From the Closed World to the Infinite Universe (01-03)

26.04.2015 09:12

From the Closed World to the Infinite Universe


École Practique des Hautes Études, Sorbonne, Paris

Baltimore, Md.: The Johns Hopkins Press


Scanned, proofed and formatted at, January 2008, by John Bruno Hare. This text is in the public domain in the United States because it was not renewed in a timely fashion at the US Copyright Office as required by law at the time.

The Hideyo Noguchi Lectureship

In 1929 the late Dr. Emanuel Libman of New York gave $10,000 to The Johns Hopkins University for the establishment of a lectureship in the History of Medicine. In accordance with Dr. Libman's wishes it was named The Hideyo Noguchi Lectureship to pay tribute to the memory of the distinguished Japanese scientist.

The present volume owes its origin to the eleventh lecture on this foundation which was delivered on December 15, 1953, at The Johns Hopkins Institute of the History of Medicine by Professor Alexandre Koyré.




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 modern philosophy are, at the same time, the root and the fruit.

This revolution or, as it has been called, this "crisis of European consciousness," has been described and explained in many different ways. Thus, whereas it is generally admitted that the development of the new cosmology, which replaced the geo- or even anthropocentric world of Greek and medieval astronomy by the heliocentric, and, later, by the centerless universe of modern astronomy, played a paramount role in this process, some historians, interested chiefly in the social implications of spiritual changes, have stressed the alleged conversion of the human mind from theoria to praxis, from the scientia contemplativa to the scientia activa et operativa, which transformed man from a spectator into an owner and master of nature; some others have stressed the replacement of the teleological and organismic pattern of thinking and explanation by the mechanical and causal pattern, leading, ultimately, to the "mechanisation of the

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world-view" so prominent in modern times, especially in the eighteenth century: still others have simply described the despair and confusion brought by the "new philosophy" into a world from which all coherence was gone and in which the skies no longer announced the glory of God.

As for myself, I have endeavored in my Galilean Studies to define the structural patterns of the old and the new world-views and to determine the changes brought forth by the revolution of the seventeenth century. They seemed to me to be reducible to two fundamental and closely connected actions that I characterised as the destruction of the cosmos and the geometrization of space, that is the substitution for the conception o he world as a finite and well-ordered whole, in which the spatial structure embodied a hierarchy of perfection and value, that of an indefinite or even infinite universe no longer united by natural subordination, but unified only by the identity of its ultimate and basic components and laws; and the replacement of the Aristotelian conception of space—a differentiated set of innerworldly places—by that of Euclidean geometry—an essentially infinite and homogenous extension—from now on considered as identical with the real space of the world. The spiritual change that I describe did not occur, of course, in a sudden mutation. Revolutions, too, need time for their accomplishment; revolutions, too, have a history. Thus the heavenly spheres that encompassed the world and held it together did not disappear at once in a mighty explosion; the world-bubble grew and swelled before bursting and merging with the space that surrounded it.

The path which led from the closed world of the ancients to the open one of the moderns was, as a matter

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of fact, not very long: barely a hundred years separate the De revolutionibus orbium coelestium of Copernicus (1543) from the Principia philosophiae of Descartes (1644); barely forty years these Principiae from the Philosophia naturalis principia mathematica (1687). On the other hand, it was rather difficult, full of obstacles and dangerous road blocks. Or, to put it in simpler language, the problems involved in the infinitization of the universe are too deep, the implications of the solutions too far-reaching and too important to allow an unimpeded progress. Science, philosophy, even theology, are, all of them, legitimately interested in questions about the nature of space, structure of matter, patterns of action and, last but not least, about the nature, structure, and value of human thinking and of human science. Thus it is science, philosophy, and theology, represented as often as not by the very same men—Kepler and Newton, Descartes and Leibniz—that join and take part in the great debate that starts with Bruno and Kepler and ends—provisionally, to be sure—with Newton and Leibniz.

I did not deal with these problems in my Galilean Studies, where I had to describe only the steps that led to the great revolution and formed, so to speak, its prehistory. But in my lectures at The Johns Hopkins University—"The Origins of Modern Science," in 1951, and "Science and Philosophy in the Age of Newton," in 1952—in which I studied the history of this revolution itself, I had the opportunity to treat as they deserved the questions that were paramount in the minds of its great protagonists. It is this history that, under the title From the Closed World to the Infinite Universe, I have endeavored to tell in the Noguchi Lecture that I had the

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honour of giving in 1953; and it is the self-same story that, taking the history of cosmology, as Ariadne's thread I am retelling in this volume: it is, indeed, only an expanded version of my Noguchi Lecture.

I would like to express my gratitude to the Noguchi Committee for its kind permission to expand my lecture to its present dimensions, and to thank Mrs. Jean Jacquot, Mrs. Janet Koudelka, and Mrs. Willard King for assistance in preparing the manuscript.

I am also indebted to Abelard-Schuman, publishers, for the permission to quote Mrs. Dorothea Waley Singer's translation of Giordano Bruno's De l’infinito universo et mondi (New York, 1950).

Alexandre Koyré












The Sky and the Heavens,






The New Astronomy and the New Metaphysics,






The New Astronomy against the New Metaphysics,






Things Never Seen Before and Thoughts Never Thought: the Discovery of New Stars in the World Space and the Materialization of Space,






Indefinite Extension or Infinite Space,






God and Space, Spirit and Matter,






Absolute Space, Absolute Time and Their Relations to God,






The Divinization of Space,






God and the World: Space, Matter, Ether and Spirit,






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Absolute Space and Absolute Time: God's Frame of Action,






The Work-Day God and the God of the Sabbath,









The Divine Artifex and the Dieu Fainéant,









Figure 1. Typical pre-Copernican diagram of the universe, 7

Figure 2. Thomas Digges's diagram of the infinite Copernican universe, 37

Figure 3. The figure M of Kepler, 79


Figure 4. Galileo's star-picture of the shield and sword of Orion, 93



It is generally admitted that the seventeenth century underwent, and accomplished, a very radical spiritual revolution of which modern science is at the same time the root and the fruit.1 This revolution can be—and was—described in a number of different ways. Thus, for instance, some historians have seen its most characteristic feature in the secularization of consciousness, its turning away from transcendent goals to immanent aims, that is, in the replacement of the concern for the other world and the other life by preoccupation with this life and this world. Some others have seen it in the discovery, by man's consciousness, of its essential subjectivity and, therefore, in the substitution of the subjectivism of the moderns for the objectivism of mediaevals and ancients; still others, in the change of relationship between θεωρία and πράξις, the old ideal of the vita contemplativa yielding its place to that of the vita activa Whereas mediaeval and ancient man aimed at the pure contemplation of nature and of being, the modern one wants domination and mastery.

These characterizations are by no means false, and they certainly point out some rather important aspects of the spiritual revolution—or crisis—of the seventeenth century, aspects that are exemplified and revealed to us, for example, by Montaigne, by Bacon, by Descartes, or by the general spread of skepticism and free thinking.

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Yet, in my opinion they are concomitants and expressions of a deeper and more fundamental process as the result of which man—as it is sometimes said—lost his place in the world, or, more correctly perhaps, lost the very world in which he was living and about which he was thinking, and had to transform and replace not only his fundamental concepts and attributes, but even the very framework of his thought.

This scientific and philosophical revolution—it is indeed impossible to separate the philosophical from the purely scientific aspects of this process: they are interdependent and closely linked together—can be described roughly as bringing forth the destruction of the Cosmos, that is, the disappearance, from philosophically and scientifically valid concepts, of the conception of the world as a finite, closed, and hierarchically ordered whole (a whole in which the hierarchy of value determined the hierarchy and structure of being, rising from the dark, heavy and imperfect earth to the higher and higher perfection of the star and heavenly spheres),2 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. 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.

It is this aspect of the seventeenth century revolution, the story of the destruction of the Cosmos and the infinitization of the universe that I will attempt to present here, at least in its main line of development.3

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The full and complete history of this process would make, indeed, a long, involved and complicated story. It would have to deal with the history of the new astronomy in its shift from geocentrical to heliocentrical conceptions and in its technical development from Copernicus to Newton, and with that of the new physics in its consistent trend toward the mathematization of nature and its concomitant and convergent emphasis upon experiment and theory. It would have to treat the revival of old, and the birth of new, philosophical doctrines allied with, and opposed to, the new science and new cosmological outlook. It would have to give an account of the formation of the " corpuscular philosophy," that strange alliance of Democritus and Plato, and of the struggle between the "plenists" and the "vacuists" as well as that of the partisans and the foes of strict mechanism and attraction. It would have to discuss the views and the work of Bacon and Hobbes, Pascal and Gassendi, Tycho Brahe and Huygens, Boyle and Guericke, and of a great many others as well.

However, in spite of this tremendous number of elements, discoveries, theories and polemics that, in their interconnections, form the complex and moving background and sequel of the great revolution, the main line of the great debate, the main steps on the road which leads from the closed world to the infinite universe, stand out clearly in the works of a few great thinkers who, in deep understanding of its primary importance, have given their full attention to the fundamental problem of the structure of the world. It is with them, and their works, that we shall be concerned here, all the more so as they present themselves to us in the form of a closely connected discussion.



I. The Sky and the Heavens

Nicholas of Cusa & Marcellus Palingenius

The conception of the infinity of the universe, like everything else or nearly everything else, originates, of course, with the Greeks; and it is certain that the speculations of the Greek thinkers about the infinity of space and the multiplicity of worlds have played an important part in the history we shall be dealing with.4 It seems to me, however, impossible to reduce the history of the infinitization of the universe to the rediscovery of the world-view of the Greek atomists which became better known through the newly discovered Lucretius5 or the newly translated Diogenes Laertius.6 We must not forget that the infinitist conceptions of the Greek atomists were rejected by the main trend, or trends, of Greek philosophical and scientific thought—the Epicurean tradition was not a scientific one7—and that for this very reason, though never forgotten, they could not be accepted by the mediaevals.

We must not forget, moreover, that "influence" is not a simple, but on the contrary, a very complex, bilateral relation. We are not influenced by everything we read or learn. In one sense, and perhaps the deepest, we ourselves

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determine the influences we are submitting to; our intellectual ancestors are by no means given to, but are freely chosen by, us. At least to a large extent.

How could we explain otherwise that, in spite of their great popularity, neither Diogenes nor even Lucretius had, for more than a century, any influence on the fifteenth century's cosmological thinking? The first man to take Lucretian cosmology seriously was Giordano Bruno. Nicholas of Cusa—it is true that it is not certain whether at the time when he wrote his Learned Ignorance (1440) he knew the De rerum natura—does not seem to have paid much attention to it. Yet it was Nicholas of Cusa, the last great philosopher of the dying Middle Ages, who first rejected the mediaeval cosmos-conception and to whom, as often as not, is ascribed the merit, or the crime, of having asserted the infinity of the universe.

It is indeed in such a way that he was interpreted by Giordano Bruno, by Kepler and, last but not least, by Descartes, who in a well-known letter to his friend Chanut (Chanut reports some reflections of Christina of Sweden, who doubted whether, in the indefinitely extended universe of Descartes, man could still occupy the central position that, according to the teaching of religion, was given to him by God in the creation of the world) tells the latter that after all "the Cardinal of Cusa and several other Divines have supposed the world to be infinite, without ever being reproached by the Church; on the contrary, it is believed that to make His works appear very great is to honor God."8 The Cartesian interpretation of the teaching of Nicholas of Cusa is rather plausible as, indeed, Nicholas of Cusa denies the finitude of the world and its enclosure by the walls of the heavenly spheres. But he

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FIGURE 1<br> <i>Typical pre-Copernican diagram of the universe</i>
Click to enlarge

Typical pre-Copernican diagram of the universe

(from the 1539 edition of Peter Apian's Cosmographia)

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does not assert its positive infinity; as a matter of fact he avoids as carefully and as consistently as Descartes himself the attribution to the universe of the qualification "infinite," which he reserves for God, and for God alone. His universe is not infinite (infinitum) but "interminate" (interminatum), which means not only that it is boundless and is not terminated by an outside shell, but also that it is not "terminated" in its constituents, that is, that it utterly lacks precision and strict determination. It never reaches the "limit"; it is, in the full sense of the word, indetermined. It cannot, therefore, be the object of total and precise knowledge, but only that of a partial and conjectural one.9 It is the recognition of this necessarily partial—and relative—character of our knowledge, of the impossibility of building a univocal and objective representation of the universe, that constitutes—in one of its aspects—the docta ignorantia, the learned ignorance, advocated by Nicholas of Cusa as a means of transcending the limitations of our rational thought.

The world-conception of Nicholas of Cusa is not based upon a criticism of contemporary astronomical or cosmological theories, and does not lead, at least in his own thinking, to a revolution in science. Nicholas of Cusa, though it has often been so claimed, is not a forerunner of Nicholas Copernicus. And yet his conception is extremely interesting and, in some of its bold assertions—or negations—it goes far beyond anything that Copernicus ever dared to think of.10

The universe of Nicholas of Cusa is an expression or a development (explicatio), though, of course, necessarily imperfect and inadequate, of God—imperfect and inadequate because it displays in the realm of multiplicity and

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separation what in God is present in an indissoluble and intimate unity (complicatio), a unity which embraces not only the different, but even the opposite, qualities or determinations of being. In its turn, every singular thing in the universe represents it—the universe—and thus also God, in its own particular manner; each in a manner different from that of all others, by "contracting" (contractio) the wealth of the universe in accordance with its own unique individuality.

