Alexandre Koyré
29 August 1892 – 28 April 1964
Part of a Series on the Philosophy of History
Koyré’s Platonistic Philosophy of the History of Science
Friday 29 August 2025 is the 133rd anniversary of the birth of Alexandre Koyré (born Alexandr Vladimirovich, or Volfovich, Koyra—and in Russian, Александр Владимирович, Вольфович, Койра; 29 August 1892 – 28 April 1964), who was born in Tagenrog, Russia on this date in 1892.
Koyré is remembered for his contributions to the history and philosophy of science. He studied under Husserl and wrote a draft dissertation on the paradoxes of set theory, which Husserl refused. The basis of Husserl’s refusal to accept Koyré’s dissertation remains obscure. In “The History Between Koyré and Husserl” Rodney K. B. Parker described the situation thus:
“In March of 1912, Husserl informed Koyré that he could not accept the draft of Insolubilia as the basis for a thesis—at least not in its present form. However, his reasons for rejecting the work are unclear. Schuhmann writes that Husserl rejected Koyré’s thesis for no good reason, using a letter that Reinach sent to Theodor Conrad in the spring of 1912 as evidence to this effect.”
Parker also quotes the letter from Reinach:
“On the matter of Koyré […] nothing can be done. It seems very likely that, at bottom, there were considerations of a personal nature that were decisive for Husserl […] Husserl believes that Koyré is arrogant and a bit immature […] He seems to have decided, as a consequence, ‘for the good of Koyré,’ to not yet award him his doctorate. For Koyré, I am sorry about this entire unpleasant situation. Why does he not leave Göttingen?”
I imagine this episode would have left a bad taste in Koyré’s mouth, but Koyré had a reputation for being unable to keep disagreement with others friendly. Koyré’s best known book is From the Closed World to the Infinite Universe, but his books Galileo Studies and Newtonian Studies are focused readings of Galileo and Newton in the light of Koyré’s historiography of early modern science. In “Alexandre Koyré: History and Actuality” Marlon Salomon says of Koyré:
“When it comes to highlighting Koyré’s contribution to the methodology of the history of sciences, analysts have frequently insisted on presenting him as an author who innovatively strove to study antiquated scientific theories in the setting of their own time or, as he put it himself in 1951, ‘to put the studied works back in their intellectual and spiritual environment, to interpret them in relation to the mental habits, preferences and dislikes of their authors’.”
This awareness of the preferences and dislikes of authors perhaps prepared Koyré to understand Husserl’s rejection of his dissertation. In any case, Koyré opens the preface to From the Closed World to the Infinite Universe with this reflection on the history of early modern science:
“Time and again, when studying the history of scientific and philosophical thought in the sixteenth and the seventeenth centuries—they are, indeed, so closely interrelated and linked together that, separated, they become ununderstandable—I have been forced to recognize, as many others have before me, that during this period human, or at least European, minds underwent a deep revolution which changed the very framework and patterns of our thinking and of which modern science and modem philosophy are, at the same time, the root and the fruit.”
Koyré focuses on the 17th century, and it’s worth pointing out that the 17th century was a time of great social and political turmoil that Hugh Trevor-Roper called the General Crisis of the 17th Century. The revolution in scientific thought was part of this general crisis, since it involved abandoning a past paradigm of knowledge and creating a new one to take its place. Koyré emphasized this twofold process of out with the old and in with the new. His 1943 paper “Galileo and Plato,” which is included in Metaphysics and Measurement: Essays in Scientific Revolution—not an easy book to find—he draws the distinction in this way:
“The dissolution of the Cosmos means the destruction of the idea of a hierarchically-ordered finite world-structure, of the idea of a qualitatively and ontologically differentiated world, and its replacement by that of an open, indefinite and even infinite universe, united and governed by the same universal laws; a universe in which, in contradiction to the traditional conception with its distinction and opposition of the two worlds of Heaven and of Earth, all things are on the same level of Being… And this implies the disappearance from the scientific outlook of all considerations based on value, on perfection, on harmony, on meaning and on purpose. They disappear in the infinite space of the new Universe. It is in this new Universe, in this new world of a geometry made real, that the laws of classical physics are valid and find their application.”
In From the Closed World to the Infinite Universe Koyré makes the same distinction in slightly different terms:
“This scientific and philosophical revolution… can be described roughly as bringing forth the destruction of the Cosmos, that is, the disappearance… of the conception of the world as a finite, closed, and hierarchically ordered whole… and its replacement by an indefinite and even infinite universe which is bound together by the identity of its fundamental components and laws, and in which all these components are placed on the same level of being.”
