 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 Leverhulme Trust. Today's episode, The Man with the Golden Thigh, Pythagoras. Philosophers have always loved mathematics. It's not hard to see why. One of the things philosophers are most interested in is knowledge. Indeed, as we found last time, one of the earliest Greek philosophers, Xenophanes, already made a contrast between really having knowledge of the truth and having mere beliefs. And, if you're looking for a nice, solid example of knowledge, mathematics is just about the best example there is. You don't merely believe that 2 plus 2 equals 4, you actually know it. Or, at least, this is what most people think, that mathematics is a kind of gold standard against which other supposed examples of knowledge can be measured. This way of looking at mathematics goes back to Greek philosophy, but mathematics itself goes back even further. I'm not just talking about counting or adding simple sums here. For instance, the Babylonians and Egyptians were accomplished in the sorts of mathematics required for land measurement and astronomy. We saw already that Thales, the first pre-Socratic philosopher, did some astronomy, and that he may have got some of his astronomical knowledge from the Egyptians. Pythagoras too, according to legend, travelled to Egypt, and may have picked up some knowledge of mathematics there. So mathematics is older than philosophy, but the two have been close companions ever since philosophy came on the scene. Plato is famous for emphasizing the links between philosophy and mathematics. Supposedly he had a sign over the entrance to his academy, reading "...let no one enter who has not studied mathematics." His student Aristotle often treats mathematics as that gold standard of knowledge, and we can find similar attitudes much later in Greek philosophy. For instance, Galen, the great doctor of the 2nd century AD, once fended off an attack of skeptical doubts by taking refuge in the certainties of mathematics. His contemporary, the equally great astronomer Ptolemy, says that among the theoretical sciences, mathematics is the only really certain discipline. But long before Galen and Ptolemy, in fact pretty long before Plato and Aristotle, there was Pythagoras. Just about everyone has heard of Pythagoras, if only because of the Pythagorean theorem. I may as well break the news straight off that there's no good evidence that Pythagoras himself discovered the Pythagorean theorem. It was however known to his followers, the Pythagoreans. Actually, that sort of sets the tone for the rest of this discussion. We know a great deal about the tradition of Pythagoreanism, which takes its name from Pythagoras, but we know hardly anything about the man himself. Among the pre-Socratics, all of whom are surrounded by a good deal of misinformation and legend, he stands out as the one figure who is more myth than man. But what a myth. He's credited with being the first to fuse philosophy with mathematics, with being a worker of miracles, being divine or semi-divine, the son of a god. The beliefs ascribed to him range from arcane metaphysical and religious ideas, for instance reincarnation, to homely ethical teachings, for instance that you shouldn't eat beans or meat. Typically there are other ancient texts that say he did eat meat. But before we get carried away with the myth, and don't worry, we'll be getting carried away shortly, since the myth is much too good to pass over in silence, let's start with what we do know about the man. We've seen that the early pre-Socratics were from the coast of Asia Minor, in modern day Turkey. Last week's subject, Xenophanes, was from there but travelled west. The same is true of Pythagoras. We have good evidence that he was from Samos, an island off the Ionian coast, but he too travelled across the Mediterranean, possibly having left his birthplace because he didn't see eye to eye with a local tyrant. The place he's most associated with is therefore not Samos, but Croton, a city in southern Italy. In fact, ancient authors like to give him credit for founding a distinctive philosophical tradition, the so-called Italian school of philosophy. Here, it might be worth mentioning again that Sicily, Italy, and other parts of the western Mediterranean had been settled by Greek colonists in the centuries previous to the emergence of the pre-Socratics. The Greeks held on in southern Italy for quite a long time, until the Romans finally pushed them out of this area which they called Magna Graecia. Pythagoras himself would have lived there in the 6th century BC, about two centuries after the settlement of Croton in the late 8th century. But getting really clear about his dates is no easy matter. We know that both Xenophanes and Heraclitus refer to him by name, so he's a rough contemporary of these thinkers, and that's good enough for our purposes. So, there's Pythagoras in southern Italy, not discovering the Pythagorean theorem. Another thing he was not