The metaphysical and epistemological conceptions of Nicholas of Cuss, his idea of the coincidence of the opposites in the absolute which transcends them, as well as the correlative concept of learned ignorance as the intellectual act that grasps this relationship which transcends discursive, rational thought, follow and develop the pattern of the mathematical paradoxes involved in the infinitization of certain relations valid for finite objects. Thus, for instance, nothing is more opposed in geometry than "straightness" and "curvilinearity"; and yet in the infinitely great circle the circumference coincides with the tangent, and in the infinitely small one, with the diameter. In both cases, moreover, the center loses its unique, determinate position; it coincides with the circumference; it is nowhere, or everywhere. But "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

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than the absolute, infinite minimum, belong to the series of the great and small. They are outside it, and therefore, as Nicholas of Cusa boldly concludes, they coincide.

Another example can be provided by kinematics. No two things, indeed, are more opposed than motion and rest. A body in motion is never in the same place; a body at rest is never outside it. And yet a body moving with infinite velocity along a circular path will always be in the place of its departure, and at the same time will always be elsewhere, a good proof that motion is a relative concept embracing the oppositions of "speedy" and "slow." Thus it follows that, just as in the sphere of purely geometrical quantity, there is no minimum and no maximum of motion, no slowest and no quickest, and that the absolute maximum of velocity (infinite speed) as well as its absolute minimum (infinite slowness or rest) are both outside it, and, as we have seen, coincide.

Nicholas of Cusa is well aware of the originality of his thought and even more so of the rather paradoxical and strange character of the conclusion to which he is led by learned ignorance.11


It is possible [he states] that those who will read things previously unheard of, and now established by Learned Ignorance, will be astonished.


Nicholas of Cusa cannot help it: it has, indeed, been established by learned ignorance12


. . . that the universe is triune; and that there is nothing that is not a unity of potentiality, actuality and connecting motion; that no one of these can subsist absolutely without the other; and that all these are in all [things] in different degrees, so different that in the universe no two [things]


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can be completely equal to each other in everything. Accordingly, if we consider the diverse motions of the [celestial] orbs, [we find that] it is impossible for the machine of the world to have any fixed and motionless center; be it this sensible earth, or the air, or fire or anything else. For there can be found no absolute minimum in motion, that is, no fixed center, because the minimum must necessarily coincide with the maximum]


[paragraph continues] Thus the centrum of the world coincides with the circumference and, as we shall see, it is not a physical, but a metaphysical "centrum," which does not belong to the world. This "centrum," which is the same as the "circumference," that is, beginning and end, foundation and limit, the "place" that "contains" it, is nothing other than the Absolute Being or God.

Indeed, pursues Nicholas of Cusa, curiously reversing a famous Aristotelian argument in favour of the limitation of the world:13


The world has no circumference, because if it had a center and a circumference, and thus had a beginning and end in itself, the world would be limited in respect to something else, and outside the world there would be something other, and space, things that are wholly lacking in truth. Since, therefore, it is impossible to enclose the world between a corporeal centrum and a circumference, it is [impossible for] our reason to have a full understanding of the world, as it implies the comprehension of God who is the center and the circumference of it.






. . . though the world is not infinite, yet it cannot be conceived as finite, since it has no limits between which it is confined. The earth, therefore, which cannot be the center,


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cannot be lacking in all motion; but it is necessary that it move in such a way that it could be moved infinitely less. Just as the earth is not the center of the world, so the sphere of the fixed stars is not its circumference, though if we compare the earth to the sky, the earth appears to be nearer to the center, and the sky to the circumference. The earth therefore is not the center, neither of the eighth nor of [any] other sphere, nor does the rising of the six signs [of the Zodiac] above the horizon imply that the earth is in the center of the eighth sphere. For even if it were somewhat distant from the center and outside the axis, which traverses the poles, so that in one part it would be elevated towards one pole, and in the other [part] depressed towards the other, nevertheless it is clear that, being at such a great distance from the poles and the horizon being just as vast, men would see only half of the sphere [and therefore believe themselves to be in its center].


Furthermore the very center of the world is no more inside the earth than outside it; for neither this earth, nor any other sphere, has a center; indeed, the center is a point equidistant from the circumference; but it is not possible that there be a true sphere or circumference such that a truer, and more precise one, could not be possible; a precise equidistance of divers [objects] cannot be found outside of God, for He alone is the infinite equality. Thus it is the blessed God who is the center of the world; He is the center of the earth and of all the spheres, and of all [the things] that are in the world, as He is at the same time the infinite circumference of all. Furthermore, there are in the sky no immovable, fixed poles, though the sky of the fixed stars appears by its motion to describe circles graduated in magnitude, lesser than the colures or than the equinoctials and also circles of an intermediate [magnitude]; yet, as a matter of fact, all the parts of the sky must move, though unequally


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in comparison with the circles described by the motion of the fixed stars. Thus, as certain stars appear to describe the maximal circle, so certain [others], the minimal, but there is no star that does not describe any. Therefore, as there is no fixed pole in the sphere, it is obvious that neither can there be found an exact mean, that is, a point equidistant from the poles. There is therefore no star in the eighth sphere which by [its] revolution would describe a maximal circle, because it would have to be equidistant from the poles which do not exist, and accordingly [the star] that would describe the minimal circle does not exist either. Thus the poles of the spheres coincide with the center and there is no other center than the pole, that is, the blessed God Himself.


The exact meaning of the conception developed by Nicholas of Cusa is not quite clear; the texts that I have quoted could be—and have been—interpreted in many different ways which I will not examine here. As for myself, I believe that we can understand it as expressing, and as stressing, the lack of precision and stability in the created world. Thus, there are no stars exactly on the poles, or on the equator of the celestial sphere. There is no fixed constant axis; the eighth, as well as all the other spheres, perform their revolutions around axes that continuously shift their positions. Moreover, these spheres are by no means exact, mathematical ("true") spheres, but only something which we should today call "spheroids"; accordingly, they have no center, in the precise meaning of this term. It follows therefore that neither the earth, nor anything else, can be placed in this center, which does not exist, and that thus nothing in this world can be completely and absolutely at rest.

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I do not believe we can go further than that and attribute to Nicholas of Cusa a purely relativistic conception of space, such as, for instance, Giordano Bruno imputes to him. Such a conception implies the denial of the very existence of celestial orbs and spheres, which we cannot ascribe to Nicholas of Cusa.

Yet, in spite of this retention of the spheres, there is a good deal of relativism in Nicholas of Cusa's world-view. Thus he continues:15


But we cannot discover motion unless it be by comparison with something fixed, that is [by referring it to] the poles or the centers and assuming them in our measurements of the motions [as being at rest]; it follows therefrom that we are always using conjectures, and err in the results [of our measurements]. And [if] we are surprised when we do not find the stars in the places where they should be according to the ancients, [it is] because we believe [wrongly] that they were right in their conceptions concerning the centers and poles as well as in their measurements.


It seems, then, that for Nicholas of Cusa the lack of agreement between the observations of the ancients and those of the moderns has to be explained by a change in the position of the axis (and poles), and, perhaps, by a shift in that of the stars themselves.

From all this, that is, from the fact that nothing in the world can be at rest, Nicholas of Cusa concludes:


. . . it is obvious that the earth moves. And because from the motion of the comets, of the air and of fire, we know by experience that the elements move, and [that] the moon [moves] less from the Orient to the Occident than Mercury or Venus, or the sun, and so on, it follows that the earth


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[paragraph continues] [considered as an element] moves less than all the others; yet [considered] as a star, it does not describe around the center or the pole a minimal circle, nor does the eighth sphere, or any other, describe the maximal, as has already been proved.


You have now to consider attentively what follows: just as the stars move around the conjectural poles of the eighth sphere, so also do the earth, the moon and the planets move in various ways and at [different] distances around a pole, which pole we have to conjecture as being [in the place] where you are accustomed to put the center. It follows therefrom that though the earth is, so to speak, the star which is nearer the central pole [than the others] it still moves, and yet does not describe in [its] motion the minimum circle, as has been shown supra. Moreover, neither the sun, nor the moon, nor any sphere—though to us it seems otherwise—can in [its] motion describe a true circle, because they do not move around a fixed base. Nowhere is there a true circle such that a truer one would not be possible, nor is [anything] ever at one time [exactly] as at another, neither does it move in a precisely equal [manner], nor does it describe an equally perfect circle, though we are not aware of it.


It is rather difficult to say precisely what kind of motion is ascribed to the earth by Nicholas of Cusa. In any case, it does not seem to be any of those that Copernicus was to attribute to it: it is neither the daily rotation around its axis, nor the annual revolution around the sun, but a kind of loose orbital gyration around a vaguely determined and constantly shifting center. This motion is of the same nature as that of all other celestial bodies, the sphere of the fixed stars included, though the slowest of

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them all, that of the sphere of the fixed stars being the quickest.

As for Nicholas of Cusa's assertions (quite unavoidable from his epistemological premises) that there is nowhere a precise circular orb or a precisely uniform motion, they must be interpreted as implying immediately (though he does not say it explicitly, it is clearly enough suggested by the context) that not only the factual content, but the very ideal of Greek and mediaeval astronomy, that is, the reduction of celestial motions to a system of interlocking uniform circular ones which would "save" the phenomena by revealing the permanent stability of the real behind the seeming irregularity of the apparent, is fallacious and must be abandoned.

Yet Nicholas of Cusa goes even further and, drawing the (penultimate) conclusion from the relativity of the perception of space (direction) and motion, he asserts that as the world-image of a given observer is determined by the place he occupies in the universe; and as none of these places can claim an absolutely privileged value (for instance, that of being the center of the universe), we have to admit the possible existence of different, equivalent world-images, the relative—in the full sense of the word—character of each of them, and the utter impossibility of forming an objectively valid representation of the universe.16


Consequently, if you want to have a better understanding of the motion of the universe, you must put together the center and the poles, with the aid of your imagination as far as you can; for if somebody were on the earth, under the arctic pole, and somebody else on the arctic pole, then just as to the man on the earth the pole will appear to be


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in the zenith, to the man on the pole it is the center that would appear to be in the zenith. And as the antipodes have, like ourselves, the sky above them, so to those who are in the poles (in both), the earth will appear to be in the zenith, and wherever the observer be he will believe himself to be in the center. Combine thus these diverse imaginations, making the center into the zenith and vice versa, and then, with the intellect, which alone can practise learned ignorance, you will see that the world and its motion cannot be represented by a figure, because it will appear almost as a wheel within a wheel, and a sphere within a sphere, having nowhere, as we have seen, either a center or a circumference.


The ancients [continues Nicholas of Cusa17] did not arrive at the things that we have brought forth, because they were deficient in learned ignorance. But for us it is clear that this earth really moves, though it does not appear to us to do so, because we do not apprehend motion except by a certain comparison with something fixed. Thus if a man in a boat, in the middle of a stream, did not know that the water was flowing and did not see the bank, how would he apprehend that the boat was moving?18 Accordingly, as it will always seem to the observer, whether he be on the earth, or on the sun or on another star, that he is in the quasi-motionless center and that all the other [things] are in motion, he will certainly determine the poles [of this motion] in relation to himself; and these poles will be different for the observer on the sun and for the one on the earth, and still different for those on the moon and Mars, and so on for the rest. Thus, the fabric of the world (machina mundi) will quasi have its center everywhere and its circumference nowhere, because the circumference and the center are God; Who is everywhere and nowhere.

It must be added that this earth is not spherical, as


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some have said, though it tends towards sphericity; indeed, the shape of the world is contrasted in its parts, as well as its motion; but when the infinite line is considered as contracted in such a way that, as contracted, it could not be more perfect or more spacious, then it is circular, and the corresponding corporeal figure [is the] spherical one. For all motion of the parts is towards the perfection of the whole; thus heavy bodies [move] towards the earth, and light ones [move] upward, earth towards earth, water towards water, fire towards fire; accordingly, the motion of the whole tends as far as it can towards the circular, and all shapes towards the spherical one, as we see in the parts of animals, in trees, and in the sky. But one motion is more circular and more perfect than another, and it is the same with shapes.


We cannot but admire the boldness and depth of Nicholas of Cusa's cosmological conceptions which culminate in the astonishing transference to the universe of the pseudo-Hermetic characterization of God: "a sphere of which the center is everywhere, and the circumference nowhere."19 But we must recognize also that, without going far beyond him, it is impossible to link them with astronomical science or to base upon them a "reformation of astronomy." This is probably why his conceptions were so utterly disregarded by his contemporaries, and even by his successors for more than a hundred years. No one, not even Lefèvre d’Etaples who edited his works, seems to have paid much attention to them,20 and it was only after Copernicus—who knew the works of Nicholas of Cusa, at least his treatise on the quadrature of the circle, but does not seem to have been influenced by him21—and even after Giordano Bruno, who drew his chief inspiration from him, that Nicholas of Cusa achieved fame as a forerunner

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of Copernicus, and even of Kepler, and could be quoted by Descartes as an advocate of the infinity of the world.

It is rather tempting to follow the example of these illustrious admirers of Nicholas of Cusa, and to read into him all kinds of anticipations of later discoveries, such, for instance, as the flattened form of the earth, the elliptic trajectories of the planets, the absolute relativity of space, the rotation of the heavenly bodies upon their axes.

Yet we must resist this temptation. As a matter of fact, Nicholas of Cusa does not assert anything of the kind. He does believe in the existence and also in the motion of heavenly spheres, that of the fixed stars being the quickest of all, as well as in the existence of a central region of the universe around which it moves as a whole, conferring this motion on all its parts. He does not assign a rotary motion to the planets, not even to this our earth. He does not assert the perfect uniformity of space. Moreover, in deep opposition to the fundamental inspiration of the founders of modern science and of the modern world-view, who, rightly or wrongly, tried to assert the panarchy of mathematics, he denies the very possibility of the mathematical treatment of nature.

