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Medieval Cosmology: Theories of Infinity, Place, Time, Void, and the Plurality of Worlds
These selections from Le système du monde , the classic ten-volume history of the physical sciences written by the great French physicist Pierre Duhem (1861-1916), focus on cosmology, Duhem's greatest interest. By reconsidering the work of such Arab and Christian scholars as Averroes, Avicenna, Gregory of Rimini, Albert of Saxony, Nicole Oresme, Duns Scotus, and William of Occam, Duhem demonstrated the sophistication of medieval science and cosmology.
642 pages, Paperback
First published January 1, 1985
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About the author
Pierre Duhem
279 books18 followersPierre Maurice Marie Duhem (French: [pjɛʁ moʁis maʁi dy.ɛm] was a French physicist, mathematician, historian and philosopher of science. He is best known for his work on chemical thermodynamics, for his philosophical writings on the indeterminacy of experimental criteria, and for his historical research into the science of the European Middle Ages. As a scientist, Duhem also contributed to hydrodynamics and to the theory of elasticity.
Duhem's views on the philosophy of science are explicated in his 1906 work The Aim and Structure of Physical Theory. In this work, he opposed Newton's statement that the Principia's law of universal mutual gravitation was deduced from 'phenomena', including Kepler's second and third laws. Newton's claims in this regard had already been attacked by critical proof-analyses of the German logician Leibniz and then most famously by Immanuel Kant, following Hume's logical critique of induction. But the novelty of Duhem's work was his proposal that Newton's theory of universal mutual gravity flatly contradicted Kepler's Laws of planetary motion because the interplanetary mutual gravitational perturbations caused deviations from Keplerian orbits. Since no proposition can be validly logically deduced from any it contradicts, according to Duhem, Newton must not have logically deduced his law of gravitation directly from Kepler's Laws.
Duhem's name is given to the under-determination or Duhem–Quine thesis, which holds that for any given set of observations there is an innumerable large number of explanations. It is, in essence, the same as Hume's critique of induction: all three variants point to the fact that empirical evidence cannot force the choice of a theory or its revision. Possible alternatives to induction are Duhem's instrumentalism and Popper's thesis that we learn from falsification.
As popular as the Duhem–Quine thesis may be in the philosophy of science, in reality, Pierre Duhem and Willard Van Orman Quine stated very different theses. Pierre Duhem believed that experimental theory in physics is fundamentally different from fields like physiology and certain branches of chemistry. Also, Duhem's conception of the theoretical group has its limits, since not all concepts are connected to each other logically. He did not include at all a priori disciplines such as logic and mathematics within these theoretical groups in physics which can be tested experimentally. Quine, on the other hand, conceived this theoretical group as a unit of a whole human knowledge. To Quine, even mathematics and logic must be revised in light of recalcitrant experience, a thesis that Duhem never held.
A quote of Duhem on physics:
A theory of physics is not an explanation. It is a system of mathematical propositions, deduced from a small number of principles, which have for their aim to represent as simply, as completely and as exactly as possible, a group of experimental laws.
Duhem's views on the philosophy of science are explicated in his 1906 work The Aim and Structure of Physical Theory. In this work, he opposed Newton's statement that the Principia's law of universal mutual gravitation was deduced from 'phenomena', including Kepler's second and third laws. Newton's claims in this regard had already been attacked by critical proof-analyses of the German logician Leibniz and then most famously by Immanuel Kant, following Hume's logical critique of induction. But the novelty of Duhem's work was his proposal that Newton's theory of universal mutual gravity flatly contradicted Kepler's Laws of planetary motion because the interplanetary mutual gravitational perturbations caused deviations from Keplerian orbits. Since no proposition can be validly logically deduced from any it contradicts, according to Duhem, Newton must not have logically deduced his law of gravitation directly from Kepler's Laws.