doing is writing books. In fact, it's rather striking that Pythagoras and Socrates are arguably the most famous philosophers prior to Plato and Aristotle, and yet neither of them wrote anything. Maybe they're so famous precisely because they never wrote anything. Socrates, like Pythagoras, became a literary character, a vessel for the ideas and imaginings of other people. And, while we like to think we have a reasonably vivid and accurate idea of the real Socrates, thanks to Plato and other authors like the historian Xenophon, in the case of Pythagoras, we are really just sifting through legends and myths. Not only is Pythagoras quite a bit earlier than Socrates, but his way of doing philosophy, if he did philosophy at all, was a lot less public than Socrates. Whereas Socrates would walk up to people in the marketplace and harass them by asking them to define virtue, Pythagoras and his young students in Croton supposedly observed a code of silence to prevent their secret teachings from being divulged to the uninitiated. Okay, maybe that code of silence is just another legend, but the fact remains that we have very little idea of what Pythagoras himself said or thought, not only because of a lack of reliable evidence, but because the stray bits of reliable evidence often seem to be deliberately obscure. To make things worse, these bits of reliable evidence are buried under an avalanche of more dubious evidence from people who thought of themselves as Pythagoreans. This tradition of Pythagoreanism is one of the most durable in ancient Greek philosophy. It begins, obviously enough, with Pythagoras himself and his immediate followers. There was then a reasonably well-defined Pythagorean movement in the 5th century BC, and in the 4th century Plato had associates and students who took up Pythagorean ideas. Aristotle found this phenomenon interesting enough that he wrote a book about Pythagoras and his followers, but unfortunately this is lost. In any case, it's really the 5th century BC Pythagoreans, after Pythagoras himself was dead, but before Plato comes along, who should get the credit for fusing philosophy with mathematics. Ideas like the harmony of the spheres, the notion that the proportions of the celestial bodies are arranged according to some kind of musical ordering, probably emerged in this period. Still, all ancient authors assumed that Pythagoras himself had an intense interest in mathematics, and we may as well go along with this, while remembering that his interests may have been more religious or symbolic than technical. The ancient authors who talk about early Pythagoreanism build up a probably fictitious contrast between two types of followers of the divine Pythagoras. There are the ones who are interested in the religious and ethical precepts that he laid down, the so-called akousmata, and then there are the math geeks. It's in the ethical precepts that we get the instruction, for instance, not to eat beans or meat. Oh, and don't ever touch a white rooster. And did I mention don't bury corpses wearing woollen clothing? These rules are hard for us to explain, and they weren't much easier for the ancients. Various symbolic explanations are given by later authors who are well-disposed towards Pythagoreanism. As for the math geeks, these are the Pythagoreans who really interest Plato and Aristotle. They get mentioned in Aristotle's existing works as well as his lost work on the Pythagoreans, which, since it's lost, like I said, we know only in fragments. These were thinkers who went so far as to say that things in the physical universe are somehow made of numbers. Aristotle claims to find this idea barely comprehensible, but if we're feeling generous, we might want to see here an anticipation of the modern idea that mathematical concepts are at the foundations of physics. We'll see in a later episode that in one of his dialogues, Plato suggests that the elements of physical objects are literally made of triangles which come together to form solid shapes. That is the sort of idea that the Pythagoreans inspired, even if it isn't something that they thought of themselves. Even the mathematically inclined Pythagoreans, the math geeks, had a deeply symbolic, maybe even mystical understanding of number. These were people like Philolaus, from Pythagoras's adopted home Croton. Philolaus and other Pythagoreans made genuine advances in mathematics, but they also used to say things like this, two and three symbolically represent woman and man, so five is the number of marriage, because it is two plus three. A particularly important number for them was ten, which among other things is the sum of the first four numbers, in other words one plus two plus three plus four equals ten. Aristotle in fact tells us that the Pythagoreans thought there must be a heavenly body which is always hidden from us, the so-called counter-earth, because the visible heavenly bodies including the sun and moon counted nine, but there must be ten of