We must now turn our attention to another aspect of the cosmology of Nicholas of Cusa, historically perhaps the most important: his rejection of the hierarchical structure of the universe, and, quite particularly, his denial—together with its central position—of the uniquely low and despicable position assigned to the earth by traditional cosmology. Alas, here too, his deep metaphysical intuition is marred by scientific conceptions that were not in advance of but rather behind his time, such as, for instance,

p. 20

the attribution to the moon, and even to the earth, of a light of their own.22


The shape of the earth is noble and spherical, and its motion is circular, though it could be more perfect. And since in the world there is no maximum in perfections, motions and figures (as is evident from what has already been said) it is not true that this earth is the vilest and lowest [of the bodies of the world], for though it seems to be more central in relation to the world, it is also, for the same reason, nearer to the pole. Neither is this earth a proportional, or aliquot part of the world, for as the world has neither maximum, nor minimum, neither has it a moiety, nor aliquot parts, any more than a man or an animal [has them]; for the hand is not an aliquot part of the man, though its weight seems to have a proportion to the body, just as it does to the dimension and the figure. Nor is the dark colour [of the earth] an argument for its baseness, because to an observer on the sun, it [the sun] would not appear as brilliant as it does to us; indeed, the body of the sun must have a certain more central part, a quasi earth, and a certain circumferential quasi-fiery lucidity, and in the middle a quasi-watery cloud and clear air, just as this earth has its elements.23 Thus someone outside the region of fire would see [the earth as] a brilliant star, just as to us, who are outside the region of the sun, the sun appears very luminous.


Having thus destroyed the very basis of the opposition of the "dark" earth and the "luminous" sun by establishing the similarity of their fundamental structure, Nicholas proclaims victoriously:24


The earth is a noble star, which has a light and a heat and an influence of its own, different from those of all other


p. 21


stars; every [star] indeed differs from every other in light, nature and influence; and thus every star communicates its light and influence to [every] other; not intentionally, for stars move and glitter only in order to exist in a more perfect manner: the participation arises as a consequence; just as light shines by its own nature, not in order that I may see it.


Indeed, in the infinitely rich and infinitely diversified and organically linked-together universe of Nicholas of Cusa, there is no center of perfection in respect to which the rest of the universe would play a subservient part; on the contrary, it is by being themselves, and asserting their own natures, that the various components of the universe contribute to the perfection of the whole. Thus the earth in its way is just as perfect as the sun, or the fixed stars. Accordingly, Nicholas of Cusa continues:25


It must not be said either that, because the earth is smaller than the sun, and receives an influence from it, it is also more vile; for the whole region of the earth, which extends to the circumference of the fire, is large. And though the earth is smaller than the sun, as is known to us from its shadow and the eclipses, still we do not know whether the region of the sun is greater or smaller than the region of the earth; however, they cannot be precisely equal, as no star can be equal to another. Nor is the earth the smallest star, for it is larger than the moon, as we are taught by the experience of the eclipses, and even, as some people say, larger than Mercury, and possibly than some other stars. Thus the argument from the dimension to the vileness is not conclusive.


Nor can it be argued that the earth is less perfect than the sun and the planets because it receives an influence

p. 22


from them: it is, as a matter of fact, quite possible that it influences them in its turn:26


It is clear therefore that it is not possible for human knowledge to determine whether the region of the earth is in a degree of greater perfection or baseness in relation to the regions of the other stars, of the sun, the moon and the rest.

Some of the arguments in favour of the relative perfection of the earth are rather curious. Thus, being convinced that the world is not only unlimited but also everywhere populated, Nicholas of Cusa tells us that no conclusion as to the imperfection of the earth can be drawn from the alleged imperfection of its inhabitants, a conclusion that nobody, as far as I know, ever made, at least not in his time. Be that as it may, in any case Nicholas of Cusa asserts that,27


. . . it cannot be said that this place of the world [is less perfect because it is] the dwelling-place of men, and animals, and vegetables that are less perfect than the inhabitants of the region of the sun and of the other stars. For although God is the center and the circumference of all the stellar regions, and although in every region inhabitants of diverse nobility of nature proceed from Him, in order that such vast regions of the skies and of the stars should not remain void, and that not only this earth be inhabited by lesser beings, still it does not seem that, according to the order of nature, there could be a more noble or more perfect nature than the intellectual nature which dwells here on this earth as in its region, even if there are in the other stars inhabitants belonging to another genus: man indeed does not desire another nature, but only the perfection of his own.


p. 23

But, of course, we have to admit that in the same genus there may be several different species which embody the same common nature in a more, or less, perfect way. Thus it seems to Nicholas of Cusa rather reasonable to conjecture that the inhabitants of the sun and the moon are placed higher on the scale of perfection than ourselves: they are more intellectual, more spiritual than we, less material, less burdened by flesh.

And, finally, the great argument from change and corruptibility to baseness is declared by Nicholas of Cusa as having no more value than the rest. For28 "since there is one universal world, and since all the particular stars influence each other in a certain proportion," there is no reason to suppose that change and decay occur only here, on the earth, and not everywhere in the universe. Nay, we have every reason to suppose—though of course we cannot know it—that it is everywhere the same, the more so as this corruption, which is presented to us as the particular feature of terrestrial being, is by no mean a real destruction, that is, total and absolute loss of existence. It is, indeed, loss of that particular form of existence.: But fundamentally it is not so much outright disappearance as dissolution, or resolution, of a being into its constitutive elements and their reunification into something else, a process that may take place—and probably does take place—in the whole universe just because the ontological structure of the world is, fundamentally, everywhere the same. Indeed it expresses everywhere in the same temporal, that is, mutable and changing, manner the immutable and eternal perfection of the Creator.

As we see, a new spirit, the spirit of the Renaissance breathes in the work of Cardinal Nicholas of Cusa. His

p. 24

world is no longer the medieval cosmos. But it is not yet, by any means, the infinite universe of the moderns.


The honor of having asserted the infinity of the universe has also been claimed by modern historians for a sixteenth century writer, Marcellus Stellatus Palingenius,29 author of a widely read and very popular book, Zodiacus vitae, which was published in Venice, in Latin, in 1534 (and translated into English in 1560); but, in my opinion, with even less reason than in the case of Nicholas of Cusa.

Palingenius, who is deeply influenced by the Neoplatonic revival of the fifteenth century and who therefore rejects the absolute authority of Aristotle, though, at other times, he quotes him with approval, may have had some knowledge of Nicholas of Cusa's world-view and have been encouraged by his example in denying the finitude of creation. Yet it is not certain, since, with the exception of the rather energetic assertion of the impossibility of imposing a limit on God's creative action, we do not find in his teaching any reference to the particular tenets of the cosmology of Nicholas of Cusa.

Thus, for instance, when in discussing the general structure of the universe he tells us30


But some have thought that every starre a worlde we may call,
The earth they count a darkened starre, whereas the least of all.


it is obvious that it is not Nicholas of Cusa, but the ancient Greek cosmologists that he has in mind. It is to be noted, moreover, that Palingenius does not share their views. His own are quite different. He does not make the earth

p. 25

a star. On the contrary he maintains consistently the opposition between the terrestrial and the celestial regions; and it is. just the imperfection of the former that leads him to the denial of its being the only populated place in the world.



                            . . . we see
The Seas and earth with sundry sorts, of creatures full to bee.
Shall then the heavens cleare be thought, as void and empty made
O rather void and empty mindes, that thus yourselves persuade.


It is clear that we cannot share the errors of these "empty mindes." It is clear, too, that32


. . . creatures doth the skies containe, and every Starre beside
Be heavenly townes and seates of Saints, where Kings and Commons bide
Not shapes and shadows vain of things (as we have present here)
But perfect Kings and people eke, all things are perfect there.


Yet Palingenius does not assert the infinity of the world. It is true that, applying consistently the principle to which Professor Lovejoy has given the name of principle of plenitude,33 he denies the finitude of God's creation, and says:34


A sorte there are that do suppose, the end of everything
Above the heavens to consist, and farther not to spring.
So that beyond them nothing is: and that above the skies p. 26
The Nature never powre to clime, but there amazed lies.
Which unto me appeareth false: and reason does me teach,
For if the ende of all be there, where skies no farther reach
Why hath not God created more? Because he had not skill
How more to make, his cunning staied and broken of his will?
Or for because he had not power? but truth both these denies,
For power of God hath never end, nor bounds his knowledge ties.
But in the State Diuine of God and Glorious maiestie
We must believe is nothing vaine since Godliest is the same:
This God what so ever he could doe assuredly did frame,
Least that his vertue were in vaine, and never should be hid.
But since he could make endlesse things, it never must be thought he did.


Nevertheless he maintains the finitude of the material world, enclosed and encompassed by the eight heavenly spheres:35


But learned Aristotle sayth there can no body bee,
But that it must of bondes consist: to this I do agree,
Because above the skies no kinde of body do we place,
But light most pure, of bodye voide, such light as doth deface
And farre excell our shining Sunne, such light as comprehend
Our eyes cannot, and endlesse light that God doth from him send.
Wherein together with their King the Sprites that are more hie
Doe dwell, the meaner sorte beneath the skies doe alwaies lie.
Therefore the reigne and position of the world consists in three, p. 27
Celestiall, Subcelestiall which with limits compast bee:
The Rest no boundes may comprehend which bright aboue the Skye
Doth shine with light most wonderfull. But here some will replye
That without body is no light, and so by this deny
That light can never there be found Above the Heavens by.


But Palingenius does not accept this theory which makes light dependent on matter and thus material itself. In any case, even if it were so for natural, physical light, it is certain that it .is not the case for God's supernatural one. Above the starry heavens there are no bodies. But light and immaterial being can well be—and are—present in the supernatural, boundless supracelestial region.

Thus it is God's heaven, not God's world, that Palingenius asserts to be infinite.



II. The New Astronomy and the New Metaphysics

N. Copernicus, Th. Digges, G. Bruno & W. Gilbert

Palingenius and Copernicus are practically contemporaries. Indeed, the Zodiacus vitae and the De revolutionibus orbium cœlestium must have been written at about the same time. Yet they have nothing, or nearly nothing, in common. They are as far away from each other as if they were separated by centuries.

As a matter of fact, they are, indeed, separated by centuries, by all those centuries during which Aristotelian cosmology and Ptolemaic astronomy dominated Western thought. Copernicus, of course, makes full use of the mathematical technics elaborated by Ptolemy—one of the greatest achievements of the human mind1—and yet, for his inspiration he goes back beyond him, and beyond Aristotle, to the golden age of Pythagoras and of Plato. He quotes Heraclides, Ecphantus and Hiketas, Philolaos and Aristarchus of Samos; and according to Rheticus, his pupil and mouthpiece, it is2


. . . following Plato and the Pythagoreans, the greatest


p. 29


mathematicians of that divine age, that [he] thought that in order to determine the cause of the phenomena, circular motions have to be ascribed to the spherical earth.


I need not insist on the overwhelming scientific and philosophical importance of Copernican astronomy, which, by removing the earth from the center of the world and placing it among the planets, undermined the very foundations of the traditional cosmic world-order with its hierarchical structure and qualitative opposition of the celestial realm of immutable being to the terrestrial or sublunar region of change and decay. Compared to the deep criticism of its metaphysical basis by Nicholas of Cusa, the Copernican revolution may appear rather half-hearted and not very radical. It was, on the other hand, much more effective, at least in the long run; for, as we know, the immediate effect of the Copernican revolution was to spread skepticism and bewilderment3 of which the famous verses of John Donne give such a striking, though somewhat belated, expression, telling us that the4


. . . new Philosophy calls all in doubt,
The Element of fire is quite put out;
The Sun is lost, and th’earth, and no mans wit
Can well direct him where to looke for it.
And freely men confesse that this world's spent,
When in the Planets, and the Firmament
They seeke so many new; then see that this
Is crumbled out againe to his Atomies.
’Tis all in peeces, all cohaerence gone;
All just supply, and all Relation.


To tell the truth, the world of Copernicus is by no means devoid of hierarchical features. Thus, if he asserts

p. 30

that it is not the skies which move, but the earth, it is not only because it seems irrational to move a tremendously big body instead of a relatively small one, "that which contains and locates and not that which is contained and located," but also because "the condition of being at rest is considered as nobler and more divine than that of change and inconsistency; the latter therefore, is more suited to the earth than to the universe."5 And it is on account of its supreme perfection and value—source of light and of life—that the place it occupies in the world is assigned to the sun; the central place which, following the Pythagorean tradition and thus reversing completely the Aristotelian and mediaeval scale, Copernicus believes to be the best and the most important one.6

Thus, though the Copernican world is no more hierarchically structured (at least not fully; it has, so to say, two poles of perfection, the sun and the sphere of the fixed stars, with the planets in between), it is still a well-ordered world. Moreover, it is still a finite one.

This finiteness of the Copernican world may appear illogical. Indeed, the only reason for assuming the existence of the sphere of the fixed stars being their common motion, the negation of that motion should lead immediately to the negation of the very existence of that sphere; moreover, since, in the Copernican world, the fixed stars must be exceedingly big7—the smallest being larger than the whole Orbis magnus—the sphere of the fixed stars must be rather thick; it seems only reasonable to extend its volume indefinitely "upwards."

It is rather natural to interpret Copernicus this way, that is, as an advocate of the infinity of the world, all the more so as he actually raises the question of the

p. 31

possibility of an indefinite spatial extension beyond the stellar sphere, though refusing to treat that problem as not scientific and turning it over to the philosophers. As a matter of fact, it is in this way that the Copernican doctrine was interpreted by Gianbattista Riccioli, by Huygens, and more recently by Mr. McColley.8

Though it seems reasonable and natural, I do not believe this interpretation to represent the actual views of Copernicus. Human thought, even that of the greatest geniuses, is never completely consequent and logical. We must not be astonished, therefore, that Copernicus, who believed in the existence of material planetary spheres because he needed them in order to explain the motion of the planets, believed also in that of a sphere of the fixed stars which he no longer needed. Moreover, though its existence did not explain anything, it still had some usefulness; the stellar sphere, which "embraced and contained everything and itself," held the world together and, besides, enabled Copernicus to assign a determined position to the sun.