Duhem's name is given to the under-determination or Duhem–Quine thesis, which holds that for any given set of observations there is an innumerable large number of explanations. It is, in essence, the same as Hume's critique of induction: all three variants point to the fact that empirical evidence cannot force the choice of a theory or its revision. Possible alternatives to induction are Duhem's instrumentalism and Popper's thesis that we learn from falsification.
As popular as the Duhem–Quine thesis may be in the philosophy of science, in reality, Pierre Duhem and Willard Van Orman Quine stated very different theses. Pierre Duhem believed that experimental theory in physics is fundamentally different from fields like physiology and certain branches of chemistry. Also, Duhem's conception of the theoretical group has its limits, since not all concepts are connected to each other logically. He did not include at all a priori disciplines such as logic and mathematics within these theoretical groups in physics which can be tested experimentally. Quine, on the other hand, conceived this theoretical group as a unit of a whole human knowledge. To Quine, even mathematics and logic must be revised in light of recalcitrant experience, a thesis that Duhem never held.
A quote of Duhem on physics:
A theory of physics is not an explanation. It is a system of mathematical propositions, deduced from a small number of principles, which have for their aim to represent as simply, as completely and as exactly as possible, a group of experimental laws.
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October 12, 2024
For a long time, it was conventional in the historiography of science to treat the Scientific Revolution of the seventeenth century as an entirely novel departure, as if sprung forth like Athena from the head of Zeus. To a large extent, this tendency reflects wishful thinking and an uncritical reception of the picture its protagonists paint of themselves. Galileo, in his inviting and entertaining dialogues, portrays his Aristotelian opponents as simple-minded and slow while giving the self-serving impression that his own ideas are completely original. In those days, scholarly standards did not demand that one credit one’s sources. The classical mechanics the great heroes of that period invented strikes one as so different in the character of its elementary principles from the Aristotelian physical cosmology that preceded it that many an historian, in a field where ever since the Renaissance humanists critical scholarship holds sway as the rule, was nonetheless inclined to accept the standard narrative of the Scientific Revolution at face value, since, after all, it plays into the widespread conceits of progress and rational superiority of modern civilization over that of the Middle Ages.
The philosophically inclined French physicist, Pierre Duhem (1861-1916), embraced in mid-life an avocation to history of science and started out by writing monographs on Leonardo da Vinci and on statics in the late sixteenth century, during the course of which he was alerted to the existence of a whole tradition of speculation into topics we today would consider to belong to astronomy and physics, unknown to Duhem’s contemporaries because extant mostly in manuscripts that had never been edited and printed. This finding prompted Duhem to expand the range of his historical studies. Thus, he created quite a stir in the scholarly world of the early decades of the twentieth century when he had the audacity to go back and trace the transmission of ideas about the natural world down through the centuries, only to find (much to his own surprise) that the architects of the seventeenth-century revolution are far more indebted to their late medieval forebears than they let on. For instance, Galileo’s graphical proof of the key mean speed theorem in his opus magnum, Two New Sciences, is lifted more or less straight from Nicole Oresme in the fourteenth century – without attribution, needless to say.
From the year 1909 up to his unfortunate sudden death to heart attack in 1916, in a remarkable feat of scholarly industry Duhem composed Le système du monde: histoire des doctrines cosmologiques de Platon à Copernic in ten volumes, not all of which he managed to see through the press but the rest of which appeared posthumously in stages through 1959. The English translator Roger Ariew – whose work is profusely praised in the foreword to the present book by the eminent historian of science Stanley Jaki – has selected texts principally related to cosmology and collected them into a single volume.
For the sake of handling a sprawling corpus such as this (601 pages in the English abridgment alone), let us give an overview of its contents and then comment on a couple of themes that emerge from Duhem’s immense labors to found the discipline of medieval scientific historiography. Part I is devoted to the two infinities, viz., the infinitely small and the infinitely large. The former engages the question as to the existence of indivisibles and, if it be supposed that they exist, as to their nature. Thus, one has to confront limiting processes and to entertain categorematic versus syncategorematic infinities. Similar issues pertain with respect to the infinitely large. The cast of characters includes Gregory of Rimini, John Buridan (against him), and Nicole Oresme and Marsilius of Inghen (for him).
