 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 – online at historyofphilosophy.net. Today's episode, Do the Math – Science in the Palaeologan Renaissance. Next time you're helping a child with her math homework and get the inevitable question, when am I ever going to need to know any of this stuff, I suggest you tell the story of Leo the philosopher, also known as Leo the mathematician. He was a 9th century Byzantine scholar whose student was captured by Muslim forces and then dazzled his captors with the learning he had received from Leo. So impressed were the Muslims that the Caliph wrote to offer Leo a position at court, but he was outbid by the emperor. Leo wound up staying in Constantinople enjoying a healthy salary. It's a particularly impressive story given the high standard of sciences in the Islamic world at that time and the fact that, as we've seen, Muslims were usually very disparaging about the state of Byzantine learning. The feeling was, for the most part, mutual. Very few Byzantines were alive to the intellectual achievement of their contemporaries in the Islamic world. In a previous episode, I've already mentioned Simeon Seth, who was that rare thing, a translator of Arabic scientific and literary material into Greek. He went so far as to borrow from Muslim medical authors while criticizing the greatest of the Greek physicians, Galen. Simeon translated works by the 9th century Persian philosopher and doctor Ahrazi, who had had the temerity to assemble a list of errors in Galenic works which he candidly titled Doubts About Galen. Simeon followed suit, mentioning places where Galen seemed to contradict himself and preferring the authority of Aristotle. More generally, the Byzantines carried on the tradition of Greek medicine, though it seems they did less to improve on Galen's medicine than their counterparts in the Islamic world. Like the Muslims, they did have hospitals, pharmacists, and surgeons. We even hear of an operation to separate conjoined twins, which was a partial success, in that one twin survived it and lived on for a few more days. A more profound engagement with science from the Islamic world can be found with the disciplines of astronomy and astrology. Simeon Seth is again relevant here. He is mentioned in Anna Komnena's Alexiad as one of the numerous astrologers present at her father's court. Already in the 11th century we see astronomical calculations being done on the basis of Arabic materials, but the most remarkable such case comes later with George Coniades. He studied in the Persian city of Tabriz in the late 13th century and translated astronomical works from Persian into Greek. There was sufficient enthusiasm for this sort of material that in the following century a theologian was moved to condemn it and one emperor banned the prediction of eclipses because they were thought to be omens of political upheaval. This made for quite a change from the days of an earlier emperor, Manuel I Komnenos, whose embrace of astrology was heavily criticized by later authors. He even wrote a treatise in defense of the discipline, insisting that astrology should not be confused with the sinful practice of magic. It's significant that when Anna mentions Simeon Seth and his intellectual interests, she calls him a matematicos. That may seem a strange way to refer to an astrologer, but in a Byzantine context it made perfect sense. Like the Latin Christians with their quadrivium, the Greeks recognized four mathematical sciences, namely arithmetic, geometry, spherics or astronomy, and harmonics or the study of music. The pursuit of these sciences might be used as a rough indicator of whether Byzantine society was flourishing in any given period, something else you might mention to your homework-shy kids. If this distracts them into a discussion of Byzantine history, there's nothing wrong with that. This peculiar type of mathematical measure would suggest that Byzantium in the 13th and 14th centuries was doing rather well. That may sound surprising given the radically reduced territory of the empire in this late period and the cataclysmic sack of Constantinople by the Crusaders in 1204. But after that disaster, there was some scientific activity around the court in exile at Nicaea, and once the capital was retaken from the Latins in the year 1261, we find a remarkable resurgence of scholarship over several generations under the Palaiologan dynasty. The scholars in question thought of themselves as reviving disciplines that had been ignored for generations, and modern day scholars have agreed, to the point that they speak of a Palaiologan Renaissance. You may feel you've heard this before. It seems that the learned men of Constantinople were constantly congratulating themselves for a revival of learning, and just recently we