In any case, Copernicus tells us quite clearly that9


. . . the universe is spherical; partly because this form, being a complete whole, needing no joints, is the most perfect of all; partly because it constitutes the most spacious form which is thus best suited to contain and retain all things; or also because all discrete parts of the world, I mean the sun, the moon and the planets, appear as spheres.


[paragraph continues] True, he rejects the Aristotelian doctrine according to which "outside the world there is no body, nor place, nor empty space, in fact that nothing at all exists" because

p. 32

it seems to him " really strange that something could be enclosed by nothing" and believes that, if we admitted that "the heavens were infinite and bounded only by their inner concavity," then we should have better reason to assert "that there is nothing outside the heavens, because everything, whatever its size, is within them,"10 in which case, of course, the heavens would have to be motionless: the infinite, indeed, cannot be moved or traversed.

Yet he never tells us that the visible world, the world of the fixed stars, is infinite, but only that it is immeasurable (immensum), that it is so large that not only the earth compared to the skies is "as a point" (this, by the way, had already been asserted by Ptolemy), but also the whole orb of the earth's annual circuit around the sun; and that we do not and cannot know the limit, the dimension of the world. Moreover, when dealing with the famous objection of Ptolemy according to which "the earth and all earthly things if set in rotation would be dissolved by the action of nature," that is, by the centrifugal forces produced by the very great speed of its revolution, Copernicus replies that this disruptive effect would be so much stronger upon the heavens as their motion is more rapid than that of the earth, and that, "if this argument were true, the extent of the heavens would become infinite." In which case, of course, they would have to stand still, which, though finite, they do.

Thus we have to admit that, even if outside the world there were not nothing but space and even matter, nevertheless the world of Copernicus would remain a finite one, encompassed by a material sphere or orb, the sphere of the fixed stars—a sphere that has a centrum, a centrum

p. 33

occupied by the sun. It seems to me that there is no other way of interpreting the teaching of Copernicus. Does he not tell us that11


. . . the first and the supreme of all [spheres] is the sphere of the fixed stars which contains everything and itself and which, therefore, is at rest. Indeed, it is the place of the world to which are referred the motion and the position of all other stars. Some [astronomers] indeed, have thought that, in a certain manner, this sphere is also subjected to change: but in our deduction of the terrestrial motion we have determined another cause why it appears so. [After the sphere of the fixed stars] comes Saturn, which performs its circuit in thirty years. After him, Jupiter, which moves in a duodecennial revolution. Then Mars which circumgirates in two years. The fourth place in this order is occupied by the annual revolution, which, as we have said, contains the Earth with the orb of the Moon as an epicycle. In the fifth place Venus revolves in nine months. Finally, the sixth place is held by Mercury, which goes around in the space of eighty days.


But in the center of all resides the Sun. Who, indeed, in this most magnificent temple would put the light in another, or in a better place than that one wherefrom it could at the same time illuminate the whole of it? Therefore it is not improperly that some people call it the lamp of the world, others its mind, others its ruler. Trismegistus [calls it] the visible God, Sophocles’ Electra, the All-Seeing. Thus, assuredly, as residing in the royal see the Sun governs the surrounding family of the stars.


We have to admit the evidence: the world of Copernicus is finite. Moreover, it seems to be psychologically quite normal that the man who took the first step, that of arresting the motion of the sphere of the fixed stars,

p. 34

hesitated before taking the second, that of dissolving it in boundless space; it was enough for one man to move the earth and to enlarge the world so as to make it immeasurable—immensum; to ask him to make it infinite is obviously asking too much.


Great importance has been attributed to the enlargement of the Copernican world as compared to the mediaeval one—its diameter is at least 2000 times greater. Yet, we must not forget, as Professor Lovejoy has already pointed out,12 that even the Aristotelian or Ptolemaic world was by no means that snug little thing that we see represented on the miniatures adorning the manuscripts of the Middle Ages and of which Sir Walter Raleigh gave us such an enchanting description.13 Though rather small by our astronomical standards, and even by those of Copernicus, it was in itself sufficiently big not to be felt as built to man's measure: about 20,000 terrestrial radii, such was the accepted figure, that is, about 125,000,000 miles.

Let us not forget, moreover, that, by comparison with the infinite, the world of Copernicus is by no means greater than that of mediaeval astronomy; they are both as nothing, because inter finitum et infinitum non est proportio. We do not approach the infinite universe by increasing the dimensions of our world. We may make it as large as we want: that does not bring us any nearer to it.14

Notwithstanding this, it remains clear that it is somewhat easier, psychologically if not logically, to pass from a very large, immeasurable and ever-growing world to an infinite one than to make this jump starting with a

p. 35

rather big, but still determinably limited sphere: the world-bubble has to swell before bursting. It is also clear that by his reform, or revolution, of astronomy Copernicus removed one of the most valid scientific objections against the infinity of the universe, based, precisely, upon the empirical, common-sense fact of the motion of the celestial spheres.

The infinite cannot be traversed, argued Aristotle; now the stars turn around, therefore . . . But the stars do not turn around; they stand still, therefore . . . It is thus not surprising that in a rather short time after Copernicus some bold minds made the step that Copernicus refused to make, and asserted that the celestial sphere, that is the sphere of the fixed stars of Copernican astronomy, does not exist, and that the starry heavens, in which the stars are placed at different distances from the earth, "extendeth itself infinitely up."

It has been commonly assumed until recent times that it was Giordano Bruno who, drawing on Lucretius and creatively misunderstanding both him and Nicholas of Cusa,15 first made this decisive step. Today, after the discovery by Professor Johnson and Dr. Larkey16—in 1934—of the Perfit Description of the Caelestiall Orbes according to the most aunciene doctrine of the Pythagoreans lately revived by Copernicus and by Geometricall Demonstrations approued, which Thomas Digges, in 1576, added to the Prognostication everlasting of his father Leonard Digges, this honor, at least partially, must be ascribed to him. Indeed, though different interpretations may be given of the text of Thomas Digges—and my own differs somewhat from that of Professor Johnson and Dr. Larkey—it is certain, in any case, that Thomas

p. 36

[paragraph continues] Digges was the first Copernican to replace his master's conception, that of a closed world, by that of an open one, and that in his Description, where he gives a fairly good, though rather free, translation of the cosmological part of the De revolutionibus orbium cœlestium, he makes some rather striking additions. First, in his description of the orb of Saturn he inserts the clause that this orb is "of all others next vnto that infinite Orbe immouable, garnished with lights innumerable"; then he substitutes for the well-known Copernican diagram of the world another one, in which the stars are placed on the whole page, above as well as below the line by which Copernicus represented the ultima sphaera mundi. The text that Thomas Digges adds to his diagram is very curious. In my opinion, it expresses the hesitation and the uncertainty of a mind—a very bold mind—which on the one hand not only accepted the Copernican world-view, but even went beyond it, and which, on the other hand, was still dominated by the religious conception—or image—of a heaven located in space. Thomas Digges begins by telling us that:


The orbe of the starres fixed infinitely up extendeth hit self in altitude sphericallye, and therefore immouable.


[paragraph continues] Yet he adds that this orbe is


the pallace of felicitye garnished with perpetuall shininge glorious lightes innumerable, farr excelling our sonne both in quantity and qualitye.


[paragraph continues] And that it is


the Court of the great God, the habitacle of the elect, and of the coelestiall angelles.


p. 37

FIGURE 2<br> <i>Thomas Digges's diagram of the infinite Copernican universe</i><br> (from <i>A Perfit Description of the Caelestiall Orbes</i>, 1576)
Click to enlarge

Thomas Digges's diagram of the infinite Copernican universe
(from A Perfit Description of the Caelestiall Orbes, 1576)

p. 38

The text accompanying the diagram develops this idea:18


Heerein can wee never sufficiently admire thys wonderfull and incomprehensible huge frame of goddes woorke proponed to our senses, seinge first the baull of ye earth wherein we moue, to the common sorte seemeth greate, and yet in respecte of the Moones Orbe is very small, but compared with the Orbis magnus wherein it is carried, it scarcely retayneth any sensible proportion, so merueillously is that Orbe of Annuall motion greater than this little darke starre wherein we liue. But that Orbis magnus beinge as is before declared but as a poynct in respect of the immensity of that immoueable heaven, we may easily consider what little portion of gods frame, our Elementare corruptible worlde is, but neuer sufficiently be able to admire the immensity of the Rest. Especially of that fixed Orbe garnished with lightes innumerable and reachinge vp in Sphaericall altitude without ende. Of which lightes Celestiall it is to bee thoughte that we only behoulde sutch as are in the inferioure partes of the same Orbe, and as they are hygher, so seeme they of lesse and lesser quantity, even tyll our syghte beinge not able farder to reache or conceyve, the greatest part rest by reason of their wonderfull distance inuisible vnto vs. And this may well be thought of vs to be the gloriouse court of ye great god, whose vnsercheable works inuisible we may partly by these his visible conjecture, to whose infinit power and maiesty such an infinit place surmountinge all other both in quantity and quality only is conueniente. But because the world hath so longe a time bin carried with an opinion of the earths stabilitye, as the contrary cannot but be nowe very imperswasible.


Thus, as we see, Thomas Digges puts his stars into a theological heaven; not into an astronomical sky. As a matter of fact, we are not very far from the conception

p. 39

of Palingenius—whom Digges knows and quotes—and, perhaps, nearer to him than to Copernicus. Palingenius, it is true, places his heaven above the stars, whereas Thomas Digges puts them into it. Yet he maintains the separation between our world—the world of the sun and the planets—and the heavenly sphere, the dwelling-place of God, the celestial angels, and the saints. Needless to say, there is no place for Paradise in the astronomical world of Copernicus.

That is the reason why, in spite of the very able defence of the priority rights of Digges made by Professor Johnson in his excellent book, Astronomical Thought in Renaissance England, I still believe that it was Bruno who, for the first time, presented to us the sketch, or the outline, of the cosmology that became dominant in the last two centuries, and I cannot but agree with Professor Lovejoy, who in his classical Great Chain of Being tells us that,19


Though the elements of the new cosmography had, then, found earlier expression in several quarters, it is Giordano Bruno who must be regarded as the principal representative of the doctrine of the decentralised, infinite and infinitely populous universe; for he not only preached it throughout western Europe with the fervour of an evangelist, but also first gave a thorough statement of the grounds on which it was to gain acceptance from the general public.


[paragraph continues] Indeed, never before has the essential infinitude of space been asserted in such an outright, definite and conscious manner.

Thus, already in the La Cena de le Ceneri,20 where, by the way, Bruno gives the best discussion, and refutation, of the classical—Aristotelian and Ptolemaic—objections

p. 40

against the motion of the earth that were ever written before Galileo,21 he proclaims that22 "the world is infinite and that, therefore, there is no body in it to which it would pertain simpliciter to be in the center, or on the center, or on the periphery, or between these two extremes" of the world (which, moreover, do not exist), but only to be among other bodies. As for the world which has its cause and its origin in an infinite cause and an infinite principle, it must be infinitely infinite according to its corporeal necessity and its mode of being. And Bruno adds:23


It is certain that . . . it will never be possible to find an even half-probable reason, why there should be a limit to this corporeal universe, and, consequently, why the stars, which are contained in its space, should be finite in number.


But we find the clearest, and most forceful, presentation of the new gospel of the unity and the infinity of the world in his vernacular dialogues De l’infinito universo e mondi and in his Latin poem De immenso et innumerabilibus.24


There is a single general space, a single vast immensity which we may freely call Void: in it are innumerable globes like this on which we live and grow; this space we declare to be infinite, since neither reason, convenience, sense-perception nor nature assign to it a limit. For there is no reason, nor defect of nature's gifts, either of active or passive power, to hinder the existence of other worlds throughout space, which is identical in natural character with our own space, that is everywhere filled with matter or at least ether.25


We have, of course, heard nearly similar things from

p. 41

[paragraph continues] Nicholas of Cusa. And yet we cannot but recognize the difference of accent. Where Nicholas of Cusa simply states the impossibility of assigning limits to the world, Giordano Bruno asserts, and rejoices in, its infinity: the superior determination and clarity of the pupil as compared to his master is striking.26


To a body of infinite size there can be ascribed neither center nor boundary. For he who speaketh of emptiness, the void or the infinite ether, ascribeth to it neither weight nor lightness, nor motion, nor upper, nor lower, nor intermediate regions; assuming moreover that there are in this space those countless bodies such as our earth and other earths, our sun and other suns, which all revolve within this infinite space, through finite and determined spaces or around their own centres. Thus we on the earth say that the earth is in the centre; and all the philosophers ancient and modern of whatever sect will proclaim without prejudice to their own principles that here is indeed the centre.




Just as we say that we are at the centre of that [universally] equidistant circle, which is the great horizon and the limit of our own encircling ethereal region, so doubtlessly the inhabitants of the moon believe themselves at the centre [of a great horizon] that embraces the earth, the sun and the other stars, and is the boundary of the radii of their own horizon. Thus the earth no more than any other world is at the centre; moreover, no points constitute determined celestial poles for our earth, just as she herself is not a definite and determined pole to any other point of the ether, or of the world-space; and the same is true of all other bodies. From various points of view these may all be regarded either as centres, or as points on the circumference, as poles, or zeniths and so forth.


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[paragraph continues] Thus the earth is not in the centre of the Universe; it is central only to our surrounding space.


Professor Lovejoy, in his treatment of Bruno, insists on the importance for the latter of the principle of plenitude, which governs his thought and dominates his metaphysics.27 Professor Lovejoy is perfectly right, of course: Bruno uses the principle of plenitude in an utterly ruthless manner, rejecting all the restrictions by which mediaeval thinkers tried to limit its applicability and boldly drawing from it all the consequences that it implies. Thus to the old and famous questio disputata: why did not God create an infinite world?—a question to which the mediaeval scholastics gave so good an answer, namely, denying the very possibility of an infinite creature—Bruno simply replies, and he is the first to do it: God did. And even: God could not do otherwise.