Part II explores the doctrine of place, both before and after the condemnations of 1277. The topic is complex and resists easy summary; Duhem discusses the contrasting views of some two dozen thinkers. Then, Part III does the same for the doctrine of time. Again, around a dozen principal thinkers are reviewed with respect to their notions of mathematical and physical time and of the possible existence of an absolute clock. Part IV takes up the void – its possibility, per se, and the aligned problem of the possibility of motion in a void. Here, Duhem gives an exposition of the views of another two dozen scholars. Lastly, Part V takes up the problem of the plurality of worlds, first in Aristotle, Simplicius and Averroes, then in scholastic philosophy before and after 1277. Here, the gallery of characters numbers around two dozen.
To whittle down ten volumes into one, the translator has had to omit a number of other topics in medieval natural philosophy of substantial intrinsic interest: impetus theory and the computists in the Merton school at Oxford, for instance. To learn about these developments, it could be recommended to acquire a reading knowledge of French so as to tackle Duhem’s full Le système du monde, or of German in order to read Anneliese Maier and Heinrich Wieleitner.
To return to the review: a first issue that bears consideration is the question as to how narrow the medieval scholastics were in their adherence to Aristotle? To call them Aristotelians requires qualification, of course, because their reception of Aristotle is heavily influenced by the commentaries of the great medieval Arabic philosophers, above all Avicenna and Averroes. But – what is more decisive – the Latin scholastics, despite the high respect in which they held his authority, could not subscribe to all of Aristotle’s positions unquestioningly. For they were Christians and, apart possibly from a small party of Latin Averroists, could scarcely accept his pagan doctrines when they conflict with revealed theology. Moreover, as we know from the history of logic – at which the medievals excelled – from the time of Peter Abelard (1079-1142) onwards, they show themselves capable of considerable independence of mind and innovation in their use of the materials they receive from antiquity. Thus, it stands to reason that one should encounter a similar phenomenon in natural philosophy, namely, a world of thought molded to be sure by the Aristotelian paradigm but increasingly minded, as the centuries wear on, to break through to unprecedented conceptions.
A second and related major theme is the bearing of theology on natural philosophy as it was conducted by the medieval scholastics. The world-historical significance of this question comes down to this: the fateful arrival of monotheism as the religion of the many (in contrast with the isolated position of the Jews, who all along were vastly outnumbered by the gentiles in the territories in which they settled during the Diaspora) could not but have momentous consequences in the intellectual realm. Already by the high Middle Ages, the church fathers had long since figured out a modus vivendi between the literary heritage of ancient pagan culture and Christianity, a great topic for another day but beside the present purpose to enter into. Yet, the ancient pagan scientific heritage itself was never truly assimilated by Christians during the patristic era. Thus, the recovery of the ancient pagan philosophical and scientific corpus that begins in earnest during the late eleventh to twelfth centuries presages a quite novel constellation in the world of ideas, for the Latin scholastics, perceiving themselves to be far behind the pagans and the great Arabic philosophers at the height of Islamic civilization, wanted to catch up and, correspondingly, entertained a keen interest in learning and mastering the natural philosophy itself.