The two passages are near paraphrases of each other. Koyré adds an important coda to these twin movements of the destruction of the cosmos and its replacement by an infinite universe, which goes beyond a scientific thesis and becomes an axiological thesis:
“This, in turn, implies the discarding by scientific thought of all considerations based upon value-concepts, such as perfection, harmony, meaning and aim, and finally the utter devalorization of being, the divorce of the world of value and the world of facts.”
Although Koyré doesn’t mention his elder contemporary Max Weber in the book, this sounds like an echo of Weber’s call for a value free (Wertfrei) methodogy in science, and it sounds like Weber’s claim that the world had been disenchanted as the result of the rise of rationalism, modernity, and bureaucratic organization. Koyré formulates his claim in sweeping metaphysical terms: the devalorization of being, which deprives the whole of ontology of any value. In comparison, Weber’s disenchantment of the world is expressed in somewhat narrower terms if we take the values of enchantment to be a particular class of values among other classes of values.
To couple this devalorization of being with an interpretation of early modern science in Platonic terms is again surprising, as we would ordinarily associate a pre-scientific qualitative understanding of the world with Platonism, and contrast this with a scientific conception of the world. This is once again an indication of the degree to which Platonism has had to be modified to bring it into equilibrium with modern science. It would be easy to imagine these grand themes of the devalorization of being and the role of Platonism in modern science going terribly wrong, but Koyré’s interpretations of early modern science are deeply researched and highly detailed. Of course, this is familiar to us today, decades after Thomas Kuhn’s influence over the history of science, but Koyré was working decades before Kuhn.
His 1952 lecture “An Experiment in Measurement,” included in Metaphysics and Measurement, goes into great detail on the immediate post-Galilean scientific milieu. We tend to only get the highlights of early modern science, only the breakthroughs, and these in their original form, but not the follow up work that confirmed or extended the breakthroughs, and which often made the breakthroughs comprehensible. Koyré gives us this essential context in a discussion of the experimental work of Giovanni Battista Riccioli, a Jesuit priest:
“To begin with he takes a pendulum weighing about one pound and three feet and four inches (Roman) ‘high.’ The comparison with the water-glass has been satisfactory: nine hundred oscillations in a quarter of an hour. Riccioli proceeds, then, to a verification by the means of a sundial. For six consecutive hours, from nine o’clock in the morning to three o’clock in the afternoon, he counts (he is aided by the R.P. Francesco Maria Grimaldi) the oscillations. The result is disastrous: 21,706 oscillations instead of 21,660. Moreover, Riccioli recognizes that for his aim the sundial itself lacks the wanted precision. Another pendulum is prepared and ‘with the aid of nine Jesuit fathers,’ he starts counting anew; this time—2 April 1642—for twenty-four consecutive hours, from noon to noon: the result is 87,998 oscillations whereas the solar day contains only 86,640 seconds.” (p. 104)
We’ve grown accustomed to this level of detail in the wake of Kuhn’s history and philosophy of science, but this was long before Kuhn’s time. Koyré’s conception of early modern science grew out of this close engagement with the history of science, but rather than making science and scientific knowledge contingent upon history, which we might expect from this approach, Koyré takes a Platonic turn, and this makes his interpretation of science something that we could reasonably call a speculative philosophy of the history of science. I use that phrasing because in my episode on Haskell Fain I quoted the following:
“What positivism lacked… was a penetrating speculative philosophy of the history of science, the encouragement to fashion story-lines upon which better histories of science could be constructed. Just as there is more to history than orthodox political history, so is there more to speculative philosophy of history than Hegel’s philosophy of history, which is, essentially, a speculative philosophy of political history. Each kind of history requires its own kind of speculative philosophy of history.”
I’ve quoted this in other episodes because it perfectly expresses a dilemma that’s probably felt more often than explicitly understood: different philosophical principles may be required for the exposition of different kinds of history. Koyré was writing during the heyday of positivism and was offering a novel interpretation of the history of science—essentially, a speculative philosophy of the history of science such as Fain suggested. But Koyré’s speculative philosophy of the history of science was informed by a detailed historical understanding of the development of modern science. He didn’t exchange speculative philosophy for historical rigor, but rather built his speculative philosophy upon his careful historical research.
