- Vittorio Hösle

# Greek Mathematics and the Origins of Science: A Conversation with Vittorio Hösle

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#### Introduction

When I first met Vittorio Hösle—a scholar who has been consulted by the Pope and widely read in all major European languages—he was carrying a bag overstuffed with children’s books for his godchildren, a Puffin classic peeking out of the top of the stack. I was surprised at the time, but I now realize there is no incongruity. One of the world’s leading philosophers and historians of Greek mathematics, Hösle is perhaps the only individual in the world to have been both a Fellow at the Institute for Advanced Studies in Princeton and the recipient of numerous other honors, as well as the author of a philosophy book for children, based on real letters a child sent him, to which he carefully responded, *Dead Philosophers’ Cafe: An Exchange of Letters for Children and Adults. *This captures the beauty and spirit of Hösle, embodying his vision of philosophy as both a rigorous academic discipline and an ancient and inclusive way of life, open to all.

He is the Paul G. Kimball Professor of Arts and Letters at Notre Dame, where he is also a Faculty Fellow at the Nanovic and Kroc Institute, and was the Founding Director of the Notre Dame Institute for Advanced Study. Hösle completed his Ph.D. at the age of 21, with a major in philosophy and two minors, one in Indology and the other in Greek; he then finished his Habilitation (a second, post-PhD degree required in Germany) four years later, published as *Hegels System*, and at 28 he was the subject of a documentary film called *Ein ganz gewöhnliches Genie [A completely normal genius*]. His work covers a wide array of topics, from the history of Greek mathematics and tragedy to Goethe, contemporary politics, and the climate crisis.

Hösle’s seminal work, *Morals and Politics*, established him as an internationally influential legal, political, and moral theorist. With Christoph Jermann he completed the first translation of Giambattista Vico’s *Principj di una Scienza Nuova *into German, and he has lectured around the world. In 1990 he delivered in Moscow a series of lectures, which eventually became his widely-translated book, *Philosophie der ökologischen Krise [Philosophy of the Ecological Crisis*], and in 2013 Pope Francis appointed Hösle to the Pontifical Academy of Social Sciences.

A prolific writer, Hösle has written and edited 57 books, nearly 200 articles, and his work has been translated into 20 languages. He has already become the subject of dissertations and scholarship, and a second documentary in 2003. His thought has had a global impact on the twenty-first century, and as *Marginalia*’s Editor it is my joy to share with you Hösle’s profound insights about science and its meaning today.

#### Interview

##### The First Scientific Revolution

SAMUEL LONCAR

Could you tell us about your science background?

VITTORIO HÖSLE

I began my studies at the University of Regensburg, a university which boasts among its luminaries Pope Benedict XVI, who at that time, however, had already left. When I began to study, he was already the Archbishop of Munich and Freising. But there was a very fascinating professor there, Imre Tóth. He was ethnically a Hungarian, with a Romanian passport. At the time, he had emigrated from Romania and had a German passport, and he was widely considered in Germany and also in Italy and France one of the most original historians and philosophers of mathematics of the twentieth century. He had barely escaped the Holocaust; his parents were murdered in Auschwitz. His sister survived but then took her life because she could not live with the horrific memories of what she had witnessed in that circle of hell. And Tóth began his studies, in fact, as a historian of modern mathematics. His first book in Hungarian was on János Bolyai, one of the founders of non-Euclidean geometries, but he then taught himself Greek. He had not learned Greek in his high school. So he acquired the language relatively late because he was extremely fascinated by Greek mathematics, and his main works are both on Greek mathematics and on nineteenth-century mathematics. He was probably the best expert on the history of non-Euclidean geometries, and he was a person with an extraordinary knowledge of the history of philosophy from the Greeks to the present. And, by the way, he was a very gifted collagist. He made a lot of collages, which express problems of the philosophy of mathematics and developments in the history of mathematics. In 2021, for his 100th birthday, the University of Regensburg published a very beautiful volume, in which several of his collages are collected.