Thus, Duhem will on occasion remark on the difference that being Christian makes to the pursuit of natural philosophy. For instance, Aristotle’s denial of potential infinity depends on not having a concept of creation [p. 73]. For, revelation introduces a formally infinite principle into the world [p. 76]. And, ‘from the moment that Christianity recognized God’s power to create new matter from nothing, the doctrine professed by the Peripatetics on the subject of the infinitely large was destroyed at its foundations’ [p. 77]. Another subject that Duhem recurs to frequently is the effect exerted by the ban on certain Aristotelian propositions issued in 1277 by Etienne Tempier, the bishop of Paris where the most prominent university faculty of theology resided. As Duhem recognizes, the ban in fact wielded an enabling influence, for it forced the scholastic philosophers to come up with their own doctrines in place of the Aristotelian ones they were no longer permitted to teach. With respect to the doctrine of time and place, for example, Duhem writes the following:
Everything that the Philosopher taught with respect to time is, in the final analysis, founded on this dogma: there does not exist and there cannot exist more than one first mobile, and hence more than one first movement; this first unique movement marks one and the same time for all the other movements. By asserting that God can, if he wishes, create several worlds, Etienne Tempier destroyed the foundation that held together the Peripatetic theory of time; in the same way, by asserting that God can impose a movement of translation to the universe, he also deprived the Peripatetic theory of place of any support. [p. 255]
Let us leave off commenting and refer the reader to the work itself for a gripping exposition of a high adventure of thought.
What if anything can we learn from medieval natural philosophy about the cosmos today? Perhaps the first lesson we can derive from the medieval scholastics is to cultivate the temerity to question the currently reigning orthodoxies in modern empirical science, just as they questioned and ultimately went beyond Aristotle. A deeper appropriation of their example would teach us something more: to internalize the perennial value of pursuing speculation within an institutional framework that prizes serious debate aimed at resolution of disagreements in order to alight upon the truth of the matter. In all honesty, one cannot say that such an environment prevails in the academic scene of the early twenty-first century, for all the lip service it offers to the ideal of disinterested pursuit of truth. For in the current institutional matrix, academic freedom is interpreted to mean that everyone does his own thing and refrains from any incisive critique of the others, lest they be proved wrong and thereby deprived of the right to support themselves by continuing research in their own specialty. If nobody is threatened with being proved wrong, everyone can keep on publishing papers immune from critique and thereby make a comfortable living in his chosen sinecure. Thus, the leading physics journals can go on filling their pages with innumerable contributions to string theory even after no trace of the supersymmetric partners was seen at CERN, nature’s verdict. Shouldn’t, however, the truth about the natural world matter? Shouldn’t our aim be to discover the truth, even if it mean letting go of cherished ideas that fail to comport with it?
The philosophically inclined French physicist, Pierre Duhem (1861-1916), embraced in mid-life an avocation to history of science and started out by writing monographs on Leonardo da Vinci and on statics in the late sixteenth century, during the course of which he was alerted to the existence of a whole tradition of speculation into topics we today would consider to belong to astronomy and physics, unknown to Duhem’s contemporaries because extant mostly in manuscripts that had never been edited and printed. This finding prompted Duhem to expand the range of his historical studies. Thus, he created quite a stir in the scholarly world of the early decades of the twentieth century when he had the audacity to go back and trace the transmission of ideas about the natural world down through the centuries, only to find (much to his own surprise) that the architects of the seventeenth-century revolution are far more indebted to their late medieval forebears than they let on. For instance, Galileo’s graphical proof of the key mean speed theorem in his opus magnum, Two New Sciences, is lifted more or less straight from Nicole Oresme in the fourteenth century – without attribution, needless to say.
From the year 1909 up to his unfortunate sudden death to heart attack in 1916, in a remarkable feat of scholarly industry Duhem composed Le système du monde: histoire des doctrines cosmologiques de Platon à Copernic in ten volumes, not all of which he managed to see through the press but the rest of which appeared posthumously in stages through 1959. The English translator Roger Ariew – whose work is profusely praised in the foreword to the present book by the eminent historian of science Stanley Jaki – has selected texts principally related to cosmology and collected them into a single volume.
For the sake of handling a sprawling corpus such as this (601 pages in the English abridgment alone), let us give an overview of its contents and then comment on a couple of themes that emerge from Duhem’s immense labors to found the discipline of medieval scientific historiography. Part I is devoted to the two infinities, viz., the infinitely small and the infinitely large. The former engages the question as to the existence of indivisibles and, if it be supposed that they exist, as to their nature. Thus, one has to confront limiting processes and to entertain categorematic versus syncategorematic infinities. Similar issues pertain with respect to the infinitely large. The cast of characters includes Gregory of Rimini, John Buridan (against him), and Nicole Oresme and Marsilius of Inghen (for him).