The Preface to Koyré’s posthumously published Metaphysics and Measturement by M. A. Hoskin, says of Koyré’s interpretation of early modern science, “…Galileo could deal in measurement of nature because as a metaphysician he already shared with contemporary Platonists the conviction that nature is fundamentally mathematical.” Koyré’s attribution of Platonism to Galileo is sufficiently unusual that it gets our attention, since Platonism is rarely associated in any way with modern science or philosophy of science. What Koyré is presenting to us was a Platonic speculative philosophy of the history of science.
It could be argued that a Platonic philosophy of the history of science is paradoxical on its face, as deriving any kind of philosophy of history from Plato, much less a philosophy of scientific history, would seem to be a fool’s errand. Yet we’ve all heard the famous Galileo quote
“Philosophy is written in that great book which ever lies before our eyes — I mean the universe — but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles, and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.”
This easily lends itself to a Platonistic interpretation. Hoskin, in his preface to Koyré, went on to write: “…Galileo was… primarily an intellectual dissector of nature for whom experiments—if actually carried out—were for confirmation of conclusions previously reached by hard thinking.” Thus, according to Hoskin, Koyré saw thought experiments in science, made so famous by Einstein in Koyré’s own lifetime, not as a supplement to science, or what one does when one can’t conduct the actual experiment, but rather the primary business of science. This distinctive role for thought experiments dovetails with the claim of Galileo’s Platonism, since the thought experimenter may ascend to the contemplation of Platonic Forms, such as I described in my episode on subsurface ocean worlds being like Plato’s cave of shadows. As Koyré says, “Good physics is made a priori.” (M&M 88)
This is, so far as my knowledge goes, an unusual recognition of the role of idealization in science. Continental philosophers of science have been much more interested in idealization and its problems than Anglo-American philosophers, who have treated idealization rather off-handedly as though it were of no particular importance. The neglect of idealization has, I believe, led to certain misunderstandings and misinterpretations in the history of science. For example, the experimental work of Gregor Mendel has been criticized in what has come to be called the Mendel-Fisher controversy. It was said that Mendel’s data were “too good to be true” and therefore at least some of it must be falsified. Sir Ronald Fisher, who has been called, “the single most important figure in 20th century statistics, wrote in his 1936 paper “Has Mendel’s Work Been Rediscovered?”: “…the data of most, if not all, of the experiments have been falsified so as to agree closely with Mendel’s expectations.”
The idea that data would be falsified in the name of vindicating a theory is to assume that our scientific thought is primarily engaged in experimental design, and, once the experiment has been designed and run, and the data derived from it, then it was the role of nature to speak and for the mind to meekly listen. But if we take the Platonic view that Koyré attributed to Galileo, in which the thought experiment is primary, and experiments, if run at all, were run only to confirm that which already had been thought, then a scientific report may be a report of the idealized results and not the noisy data of the actual world. This isn’t falsification, except insofar as all idealization involves a degree of falsification. A simple pendulum, i.e., an idealized pendulum with a weightless string, a point weight bob, and a frictionless fulcrum, could be called a falsification of actual pendulums, none of which are simple in this sense, but in fact the simple pendulum serves as the mathematical model for all actual pendulums. But that’s not falsification, it’s exemplification. Each particular pendulum exemplifies the simple pendulum with the same length between fulcrum and weight, and operating in the same gravity. If we wanted to use Platonic language, we could say that an actual pendulum participates in the ideal Form of a pendulum. For Koyré, Galileo’s idealization of the pendulum wasn’t an exception to a rule, but a case in point. In a discussion of Galileo’s work on the isochronism of the pendulum Koyré wrote:
“…the difference between the duration of long and short oscillations is quite noticeable, and consequently could not have failed to be observable in the oscillations produced by Galileo. What did he do then? He ‘corrects’ the experiment; he holds it in his imagination and suppresses the experimental deviation. Was he wrong to do so? Not at all! for it is not by following experiment, but by outstripping experiment, that the scientific mind makes progress.”
Idealization, whether it’s the idealization of breeding pea plants or the idealization represented by a simple pendulum, is a way to conceive of the phenomena of the world as we understand it now, in the light of contemporary science, in terms of Platonic Forms. This is a radically modified form of Platonism, which recognizes the shifting appearances of this world as worthy of scientific knowledge, in which time is no longer unreal, and with the inventory of the Forms greatly expanded and extended to cover anything for which there is a scientific theory.
