 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, Man of Discoveries, Girolamo Cardano. I don't have much in common with Georg Friedrich Wilhelm Hegel, one of the greatest philosophers of the 19th century, but I can at least say that, like him, I have spent a lot of time teaching German students about the history of philosophy. Hegel lectured on this subject many times, in Jena, in Heidelberg, and then in Berlin every year over the last decade of his life. His approach to the subject was rather different from mine, not least in his notorious dismissal of philosophy written in Arabic as involving no proper principle and stage in the development of philosophy. But I rather like the choice he makes when he comes to philosophy in the Renaissance. He starts off not with an obvious figure like Bruni, Ficino, or Machiavelli, but with several pages on Girolamo Cardano. Hegel's remarks are based especially on Cardano's autobiography, which he summarizes in part as follows, In his habits, outer life, and conduct, he went from one extreme to the other. At one moment he was calm, at another like a madman o lunatic, now industrious and studious, now dissolute and squandering all his goods. Naturally, in these circumstances, he brought off his children very badly. I can readily understand why Hegel latched onto Cardano, since he might be the philosopher from the Italian Renaissance whose personality comes down to us most vividly today. He was a prolific writer, as we'll be seeing, and scattered personal remarks throughout his many works. But it is his autobiography that gives the strongest sense of his personality. It covers the main events of his life. Born in Pavia in 1501, he studied in his home city and Padua, and taught mathematics and medicine at several universities, including Bologna in the 1560s. This followed the execution of Cardano's son in 1560, on the grounds that the young man had poisoned his wife, which no doubt encouraged Hegel's remark about Cardano's imperfect child-rearing. As if this tragedy were not enough, ten years later Cardano himself was charged with heresy, imprisoned for a couple of months, and made to recant his supposedly unorthodox views. But it's not for these biographical milestones that one reads Cardano's account of his own life, it's for such details as a description of his favorite meal, veal cooked in its own juice, the strange dreams and portents that have followed him through life, his talent for name dropping, with a whole chapter devoted to listing his friends, and another to listing the various prominent men who have praised him. To say nothing of Cardano's evident delight at his own genius, as when he tells us how many languages he was able to learn with no effort or study whatsoever. Indeed, a keynote of the text is its self-aware boastfulness. He informs us, twice, that a friend dubbed him the man of discoveries and was right to do so. Cardano reckons he has 40,000 significant discoveries to his name and about 200,000 minor ones. Cardano has no need to choose between the Aristotelian goal of contemplative fulfillment and the Stoic ideal of withstanding all misfortune, he finds it possible to achieve both. At one point, he even manages to brag about being average when describing his own appearance, "...so truly commonplace that several painters who have come from afar to make my portrait have found no feature by which they could so characterize me that I might be distinguished." Medicine, perhaps the most central of Cardano's many fields of expertise, is mentioned throughout the autobiography. No reader will soon forget the way he obsessively and frankly catalogues his physical and psychological ailments, which include fear of heights, insomnia, stuttering, excessive urination, and a decade of sexual impotence. Good thing then for his medical expertise, which has enabled him to devise the ideal exercise regime for preserving health. "...I have," he willingly remarks, "...reduced the whole to a system as is the fashion in matters of theology, with much profound meditation and brilliant reasoning." He wouldn't necessarily claim to be better at medicine than Galen and Apasenna, but it's only fair he should mention having lived longer than either of them managed. Actually, the talent for self-presentation is something else Cardano learned from Galen and then perfected. Cardano names Galen as a precedent for autobiographical writing, and many aspects of his life story ring Galenic bells. Like Galen, Cardano revels in telling stories where he humiliated rival scholars in debate or through superior medical diagnosis. He offers us a list of his own books, as Galen did, and like him is not shy in criticizing the books of others. In fact, the targets include Galen himself, whom Cardano does not hesitate to correct on points of medical therapy. Cardano freely admits that writing has itself been a way for him to fend off grief and maintain his mental and physical health. This might be why he wrote so darn much. About half of his voluminous output is on medicine, and goes well beyond the kind of book learning that he could have gleaned from reading Galen and Apasenna. He was a practicing doctor and, again like Galen, wrote up detailed case studies, most notably concerning his attendance on the Archbishop of St Andrews, whom he traveled all the way to Scotland to treat in 1552. He told the bishop to eat dry foods, since his body had been made overly moist by illness, and to chew gum, actually pistachio resin, to excite saliva, which would draw moisture out of the brain. Also, and more likely to be helpful, the bishop should get plenty of rest. While confessing to lack of expertise in surgery, Cardano encouraged the study of hands-on medical skills, complaining that contemporary medical education passes over such important disciplines as obstetrics, dentistry, surgery, and pediatrics, all the areas, as he wryly remarked, where the doctor's failure would be obvious. He was a great believer in maintaining and restoring health through careful regimen. Alongside his aforementioned program of exercise, he recommended a vegetarian diet, while avoiding some fruits. He blamed a bout of dysentery in his own childhood on eating grapes, and deemed melons so dangerous that they ought to be made illegal. Despite the occasional point of correction, Cardano was largely an admirer of Galen, though in what seems to have been a rhetorical