Tóth gave splendid classes on the history of Greek mathematics at the University of Regensburg. I read with him the first book of Euclid very thoroughly and with a lot of nuances. Tóth’s main discovery—I think it is a discovery even if in some points I deviate from his interpretation—was that the Greeks had already understood that in principle, you could have two consistent alternatives to Euclidean geometry. (The acknowledgment of their consistency, however, in my eyes, does not entail that they considered such geometries true.) So his famous claim was that the problem of parallels is not something that develops out of the parallel postulate of Euclid (the fifth one of his postulates), but the other way around. The parallel postulate of Euclid is a response to a discovery within the Platonic Academy that logically you could develop geometrical systems that deviate from Euclidean geometry. I know it sounds, for the layperson, very surprising; but Tóth collected 20 passages in Aristotle that point very clearly in that direction.

He also always insisted on the peculiar structure of the first book of Euclid. The first 28 theorems of the first book of Euclid are theorems of what is today called the absolute geometry of Bolyai. This means they do not presuppose the postulate of the parallels that we know from Euclid nor its negation assumed in hyperbolic geometry. And one of the things that already surprised the greatest preserved commentator of Euclid, Proclus—the Neoplatonic philosopher who wrote a splendid commentary on the first book of Euclid’s *Elements*—is that Euclid proved certain theorems in the first part of his first book: for example, that the sum of two angles in a triangle is less than 180° (I 17), not yet using the parallel postulate. And it seems superfluous to prove such a theorem because it follows immediately from the theorem I 32, which says, after you have introduced the parallel postulate, that the sum of a triangle is exactly 180° degrees, from which it follows immediately that the sum of two angles in a triangle must be less than 180°. Why does he prove it if it’s such a trivial corollary of I 32? Well, the point is that he wants so show that you can prove this without using the parallel postulate, and that is indeed surprising. In fact, already Charles Sanders Peirce, perhaps the greatest American philosopher, who did not know the Aristotle passages, had claimed that Euclid was somehow a non-Euclidean geometer. It shows the enormous understanding that Peirce had of the history of science. He was not only a very good scientist and philosopher, but also had a good grasp of the history of science.

And my first essay—which was published in 1982—was continuing the studies of Tóth and trying to show that two passages in Plato, in the* Republic* and particularly in the *Cratylus*, can best be made sense of if we assume that in the Platonic Academy people were aware of what was known to Aristotle. It’s also quite clear from the beginning that Aristotle’s Peripatos did not have great mathematicians—a lot of excellent pupils, but the great mathematicians are collected in the Platonic Academy. And so it is quite clear that these results must go back to Plato’s school.

I then later published on Plato’s philosophy of numbers and tried to show that the doctrine ascribed to Plato as one of the so-called unwritten doctrines by Aristotle and other ancient philosophers is, in fact, quite similar to a theory in the philosophy of mathematics that was developed at the beginning of the twentieth century by the great Dutch mathematician Brouwer. Brouwer assumes that the original concept of mathematics is twoity, and in Plato it’s* the ahoristos dyas,* the indeterminate dyad. Brouwer did not know about Plato, but he develops a theory that is relatively similar.

So I’ve gone on with work in this area; for example, I was able, I think, to show conclusively that in a Platonic dialogue, the* Phaedrus*, there’s a deliberate allusion to the use of the golden section as a building principle for the dialogue. The golden section is of course known to Euclid. Probably it was the first irrational magnitude that the Greeks had discovered by analyzing the regular pentagon. But the first claim that the golden section is also useful as an aesthetical principle is found only at the beginning of the nineteenth century, and so many people thought that the golden section was never used as an aesthetical principle earlier. And while I cannot prove it for the visual arts in the Greek and Roman time, I think that the passage that I’ve analyzed shows that Plato deliberately used the golden section as a way to structure the *Phaedrus*’s two parts; they are related to each other in the golden section.