them, because ten is the most important number. After Aristotle and Plato's immediate followers, the Pythagoreans fade away a bit, but they make a big comeback in the first century BC. At this point we begin to see a powerful tendency to combine Plato's ideas with Pythagorean ideas like number symbolism. This tendency lives on until the end of pagan Greek philosophy, with the tradition we nowadays refer to as Neoplatonism. We call the late ancient philosophers of the 3rd to 6th centuries AD Neoplatonists because they were followers of Plato, but also had a lot of new ideas, which modern scholars do not find in Plato, hence the Neo in Neoplatonism. For them, one of the biggest influences was the tradition of Pythagoras whom they saw as an ultimate source of Plato's own ideas. Thus Pythagoras, one of the very earliest Greek thinkers, became one of the most important authorities and intellectual heroes of the Greek thinkers in late antiquity a full millennium later. One of the Neoplatonists who most admired Pythagoras was Eamblichus, who lived in the 3rd to 4th century AD. We'll get to him as a philosopher in his own right eventually, though it will be a while, at the rate we're going. I mention him now because he wrote a work called On the Pythagorean Way of Life, which shows the way Pythagoras was perceived by that much later period of Greek philosophy. By Eamblichus' day, the legend of Pythagoras has blossomed so that he is seen as the definitive sage, able to work miracles, and apparently inexhaustible in his wisdom. Eamblichus mentions many miraculous events, some of which were already reported much earlier, for instance by Aristotle. For example, Pythagoras is said to have had a thigh made of gold, which he once exhibited at Olympia. He's able to see the future, for instance by predicting an earthquake. He can talk to animals and even give them instructions. Eamblichus has him confronting a bear who had been attacking people in the local area and persuading the bear to mind its manners. And if that's not enough to impress you, he can also talk to geographical features. Eamblichus tells us that he was once greeted by a river. This sort of thing may strike us as somewhat amusing now, but it had a serious purpose at its time. It's been suggested that the Pythagoras legend was emphasized by authors like Eamblichus because they lived in a time when their pagan religious beliefs were under pressure from the rapid spread of Christianity. For a Platonist pagan like Eamblichus, or his teacher Porphyry, who wrote venomous attacks on the Christians, Pythagoras could serve as an ideal holy man to rival Jesus. His piety and religious teachings are emphasized throughout, and we hear Pythagoras' advice about how to behave towards the gods and their temples. For instance, he says you should never visit a temple unless it is the primary reason for your journey. Just stopping off at a temple on the way to somewhere else is inappropriate, even if you're walking right by one. On the other hand, Eamblichus most definitely sees Pythagoras as a philosopher. He sees him in fact as THE philosopher, the founder of Eamblichus' own intellectual tradition, and even the first man to call himself a philosophos, which means lover of wisdom, sophia being the Greek word for wisdom. On this account, Pythagoras was the first to make the love of wisdom into a way of life. As we might expect, Eamblichus also emphasizes Pythagoras' connections with the mathematics, especially music. From very early on in the Pythagorean tradition, music and mathematics were intimately related. And no wonder, because the relationships between notes are just examples of mathematical ratios. In fact, you would make a Greek lyre by stretching numerous strings at the same tension. The different lengths of the strings gives you the different notes. Eamblichus tells a picturesque story, in which Pythagoras hits upon this insight when he's walking by a blacksmith's shop and hears the hammer beating against the metal, ringing out at different tones. Pythagoras then goes home and experiments with stretching strings on weights to get the different musical ratios, such as the octave. Eamblichus adds the exceedingly implausible idea that Pythagoras actually invented a whole range of musical instruments. The Pythagoreans believed that the musical harmonies had some kind of affinity with and effect on the human soul. Another feat ascribed to Pythagoras, and one you can try at home, is using different kinds of music to induce different emotional states. Eamblichus tells how Pythagoras once managed to calm down a ragingly drunk man just by having someone play the right sort of music on a set of pipes. The idea that the soul and its states would somehow resonate to music, if you will, chimes with the idea that the soul itself might be a kind of harmony. Plato and Aristotle both discuss this Pythagorean idea, and the theory may seem to us strikingly plausible in its way. On this view, the soul is not some