Indeed, Bruno's God, the somewhat misunderstood infinitas complicata of Nicholas of Cusa, could not but explicate and express himself in an infinite, infinitely rich, and infinitely extended world.28


Thus is the excellence of God magnified and the greatness of his kingdom made manifest; he is glorified not in one, but in countless suns; not in a single earth, but in a thousand, I say, in an infinity of worlds.


Thus not in vain the power of the intellect which ever seeketh, yea, and achieveth the addition of space to space, mass to mass, unity to unity, number to number, by the science that dischargeth us from the fetters of a most narrow kingdom and promoteth us to the freedom of a truly august realm, which freeth us from an imagined poverty and straineth to the possession of the myriad riches of so vast a space, of so worthy a field of so many cultivated


p. 43


worlds. This science does not permit that the arch of the horizon that our deluded vision imagineth over the Earth and that by our phantasy is feigned in the spacious ether, shall imprison our spirit under the custody of a Pluto or at the mercy of a Jove. We are spared the thought of so wealthy an owner and subsequently of so miserly, sordid and avaricious a donor.


It has often been pointed out—and rightly, of course—that the destruction of the cosmos, the loss, by the earth, of its central and thus unique (though by no means privileged) situation, led inevitably to the loss, by man, of his unique and privileged position in the theo-cosmic drama of the creation, of which man was, until then, both the central figure and the stake. At the end of the development we find the mute and terrifying world of Pascal's "libertin,"29 the senseless world of modern scientific philosophy. At the end we find nihilism and despair.

Yet this was not so in the beginning. The displacement of the earth from the centrum of the world was not felt to be a demotion. Quite the contrary: it is with satisfaction that Nicholas of Cusa asserts its promotion to the rank of the noble stars; and, as for Giordano Bruno, it is with a burning enthusiasm—that of a prisoner who sees the walls of his jail crumble—that he announces the bursting of the spheres that separated us from the wide open spaces and inexhaustible treasures of the ever-changing, eternal and infinite universe. Ever-changing! We are, once more, reminded of Nicholas of Cusa, and, once more, we have to state the difference of their fundamental world views—or world feelings. Nicholas of Cusa states that immutability can nowhere be found in the whole universe; Giordano Bruno goes far beyond this

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mere statement; for him motion and change are signs of perfection and not of a lack of it. An immutable universe would be a dead universe; a living one must be able to move and to change.30


There are no ends, boundaries, limits or walls which can defraud or deprive us of the infinite multitude of things. Therefore the earth and the ocean thereof are fecund; therefore the sun's blaze is everlasting, so that eternally fuel is provided for the voracious fires, and moisture replenishes the attenuated seas. For from infinity is born an ever fresh abundance of matter.


Thus Democritus and Epicurus, who maintained that everything throughout infinity suffereth renewal and restoration, understood these matters more truly than those who at all costs maintain a belief in the immutability of the Universe, alleging a constant and unchanging number of particles of identical material that perpetually undergo transformation, one into another.


The importance for Bruno's thought of the principle of plenitude cannot be overvalued. Yet there are in it two other features that seem to me to be of as great an importance as this principle. They are: (a) the use of a principle that a century later Leibniz—who certainly knew Bruno and was influenced by him—was to call the principle of sufficient reason, which supplements the principle of plenitude and, in due time, superseded it; and (b) the decisive shift (adumbrated indeed by Nicholas of Cusa) from sensual to intellectual cognition in its relation to thought (intellect). Thus, at the very beginning of his Dialogue on the Infinite Universe and the Worlds, Bruno (Philotheo) asserts that sense-perception, as such,

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is confused and erroneous and cannot be made the basis of scientific and philosophical knowledge. Later on he explains that whereas for sense-perception and imagination infinity is inaccessible and unrepresentable, for the intellect, on the contrary, it is its primary and most certain concept.31


Philotheo—No corporeal sense can perceive the infinite. None of our senses can be expected to furnish this conclusion; for the infinite cannot be the object of sense-perception; therefore he who demandeth to obtain this knowledge through the senses is like unto one who would desire to see with his eyes both substance and essence. And he who would deny the existence of a thing merely because it cannot be apprehended by the senses, nor is visible, would presently be led to the denial of his own substance and being. Wherefore there must be some measure in the demand for evidence from our sense-perception, for this we can accept only in regard to sensible objects, and even there it is not above all suspicion unless it cometh before the court aided by good judgment. It is the part of the intellect to judge yielding due weight to factors absent and separated by distance of time and by space intervals. And in this matter our sense-perception doth suffice us and doth yield us adequate testimony, since it is unable to gainsay us; moreover it advertiseth and confesseth its own feebleness and inadequacy by the impression it giveth us of a finite horizon, an impression moreover which is ever changing. Since then we have experience that sense-perception deceiveth us concerning the surface of this globe on which we live, much more should we hold suspect the impression it giveth us of a limit to the starry sphere.


Elpino—Of what use are the senses to us? tell me that.

Phil.—Solely to stimulate our reason, to accuse, to indicate,


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to testify in part . . . truth is in but a very small degree derived from the senses as from a frail origin, and doth by no means reside in the senses.


Elp.—Where then?

Phil.—In the sensible object as in a mirror; in reason, by process of argument and discussion. In the intellect, either through origin or by conclusion. In the mind, in its proper and vital form.


As for the principle of sufficient reason, Bruno applies it in his discussion of space and of the spatially extended universe. Bruno's space, the space of an infinite universe and at the same time the (somewhat misunderstood) infinite "void" of Lucretius, is perfectly homogeneous and similar to itself everywhere: indeed, how could the "void" space be anything but uniform—or vice versa, how could the uniform "void" be anything but unlimited and infinite? Accordingly, from Bruno's point of view, the Aristotelian conception of a closed innerworldly space is not only false, it is absurd.32


Philotheo—If the world is finite and if nothing is beyond, I ask you where is the world? Where is the universe? Aristotle replieth: it is in itself. The convex surface of the primal heaven is universal space, which being the primal container is by nought contained.


Fracastoro—The world then will be nowhere. Everything will be in nothing.

Phil.—If thou wilt excuse thyself by asserting that where nought is, and nothing existeth, there can be no question of position in space, nor of beyond, nor outside, yet I shall in no wise be satisfied. For these are mere words and excuses which cannot form part of our thought. For it is wholly impossible that in any sense or fantasy (even


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though there may be various senses and various fantasies), it is, I say, impossible that I can with any true meaning assert that there existeth such a surface, boundary or limit, beyond which is neither body, nor empty space, even though God be there.


We can pretend, as Aristotle does, that this world encloses all being, and that outside this world there is nothing; nec plenum nec vacuum. But nobody can think, or even imagine it. "Outside" the world will be space. And this space, just as ours, will not be "void"; it will be filled with "ether."

Bruno's criticism of Aristotle (like that of Nicholas of Cusa) is, of course, wrong. He does not understand him and substitutes a geometrical "space" for the place-continuum of the Greek philosopher. Thus he repeats the classical objection: what would happen if somebody stretched his hand through the surface of the heaven?33 And though he gives to this question a nearly correct answer (from the point of view of Aristotle),34


Burchio—Certainly I think that one must reply to this fellow that if a person would stretch out his hand beyond the convex sphere of heaven, the hand would occupy no position in space, nor any place, and in consequence would not exist.


he rejects it on the perfectly fallacious ground that this "inner surface," being a purely mathematical conception, cannot oppose a resistance to the motion of a real body. Furthermore, even if it did, the problem of what is beyond it would remain unanswered:35


Philotheo—Thus, let the surface be what it will, I must always put the question: what is beyond? If the reply


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is: nothing, then I call that the void, or empty-ness. And such a Void or Emptiness hath no measure nor outer limit, though it hath an inner; and this is harder to imagine than is an infinite or immense universe. For if we insist on a finite universe, we cannot escape the void. And let us now see whether there can be such a space, in which is nought. In this infinite space is placed our universe (whether by chance, by necessity or by providence I do not now consider). I ask now whether this space which indeed containeth the world is better fitted to do so than is another space beyond?


Fracastoro—It certainly appeareth to me not so. For where there is nothing there can be no differentiation; where there is no differentiation there is no destruction of quality and perhaps there is even less of quality where there is nought whatsoever.


Thus the space occupied by our world, and the space outside it, will be the same. And if they are the same, it is impossible that "outside" space should be treated by God in any different way from that which is "inside." We are therefore bound to admit that not only space, but also being in space is everywhere constituted in the same way, and that if in our part of the infinite space there is a world, a sun-star surrounded by planets, it is the same everywhere in the universe. Our world is not the universe, but only this machina, surrounded by an infinite number of other similar or analogous "worlds"—the worlds of star-suns scattered in the etheric ocean of the sky.36

Indeed, if it was, and is, possible for God to create a world in this our space, it is, and it was, just as possible for Him to create it elsewhere. But the uniformity of

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space—pure receptacle of being—deprives God of any reason to create it here, and not elsewhere. Accordingly, the limitation of God's creative action is unthinkable. In this case, the possibility implies actuality. The infinite world can be; therefore it must be; therefore it is.37


For just as it would be ill that this our space were not filled, that is our world were not to exist, then, since the spaces are indistinguishable, it would be no less ill if the whole of space were not filled. Thus we see that the universe is of indefinite size and the worlds therein without number.


[paragraph continues] Or, as the Aristotelian adversary of Bruno, Elpino, now converted to his views, formulates it:33


I declare that which I cannot deny, namely, that within infinite space either there may be an infinity of worlds similar to our own; or that this universe may have extended its capacity in order to contain many bodies such as those we name stars; or again that whether these worlds be similar or dissimilar to one another, it may with no less reason be well that one, than that another should exist. For the existence of one is no less reasonable than that of another; and the existence of many no less so than of one or of the other; and the existence of an infinity of them no less so than the existence of a large number. Wherefore, even as the abolition and non-existence of this world would be an evil, so would it be of innumerable others.


More concretely:39


Elp.—There are then innumerable suns, and an infinite number of earths revolve around these suns, just as the seven we can observe revolve around this sun which is close to us.


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Phil.—So it is.


Elp.—Why then do we not see the other bright bodies which are the earths circling around the bright bodies which are suns? For beyond these we can detect no motion whatsoever; and why do all the other mundane bodies appear always (except those known as comets) in the same order and at the same distance?


Elpino's question is rather good. And the answer given to it by Bruno is rather good, too, in spite of an optical error of believing that, in order to be seen, the planets must be formed on the pattern of spherical mirrors and possess a polished, smooth, "watery" surface, for which, moreover, he is not responsible as it was common belief until Galileo:40


Phil.—The reason is that we discern only the largest suns, immense bodies. But we do not discern the earths because, being much smaller they are invisible to us. Similarly, it is not impossible that other earths revolve around our sun and are invisible to us either on account of greater distance or smaller size, or because they have but little watery surface, or because such watery surface is not turned toward us and opposed to the sun, whereby it would be made visible as a crystal mirror which receiveth luminous rays; whence we perceive that it is not marvellous or contrary to nature that often we hear that the sun has been partially eclipsed though the moon hath not been interpolated between him and our sight. There may be innumerable watery luminous bodies—that is earths consisting in part of water circulating around the sun, besides those visible to us; but the difference in their orbits is indiscernible by us on account of their great distance, wherefore we perceive no difference in the very slow motion


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discernible of those visible above or beyond Saturn; still less doth there appear any order in the motion of all around the centre, whether we place our earth or our sun as that centre.


The question then arises whether the fixed stars of the heavens are really suns, and centers of worlds comparable to ours.41


Elp.—Therefore you consider that if the stars beyond Saturn are really motionless as they appear, then they are those innumerable suns or fires more or less visible to us around which travel their own neighbouring earths which are not discernible by us.


One would expect a positive answer. But for once Bruno is prudent:42


Phil.—Not so for I do not know whether all or whether the majority is without motion, or whether some circle around others, since none hath observed them. Moreover they are not easy to observe, for it is not easy to detect the motion and progress of a remote object, since at a great distance change of position cannot easily be detected, as happeneth when we would observe ships in a high sea. But however that may be, the universe being infinite, there must be ultimately other suns. For it is impossible that heat and light from one single body should be diffused throughout immensity, as was supposed by Epicurus if we may credit what others relate of him. Therefore it followeth that there must be innumerable suns, of which many appear to us as small bodies; but that star will appear smaller which is in fact much larger than that which appeareth much greater.


The infinity of the universe thus seems to be perfectly

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assured. But what about the old objection that the concept of infinity can be applied only to God, that is, to a purely spiritual, incorporeal Being, an objection which led Nicholas of Cusa—and later Descartes—to avoid calling their worlds "infinite," but only "interminate," or "indefinite"? Bruno replies that he does not deny, of course, the utter difference of the intensive and perfectly simple infinity of God from the extensive and multiple infinity of the world. Compared to God, the world is as a mere point, as a nothing.43


Phil.—We are then at one concerning the incorporeal infinite; but what preventeth the similar acceptability of the good, corporeal and infinite being? And why should not that infinite which is implicit in the utterly simple and indivisible Prime Origin rather become explicit in his own infinite and boundless image able to contain innumerable worlds, than become explicit within such narrow bounds? So that it appeareth indeed shameful to refuse to credit that this world which seemeth to us so vast may not in the divine regard appear a mere point, even a nullity?


Yet it is just that "nullity" of the world and of all the bodies that constitute it that implies its infinity. There is no reason for God to create one particular kind of beings in preference to another. The principle of sufficient reason reinforces the principle of plenitude. God's creation, in order to be perfect and worthy of the Creator, must therefore contain all that is possible, that is, innumerable individual beings, innumerable earths, innumerable stars and suns—thus we could say that God needs an infinite space in order to place in it this infinite world.