I published also on the philosophy of the mathematics of the Neoplatonists and worked on philosophy and mathematics in Nicholas of Cusa and in my book on Hegel I deal with his contributions to mathematical discourse. So that was my background, coming from Imre Tóth’s school, and when I went to Tübingen, where I then got my PhD, I studied with Hans Krämer and Konrad Gaiser, who had founded the so-called “Tübingen School of Plato interpretation,” and not Krämer but Gaiser was also very well versed in ancient mathematics, and he also thought that in order to understand Plato correctly, you must have a background in the mathematics of his time, because we should never forget that Plato did not only write dialogues, but he was the head of a school to which some of the greatest mathematicians of world history have belonged, to name only Eudoxus, Theaetetus, and Menaechmus.

SAMUEL LONCAR

Extraordinary. I didn’t know about Imre Tóth’s discovery, and my mind is reeling, partly because it’s striking that he discovered that if the Greeks were aware of non-Euclidean geometries, in a sense they were more aware of the contingency of the structure of the natural world than even Immanuel Kant at the end of the eighteenth century. We don’t need to bog down non-specialists further, but it is significant. Of course, as you know much better than I, the issue of whether Kantian transcendental philosophy assumes Euclidean geometry is controversial. So it’s all the more extraordinary that Euclid himself was not assuming Euclidean geometry as logically necessary.

VITTORIO HÖSLE

Well, let me say two things. Kant’s philosophy of mathematics—which by the way, my teacher Tóth absolutely disliked because he rejected transcendental idealism, which he considered a form of psychologism—is a philosophy, in fact, of the applicability of mathematics to the natural world. This problem does not play a great role in the ancient world, because we do not yet have a strong mathematization of the world. It begins, however, with Plato in the *Timaeus*, but these are only small steps towards the mathematization of the natural world. In the ancient world, the area where it happened most was astronomy. But the ancient belief was that there was a radical break between the sublunar world and the supralunar world; they thought that very different principles of physics applied in one and in the other. The rejection of this divide is one of the great discoveries of the seventeenth century that led to a very different concept of science.

So, in this sense, Kant has a different focus than the discussions that must have taken place in the Academy and in the Peripatos, but Kant himself, unlike Leibniz, recognized that Euclidean geometry is based on synthetic propositions *a priori*. So, in this sense, Kant was closer to Plato than, for example, Leibniz, who had no doubt about the analyticity of the Euclidean geometry, while both Plato, Aristotle, and Kant understood that this is not the case.

The question, however, whether alternative geometries are reasonable, i.e., whether consistency is sufficient to make a geometrical system mathematically legitimate, is a different issue. Kant thought that we have to appeal to pure intuition beyond logic in order to justify Euclidean geometry, while in the case of Plato and Aristotle there’s no appeal to pure intuition. If there’s a philosopher of mathematics in the ancient world who somehow moves in the direction of the Kantian concept, it’s only Proclus—but neither Plato nor Aristotle.

I think the Greeks must have assumed that Euclidean geometry is by far preferable to the alternatives because of its determinacy. In Euclidean geometry, all triangles have a sum that equals 180°; in the hyperbolic geometry, it’s less than that, in the elliptic geometry it’s more. And probably the Greeks already understood that only in the Euclidean geometry you have figures that are similar, but not congruent—they cannot exist in the other two geometries. And that may well have played an important role given the theory of proportions developed by Eudoxus in the Academy. So I think that both Kant and Plato/Aristotle clearly preferred Euclidean geometry. But they seem to have recognized the possibility of consistent alternatives to Euclidean geometry even if they rejected them for different reasons.

##### Modern Science as Rupture: Competing Narratives

SAMUEL LONCAR

That’s very helpful, and you’ve touched on a couple of big issues. So I’ll frame a question to you and you can reject both options, but it’ll allow you to position your own work. You referenced the major change in the seventeenth century in the concept of science with the rejection of the idea that there are fundamentally different laws governing different aspects of the cosmos—the world above the moon and the world below the moon, as the ancients thought, and as Aristotle, in particular, influentially canonized for the scholastic, medieval scientific tradition.