exercise, he did compose a damning critique of his ancient role model as having had more luck than learning and displayed more vice than virtue. Of all medical authorities, though, the one he most admired was Hippocrates. Along with Ptolemy and Plotinus, Cardano named him as one of the three figures who were close to divinity in their level of insight, literally incomparable to other scholars, which is why he deliberately excluded them from his list of the greats. He excoriated the doctors of his own day for any departure from the advice given by Hippocrates, not least his ban on eating melons, and composed a series of commentaries on the Hippocratic Corpus, on which he lectured during his years at Bologna. Cardano also lavished praise on Avicenna, even preferring him to Galen, because of his superior moral character and the better organization of his works. Among his contemporaries, one figure he greatly esteemed was the anatomist Vesalius. In part this was because he thought the Vesalian theories were in harmony with the Hippocratic Corpus, and helpful in correcting the errors of Galenic anatomy. Always wary of uncritically following anyone, though, Cardano assured his readers that his policy was to believe not Vesalius, but his own eyes. Cardano thought far less, by the way, of Leonardo da Vinci. Having viewed the artist's anatomical drawings, he said that they were, "...by all means beautiful and worthy of such a famous artist, but completely useless, being the work of one who did not know the number of intestines. The fact is that he was a mere painter, not a physician nor a philosopher." Among the many things Cardano found to admire in Hippocrates was his teaching on the soul. This is on the face of it rather strange, because Cardano was a proponent of the soul's immateriality, whereas he ascribes to Hippocrates the view that the soul is nothing but heat. The reason Cardano likes this view is that it makes life and soul pervasive in the cosmos. Wherever you find heat, there would be some sort of soul present. Departing from Aristotelian cosmology, he asserted that even the celestial bodies possess heat, since they are alive. Still, the Hippocratic idea of soul as heat does in a way establish the immortality of soul because heat is never extinguished, but is a permanent feature of the universe. These ideas resonate with at least some of what Cardano himself wrote about the soul and the mind. I say some of, because he puts forward different ideas in different places and admits to difficulty in reaching a firm conclusion. Shortly before his death, he was still saying, I know souls are immortal, but I'm not sure how. One thing he was sure about is that Pompanazzi had been wrong to suggest that the human soul is tied to its body, needs the body as a basis for its operations, and dies along with it. To the contrary, Cardano argued, materiality impedes thought. This is why animals cannot think, because their bodies make this impossible for them. And the intellect of soul can certainly survive independently of the body. He is confident that Aristotle would agree with this, and goes so far as to argue that for Aristotle it should be possible that individual souls are reincarnated, being associated now with one body and then with another. Of course, Cardano doesn't dare to endorse the transmigration of souls himself, but he does flirt with the notorious doctrine of Averroism, which envisions a single intellect shared by all humans as the sole guarantor of immortality. Cardano likewise makes the intellect alone to be immortal, while lower functions like imagination and memory die with the body. He also intimates that there is a kind of universal, active intellectual power in whose immortality we partake. As he nicely puts it, the origin of all intellects seems to be the same for all, since human beings from very early on are endowed with the same principles, as in all swallows there is the same ability to build a nest. Still, Cardano distances himself from the Averroist notion that there is only one universal mind. Instead, each of us gets a portion of intellect, which is why we each have our own acts of understanding that are not shared with others. As Cardano says, the active intellect is within us and a part of us. Sadly, we cannot enjoy the activities of this intellect nonstop. It's an effort to divert the mind from, as Cardano puts it, the vexations of the body and the senses, such as pain, fear, pleasures, and hope. He knew whereof he spoke. If this was a man who got more than his share of intellect, he also experienced more than his share of pain and grief. It seems he was trying to distract himself from these travails by making all those discoveries and writing so many books. By reading and writing about science, he could retreat temporarily from a troubled bodily existence. I find his remarks about this rather moving. While I am actually writing this, my intellect is the things you grasp through what I have written. Medicine, while I discuss medical matters, arithmetic at the time that I was writing about numbers. So much so that, as must happen to everyone else who has been an author of various works, while I read over what I have written, I think myself different from the person I now am. Elsewhere, he speaks of the way that physical pain can be escaped by intense intellectual focus, though conversely, the pain may make thinking impossible. Fortunately, Cardano had a plan B, have fun. His autobiography contains a whole chapter on things in which he takes pleasure, to his credit, these include the joys of reading authors like Aristotle and Plotinus, but Cardano was also partial to a bit of gambling. Well, more than a bit actually. He makes it fairly clear that he is a gambling addict, even admitting that he once had to pawn his wife's jewelry and some family furniture to pay off debts. No wonder that, as he cheerfully remarks, he has wound up richer in the knowledge of nature's secrets than in muddy. The loss to his bank account turned out to be a gain to the storehouse of human knowledge, because his fascination with gambling led him to write a remarkable study of the mathematics of dice and card games. This pioneering work has been called the first text on the theory of probability. It sets out observations that may now seem obvious, for instance that the probability of a favorable outcome is the number of good outcomes divided by the total