Part II explores the doctrine of place, both before and after the condemnations of 1277. The topic is complex and resists easy summary; Duhem discusses the contrasting views of some two dozen thinkers. Then, Part III does the same for the doctrine of time. Again, around a dozen principal thinkers are reviewed with respect to their notions of mathematical and physical time and of the possible existence of an absolute clock. Part IV takes up the void – its possibility, per se, and the aligned problem of the possibility of motion in a void. Here, Duhem gives an exposition of the views of another two dozen scholars. Lastly, Part V takes up the problem of the plurality of worlds, first in Aristotle, Simplicius and Averroes, then in scholastic philosophy before and after 1277. Here, the gallery of characters numbers around two dozen.
To whittle down ten volumes into one, the translator has had to omit a number of other topics in medieval natural philosophy of substantial intrinsic interest: impetus theory and the computists in the Merton school at Oxford, for instance. To learn about these developments, it could be recommended to acquire a reading knowledge of French so as to tackle Duhem’s full Le système du monde, or of German in order to read Anneliese Maier and Heinrich Wieleitner.
To return to the review: a first issue that bears consideration is the question as to how narrow the medieval scholastics were in their adherence to Aristotle? To call them Aristotelians requires qualification, of course, because their reception of Aristotle is heavily influenced by the commentaries of the great medieval Arabic philosophers, above all Avicenna and Averroes. But – what is more decisive – the Latin scholastics, despite the high respect in which they held his authority, could not subscribe to all of Aristotle’s positions unquestioningly. For they were Christians and, apart possibly from a small party of Latin Averroists, could scarcely accept his pagan doctrines when they conflict with revealed theology. Moreover, as we know from the history of logic – at which the medievals excelled – from the time of Peter Abelard (1079-1142) onwards, they show themselves capable of considerable independence of mind and innovation in their use of the materials they receive from antiquity. Thus, it stands to reason that one should encounter a similar phenomenon in natural philosophy, namely, a world of thought molded to be sure by the Aristotelian paradigm but increasingly minded, as the centuries wear on, to break through to unprecedented conceptions.
A second and related major theme is the bearing of theology on natural philosophy as it was conducted by the medieval scholastics. The world-historical significance of this question comes down to this: the fateful arrival of monotheism as the religion of the many (in contrast with the isolated position of the Jews, who all along were vastly outnumbered by the gentiles in the territories in which they settled during the Diaspora) could not but have momentous consequences in the intellectual realm. Already by the high Middle Ages, the church fathers had long since figured out a modus vivendi between the literary heritage of ancient pagan culture and Christianity, a great topic for another day but beside the present purpose to enter into. Yet, the ancient pagan scientific heritage itself was never truly assimilated by Christians during the patristic era. Thus, the recovery of the ancient pagan philosophical and scientific corpus that begins in earnest during the late eleventh to twelfth centuries presages a quite novel constellation in the world of ideas, for the Latin scholastics, perceiving themselves to be far behind the pagans and the great Arabic philosophers at the height of Islamic civilization, wanted to catch up and, correspondingly, entertained a keen interest in learning and mastering the natural philosophy itself.