Let’s say there’s a commonsense philosophy of science among scientists, which is not deeply aware of the historical nuances of the scientific tradition, but is often part of an Enlightenment narrative in which Science is basically seen as getting a start with the Greeks, somehow being ruined by religion—you know, in this Enlightenment narrative—and then, of course, famously in Pope’s summation, beginning again with Newton. And so you get the origins of a strong philosophy of the modern scientific revolution as a rupture, or a massive transformation, in the history of human thought and culture. So that’s the big topic I want to ask about.

And I know you don’t subscribe to anything as simple as the Enlightenment narrative. But you have then a lot of competing narratives that are all very large-structure stories about modernity, Western culture, religion, science—everything from Hans Blumenberg to others, who will argue that there are very deep metaphysical questions that arise from the ancient world and develop in Christianity that shaped the formation of modern science for good or ill. How do you think about the history of what we call science in the English-speaking world? Natural Science, mathematical physics? Do you see a long, relatively complex, but progressive story? Or do you see a story of rupture that requires a great deal of historical sympathy to reconstruct?

VITTORIO HÖSLE

I think the two alternatives are, in fact, not mutually exclusive. In the long term, I subscribe to the progress narrative. There has obviously been progress in science. We have a possibility of predicting natural events today that is far, far superior to the capacity that any culture ever had. So we cannot deny that. But it is also true that history is not as smooth as people would like to have it. First of all, I subscribe to the theory of the history of natural sciences that Piama Gaidenko developed. Gaidenko was an excellent Russian historian of science. (I had a lot of talks with her in 1990 when I spent four months in Moscow. She passed recently, in 2021.) You should not forget that while in the Institute of Philosophy of the Academy of Sciences of the Soviet Union, you could not have free discussions on political philosophy, in the realms of the history of philosophy and the history of science, there was first-rate research. And Gaidenko published two books on the two scientific revolutions. In two volumes, published in Moscow in 1980 and in 1987, she deals with the “Evolution of the Concept of Science.” And the central theory is that there were, in fact, two scientific revolutions in history: the one occurred in the fifth and fourth centuries BC, the other in the seventeenth and eighteenth centuries, and these are the two major events in the history of science.

In fact, another book that is important in this context is by Lucio Russo, an Italian historian of science. It was translated into German and English, into the latter in 2004 with the title* The Forgotten Revolution*. It deals with the ancient revolution of science (which he dates, too late in my eyes, to the Hellenistic age) and the loss of its discoveries in the Middle Ages.

So Gaidenko and Russo are certainly very important in the history of science, because they insisted on the scientific nature of the Greek epistemic system. What the Greeks achieved is indeed extraordinary, particularly in mathematics. We spoke about the recognition of the logical possibility of non-Euclidean geometries in ancient mathematics, but two other astonishing achievements of Euclid are to be found, first, in the fifth book—the doctrine of proportions elaborated by Eudoxus. Even if the Greeks of the classical time recognized as numbers only what we call natural numbers (furthermore, excluding 1), Eudoxus’ theory covers both rational and irrational magnitudes and is analogous to Richard Dedekind’s theory of irrational numbers, which was developed in the second half of the nineteenth century. (Oddly enough, only in that time rigorous theories of irrational numbers were proposed, beside Dedekind also by Karl Weierstrass and Georg Cantor.)

In fact, when Dedekind published his famous book, *Was sind und was sollen die Zahlen?*, Rudolf Lipschitz, a friend and colleague of his, said, “But what you’re doing is nothing else than what Euclid already said.” And he said, “No, because I explicitly claim the existence of irrational numbers.” But the gist of his mathematical idea is fundamentally the same that you have in Eudoxus’ theory – a theory so general that it applies both to geometrical and arithmetical magnitudes.