number of outcomes. For instance, if you need to roll 3 on a six-sided die, your chance of doing so is 1 out of 6. He also tries to work out the average result that should be expected over repeated trials, for instance what the average roll will be if you roll three dice over and over. In addition to articulating genuine insights about probability, Cardano also inadvertently displays how easily our intuitions go astray when thinking about it. He assumes, wrongly, that the chance of success over a certain number of trials is the number of trials times the chance of succeeding in one trial. Thus, if you need to roll a 3 on one six-sided die, then your chance of doing so in two rolls should be double of what it is in one roll, so 2 in 6. To see that this is wrong, consider that your chances of rolling a 3 after 6 rolls would be 6 out of 6, so a guaranteed success, but of course that is not the case. Cardano also makes some comments connecting the topic of probability to standard philosophical issues. He speculates about the connection between fate and luck, expressing doubt that the order of the universe would bother to affect a card game. But he also expresses a certain fatalism, suggesting that the outcome of a game of chance may be settled in advance, so it makes no difference what you do. He compares this to the way you are subject to the authority of the prince, whether you decide to stay at home or go out. With Cardano being Cardano, he wrote a number of mathematical works, of which the most famous is his Great Art, a study of algebra. Alongside some nice mathematical observations that even I can appreciate, for instance that the square root of a positive number can be negative, this book is revealing as concerns ideas of scientific originality and priority in the 16th century. For one thing, there is Cardano's characteristic boast at the outset that the work is so replete with new discoveries and demonstrations by the author, more than 70 of them, that its forerunners are of little account. Then there is his notorious inclusion of the method for solving cubic equations, which, stay with me here, have the form x to the third plus ax equals b. Cardano does not claim this among his many novel discoveries. He credits Niccolò Tartaglia for it and admits that Tartaglia would not want him to publish the secret, and in the event, Tartaglia was indeed furious. But Cardano claims an excuse, namely that another mathematician had discovered the same method a few decades ago, after which it was forgotten. This vignette could hardly be a more eloquent demonstration of the way ideas about originality were gradually changing in the Renaissance. Increasingly, scholars wanted to claim new innovations for themselves, which is also why Cardano was so flattered to be called man of discoveries. But the rules for scientific precedent remain unclear, and propriety was a matter of individual judgment, not commonly accepted practice. Perhaps Cardano was willing to risk annoying his colleague Tartaglia simply because he was so used to annoying people. His autobiography includes a long list of his critics and enemies, as if to balance out the list of friends and admirers. Among those who Cardano accused of attacking him for the sake of making a reputation for themselves, none was a more bitter opponent than fellow philosopher Julius Scaliger. Scaliger took issue with one of Cardano's most significant works on subtlety, a wide-ranging and enormous treatise dedicated to the most obscure aspect in each branch of study, as Cardano puts it with typical modesty. Scaliger hated it. He wrote a treatise containing 365 chapters, presumably so the reader might spend every day of the year contemplating Cardano's shortcomings. Anthony Grafton has called it the most savage book review in the bitter annals of literary invective. It attacked everything from Cardano's pitiful Latin skills to the aforementioned ideas about soul and intellect. Remember that moving passage about transforming one's mind into the object of one's contemplation? Well, it moves Scaliger only to sarcastic abuse. Well done, Cardano, you who say that when you think of a horse, your intellect is nothing other than a horse. I wouldn't dream of taking a side in this dispute, but if I did, then Cardano would have just the book for me. It's a whole treatise on dreams, based to a large extent on an ancient guide to dream interpretation by an author named Synesius. Cardano offers a whole theory as to how different kinds of dreams are caused. They may, for instance, result from bad digestion or, on the other hand, from contact with the intelligible realm. In the latter case, they may divulge visions of future events. This sounds pretty far from anything we now recognize as genuinely scientific, but for Cardano the topic of prophetic dreams is closely connected to medicine. We receive prophetic dreams when the spirit that flows through the body is well prepared and at rest, which is why the dreams come when we sleep. The skilled interpreter, like the skilled doctor approaching each patient, must take into account the dreamer's way of life and his individual disposition. Cardano himself enjoyed many prophetic dreams and recounts them in his autobiography. He thinks that, at least in retrospect, he can understand the meaning of his visions. On one occasion he was on the verge of administering what would have been a fatal therapy to a patient, but was held back by a dream warning. Still, he admits that interpretation, like medicine, will always remain an uncertain business. Not only must the nature of dreams be infinite, the very analysis of them is infinite, the mind is infinite in its power, and the number of things is infinite too. No wonder he wrote so much. Cardano was obviously a remarkable individual, even by the standards of Renaissance Italy, which boasted plenty of remarkable individuals. Appropriately for an expert mathematician, he sums up the themes we've been pursuing in recent episodes, while also having interesting things about astrology and divination, a topic I predict we'll be covering soon. First though I want to dwell a little longer on the discipline that occupied so much of Cardano's attention. Not gambling, but medicine, though I bet you'll be fascinated by my discussion of health and illness in the Renaissance with Guido Giglioni next time here on The History of Polonio. Philosophy without any gaps.