were speaking of a Syriac Renaissance. But to quote Gaudier Boudin, who has done fundamental studies of the scientific output of this period, even though in Byzantium Renaissance is a hackneyed idea, it normally contains a germ of truth. Scholars of the time complain of difficulty finding books and teachers, and though that may be in part an attempt to claim originality for themselves, it's clear that the waning political fortunes of the empire really did lead to poor conditions for intellectual activity in previous generations. The good news is that this is the last Renaissance I'll be mentioning before I get to the real thing. In fact, you could say that in a sense, we have now finally arrived at the real thing. We'll be seeing in numerous episodes to come that the work of late Byzantine scholars anticipated, and contributed directly to, the blossoming of humanism in Renaissance Italy. That's most obvious with figures like Gymistos Platon, who actually traveled to Italy in the 15th century. But it applies already to authors of the Nicene and Palaiologan periods who engaged in many of the activities characteristic of Italian humanism, editing Greek texts, writing commentaries, and of course mastering a wide range of disciplines as befits true Renaissance men. Consider Nikephorus Blemides, who actually survived the sack of Constantinople as a child and was trained at Prusa and Nicaea. Though he was offered a post at the Nicaean court, Blemides decided instead to join the church, where he rose to a high rank. He was tutored to Theodore II Lascaris, whom you might remember from our look at Byzantine political philosophy. Blemides has even been given credit for inspiring Lascaris to try to become a kind of philosopher-emperor. In an account of his own life, Blemides tells us of travelling extensively as he tried to track down manuscripts. He saw precious books at the monastery of Mount Atos that could not be found elsewhere. Among his own works are an introductory epitome on logic and natural philosophy. It draws on Aristotle of course, but also commentaries by figures like the late ancient Platonist Simplicius. Alongside Theodore Lascaris, another of Blemides's students was George Acropolitis, who brings us back to Constantinople. He was the first head of an imperial school re-established at the capital under the Peleologan emperor Michael VIII. He features in an incident that has been taken of emblematic of the way that these scholars were restoring science after an age of ignorance. While still at the court of Nicaea, Acropolitis was asked to explain why eclipses happen and gave a correct answer that he had learned from Blemides. This was greeted with mockery by another scholar who was present and by the Empress herself. Another author of the time was Kinder, praising Acropolitis as the equal of Aristotle in logic and natural philosophy and of Plato in theology and Attic Greek. Perhaps he was their equal as a teacher too, because one of his students was among the most outstanding of these men we might call Byzantine humanists. This was Maximus Plonides, who was highly placed under Andronicus II. We still have a letter he wrote to this emperor and speeches he gave at court. Plonides copied and edited Greek works on an impressive range of subjects, from Plato's dialogues to Plutarch's Moralia, from Ptolemy's treatise on geography to the arithmetic of Diophantos on which he also wrote a commentary. He even copied from Marcus Aurelius' Meditations. Actually, I just said that these Byzantine humanists were men, but we know that at least one woman shared Plonides' scholarly interests. The Adora, the emperor's niece, also collected books and wrote to him asking that he correct her copy of a work on harmonics. With Plonides we are in the happy situation of having manuscripts that actually belong to him, something that will become more and more common as we move forward into the Italian Renaissance and philosophy in early modern Europe. This is exciting because we'll be able to know exactly what various philosophers were reading, sometimes we even have notes they made on these texts. Modern day researchers can reconstruct entire scholarly libraries, even hold in their hands the very copies of the books used by these long dead philosophers. But let's not get ahead of ourselves, I still need to mention a scholar who is perhaps most central for the story of this episode, one who also flourished during the reign of Andronicus II. In fact, he was even this emperor's chief minister. His name was Theodor Metochites. Like Vlamides, he wrote epitomes or paraphrases of works by Aristotle for this purpose drawing on earlier commentators like Michael of Ephesus. But Metochites was not by any means a slavish follower of Aristotle. To the contrary, he found Aristotle's criticisms