entity separate from the body, but is rather the attunement or proportion that keeps the body in functioning order. Just like a lyre will play badly, or not at all, if its strings are taken out of the correct harmonic tension, so a body will become defective, for instance, ill, or just die if its attunement is disrupted. But there's something of a puzzle here. Although in a sense, it isn't surprising to see that music and mathematics obsess Pythagorean, setting forth this sort of theory about the soul, it is almost certainly not the theory of soul Pythagoras adopted. For according to Pythagoras, the soul can leave one body and go on to reside in other bodies, including the bodies of animals. In other words, Pythagoras believed in reincarnation. Part of his legend is that unlike the rest of us, he was able to remember who he had been in his former lives. For example, he was the chap who killed Patroclus, the bosom companion of Achilles in the Trojan War. But again, there's more here than just legend. You might remember my saying last time that Xenophanes refers to Pythagoras by name. He says that Pythagoras once heard a puppy whining as it was beaten, and cried out, stop, for I recognize that its voice belongs to a friend of mine. This is a little joke at Pythagoras's expense, but one that only makes sense if he was already known to believe in reincarnation. Perhaps you're not convinced that this counts as philosophy. I guess if you met someone at a party who was convinced that she used to be Marie Antoinette, and then after a trip to the guillotine was a giraffe, you wouldn't think, aha, a philosopher. But this theory of reincarnation at least relates to, and maybe even inaugurates, a philosophical theory with a grand lineage, dualism. Dualism is simply the view that the soul and the body are two distinct things. Many dualists draw the further inference that one can therefore exist without the other. This is implied by reincarnation, the soul survives the death of one body, namely Marie Antoinette's, before entering the next, namely that of a giraffe. Perhaps Pythagoras's view was even stronger, that the soul and the body are completely different metaphysical entities. They would be more different than, say, your nose and my nose. These are distinct things, and one can exist without the other, but they are the same sort of thing. By contrast, according to most Pythagoreans in ancient philosophy, the soul and the body are utterly different sorts of thing. The soul is immaterial, and probably indestructible. The body is material, and will inevitably be destroyed. This view is what philosophers usually mean when they use the word dualism, and it will be defended by many famous philosophers. Plato and Descartes, especially, leap to mind here. There's some reason to think that Plato had Pythagoreanism in mind when he developed his particular version of dualism, so we've taken a big step in the direction of understanding Plato's background, or at least the background of one major theme in his philosophy. And now, if you'll pardon the pun, we've come full circle, back to the Pythagorean's interest in things like circles, numbers, shapes, and all the other objects studied in mathematics. It's no coincidence, I think, that Pythagoreanism is associated both with dualist theories about the soul, and with an emphasis on mathematics. The soul postulated by the dualist has a great deal in common with numbers. Both are abstract, immaterial entities, and look like they will always exist, assuming they exist at all. How are you going to kill an immaterial soul, or assassinate the number seven? One reason Platonism and Pythagoreanism were able to combine together so easily is that both Plato and the followers of Pythagoras were interested in these stable, immaterial objects. They wanted to get away from the messiness of physical objects with the way they constantly change and they're being subject to an infinite number of various features. That certainly isn't the only idea that drives Plato, but it seems to be one of the most important, and it is even more important for later thinkers who see Pythagoras as the inventor of Platonic philosophy like our friend Iamblichus. In all this, the Pythagorean tradition is very different from what we'll be looking at next, the philosophy of Heraclitus. His interest in the phenomenon of change is nearly as famous as Pythagoras' obsession with mathematics, and in one of his many rather mysterious remarks he says the things he values most are those things he can see, hear, and learn about. He was, in other words, a man for the concrete. Yet he was also a man with a taste for riddles and paradoxes. His memorable, but puzzling one-liners epitomize the fragmentary, suggestive sort of philosophy we get from the pre-Socratics. His remark that you can't step into the same river twice is only the most famous example. So go with the flow, and join me for Heraclitus next week on the History of Philosophy without any gaps.