And the other awe-inspiring achievement in Euclid’s *Elements* is the twelfth book, which like the fifth book goes back to Eudoxus, in which we find a method to prove theorems that today we prove by calculus—the so-called “method of exhaustion.” That term was only coined in the seventeenth century, when calculus began to be developed. But people understood that the Greeks already had a far less powerful method to prove some of the theorems which cannot be proved with normal elementary geometrical means. There are, however, two important differences between Eudoxus’ method of exhaustion and modern infinitesimal calculus. On the one hand, the method of exhaustion is based on an apagogic proof; it proves an equality by excluding that an area could be either greater or smaller than a given value. A positive proof by assuming an actual increase or decrease without end is alien to the Greeks, for they reject the actually infinite – and thus, their method is much less powerful than the modern one.

On the other hand, when, in the seventeenth century, people like Fermat, Newton, and Leibniz developed calculus, their ideas were not consistent. The first person who manages to offer a rigorous proof in calculus was Cauchy at the beginning of the nineteenth century. It took almost two centuries until people were able to offer for the first time a rigorous proof. But even Cauchy had an inconsistency, and this inconsistency was only eliminated at the end of the nineteenth century by Weierstrass. So it took more than two centuries to get to a consistent theory. The method of exhaustion of Eudoxus, however, is logically perfect from the start. There is no gap. Again, it’s much less powerful than calculus; we are all very happy to have calculus. But it shows you the instinctive logical genius of the Greeks. I say “instinctive,” for Eudoxus operated in a time when logic as a science did not yet exist. A small part of logic, syllogistics, was developed shortly afterwards by Aristotle, who achieved an axiomatization of this discipline comparable to that laid out by the Greek mathematicians within the Academy for planimetry (not, however, for arithmetics and stereometry, the other two disciplines contained in Euclid’s *Elements*). Both the axiomatization and the rigor of the proofs are something which clearly distinguishes Greek mathematics from that of other ancient civilizations like the Mesopotamian, Indian, and Chinese. Also, the interest in concepts that had no empirical relevance is a hallmark of Greek mathematics – the Babylonians developed complex mathematical techniques but never hit upon the existence of irrational magnitudes, which are irrelevant for practical purposes since in this realm we must always live with approximations. But the Greeks demonstrated their existence already in the middle of the fifth century.

Now let us go to some of the differences between the first and the second scientific revolution, on which I dealt in the second chapter of my book *Philosophie der ökologischen Krise*, where I discuss the intellectual presuppositions of the ecological crisis,[10] which, alas, was never translated into English, even if into eight other languages. One of the big differences is that in the ancient world, science and technology are not really connected. There is one great exception: the absolutely titanic figure of Archimedes. He was, first, one of the most ingenious mathematicians of all times (as such, he developed further the method of exhaustion and proved a lot of important theorems; for example, he was able to determine the volume of the sphere and the cylinder). He was, second, also an excellent physicist. He discovered the law of the lever (even if, in fact, his “proof” contains one of the few logical errors in his work) as well as “Archimedes’ principle” on the apparent loss of weight by bodies immersed in fluids.

And, third, he was a first-class engineer; he was involved in the defense of Syracuse, when Marcellus, in 212, besieged and then finally captured the city, and then during the process of the fall of Syracuse, Archimedes was killed. He was the exception that united these three disciplines. The Platonic Academy was a place for absolutely first-class mathematical research and for very important astronomical research, but they were far less interested in trying to find laws for the terrestrial world. This of course happened in the seventeenth century with Galileo’s discovery of the law of fall – which blatantly contradicts what Aristotle had laid out on the fall of bodies in the fourth book of his *Physics*.

But the rise of modern science is not only driven by theoretical interests. Particularly if you’re reading both Bacon’s *Novum Organon* and *New Atlantis*, you find a new justification of science. Science is not primarily important because it manifests a hidden order of reality, but because it will help if applied to the empirical world to make human life better. Bacon himself, for example, had no mathematical training. If you’re reading *Novum Organon*, you’re quite surprised how ignorant in mathematics he is. There’s no doubt that people in Plato’s Academy had a mathematical training far superior to that which Bacon had. But Bacon combines the idea that we have to engage in science with a program of easing human life—somehow with the anticipation that the Scientific Revolution will lead to an Industrial Revolution.