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To sum up:44


Phil.—This indeed is what I had to add; for, having pronounced that the Universe must itself be infinite because of the capacity and aptness of infinite space; on account also of the possibility and convenience of accepting the existence of innumerable worlds like to our own; it remaineth still to prove it. Now both from the circumstances of this efficient cause which must have produced the Universe such as it is, or rather, must ever produce it such as it is, and also from the conditions of our mode of understanding, we may easily argue that infinite space is similar to this which we see, rather than argue that it is that which we do not see either by example or by similitude, or by proportion, or indeed, by any effort of imagination which doth not finally destroy itself. Now to begin. Why should we, or could we imagine that divine power were otiose? Divine goodness can indeed be communicated to infinite things and can be infinitely diffused; why then should we wish to assert that it would choose to be scarce and to reduce itself to nought—for every finite thing is as nought in relation to the infinite? Why do you desire that centre of divinity which can (if one may so express it) extend indefinitely to an infinite sphere, why do you desire that it should remain grudgingly sterile rather than extend itself as a father, fecund, ornate and beautiful? Why should you prefer that it should be less, or indeed by no means communicated, rather than that it should fulfil the scheme of its glorious power and being? Why should infinite amplitude be frustrated, the possibility of an infinity of worlds be defrauded? Why should be prejudiced the excellency of the divine image which ought rather to glow in an unrestricted mirror, infinite, immense, according to the law of its being? . . . Why wouldst thou that God should in power, in act and in effect (which in him are


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identical) be determined as the limit of the convexity of a sphere rather than that he should be, as we may say, the undetermined limit of the boundless?


Let us not, adds Bruno, be embarrassed by the old objection that the infinite is neither accessible, nor understandable. It is the opposite that is true: the infinite is necessary, and is even the first thing that naturally cadit sub intellectus.


Giordano Bruno, I regret to say, is not a very good philosopher. The blending together of Lucretius and Nicholas of Cusa does not produce a very consistent mixture; and though, as I have already said, his treatment of the traditional objections against the motion of the earth is rather good, the best given to them before Galileo, he is a very poor scientist, he does not understand mathematics, and his conception of the celestial motions is rather strange. My sketch of his cosmology is, indeed, somewhat unilateral and not quite complete. As a matter of fact, Bruno's world-view is vitalistic, magical; his planets are animated beings that move freely through space of their own accord like those of Plato or of Pattrizzi. Bruno's is not a modern mind by any means. Yet his conception is so powerful and so prophetic, so reasonable and so poetic that we cannot but admire it and him. And it has—at least in its formal features—so deeply influenced modern science and modern philosophy, that we cannot but assign to Bruno a very important place in the history of the human mind.


I do not know whether Bruno had a great influence on his immediate contemporaries, or even whether he

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influenced them at all. Personally, I doubt it very much. He was, in his teaching, far ahead of his time.45 Thus his influence seems to me to have been a delayed one. It was only after the great telescopic discoveries of Galileo that it was accepted and became a factor, and an important one, of the seventeenth century world-view.

Kepler, as a matter of fact, links Bruno with Gilbert and seems to suggest that it was from the former that the great British scientist received his belief in the infinity of the universe.

This is, of course, quite possible: the thorough criticism of the Aristotelian cosmology may have impressed Gilbert. Yet it would be the only point where the teaching of the Italian philosopher was accepted by him. There is, indeed, not much similarity (besides the animism, common to both) between the "magnetic philosophy" of William Gilbert and the metaphysics of Giordano Bruno. Professor Johnson believes that Gilbert was influenced by Digges, and that, having asserted the indefinite extension of the world "of which the limit is not known, and cannot be known," Gilbert, "to enforce his point, adopted without qualification Digges' idea that the stars were infinite in number, and located at varying and infinite distances from the center of the Universe."46

This is quite possible, too. Yet, if he adopted this idea of Digges, he completely rejected his predecessor's immersion of the celestial bodies into the theological heavens: he has nothing to tell us about the angels and the saints.

On the other hand, neither Bruno nor Digges succeeded in persuading Gilbert to accept, in its entirety, the astronomical theory of Copernicus of which he seems to have admitted only the least important part, that is, the diurnal

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motion of the earth, and not the much more important annual one. Gilbert, it is true, does not reject this latter: he simply ignores it, whereas he devotes a number of very eloquent pages to the defence and explanation (on the basis of his magnetic philosophy) of the daily rotation of the earth on its axis and to the refutation of the Aristotelian and Ptolemaic conception of the motion of the celestial sphere, and also to the denial of its very existence.

As to this latter point, we must not forget, however, that the solid orbs of classical—and Copernican—astronomy had, in the meantime, been "destroyed" by Tycho Brahe. Gilbert, therefore, in contradistinction to Copernicus himself, can so much more easily dispense with the perfectly useless sphere of the fixed stars, as he does not have to admit the existence of the potentially useful planetary ones. Thus he tells us:


But in the first place, it is not likely that the highest heaven and all these visible splendours of the fixed stars are impelled along that most rapid and useless course. Besides, who is the Master who has ever made out that the stars which we call fixed are in one and the same sphere, or has established by any reasoning that there are any real, and, as it were, adamantine spheres? No one has ever proved this as a fact; nor is there a doubt but that just as the planets are at unequal distances from the earth, so are those vast and multitudinous lights separated from the earth by varying and very remote altitudes; they are not set in any sphaerick frame of firmament (as is feigned), nor in any vaulted body; accordingly the intervals of some are, from their unfathomable distance, matter of opinion rather than of verification; others do much exceed them and


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are very far remote, and these being located in the heaven at varying distances, either in the thinnest aether, or in that most subtle quintessence, or in the void; how are they to remain in their position during such a mighty swirl of the vast orbe of such uncertain substance . . .


Astronomers have observed 1022 stars; besides these innumerable other stars appear minute to our senses; as regards still others, our sight grows dim, and they are hardly discernible save by the keenest eye; nor is there any possessing the best power of vision that will not, while the moon is below the horizon and the atmosphere is clear, feel that there are many more, indeterminable and vacillating by reason of their faint light, obscured because of the distance.

How immeasurable then must be the space which stretches to those remotest of the fixed stars! How vast and immense the depth of that imaginary sphere! How far removed from the earth must the most widely separated stars be and at a distance transcending all sight, all skill and thought! How monstrous then such a motion would be!

It is evident then that all the heavenly bodies, set as if in a destined place, are there formed unto spheres, that they tend to their own centres and that round them there is a confluence of all their parts. And if they have motion that motion will rather be that of each round its own centre, as that of the earth is, or a forward movement of the centre in an orbit as that of the Moon.

But there can be no movement of infinity and of an infinite body, and therefore no diurnal revolution of the Primum Mobile.47



III. The New Astronomy Against the New Metaphysics

Johannes Kepler's Rejection of Infinity

The conception of the infinity of the universe is, of course, a purely metaphysical doctrine that may well—as it did—form the basis of empirical science; it can never be based on empiricism. This was very well understood by Kepler who rejects it therefore—and this is very interesting and instructive—not only for metaphysical, but also for purely scientific reasons; who even, in anticipation of some present-day epistemologies, declares it scientifically meaningless.1

As for the metaphysical reasons for which Kepler denies the infinity of the universe, they are derived chiefly from his religious beliefs. Indeed, Kepler, a devout though somewhat heretical Christian, sees in the world an expression of God, symbolizing the Trinity2 and embodying in its structure a mathematical order and harmony. Order and harmony that cannot be found in the infinite and therefore perfectly formless—or uniform—universe of Bruno.

Yet it is not this conception of God's creative action,

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but a conception of astronomical science, as based upon, and limited by, the phenomena that Kepler opposes to Bruno and to those who share his views. Thus, discussing the interpretation to be given to the appearance of a new star in the foot of the Serpentarius, Kepler raises the question whether this amazing and striking phenomenon does not imply the infinity of the universe. He does not think so, yet he knows, and tells us that,3


. . . there is a sect of philosophers, who (to quote the judgment of Aristotle, unmerited however, about the doctrine of the Pythagoreans lately revived by Copernicus) do not start their ratiocinations with sense-perception or accommodate the causes of the things to experience: but who immediately and as if inspired (by some kind of enthusiasm) conceive and develop in their heads a certain opinion about the constitution of the world; once they have embraced it, they stick to it; and they drag in by the hair [things] which occur and are experienced every day in order to accommodate them to their axioms. These people want this new star and all others of its kind to descend little by little from the depths of nature, which, they assert, extend to an infinite altitude, until according to the laws of optics it becomes very large and attracts the eyes of men; then it goes back to an infinite altitude and every day [becomes] so much smaller as it moves higher.


Those who hold this opinion consider that the nature of the skies conforms to the law of the circle; therefore the descent is bound to engender the opposite ascent, as is the case with wheels.

But they can easily be refuted; they indulge indeed in their vision, born within them, with eyes closed, and their ideas and opinions are not received by them [from valid experience] but produced by themselves.


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This general criticism may be sufficient. Yet Kepler does not content himself with it and continues:4


We shall show them that by admitting the infinity of the fixed stars they become involved in inextricable labyrinths.


Furthermore we shall, if possible, take this immensity away from them: then, indeed, the assertion will fall of itself.


Kepler knows quite well that this particular opinion concerning the infinity of the world goes back to the ancient heathen philosophers, criticized—rightly, according to him—by Aristotle.5


This particular school of the ancient heathen philosophers is chiefly refuted by the argument by which Aristotle demonstrated the finitude of the world from motion.


As for the moderns, he tells us that the infinity of the world6


. . . was defended by the unfortunate Jord. Bruno. It was also asserted in a by no means obscure way, though he expressed himself as if he doubted it, by William Gilbert in the otherwise most admirable book De magnete. Gilbert's religious feeling was so strong that, according to him, the infinite power of God could be understood in no other way than by attributing to Him the creation of an infinite world. But Bruno made the world so infinite that [he posits] as many worlds as there are fixed stars. And he made this our region of the movable [planets] one of the innumerable worlds scarcely distinct from the others which surround it; so that to somebody on the Dog Star (as, for instance, one of the Cynocephals of Lucian) the world would appear from there just as the fixed stars appear to us from our world. Thus according to them, the new star was a new world.


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Neither Bruno's enthusiasm for the infinity of the universe, nor even Gilbert's desire to enhance God's infinite power, is shared by Kepler. Quite the contrary, he feels that7


This very cogitation carries with it I don't know what secret, hidden horror; indeed one finds oneself wandering in this immensity, to which are denied limits and center and therefore also all determinate places.


[paragraph continues] From the purely religious point of view, it would be sufficient, perhaps, to make an appeal to the authority of Moses. Yet the question we are discussing is not a dogmatic one; it has to be dealt with not by recourse to revelation, but by scientific reasoning,5


But because this sect misuses the authority of Copernicus as well as that of astronomy in general, which prove—particularly the Copernican one—that the fixed stars are at an incredible altitude: well then we will seek the remedy in astronomy itself.


[paragraph continues] Thus by the same means which seem to those philosophers to enable them to break out of the limits of the world into the immensity of infinite space, we will bring them back. "It is not good for the wanderer to stray in that infinity."

Kepler's refutation of the infinitist conception of the universe may appear to the modern reader unconvincing and even illogical. Yet, as a matter of fact, it is a perfectly consistent and very well-reasoned argument. It is based on two premises, which, by the way, Kepler shared with his opponents. The first one is a direct consequence of the principle of sufficient reason and consists in admitting

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that, if the world has no limits and no particular, determined, structure, that is, if the world-space is infinite and uniform, then the distribution of the fixed stars in this universe must be uniform, too.9 The second premise concerns the science of astronomy as such. It postulates its empirical character; it tells us that astronomy, as such, has to deal with observable data, that is, with the appearances (φαινόμενα); that it has to adapt its hypotheses—for instance, the hypotheses concerning the celestial motions—to these appearances, and that it has no right to transcend them by positing the existence of things that are either incompatible with them, or, even worse, of things that do not and cannot "appear." Now these "appearances"—we must not forget that Kepler is writing in 1606, that is, before the enlargement of the observable data by the discovery and the use of the telescope—are the aspects of the world that we see. Astronomy therefore is closely related to sight, that is, to optics. It cannot admit things that contradict optical laws.

Let us now turn back to Kepler:10


To begin with, it can most certainly be learnt from astronomy that the region of the fixed stars is limited downwards; . . . moreover it is not true . . . that this inferior world with its sun differs in no way in its aspect from any one of the fixed stars; that is, [that there is no difference] of one region or place from another.


For, be it admitted as a principle that the fixed stars extend themselves in infinitum. Nevertheless it is a fact that in their innermost bosom there will be an immense cavity, distinct and different in its proportions from the spaces that are between the fixed stars. So that if it occurred


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to somebody to examine only this cavity, even [if he were] ignorant of the eight small bodies which fly around the centrum of this space at a very small distance from it, and did not know what they are, or how many; nevertheless from the sole comparison of this void with the surrounding spherical region, fitted with stars, he certainly would be obliged to conclude that this is a certain particular place and the main cavity of the world. Indeed, let us take, for instance, three stars of the second magnitude in the belt of Orion, distant from each other by 81´, being, each one, of at least 2 minutes in diameter. Thus, if they were placed on the same spherical surface of which we are the center, the eye located on one of them would see the other as having the angular magnitude of about 2¾°; [a magnitude] that for us on the earth would not be occupied by five suns placed in line and touching each other. And yet these fixed stars are by no means those that are the nearest to each other; for there are innumerable smaller ones that are interspersed [between them]. Thus if somebody were placed in this belt of Orion, having our sun and the center of the world above him, he would see, first, on the horizon, a kind of unbroken sea of immense stars quasi-touching each other, at least to the sight; and from there, the more he raised his eyes, the fewer stars would he see; moreover, the stars will no longer be in contact, but will gradually [appear to be] more rare and more dispersed; and looking straight upward he will see the same [stars] as we see, but twice as small and twice as near to each other.


