killed there. This calamity was a foretaste of what would come almost exactly a century later with the total expulsion of Jews from Spain. As a high-ranking Jewish leader, Kreskus worked to find safe havens for his co-religionists. He also went on the offensive against the Christians, at least in writing. Among his works is a treatise written in Catalan, which criticizes ten principles of the Christian faith such as original sin, the doctrines of the Trinity and Incarnation, the virginity of Mary, and so on. Under the circumstances, this may sound remarkably provocative, but the intended audience was probably Kreskus's fellow Jews, or converts, who he hoped might recant and return to Judaism. Within Judaism too, Kreskus's great preoccupation was the principles of religion. His greatest work, the one that contains his reflections on Aristotelian natural philosophy, is entitled Or Hashem, or Light of the Lord. It was occasioned by the philosophical approach to the Jewish law that Kreskus found in Maimonides's Mishneh Torah. Maimonides followed the traditional count of 613 commandments in the law. Among these, he put one above all others, the commandment to believe in God. Also in the Mishneh Torah, as well as in his commentary on the Mishnah, Maimonides itemized thirteen principles of the Jewish religion. These again included the existence of God, as well as God's incorporeality, divine providence, prophecy in general, and the special prophethood of Moses in particular, and so on. Following previous authors who had simplified this list, Kreskus distilled Maimonides's dogma into three main claims. God exists, he is one, and he has no body. Naturally, Kreskus thought all three of these claims are true. In fact, he thought they are held in common by all reasonable religions, never mind the true religion, which is Judaism. But he did not think that Maimonides, or for that matter Aristotle or Gersonides, had managed to prove them. The purpose of the light of the Lord is thus to expose the flaws in Maimonides's arguments, which were drawn largely from Aristotle. Thereby, Kreskus intended to make room, not for modern physics, but for a clearer understanding of how and why we should accept these paramount principles of Judaism. Kreskus worried that Maimonides had placed the majestic edifice of Jewish law on the shaky foundations of Aristotelian science. The light of the Lord offers an explosion of arguments designed to knock down this whole condemned structure, so that Kreskus can raise something more solid in its place. Kreskus already makes a fundamental point against Maimonides's handling of the first and chief principle, the existence of God. As I just mentioned, Maimonides counts belief in God as a commandment laid upon us by God himself. This, Kreskus argues, simply makes no sense. For one thing, why would anyone follow a command from God without already believing that God exists? The existence of God is a principle presupposed by the commandments of the law, not itself among those commandments. Furthermore, it is not just up to us to decide what we believe. And if something is not a matter of choice, then it is incoherent to issue commands about it. Here, Kreskus has made an interesting philosophical point about the nature of belief, that it responds to things like good evidence or good reasons, and not to a decision made by the believer. Suppose I command you to believe that Buster Keaton is the greatest figure in the history of cinema. In fact, suppose I offer you a tall stack of money to believe that. No matter how much you like the deal, you can't just decide to believe this, or anything else. Our beliefs respond not to bribes or threats, but to what we find convincing, a point lost on those Christians who tried to compel Kreskus and his fellow Jews to convert. If you were minded to accept my bribe, the most you could do would be to seek out good evidence that Keaton really is as great as I claim, for instance by watching some of his films. Likewise, Kreskus says, we believe in God because we have reasons to do so, not because it is commanded. But all this is merely a skirmish before the main battle which is fought over the premises used by Maimonides to demonstrate what he thinks we are commanded to believe, that God exists, is one, and is immaterial. As we saw when we looked at Maimonides, he offered two methods for proving God's existence. The easy method is to presuppose that the cosmos began in time, and infer from this that such a cosmos would need a creator. The other method is the one attacked by Kreskus. In this case we instead begin by arguing that the cosmos is eternal. We show that the heavens of the cosmos are eternally moving. Since time is the measure of motion, as Aristotle tells us, time must be eternal too. On the other hand, the body of the cosmos is finite in size. It has an edge, namely the outer surface of the furthermost heavenly sphere which is surrounded by nothing, not even empty void. Since the cosmos is finite in this way, it cannot contain within itself the power needed to generate an eternal motion. Instead there must be an immaterial mover capable of causing the everlasting motion of the heavens, and this is God. To his credit, Maimonides is very forthcoming about the principles that need to be accepted or established if this argument is to work. He counts 26 of them, and sets them out at the beginning of the second part of his Guide for the Perplexed. As you might have noticed from the summary I just gave, the premises include practically every core idea of Aristotle's physics, the eternity and finite size of the universe, the nature of time, and the impossibility of void. Crescus is going to raise serious doubts about these premises and all the arguments that had been used to support them. He will thus threaten to sweep away the whole of natural philosophy as it was known in the medieval period. Again, he does this not because he has a better physics to put in its place, but simply because he sees the Aristotelian system as an inadequate basis for belief in God. Since there are 26 premises to consider, I won't be able to go through them all, but a look at the highlights, like a viewing of one or two Buster Keaton movies, should be apple proof of greatness. At the risk of making it sound like