And this now leads us to the other part of your question: How did this come about? And here we see how you cannot write a history of science exclusively based on inner-scientific developments. Scientific developments are of course extremely important. It’s clear that certain mathematical problems lead to other mathematical problems, simply because they are logically connected; when you try to work on one of them and possibly solve it, you understand that you will make progress if you generalize your theory, address other problems first, etc. So this is obviously a very important factor of the inner evolution of science, and it plays a great role in Galileo and Descartes. Take *The Geometry* of Descartes. Descartes wants to solve a geometrical problem discussed by Pappus, a fourth-century-AD Greek mathematician, so it’s an inner-mathematical problem, but he understands that he can solve this and many other problems if he makes a step of abstraction that would have been hardly conceivable for the Greeks, and this leads to analytical geometry—if you want, to an algebraization of geometry. The history of science often has to do with the rise, on more general levels, of the power of abstraction, which allows one to see certain problems from a distance where they become easier. Paradoxically, one needs an enormous intellectual effort to get to the level of abstraction needed, but once one is there, one can solve problems more easily than before. (But Descartes was of course wrong in hoping that the new method would render the discovery of proofs almost inevitable.)

But what you can learn when you are studying the second scientific revolution is that in the case of Bacon, what drives him are mainly extra-scientific concerns—namely, the concern to render the world subject to humans, and there is no doubt that this concern is deeply motivated by Christian ideas. Therefore, in *New Atlantis* we have the House of Salomon, which clearly continues a religious vocation.

People begin to think that we have a moral duty to try to use our scientific knowledge to make life less hard, to overcome misery, to extend the lifespan of humans, to overcome terrible diseases. All this is a very important motive that did not really play a role in ancient science. And this has to do with the fact that ancient science is an aristocratic activity of intellectuals, who are not really thinking about how they could ease the life of the lower classes, while this becomes a motive that is very strong in the second scientific revolution and that has Christian roots. While Galileo moves in the direction of questioning the radical divide between terrestrial and celestial physics, his main achievements were in terrestrial physics: the development of the principles of mechanics. However, he challenges another divide of the ancients.

Ancient science not only has a divide between sublunar and supralunar physics. The ancient worldview assumed that mechanics, the discipline of how you can build machines, has nothing to do with physics. In the *Corpus Aristotelicum*, we have a work called *Problemata Mechanica*, probably not by Aristotle but by one of his students, in which questions of building machines are discussed, but they’re not connected with the principles of physics. It’s a completely independent discipline. And Galileo was the first to understand that, ultimately, our engineering capacities, thanks to which we build machines, are based on the same principles that are discovered by science. The Greek word “mechanics” has to do with “*mechane*” – which means “ruse.” But engineering can outwit nature only by using it, by changing antecedent conditions in such a way that thanks to the same laws that dominate nature humans achieve more favored outcomes. So science and engineering are much more deeply connected than the Greeks thought. And that, of course, was a very important step forward for the development of the union between science and technology.

Arnold Gehlen, the great German philosopher and anthropologist, in his extraordinary book of 1957, *The Soul in the Technical Age (Die Seele im technischen Zeitalter*), argues that what happened in early modernity, in the seventeenth and eighteenth century, is a combination of three things that in antiquity were not connected: science (which, again, existed in antiquity at a very high level, but in isolation), technology, and capitalism. His argument is that modern science, unlike the ancient sciences of mathematics or even astronomy, is experimental. Astronomy is an empirical science; it tries to render justice to the movements of the celestial bodies that we see, “to save the phenomena,” as the ancients said.