Kepler's reasoning is, of course, erroneous. But only because the data available to him are faulty. In itself it is quite correct. Indeed, if we assume that the fixed stars, or at least the equally bright ones, are at an approximately equal distance from us, if we assume, moreover,

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that their visible diameter corresponds to their real one, we are bound to admit that the two big stars in the belt of Orion, separated by the angular distance of 81´, will be seen from each other as covering more surface of the sky than five suns put together; the same will be the case for a great number of the other fixed stars, and therefore the visible aspect of the sky will be, for the observer placed on the fixed stars, quite different from its aspect for us. This implies, of course, a variation in the pattern of the real distribution of the fixed stars in space, that is, the negation of the homogeneity and the uniformity of the universe. Once more, let us not forget that Kepler wrote before the invention of the telescope and did not—and even could not—know that the visible diameter of the fixed stars is a pure optical illusion that gives us no information about their size and distance. Not knowing it, he was entitled to conclude:11


For us the fact of the sky is quite different. Indeed we see everywhere stars of different magnitude, and [we see them] also equally distributed everywhere. Thus around Orion and the Twins we see many of them big and closely packed together: the eye of the Bull, the Capella, the heads of the Twins, the Dog, the shoulders, the belt and the foot of Orion. And in the opposite part of the sky there are equally large ones: the Lyre, the Eagle, the heart and the brow of the Scorpion, the Serpentarius, the arms of the Balance; and before them Arcturus; the head of the Virgin; also after them the last star of the Water Bearer and so on.


I have just pointed out that Kepler's discussion of the astronomical data that enabled him to assert the particular, unique structure of our site in the world-space was based on the assumption of the equidistance—from us

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—of the fixed stars. Couldn't this conclusion be avoided if we admitted that the stars are so far away from us—and therefore from each other—that, seen from each other, they will not appear as big as we have calculated? Or couldn't we go even farther and admit that our fundamental assumption could, possibly, be incorrect and that stars which appear to be near each other could, in point of fact, be separated by an enormous distance, the one being near us and the other exceedingly far away? As we shall see, even if it were so, it would not change the fundamental fact of the singularity of our world-space. But the objection has to be dealt with. Kepler, therefore, proceeds:12


When, some time ago, I advanced these views [just developed] some people, to try me, vigorously defended the cause of infinity, which they had taken from the above-mentioned philosophers. They asserted that, granting infinity, it was easy for them to separate the pairs of fixed stars (which we on the earth perceive as being very near each other) by as great a distance as that which separates us from them. Yet this is impossible. Even admitting that you can arbitrarily elevate13 the double fixed stars [that are] equally distant from the center of the world, it must be remembered that, if we elevate the fixed stars, the void which is in the middle, and also the circular envelope of the fixed stars, increase at the same time. Indeed, [these people] assume thoughtlessly that, the fixed stars being elevated, the void will remain the same.


[paragraph continues] As it will not, the singular character of our site will be maintained.14


But what, they say, if, of the two stars of the belt of Orion, we assume one to remain in its sphere, because the


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theory of parallaxes does not admit an inferior position,15 and the other to be higher by an infinite distance? Shall we not, in this way, obtain that, seen from each other, they appear as small as they appear to us? and that there will be a distance between them, void of stars, equal to the distances between us and them?


I answer that, perhaps, one could use this method if there were only two stars, or only a few of them, and if they were not dispersed and disseminated in a circle. Indeed, you either alternately remove the stars to a greater distance and let them stay where they are or [you remove them] all together. If alternately, you do not solve the problem, though you decrease somewhat the difficulty. For, concerning those that will remain near, the affirmation [made by us] will still be just as valid. The pairs of stars will be nearer to each other than to the sun, and their diameters, as seen from each other, larger [than they are as seen by us]. But those that are removed higher will, of course, be more distant [from each other], yet nevertheless they will be comparatively large [as seen from each other]. And I would even easily concede, without endangering my cause, that all the fixed stars are of the same magnitude; and that those which to us appear large are near to us, and those [which appear small] are so much farther. As sings Manilius:15a 'Not because less bright, but because they are removed to a greater altitude.'

I say: I will concede not: I will assert. For it is just as easy to believe that [the stars] differ really in brightness, in color and also in magnitude. And it is possible that both [opinions] are true, as is the case with the planets, of . which some are really larger than others, whereas some others only appear to be larger though in themselves they are smaller, namely because they are nearer to us.


[paragraph continues] The consequences of these hypotheses will be seen later.

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[paragraph continues] For the moment we have to discuss the implications for the φαινόμενα of a really uniform distribution of the fixed stars in the world-space, that is, of a distribution according to which they would be separated from each other by equal distances, namely by the same distance that separates them from us.16


But let us pass to the other member [of the argument], and say what would result if all the stars were separated from each other by the same distance, in such a way that the nearest ones would retain the propinquity which astronomy imposes as a limit to all [stars], not allowing any one to be nearer, and all the others would be elevated in respect to it, and removed to an altitude equal to the distance of the nearest one to us.


As a matter of fact nothing will result from all this. It will never be the case that the [starry heavens] would appear to those whom we may imagine observing them from these stars as they appear to us. From which it follows that this place, in which we are, will always have a certain peculiarity that cannot be attributed to any other place in all this infinity.


Once more, in order to understand Kepler's reasoning, we have to remember that we are not discussing the abstract possibility of a certain distribution of stars in the world-space, but the concrete distribution of stars corresponding to the appearance of the sky; that is, we are dealing with the distribution of visible stars, of those that we actually see. It is their distance from us that is in question, and it is for them that the possibility of a uniform distribution, which would place most of them at very great, and regularly increasing, distances from us, is denied.17

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For, if the state of affairs were such as has been said, it is certain that those stars that are two, three, a hundred times higher will also be two, three, a hundred times larger. Indeed, let a star be as elevated as you wish, you will never obtain that it would be seen by us as having a diameter of two minutes.18 Thus the diameter will always be two thousandth, one thousandth, or so of the distance from us; but this diameter will be a much larger part of the mutual distances between two fixed stars (since these distances are much smaller than their distance from us). And though from a star near us the face of the sky will appear nearly the same as it does to us; yet from the other stars the aspect of the world will be different, and all the more different in that they are farther. Indeed, if the intervals of the pairs of stars (which to us appear as nearest each other) remain constant, their aspects [dimensions], as seen from each other, will increase [with their distance from us]. For the more you remove the stars to an infinite altitude, the more monstrous you imagine their dimensions, such as are not seen from this place of our world.


An observer starting from the earth and moving upwards to the outer spaces would, therefore, find the "appearance" of the world constantly changing, and the fixed stars always increasing in their real as well as visible dimensions. Besides,19


The same must be said concerning the space that for such a traveler increases continuously, every time he transfers the stars from one order to the next and moves them higher. You may say that he is building the shell of a snail, which becomes ever wider towards the exterior.


You cannot, indeed, separate the stars [by moving them] downward; the theory of the parallaxes does not allow it


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because it puts a certain limit to the approximation; you cannot separate them sideways, as they possess already their places determined by sight; it remains thus to separate the stars by moving them upward, but in this case the space that surrounds us and in which are found no stars whatever except the eight small globes in the very centre of this void, grows at the same time.


Thus it is obvious that we may assume the world to be as large as we like; still the disposition of the fixed stars as seen by us will be such that this our place will appear as possessing a certain particularity and as having a certain manifest property (the absence of fixed stars in the vast void) by which it is distinct from all other places.

Kepler is perfectly right. We can make the world as big as we wish, and yet, if we have to restrict its contents to the visible stars, which moreover appear to us as finite, measurable bodies—not points of light—we will never be able to assign to them a uniform distribution that would "save" the phenomena. Our world will always be distinguished by a particular structure.20


It is certain that, on the inside, toward the sun and the planets, the world is finite and, so to say, excavated. What remains belongs to metaphysics. For, if there is such a place [as our world] in this infinite body, then this place will be in the center of the whole body. But the fixed stars which surround it will not, in respect to it, be in a position similar [to that of our sun] as they should be if there were everywhere worlds similar to ours. But they will form a closed sphere around this [void]. This is most obvious in the case of the Milky Way which passes through [the heavenly sphere] in an uninterrupted circle, holding us in


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the middle. Thus both the Milky Way and the fixed stars play the role of extremities. They limit this our space, and in turn are limited on the exterior. Is it, indeed, credible that, having a limit on this side, they extend on the other side to infinity? How can we find in infinity a centrum which, in infinity, is everywhere? For every point taken in the infinity is equally, that is, infinitely, separated from the extremities which are infinitely distant. From which it would result that the same [place] would be the center and would not be [the center], and many other contradictory things, which most correctly will be avoided by the one who, as he found the sky of the fixed stars limited from inside, also limits it on the outside.


Yet, can we not assume that the region of the fixed stars is boundless and that stars follow upon stars, though some, or even most of them, are so far away that we do not see them? Assuredly we can. But it will be a purely gratuitous assumption, not based on experience, that is, on sight. These invisible stars are not an object of astronomy and their existence cannot in any way be demonstrated.

In any case there cannot be stars—especially visible ones—at an actually infinite distance from us. Indeed, they should necessarily be infinitely large. And an infinitely large body is utterly impossible because it is contradictory.

Once more Kepler is right. A visible star cannot be at an infinite distance; nor, by the way, can an invisible one:21


If there were an infinite altitude of the sphere of the fixed stars, that is, if some fixed stars were infinitely high, they would also be in themselves of an infinite corporeal bulk.


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[paragraph continues] Imagine, indeed, a star, seen under a certain angle, for instance, 4´; the amplitude of such a body is always a thousandth part of its distance, as we know from geometry. Consequently if the distance is infinite, the diameter of the star will be the thousandth part of the infinite. But all the aliquot parts of the infinite are infinite. Yet at the same time it will be finite, because it has a form: all form is circumscribed by certain bounds, that is, [all form] is finite or limited. But we have given it a form when we have posited it as visible under a certain angle.


The impossibility of a visible star's being at an infinite distance thus demonstrated, there remains the case of an invisible one.22


But what, you will ask, if it were so small as not to be seen? I answer that the result is the same. It is necessary, indeed, that it occupy an aliquot part of the circumference that passes through it. But a circumference of which the diameter is infinite is itself infinite. Thus it follows that no star, either visible, or having vanished because of its smallness, is separated from us by an infinite distance.


It remains only to ask ourselves whether an infinite space without stars can be posited. Kepler replies that such an assertion is utterly meaningless, since wherever you put a star you will be at a finite distance (from the earth) and if you go beyond, you cannot speak of a distance.23


Finally, even if you extend the place without stars to infinity, it is certain that wherever you put a star into it, you will have a finite interval and a finite circumference determined by the star; thus, those who say that the sphere of the fixed stars is infinite commit a contradiction in adjecto.


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[paragraph continues] In truth, an infinite body cannot be comprehended by thought. For the concepts of the mind concerning the infinite are either about the meaning of the term " infinite," or about something which exceeds all conceived numerical, visual, tactual measure: that is, something which is not infinite in actu, as an infinite measure can never be thought of.


Kepler, once more, is perfectly, or at least partially, right. It is quite certain that wherever you put a star you will find yourself at a finite distance from your starting point, as well as from all other stars in the universe. A really infinite distance between two bodies is unthinkable, just as an infinite integer is unthinkable: all integers that we can reach by counting (or any other arithmetical operation) are necessarily finite. Yet it is perhaps too rash to conclude therefore that we have no concept of the infinite: does it not mean precisely—as Kepler tells us himself—that it is what is "beyond" all number and all measure?

Furthermore, just as in spite of—or because of—the finiteness of all numbers we can go on counting without end, can we not also go on putting stars in space, all, of course, at finite distances, without ever coming to an end? Certainly we can, provided we abandon Kepler's empirical, that is, Aristotelian or semi-Aristotelian, epistemology which precludes this operation, and replace it by another: an a priori Platonic or at least semi-Platonic one.


In my analysis of Kepler's objections to the infinity of the world I have pointed out that they were formulated several years before the great astronomical (telescopical) discoveries of Galileo. These discoveries, which so tremendously

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enlarged the field of observable stars and so deeply modified the aspect of the celestial vault, discoveries which Kepler accepted and defended with joy, and which he supported not only with the weight of his undisputed authority but also by establishing the theory of the instrument—the telescope—used by Galileo, obliged him, of course, to modify some of the views he had expressed in his treatise on the new star. However, and this seems to me extremely interesting and significant, they did not lead him to the acceptance of the infinitist cosmology. On the contrary, they seemed to him to confirm his own finitistic world-view and to bring new data in favor of the unicity of the solar system and of the essential distinction of our moving world and the motionless congeries of the fixed stars.

Thus in his famous Dissertatio cum nuntio sidereo he tells us that at first, before having in hand the publication of Galileo, he was somewhat disturbed by the conflicting reports about the latter's discoveries, namely, whether the new stars were new planets moving around the sun, new "moons" accompanying the solar planets, or, as his friend Mattheus Wackher believed, planets revolving around some fixed stars: a strong argument in favor of Bruno's conception of the uniformity of the world. In this case, indeed,24


. . . nothing could prevent us from believing that numberless others would be discovered later on, and that either this our world were infinite as Melissos and the author of magnetic philosophy, William Gilbert, held, or that there was an infinity of worlds and earths (besides this one) as was believed by Democritus and Leucippus and, among the moderns, by Bruno, Brutus, Wacherus and, possibly also, by Galileo.


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The perusal of the Nuntius tranquillized Kepler. The new stars were not planets: they were moons, Jupiter's moons. Now, if the discovery of planets—whether revolving around fixed stars or around the sun—would have been extremely disagreeable for Kepler, the discovery of new moons did not affect him at all. Why, indeed, should the earth be the only planet to possess a moon? Why should the other ones not be similarly endowed with satellites? There is no reason why the earth should have this privilege. Nay, Kepler thinks that there are good reasons why all the planets—with the exception perhaps of Mercury, too near the sun to need one—should be surrounded with moons.