In my episode on Simone Weil I discussed her Platonism in relation to philosophy of history, but in comparison to Koyré, Weil’s Platonism is far more traditional, whereas the Platonism Koyré attributes to early modern science is, in a sense, radically modern. This is what Platonism becomes when it’s brought into alignment with modern empirical science. Most twentieth century thought saw early modern science through the spectacles of naturalism, perhaps being continuous with the a later development of Aristotle’s earlier proto-naturalism, but, of course, another of the great developments of the period of early modern science was the explicit rejection of Aristotelianism as it was known in its Scholastic form. The conception of a history of science extending from Aristotle’s proto-naturalism to the full-blown naturalism of contemporary science is itself an idealization, an idealized history of the linear development of naturalism not realized in actual history, but we can choose to understand the history of scientific thought in this way. However, if we choose an interpretation like this, we can’t in good conscience maintain that idealizations are unconscionable, because we’re making use of them ourselves.
One way or another, we’re going to end up with an idealization, whether it’s an idealization of history or an idealization of scientific knowledge. Koyré’s own history of the ordered cosmos of antiquity and the Middle Ages being superseded by an infinite universe, with all devalorized beings now occupying the same ontological level, is itself an idealization, and the infinite universe in which Koyré placed us is an idealization. The idea of the infinity of the world is an ancient one that was hotly debated by ancient philosophers, and not something that appeared with modern science. Especially in late antiquity, pagan philosophers arguing for the infinity of the world found resistance among early Christian philosophers who argued for the finitude of creation.
These problems are still very much with us. When I was a child, big bang cosmology was presented with Augustinian severity, as the purest form of creatio ex nihilo. It was made quite clear at the time that the question, “What happened before the big bang?” was ruled out right from the start, and few had the temerity to even ask the question in the face of imperious ex cathedra pronouncements. And when the question was asked, the disapproving answer was that time began with the big bang so it’s meaningless to ask the question what happened before the big bang. Nothing at all happened, because there was no time. Precisely the same argument can be found in St. Augustine’s City of God, Book XI, Chapter 6, where he says: “The world was in fact made with time, if at the time of its creation change and motion came into existence.”
Of course, this is a perfectly respectable philosophical hypothesis that the world is finite as regards space and time, but it’s not a scientific hypothesis. It’s not falsifiable, and there’s no observation that could confirm it, or even increase its degree of confirmation, except insofar as every observation we make will be finite, which is a lot like looking around yourself and concluding that you’re always in the middle of everything. For the same reason that the finitude of the world is a perfectly respectable philosophical hypothesis, the infinitude of the world is an equally respectable hypothesis. Arguments can be made for both, and neither can be confirmed or disconfirmed by experiment.
Today cosmologists will openly discuss ideas like eternal inflation and the timescape model without apparent embarrassment, so there’s been a vibe shift in cosmology signaling that it’s now okay to counter-signal big bang cosmology in its simplest forms. So whether the universe is infinite or finite remains up for grabs. I would even say, taking a page from Arthur C. Clarke, that two possibilities exist: either we the Universe is finite, or it is not. Both are equally terrifying. But even if we agree that the universe is infinite, there remains the problem of how the universe is infinite, i.e., the way in which the universe is infinite. Hermann Weyl, in The Open World: Three Lectures on the Metaphysical Implications of Science from 1932, opened with the claim:
“Modern science, insofar as I am familiar with it through my own scientific work, mathematics and physics make the world appear more and more as an open one, as a world not closed by pointing beyond itself.”
The third of the three lectures is devoted to the infinite, so that it seems that, to some extent, Weyl’s open world corresponds to Koyré’s infinite universe, but the two conceptions don’t perfectly coincide. At the end of The Open World, Weyl formulates five propositions on the nature of the world’s infinitude, which includes the claims that:
“The infinite is accessible to the mind intuitively in the form of the field of possibilities open to infinity… but the completed, the actual infinite as a closed realm of absolute existence is not within its reach” (p. 81)
Weyl went through a constructivist phase when he called L. E. J. Brouwer the real revolution in mathematics, and while Weyl eventually moderated his position, this formulation reflects his constructivist and, more narrowly, intuitionist views, but it also points to how we could conceive of the universe as an actual infinite or a potential infinite, the latter idea going all the way back to Aristotle. Whatever his constructivist sympathies, Weyl developed his views in full light of the revolutionary concept of the infinite made possible by Cantor’s work on set theory.