But astronomy, even if it’s an empirical science and based on systematic observations, is not, or was not earlier, an experimental science, because one cannot make experiments with stars. One has to observe how they move, but one cannot change the conditions to alter the movements, while Galileo did engage in an experimental science when he dropped weights off of the Leaning Tower in Pisa. And now Gehlen righty remarks that the structure of an experiment very easily can become an engine; it’s an engine *in nuce*, because one tries to isolate certain parameters to see their connections, and by doing so, one can easily develop the idea how one could build an engine. But also the other way around. Once you have developed an engine for practical purposes, to satisfy certain needs, you understand that this new machine may shed light on certain physical principles. And so since the seventeenth and particularly the eighteenth century, science and industry, science and technology, go hand in hand. Probably this is connected to a new appreciation of manual labor, which was alien to antiquity. The mathematization of nature, on the other hand, while almost absent in Aristotle, has some appearance in Plato’s *Timaeus*, as I already mentioned; and therefore, the revolt against scholasticism and Aristotelianism, which characterizes the scientific revolution of the seventeenth century, could go hand in hand with a deep admiration for Plato – suffice it to mention Johannes Kepler.

Now, the more complex the experiments are—think today about CERN; I’ve once visited the CERN in Geneva, and it’s indeed an incredible structure—the more you need capital. Capitalism is necessary both for the development of industry and for the development of complex experiments, and therefore science and technology have to be connected with capitalism. And Gehlen argues that this triumph of science, technology and capitalism is what created modernity and what distinguishes it radically from antiquity.

However, people who have not read the ancient scientists often completely underrate ancient science, because they think that science must be connected with technology. I’m not at all an expert in ancient technology, but also here, even if it was to a large extent disconnected from science in a rigorous sense, the Greeks were better than many people think. You may have heard about the Antikythera mechanism that had already been found in 1901, but was correctly interpreted only after many decades, most extensively in the last fifteen years. It was a mechanism to predict celestial phenomena such as eclipses and functioned as multiple calendars. But it remains true that, fundamentally, in the ancient world the main source of energy was muscular energy, of animals and of humans, usually slaves. Sure, water mills were brought occasionally to use (the first description of them is due to Philo of Byzantium from the third century BC) but the whole idea that you could systematically harness energy from nature in order to render a human life less laborious (and therefore, for example, abolish slavery) is much later.

##### Science as a Humanitarian Project

VITTORIO HÖSLE

Despite the far superior physical and mathematical intelligence of Galileo and Descartes compared with Bacon, it’s clear that they too are deeply driven by Christian motives. The fact that Galileo was condemned by the Church often lets the layperson overlook the fact that Galileo was a serious Catholic. Let us not forget that his two daughters became nuns. And when we discuss, for example, the rejection of the geocentric Ptolemaic astronomy, the first great alternative theory was due to a chapter canon, who may or may not have been ordained as a priest, Nicolaus Copernicus. Certainly, the Ptolemaic astronomy was not only rejected because the system of epicycles became more and more worrisome and could not really render justice to the data. Besides the purely astronomical reasons there was an intellectual fascination with the new paradigm, which, even if the Ptolemaic system had been the intellectual staple food of the medieval worldview (think only of Dante’s *Comedy*), was paradoxically inspired itself by Christian motives.

This is already visible in Nicholas of Cusa, who later became Prince-Bishop and Cardinal. He is one of the first people who, in the second book of *On Learned Ignorance* (*De Docta Ignorantia*), challenged the Ptolemaic system; and Giordano Bruno, who, however, was burned at the stake in 1600, was strongly influenced by Cusanus, whom he admired deeply. Their fascination for an infinite universe has nothing to do with the necessity of cooperating with industry and technology, but is prompted by radical metaphysical changes, which in the course of medieval philosophy challenged traditional metaphysical ideas.

One such idea is that of an infinite God: Nicholas of Cusa argues that it’s more natural for an infinite God to create a world that is potentially infinite and not limited. Also, Nicholas’ extremely original philosophy of mathematics points to its Christian roots: His partial anti-Platonism according to which humans *create* mathematical entities, which the Greeks had considered as pre-existent entities, is based on his belief that the human mind is made in the image of the creator God and thus must be itself creative.