of his own teacher Plato distasteful and thought that in these passages Aristotle was being needlessly contentious and competitive since in fact the two great philosophers agreed about pretty well everything. You may have noticed just a moment ago that when George Acropolitis was compared to Aristotle, mention was made specifically of prowess in logic and natural philosophy. This corresponds to the way that Metochites saw Aristotle as authoritative for the rather introductory subject of logic and the study of crude material things, but not a specialist in the more refined discipline of mathematics. Metochites had philosophical reasons for this preference. In the preface to a work on astronomy, he expresses the classically Platonic attitude that physical things are subject to inevitable change and variation unlike the secure and immutable truths of mathematics. In light of this, he rates the natural sciences rather low in epistemic terms. They can provide no certainty, as can the mathematical arts and also theology thanks to the certitude that comes with faith. And here we have yet another anticipation of Renaissance Italy where the rediscovery of the Hellenistic philosophical schools will have a huge impact. Metochites shows a remarkable awareness of the skeptical school of the Hellenistic period. He sees the skeptics as fundamentally agreeing with his own Platonic stance on the unknowability of a world that is in constant flux. For him, then, skepticism amounts to a negative claim, namely that the human mind cannot achieve knowledge of things. Metochites does not seem to adopt the more subtle approach of the Pyronist skeptic who simply suspends judgment about everything, including the question of whether knowledge is possible. This despite the fact that the work of the great exponent of Pyronian skepticism, Sextus Empiricus, was being copied at about this same period in the late 13th century. By an irony of history, or just because these Byzantines weren't very creative when it came to naming their kids, who you can bet did their math homework without complaining, Metochites' greatest rival and his most accomplished student were both named Nikephorus. The rival was Nikephorus Comnos, another minister under Andronicus II. Things between them started politely enough, with Comnos seeking Metochites' judgment on works he had written about topics in natural philosophy. But when Comnos wrote a diatribe about poor writing style and Metochites understood himself to be the target, their relationship soured. They sniped at each other over topics such as astronomy and the correct exegesis of Plato and Aristotle. As one scholar has remarked of this unedifying spectacle, one observes with mixed wonder and distaste that a contest for supreme political power between two leading imperial ministers should produce this offshoot of scholastic controversy. Metochites had a more favorable reception from his student Nikephorus Gregoras, who called his teacher a living library and said that the souls of Homer, Plato, Ptolemy, and Plutarch were united in Metochites. Gregoras inherited his master's scientific interests. He proposed a calendrical reform that anticipated by some two and a half centuries the changes that would be made to produce the Gregorian calendar in the West. He also seems to have shared Metochites' philosophical posture, as we can see from a dialogue Gregoras wrote called the Florencius. Here he echoes Metochites by charging Aristotle with disrespect towards Plato. He also shows independence of mind when it comes to specific doctrines of Aristotelian natural philosophy. Some of those doctrines were of course routinely rejected in Byzantine culture, obvious examples being Aristotle's claim that the soul cannot survive bodily death and his view that things are always made from pre-existing matter, which would rule out God's power to create from nothing. But Gregoras and other Palaeologan thinkers also make such un-Aristotelian moves as accepting the existence of void, both outside and inside the cosmos, rejecting Aristotle's account of how vision works, and denying that the heavens are made of a fifth element distinct from those we find in the earthly realm. The nature of the elements was in fact much debated at this time. One point of contention was Nikephoros Komnos' surprising claim that air is wetter or more moist than water. His namesake, Nikephoros Gregoras, thought that Komnos was, if you'll pardon the expression, all wet. It seems obvious that Gregoras has the better side of the argument here, surely water is as moist as anything could be and thus more wet than air? But we should step back and ask ourselves why Komnos would have made such an outlandish claim. It was firstly a matter of conceptual tidiness. Komnos wanted to take each of Aristotle's