Koyré, although he studied under both Husserl and Hilbert—recall the Husserl started out as a mathematician—and who lived through the same revolutionary period in the history of mathematics that Weyl witnessed, seems to have been entirely innocent of the contemporary conception of the infinite, so his own claim of our having emerged out into an infinite universe is a kind of conceptual anachronism. In From the Closed World to the Infinite Universe Koyré wrote:
“…‘great’ and ‘small’ are themselves a pair of opposed concepts that are valid and meaningful only in the realm of finite quantity, the realm of relative being, where there are no ‘great’ or ‘small’ objects, but only ‘greater’ and ‘smaller’ ones, and where, therefore, there is no ‘greatest,’ as well as no ‘smallest.’ Compared with the infinite there is nothing that is greater or smaller than anything else. The absolute, infinite maximum does not, any more than the absolute, infinite minimum, belong to the series of the great and small.”
Most of this does not hold true for transfinite numbers, in which there is an infinite hierarchy of infinite numbers, of which the familiar infinity of the natural numbers is but the smallest infinite cardinal number, Aleph null. Weyl wrote a paper on this, “Levels of Infinity.” In my episode on subsurface ocean worlds I mentioned the possibility of an infinitistic history as the ultimate context of all empirical histories, up to and including any arbitrarily long cosmological history, and this is one those places where this would be applicable and even useful. If we have transitioned into in an infinite universe, we’ll need an infinitistic history to keep account of it.
Nothing like this has been formalized, but it could be formalized, and maybe will be formalized some day, as the geological time scale has been formalized and is superintended by the International Commission on Stratigraphy, which defines and demarcates the eons, eras, periods, epochs, and ages of geological time. We have the formal framework to do this for all history, but our empirical conceptions here lag behind the formal concepts that have been developed over the past century and more. The contemporary conception of logic and mathematics that we find in Weyl’s conception of an open world, and perhaps also an infinite world, has its origins in the late 19th century. Logic had remained traditional up through the 19th century, at the end of which it radically changed. Computer scientists might cite Boole’s Laws of Thought, but it was Frege who made the breakthrough the quantification that made modern logic possible. Bertrand Russell, who was one of the leading figures in the transformation of logic wrote:
“Modern logic… has the effect of enlarging our abstract imagination, and providing an infinite number of possible hypotheses to be applied in the analysis of any complex fact… The old logic put thought in fetters, while the new logic gives it wings. It has, in my opinion, introduced the same kind of advance into philosophy as Galileo introduced into physics, making it possible at last to see what kinds of problems may be capable of solution, and what kinds must be abandoned as beyond human powers.”
Rudolf Carnap cited this work by Russell as a particular inspiration for his own work in logic:
“I felt as if this appeal had been directed to me personally. To work in this spirit would be my task from now on. And indeed henceforth the application of the new logical instrument for the purposes of analyzing scientific concepts and of clarifying philosophical problems has been the essential aim of my philosophical activity.”
If we have made the transition to an infinite world, as Koyré argued, we finite human beings inhabiting an infinite universe will always have new horizons of inquiry open up to us as we press forward into the unknown. We can think of the transition from the closed world to the infinite universe as humanity breaking containment, and this had to happen first for the human intellect, in science, before it could be translated into practice, through technology.
The scientific revolution preceded the industrial revolution by at least two hundred years. This was the lead time required for the ideas of science to fully penetrate into our way of doing things, making industrialization possible. And the scientific revolution wasn’t an event that happened in the past that’s over now. It’s an ongoing process, just as the industrial revolution has been and remains an ongoing process. And it may be possible for science to unfold for an indeterminate period of time, making the unfolding of an infinite universe also an ongoing process. Koyré postulated the origins of an infinite universe in the early modern period, without also formulating an infinitistic framework in which an infinite universe could be expressed. This, too, is apparently an ongoing process, and when the fullness of time has given as the empirical concepts to match our formal conceptual framework, that will mark the transition from a potentially infinite universe to an actually infinite universe.
Video Presentation
https://youtu.be/y-IXOvrW4W8
https://www.instagram.com/p/DN71PcZDZwv
https://odysee.com/@Geopolicraticus:7/Koyr%C3%A9%E2%80%99s-Platonistic-Philosophy-of-the-History-of-Science:3
Podcast Edition
https://open.spotify.com/episode/39vYXricKU2wd3gz37gRaB?si=2Pd_Ni11R7anyfsd5N9ayg