this episode is going to be an awfully long one, let's start with infinity. Aristotle accepted the possibility of what is called a potential infinity, which is when you have a situation of indefinite increase, like counting up through numbers. There's no end to the process, but you will never get to an actually infinite number, so this is perfectly possible. It's impossible, though, that anything be actually infinite, for instance that the body of the universe be unlimited in size. Aristotle devised clever arguments to show the impossibility of such a scenario. Imagine, for instance, an infinitely large disk that is rotating around a central point. Now picture an endless line drawn from that center point across the disk, like an infinitely long spoke in an infinitely large wheel. Aristotle realizes that in a rotating circle, a point further from the center will move faster than one closer to the center. For instance, in a normal, finitely sized wheel, a point on the wheel's rim moves faster as the wheel spins than a point on a spoke right near the middle. So a point infinitely distant from the center on our infinitely long line would need to move infinitely fast, if it is to move along in this rotation. But infinitely fast motion is absurd, so there cannot be an infinitely large body. Against this sort of argument, Kresge uses a tactic Aristotle himself had employed in thinking about potential infinity. Aristotle had said, for instance, that any finite body can always be divided, then divided again and again. In principle, there is no limit to how small the divisions can be, though of course there is a practical limit to how finely we can chop things up. Similarly, Aristotle would explain the infinity of the eternal past like this. For any number of years you choose to name, the universe has existed for longer than that number of years. In other words, if you say, has the world existed for one million years? Aristotle will be willing to say, sure, in fact, for longer than that, and he'll give you the same response no matter what number you choose. Just as with dividing a body or counting upwards through the numbers, you never have to stop, but neither do you ever finish the process by arriving at an actually infinite number of past years. Now Kresge proposes that the same thing can be applied to Aristotle's thought experiment of the infinitely long line on the infinite disk. Take any point on the line you like. It will always be true to say that the line extends past that point as it stretches away from the center of the disk. Yet there is no particular point that is infinitely far from the center, no point that would need to be moving infinitely fast for the rotation to succeed. Rather, the points on the line are at indefinitely increasing, yet in each case finite, distances from the center of the disk. In a stroke of genius, Kresge thinks to compare this to an already well-known result in geometry in which two lines can approach each other indefinitely, getting closer and closer without ever meeting. You might remember the word asymptote from high school. That's what Kresge is referring to. If the distance between two lines can get smaller and smaller forever without ever going to zero, then likewise the line's length can get bigger and bigger forever while remaining limited at any given point. And like this imaginary line, Kresge isn't done. He adds several more points of his own that controvert age-old assumptions about infinity. For instance, he states that a line bounded in one direction and infinite in the other is no smaller than a line that is infinite in both directions. Here Kresge is rejecting an assumption made even by other critics of Aristotle, like Akinde in his arguments against the eternity of the universe. Akinde and pretty much everyone else had assumed that one infinite quantity cannot form only a part of another infinite quantity while both are equal in size. Imagine for instance an infinite pile of marbles, half of which are red and half of which are black. Before Kresge, most philosophers would see this as impossible because the red marbles would be infinite in number yet only half as many as the infinite total number of marbles. Kresge fails to see the problem. In his example, the two lines are obviously going to be the same size, even though one is bounded at one end while the other is not. After all, both lines are of indefinite and unmeasurable length. This is all that infinite means, without a limit. Kresge doesn't develop this idea at length, so to speak. Aristotle and Akinde would probably say he has lost his marbles. But in fact he has made a fundamental breakthrough, one that would make it possible to accept, for instance, that the set of positive integers is the same size as the set of even positive integers. After all, that case is just like our example of the infinite pile of marbles, half of which are red. Kresge's new conception of infinity has implications for how we conceive of the physical universe. Aristotle, Maimonides, and friends assumed that the cosmos ends at the sphere of fixed stars, and that there is no empty space beyond that sphere. But Kresge again sees no problem with supposing an infinite void around the cosmos, as the Stoics had suggested in antiquity. After all, he's shown with his example of the infinitely long line on the disk that there is nothing absurd with supposing that space extends indefinitely. Hang on a minute though, because Aristotle has another way of blocking this move. He argued that, infinite or not, void space is impossible. His most persuasive argument was that the speed of any motion is inversely related to the density of the medium it passes through. There is, for instance, the well-known phenomenon that giraffes lope more quickly through the fresh air of the savanna than they do through honey. But a void space has zero density, so the speed of any motion through it should be infinitely fast—the same absurdity we had before with the infinite line on the infinite disk. Against this, Kresge deploys an idea that had already been suggested by Philoponus and Ibn Bajja, that the effect of a dense medium is only to slow down a motion's intrinsic speed. With a void, there would be no slowing effect at all, so the speed would be determined solely by the