Thus, Duhem will on occasion remark on the difference that being Christian makes to the pursuit of natural philosophy. For instance, Aristotle’s denial of potential infinity depends on not having a concept of creation [p. 73]. For, revelation introduces a formally infinite principle into the world [p. 76]. And, ‘from the moment that Christianity recognized God’s power to create new matter from nothing, the doctrine professed by the Peripatetics on the subject of the infinitely large was destroyed at its foundations’ [p. 77]. Another subject that Duhem recurs to frequently is the effect exerted by the ban on certain Aristotelian propositions issued in 1277 by Etienne Tempier, the bishop of Paris where the most prominent university faculty of theology resided. As Duhem recognizes, the ban in fact wielded an enabling influence, for it forced the scholastic philosophers to come up with their own doctrines in place of the Aristotelian ones they were no longer permitted to teach. With respect to the doctrine of time and place, for example, Duhem writes the following:
Everything that the Philosopher taught with respect to time is, in the final analysis, founded on this dogma: there does not exist and there cannot exist more than one first mobile, and hence more than one first movement; this first unique movement marks one and the same time for all the other movements. By asserting that God can, if he wishes, create several worlds, Etienne Tempier destroyed the foundation that held together the Peripatetic theory of time; in the same way, by asserting that God can impose a movement of translation to the universe, he also deprived the Peripatetic theory of place of any support. [p. 255]
Let us leave off commenting and refer the reader to the work itself for a gripping exposition of a high adventure of thought.
What if anything can we learn from medieval natural philosophy about the cosmos today? Perhaps the first lesson we can derive from the medieval scholastics is to cultivate the temerity to question the currently reigning orthodoxies in modern empirical science, just as they questioned and ultimately went beyond Aristotle. A deeper appropriation of their example would teach us something more: to internalize the perennial value of pursuing speculation within an institutional framework that prizes serious debate aimed at resolution of disagreements in order to alight upon the truth of the matter. In all honesty, one cannot say that such an environment prevails in the academic scene of the early twenty-first century, for all the lip service it offers to the ideal of disinterested pursuit of truth. For in the current institutional matrix, academic freedom is interpreted to mean that everyone does his own thing and refrains from any incisive critique of the others, lest they be proved wrong and thereby deprived of the right to support themselves by continuing research in their own specialty. If nobody is threatened with being proved wrong, everyone can keep on publishing papers immune from critique and thereby make a comfortable living in his chosen sinecure. Thus, the leading physics journals can go on filling their pages with innumerable contributions to string theory even after no trace of the supersymmetric partners was seen at CERN, nature’s verdict. Shouldn’t, however, the truth about the natural world matter? Shouldn’t our aim be to discover the truth, even if it mean letting go of cherished ideas that fail to comport with it?
May 16, 2016
The Middle Age physicists were able to formulate precise, very modern questions and offer penetratingly clear answers to questions on infinity (laying the foundations of calculus) and on the fundamentals undergirding even modern physics: place, time (and its relativity), void, and the "plurality of the worlds" (i.e., what's called "parallel universes" today).
January 3, 2025
Take this review with a pinch of salt: I am not the intended audience for this book.
I went into this book thinking cosmology was something different to what it actually is, so when I started reading I was confused before I actually looked up the term and found out it was a physics thing. This is quite clearly my own fault, but I decided to stick with the book anyway as a Medievalist. Unfortunately my confusion did not clear up - I was still very confused about many of the concepts by the end of it. I also didn't love the writing style of the book. It was very quote heavy, some quotes lasting several pages long.
It wasn't all bad, however. It was interesting to see how medieval philosophers theorised physics in a way that was still in line with Catholic Church doctrine. I especially like the fact that Very glad this was included.
It's very high level and clearly made for History of Science or Philosophy scholars so I would recommend this book to them as they could probably get a lot more out of it than I did and are quite clearly the intended audience.
I went into this book thinking cosmology was something different to what it actually is, so when I started reading I was confused before I actually looked up the term and found out it was a physics thing. This is quite clearly my own fault, but I decided to stick with the book anyway as a Medievalist. Unfortunately my confusion did not clear up - I was still very confused about many of the concepts by the end of it. I also didn't love the writing style of the book. It was very quote heavy, some quotes lasting several pages long.
It wasn't all bad, however. It was interesting to see how medieval philosophers theorised physics in a way that was still in line with Catholic Church doctrine. I especially like the fact that Very glad this was included.
It's very high level and clearly made for History of Science or Philosophy scholars so I would recommend this book to them as they could probably get a lot more out of it than I did and are quite clearly the intended audience.
Displaying 1 - 3 of 3 reviews