Another important idea is the development of the concept of possible worlds in the late Middle Ages, beginning with Henry of Ghent and Duns Scotus. This unleashes the scientific imagination, because people began to think about possible worlds in a way that for the Greeks would not have been possible. The concept of possibility of the Greeks is completely different from that of a possible world, because possibility is something within the actual world that is about and may fail to develop towards its own *telos*. The possible worlds of Duns Scotus are alternatives to the actual world, not something within the actual world. Such metaphysical concepts have had an enormous impact on the development of scientific theories, and probably the scientific decay at the end of antiquity and in the early Middle Ages was not too high a price for bringing forth in a slow process a new metaphysics that rendered the specific differences of modern science possible.

I want to mention another important point. While the superficial secular narrative insisted mainly on the opposition between religion and science, pointing, for example, to the shameful trial against Galileo, a more objective account, as proposed, for example, in the admirable recent works by Peter Harrison, insists on the religious roots of the fathers of modern science. Descartes was like Galileo a serious Catholic, Kepler a committed Lutheran—and even if Newton was an Arian, he was a convinced theist. These are not simply biographical facts; the theistic framework makes it much more plausible to believe in one coherent system of laws of nature. The skepticism of Hume, on the other hand, is hardly conducive to the project of modern science, for such a project must trust in the intelligibility of the universe, denied by skepticism, and such a trust is justified if nature is itself the result of a mind.

One of the greatest achievements of Descartes in philosophy was the idea that you can have a philosophy in the first person. This means: by abstracting from your own body, and this possibility of epistemically distinguishing between one’s body and one’s mind is the basis for his metaphysical dualism of body and mind. It’s a radically new theory. There is only one person in antiquity who has come relatively close to him, and that’s Augustine. But it’s a doctrine completely alien, for example, to the Aristotelian tradition, also to Thomas Aquinas.

And if you read the antischolastic letter by Michelangelo Fardella, a Catholic priest, an Augustinian, a Cartesian, and a correspondent of Leibniz, you find him insisting (correctly, as I believe) that the Christian belief in the immortality of the soul is best grounded in the Cartesian theory. If the soul is nothing else than the form of an organic body, as Aristotle and Aquinas teach, when we have the dissolution of the body, the soul must dissolve too. For all these reasons making a radical break between Christianity and modern science is deeply misleading. Modern science and the philosophical ideas of modern scientists, like Descartes, are strongly inspired by basic changes in the metaphysical worldview that occurred in the Middle Ages...

*Part Two Forthcoming*

*Vittorio G. Hösle is the Paul Kimball Professor of Arts and Letters, Department of German and Russian Languages and Literatures, Concurrent Professor of Philosophy and of Political Science. His scholarly interests are in the areas of systematic philosophy (metaphysics, ethics, aesthetics, political theory) and the history of philosophy (mainly ancient and modern). He has recently published a book on philosophical literature, *Philosophische Literatur-Interpretationen von Dante bis le Carré *(2023), and one on the *Ukraine War, Mit dem Rücken zu Russland. Der Ukrainekrieg und die Fehler des Westens *(2022). This year he has published with Jieon Kim a translation of the *Commentary on the Song of Songs* by Rupert of Deutz. Hösle has written or edited 57 books and published nearly 200 articles. His work has appeared in 20 languages. Among other prizes and awards, he received the Fritz-Winter Prize of the Bavarian Academy of Sciences and has had visiting professorships in many countries and fellowships at various institutions, such as the Institute for Advanced Study in Princeton.*

*Samuel Loncar is a philosopher and the Editor of the *Marginalia Review of Books*. He is writing a book on science as a spiritual revolution for Columbia University Press. Learn more at **www.samuelloncar.com**. Tweets @samuelloncar*

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