motion's impetus. But of course, this speed will remain finite. Kresge sees another problem for Aristotle and Maimonides here. Motions are indeed impeded and slowed down by the friction of the media they pass through, but this is never going to happen in the case of the rotation of the heavens, since in Aristotle's own cosmology, there is no friction applied to them. Why then do we need an infinite power to make them move? It would be one thing if the heavens moved infinitely quickly. That would indeed call for a power of infinite intensity to make them go. But on Aristotle's own reckoning, the heavens are instead moving at a finite speed, albeit for an infinitely long time. No infinite or immaterial cause is needed to explain this, argues Kresge. Rather, a finite amount of power could be applied to set them into motion, and they will just rotate forever, since there is nothing to slow them down or stop them. And another thing, while we're at it, it doesn't actually seem that any external cause is necessary to move the heavens, whether the cause would be finite or infinite in power. The heavens are surely alive and capable of moving themselves, after all. If not, they would be less impressive than even a humble insect down here on earth. Maimonides's proof for God's existence is by now in tatters, and Aristotelian natural philosophy has suffered a lot of collateral damage in the process. This is all that Kresge set out to achieve. But he also points out that, given the shakiness of Aristotle's physics, we could easily imagine that our universe is radically different from the one supposed in the philosophical tradition. For instance, if actual infinity is possible, and if there is an infinite void, there could well be other worlds out there in the emptiness, a hypothesis last seriously entertained by ancient atomists. In fact, our own cosmos might be only one in an infinite series of worlds created and then destroyed by God. Of course, this would presuppose that time stretches back beyond the existence of our world, something Aristotle would reject, but I'm guessing you won't be surprised to hear that Kresge sees no problem here. Like the early unorthodox Muslim philosopher Ar-Razi, Kresge is giving up on the Aristotelian understanding of time as dependent on motion, and of place as the limit surrounding a body. Rather, place is simply the void or emptiness whose possibility Kresge has now established. As for time, Aristotle had defined it as the measure of motion in respect of prior and posterior. Not really, says Kresge. For one thing, time could measure bodies at rest, too, or even the extended existence of immaterial things. He admits that Aristotle was right, for once, to define time as a measure, but it is a measure that we ourselves impose when we evaluate the interval between any two moments, as when we say that the starting and end point for one revolution of the sun are a year apart. So here, Kresge is unlike Ar-Razi, for whom time was an independent, eternal principle of the universe. For Kresge, time is instead brought into being by our mental activity, so it exists only in the soul. As a result, Kresge has no trouble in supposing that time stretches back to before our cosmos existed. That just means we can mentally entertain longer periods than the finite time during which the cosmos has been around. If he's serious about all this, Kresge is proposing that God creates a universe containing infinitely many worlds existing now, and a further infinity of worlds in the past and in the future. Which just goes to show how lucky we are to live in the world that had Buster Keaton in it. Kresge's demolition job on Aristotelian physics is his most famous achievement, and probably deservedly so. But it should not distract us from the important fact that he actually accepts the point Maimonides was trying to prove with his 26 premises. God does exist, and we can even prove it. How? Well, basically by using Avicenna's method. If we consider the whole of Kresge's universe with all its worlds, we may be grappling with something that is infinite, but it is still something that could have failed to exist. There must be a necessary existent to explain why this infinite contingency has been realized, and of course that necessary existent is God. Actually, Maimonides knew and made use of Avicenna's proof too, but Kresge thinks he didn't understand it properly. In his version of Avicenna's argument, Maimonides mentioned that if all things are possibly non-existent, then at some point in eternal time this possibility would be realized, and at that point there would be nothing. Kresge rejects this, seeing that the proof from contingency needs to assume nothing about eternity or for that matter about whether the things God has created are finite or infinite. Rather, Avicenna's insight was to label the whole aggregate of created things, finite or infinite, as contingent, and argue from there to the need for an external necessary cause to explain why this contingency has been realized. We can tell from this that Kresge was no implacable foe of philosophy in all its forms. Rather, like Al-Ghazali in the Eastern Islamic world, he held philosophers to their own standards, pointing out the holes in their supposedly demonstrative arguments. Yet he made use of philosophical ideas himself when he turned to the question of how the Jewish law could be grounded. It's tempting to buttonhole Gersonides and Kresge, the two great thinkers of medieval Judaism after Maimonides, as representing the rationalist and anti-rationalist paths open to Jews in this period. There's something to that idea. Yet Gersonides, despite his enthusiasm for Averroes, was also a critic of the previous philosophical tradition, and Kresge structured his Light of the Lord in pretty much the same way as Gersonides structured his Wars of the Lord. Both proceed by listing classic arguments of philosophy and then passing judgment upon them. For Kresge, there is a time and place for everything, even philosophy. So, both these thinkers were complex characters, which makes it worth our while to spend one more episode in their company. Please join me for an interview with an expert on both of them, Tamar Rudofsky, at the same time and same place, The History of Philosophy, without any gaps.