basic qualities, namely heat, cold, wetness, and dryness, to be the dominant feature of one of the four elements. Clearly, fire is the element that is primarily hot, and earth is primarily dry. Since air is not cold at all in the Aristotelian scheme, but rather both hot and wet, that leaves only water to be primarily cold. So by process of elimination, it's apparently air that is primarily wet. Perhaps then we should just give up on assigning the four qualities to the four elements, however tidy it would be. But there is a more profound rationale underlying Komnos' view, which is that wetness is not actually what you might suppose it to be. The wet or moist is not necessarily what soaks or quenches thirst. Rather, it is most fundamentally that which is fluid, just as the dry is that which is solid. Looked at in this way, we realize that air is indeed more fluid than water, even if water too is fluid. Air is more easily moved, and less apt to retain a shape. So we gain a useful insight from what may seem to be, if you'll pardon another expression, a rather dry scholastic debate. It calls our attention to the fact that Aristotelian elemental theory is more like modern chemistry than you might suppose. The qualities and elements it invoked were not just the everyday things we experience, like clods of earth, flickering flames, or the sopping wetness of a sponge. They were instead theoretical postulates that underlie and explain such phenomena. You will never encounter pure fire or pure earth, only bodies that are mixed out of pure elements, and the properties those pure elements possess may, as Comnos realized, be defined in quite abstract terms. If this debate shows how intricately the Peleologan scholars engaged with Aristotelian natural philosophy, their devotion to the mathematical sciences shows them adopting a fundamentally Platonic outlook. Plato had, after all, said in more than one dialogue that astronomy or mathematics is a step towards higher philosophy, one that must be studied and mastered before attaining true wisdom. In keeping with this, Michael Bselos had described mathematics as a rung on the ladder of disciplines he had ascended which culminated in metaphysics. In the same spirit, Nikephoros Gagoras states that the mathematical art of astronomy is a ladder adjacent to theology. Lest we miss the Platonist overtones, he adds that its study helps us to separate the soul's concerns from the corrupting pleasures of the body. It's easy to miss the broader theological motives and context of works that look more or less like faithful repetition of Aristotelian physics or other ancient Greek scientific works. But these were deeply pious scholars, and their pursuit of science cannot be disentangled from that piety. This emerges at the end of a commentary on Aristotle's physics by yet another Byzantine humanist of this period, George Pachimeris. The commentary is rounded off with a poem in ecstatic praise of Aristotle who, says Pachimeris, understood what pagans did not teach. But hang on a second, wasn't Aristotle a pagan? Of course, but Pachimeris thinks that Aristotle has outdone the other pagans with his account of a first cause of all motion, a theory that shows him glimpsing the nature of the Christian God. Pachimeris, by the way, is another scholar whose books still survive. We have copies of Platonic dialogues and works by Proclus in his handwriting, and also the autograph of Pachimeris' own commentary on the physics, only one of numerous Aristotelian works to get this treatment from his pen. With a revival of philosophy and science, the Nicene and Peleologian authors show us the remarkable endurance of Byzantine intellectual culture. And the fortune of their own works confirms the same point. The writings of these men were read in Renaissance Italy, whose culture they did so much to anticipate and to facilitate. They were also recycled and recopied in the later Greek tradition, with a compilation by Pachimeris on philosophy being used in further compilations, and manuscripts of Blemades still being made as late as the 19th century. But we're not ready to look ahead that far just yet. More immediately, we need to consider a dispute in which theological concerns were far more evident. A famous set piece of late Byzantine culture involved one of the figures we've just met, namely Nikephoros Gregoras. But its main character, and Gregoras's main opponent, was a dominant personality of the time, and indeed of the whole history of Byzantine theology. At stake was nothing less than the capacity of the human mind to understand God. Join me next time to achieve something slightly less daunting than that, but still worthwhile, an understanding of Gregory Palamas and the Hezekiah's controversy here on The History of Philosophy Without Any Gaps.