It could be said, of course, that the earth has a moon because it is inhabited. Thus, if the planets had moons, they should be inhabited too. And why shouldn't they be? There is, according to Kepler—who, for our world, accepts the teachings of Nicholas of Cusa and Bruno—no reason to deny this possibility.

As for the other discoveries of Galileo, namely, those concerning the fixed stars, Kepler points out that they enhance the difference between the stars and the planets. Whereas the latter are strongly magnified by the telescope and appear as well-defined discs, the former hardly increase their dimensions for, seen through the telescope, they are deprived of the luminous haze that surrounds them,25 a fact of tremendous importance because it shows that this haze belongs not to the seen stars but to the seeing eye, in other words, that it is not an objective but a subjective phenomenon and that, whereas the visible dimensions of the planets have a determinate relation to their real ones, this is not the case for the fixed stars.

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[paragraph continues] Thus we can calculate the dimensions of the planets, but we cannot do it, at least not as easily, for the fixed stars.

The explanation of this fact is easy: whereas the planets shine by the reflected light of the sun, the fixed stars shine by their own, like the sun. But if so, are they not really suns as Bruno has asserted? By no means. The very number of the new stars discovered by Galileo proves that the fixed stars, generally speaking, are much smaller than the sun, and that there is in the whole world not a single one which in dimensions, as well as in luminosity, can be equal to our sun. Indeed, if our sun were not incommensurably brighter than the fixed stars, or these so much less bright than it, the celestial vault would be as luminous as the sun.

The very existence of a tremendous number of fixed stars which we do not see, but which observers placed upon one of them would, is a proof, according to Kepler, that his fundamental objection to the infinitist cosmology, namely, that for no observer in the world would the aspect of the sky be the same as it is for us, is even better grounded in the facts than he had imagined. Thus the conclusion formerly drawn from the analysis of the phenomena accessible to the unassisted eye finds itself confirmed by the adjunction to them of the phenomena revealed by the telescope: our moving world, with its sun and planets, is not one of many, but a unique world, placed in a unique void, surrounded by a unique conglomeration of innumerable fixed—in the full sense of the term—stars.

Kepler thus maintains his position. Of the two possible interpretations of the telescopic discoveries of Galileo, that the new (fixed) stars are not seen by the unassisted eye

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because they are too far, and that they are not seen because they are too small, he resolutely adopts the second.

He is wrong, of course; and yet, from the point of view of pure empiricism, he is blameless because there are, for him, on the one hand, no means of determining the intervals that separate us from the stars and no reason therefore to assume that they are not very different in size; all the more so as there are, on the other hand, some examples—the "Medicean" planets, in fact—of celestial objects imperceptible because they are too small to be seen.

Let us turn now to the Epitome astronomiae Copernicanae, the last, and the most mature, great work of Kepler. We shall find the rejection of the infinity of the world presented just as vigorously, or perhaps even more vigorously, than ever before. To the question26


What is to be held concerning the shape of the sky?


the reply is given:


Though we cannot perceive with our eyes the matter of the etheric aura, there is nothing, however, to prevent us from believing that it is spread through the whole amplitude of the world on all sides surrounding the elementary sphere. That the army of the stars completely encircles the earth and thus forms a certain quasi-circular vault is clear from the fact that, while the earth is round, men, wherever they go, see the stars above their heads, as we do.


Thus if we turned around the earth, or if the earth turned around with us, we would see the whole troop of the stars

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arranged in a closed circuit. But that is not an answer to the question asked, as nobody doubts that the earth is surrounded by stars. What we have to find out is something quite different, namely, whether this quasi vault is more than a simple appearance, that is whether21


the centres of the stars are placed on the same spherical surface.


[paragraph continues] At this stage of the discussion Kepler does not want to commit himself. Thus he gives a rather cautious answer:


This is rather uncertain. As some of them are small, and others big, it is not impossible that the small ones appear such because they are far away in the high ether, and the large [do so] because they are nearer to us. Nor is it absurd that two fixed [stars] of different apparent magnitude be distant from us by the same interval.


As for the planets, it is certain that they are not in the same spherical surface as the fixed stars; indeed they eclipse the fixed stars but are not eclipsed by these.


[paragraph continues] But in this case, that is, if we can neither determine the intervals that separate us from the fixed stars nor decide whether their apparent magnitude is a function of their real size or only of their distance, why should we not admit that their "region" is unlimited or infinite? Indeed,28


If there is no more certain knowledge concerning the fixed stars, it would seem that their region is infinite; nor will this our sun be anything other than one of the fixed stars, larger and better seen by us, because [it is] nearer to us than the fixed stars; and in this case around any one of the fixed stars there may be such a world as there is around us; or, which is exactly the same, among the innumerable places in that infinite assembly of the fixed stars


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our world with its sun will be one [place] in no way different from other places around other fixed stars, as [represented] by the adjoined figure M.


The supposition seems reasonable or, at least, admissible. Yet Kepler rejects it, and does so for the same reasons he had twelve years before: from the hypothesis of infinity, that is, of a uniform distribution of the fixed stars in space, would follow an aspect of the sky that is not in accordance with the phenomena. For Kepler, indeed, the infinity of the world necessarily implies a perfect uniformity of its structure and contents. An irregular, irrational scattering of fixed stars in space is unthinkable; finite or infinite, the world must embody a geometrical pattern. But whereas for a finite world it is reasonable to choose a particular pattern, the principle of sufficient reason prevents the geometrically minded God of Kepler from doing it in an infinite one. As already explained by Bruno, there is no reason (or even possibility) for God to make a distinction between the "places" of a perfectly homogeneous space, and to treat them in a different way. Kepler thus states:29


This [the infinity of the world] indeed [was asserted] by Bruno and some others. But [even] if the centers of the fixed stars are not on the same spherical surface, it does not follow that the region in which they are dispersed is everywhere similar to itself.


As a matter of fact, in the midst of it [the region of the fixed stars] there is assuredly a certain immense void, a hollow cavity, surrounded in close order by the fixed stars, enclosed and circumscribed as by a wall or vault; it is in the bosom of this immense cavity that our earth with the sun and the moving stars [planets] is situated.


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FIGURE 3<br> The figure M of Kepler<br> (from the Epitome astronomiae Copernicanae, 1618)
Click to enlarge

The figure M of Kepler
(from the Epitome astronomiae Copernicanae, 1618)

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In order to demonstrate this assertion, Kepler gives us a detailed description of the aspect that the sky would have in the case of a uniform distribution of the fixed stars (which, moreover, in this case would have to be assumed as being, all of them, of the same size), and opposes this hypothetical picture to the actual one.30


If the region of the fixed stars were everywhere similarly set with stars, even in the vicinity of our movable world, so that the region of our world and of our sun had no peculiar outline compared to the other regions, then only a few enormous fixed stars would be seen by us, and not more than twelve (the number of the angles of the icosahedron) could be at the same distance from us and of the same [visible] magnitude; the following ones would be scarcely more numerous, yet they would be twice as distant as the nearest ones; the next higher would be three times as far, and so on, always increasing their distance [in the same manner].


But as the biggest of all appear so small that they can hardly be noted or measured by instruments, those that would be two or three times farther off, if we assume them to be of the same true magnitude, would appear two or three times smaller. Accordingly we should quickly arrive at those which would be completely imperceptible. Thus very few stars would be seen, and they would be very different from each other.

But what is seen by us in fact is quite different. We see, indeed, fixed stars of the same apparent magnitude packed together in a very great number. The Greek astronomers counted a thousand of the biggest, and the Hebrews eleven thousand; nor is the difference of their apparent magnitudes very great. All these stars being equal to the sight, it is not reasonable that they should be at very unequal distances from us.


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Thus, as the general appearance of the fixed stars is everywhere nearly the same in respect to their number and magnitude, the visible sky is also everywhere raised above us by nearly the same distance. There is therefore an immense cavity in the midst of the region of the fixed stars, a visible conglomeration of fixed stars around it, in which enclosure we are.


In the belt of Orion there are three big stars which are distant from each other by an interval of 83´; let us suppose the visible semidiameter of each to be only of one minute; accordingly it will appear to the sight as being of 83´, that is, nearly three times the breadth of the sun, and as for the surface, it would be eight times larger than the sun itself. Consequently the appearance of the fixed stars as seen from each other is not the same as it is from our world, and accordingly we are farther away from the fixed stars than the neighbouring fixed stars are from each other.


As we see, the telescope did not change the pattern of Keplerian reasoning: it only made him diminish somewhat the visible dimensions of the fixed stars. And, of course, as long as this visible dimension is not completely removed from the objective sphere to the subjective one, Kepler's deduction can be upheld.

Yet, it may be objected, its second premise, that of the uniform size of the fixed stars, is gratuitous. It seems that,31


The strength of this argument can be weakened by assuming that the stars are so much larger as they are higher [farther] from the earth. For, if among the so numerous stars that are seen under nearly the same angle, some were assumed to have small bodies, and others enormous ones, it would follow that the former are near us and the latter exceedingly far; and thus, in this case, stars which


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are seen by us as very near [to each other] could in point of fact be very distant.


This is a possible assumption, but, as we know, a rather improbable one, since it would imply an extremely unlikely star distribution, a distribution, moreover, completely incompatible with our fundamental assumption of a homogeneous, uniform universe:32


In this case, this region would be conspicuous if not by its vacuity then by the smallness of the stars in the neighbourhood of our moving world, and thus the very minuteness of the stars would present a kind of void, whereas the increasing magnitude of the stars on the exterior would play the role of the vault. In the universe there would be less stellar matter in this cavity in which our moving world is located, and more matter in the circumference which contains and limits it. Thus it would still remain true that this place is singular and notable compared to all the remaining parts of the region of the fixed stars.


Moreover, it is more probable that those [stars] that are nearly of the same sensible magnitude are separated from us by nearly the same distance, and that a kind of hollow sphere is formed by the packing closely together of so many stars.


The arguments already developed are more than sufficient to enable us to maintain the unicity of this our moving and sun-centered world, and to oppose it to the realm of the fixed stars. We can, however, supplement them by more direct ones, and show that the phenomena clearly point out our (the solar system's) central position in the midst of the peripheral accumulation of stars. The appearance of the Milky Way—in spite of its resolution

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by Galileo into an innumerable multitude of stars—still seems to Kepler to preclude any other conclusion. Thus, elaborating the demonstration outlined in the De stella nova, Kepler continues:33


Do you have any other argument demonstrating that this place in the midst of which are the earth and the planets is particularly distinguished in respect to all other places in the region of the fixed stars?


The way called by the Greeks the Milky Way and by us the Road of St. Jacob is spread around in the middle of the orb of the fixed stars (as the orb appears to us), dividing it into two apparent hemispheres; and though this circle is of unequal breadth, still it is, all around, not very dissimilar to itself. Thus the Milky Way conspicuously determines the place of the earth and of the moving world in relation to all other places in the region of the fixed stars.

For if we assume that the earth is on one side of the semidiameter of the Milky Way, then this Milky Way would appear to it [the earth] as a small circle or small ellipse . . . it would be visible at one glance, whereas now not more than half of it can be seen at any moment. On the other hand, if we assumed that the earth were indeed in the plane of the Milky Way, but in the vicinity of its very circumference: then this part of the Milky Way would appear enormous, and the opposite part, narrow.

Thus the sphere of the fixed stars is limited downwards, towards us, not only by the stellar orb but also by the circle of the Milky Way.


Still, in spite of being thus limited "downwards," the sphere of the fixed stars could nevertheless extend indefinitely "upwards"; the walls of the world-bubble could be indefinitely, or infinitely, thick. Once more we see

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[paragraph continues] Kepler reject this supposition as groundless and perfectly unscientific. Astronomy, indeed, is an empirical science. Its field is coextensive with that of observable data. Astronomy has nothing to say about things that are not, and cannot, be seen.34


But then is not the region of the fixed stars infinite upwards? Here astronomy makes no judgment, because in such an altitude it is deprived of the sense of seeing. Astronomy teaches only this: as far as the stars, even the least ones, are seen, space is finite.


Kepler does not mention Galileo in this discussion, and we can understand why: the telescope does not change the situation. It allows us to see more stars than we did before its invention; it enables us to transcend the factual limitation of our sense of seeing; but it does not remove its essential structure. With as without the telescope, things at an infinite distance cannot be seen. The optical world is finite.

Thus to the question:35


But is it not possible for some of the visible stars to be separated from us by an infinite distance?


[paragraph continues] Kepler replies:


[paragraph continues] No; because everything that is seen, is seen by its extremities. Consequently a visible star has limits all around. But if the star receded to a really infinite distance, these limits too would be distant from one another by an infinite space. For everything at once, that is, the whole body of the star, would participate in the infinity of this altitude. Therefore, if the angle of vision remained the same, the diameter of the star, which is the line between its limits, would be increased proportionally to the distance; thus the


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diameter of a [star] twice as distant will be twice as large as the diameter of the nearer one, the diameter of a [star] distant by a finite space will be finite, but when a body is assumed to acquire an infinitely increased distance [its diameter] also becomes infinitely great.


Indeed, to be infinite and to be limited is incompatible, just as it is incompatible to be infinite and to have a certain, that is, determinate, proportion to something finite. Consequently, nothing that is visible is separated from us by an infinite distance.


So much for the visible world. But can we not assume that outside and beyond the world, or the part of the world that is seen by us, space, and stars in space, continue to exist without end? It may be meaningless from the point of view of astronomy, it may be metaphysics. . . . But is it a good one? Not according to Kepler, who held that this concept—that of modern science—is bad, as a really infinite number of finite bodies is something unthinkable, even contradictory:36


But what if there were in reality stars, of finite body, scattered upwards in the infinite spaces, [stars] which, because of so great a distance, were not seen by us?


First, if they are not seen, they in no way concern astronomy. Then, if the region of the fixed stars is at all limited, namely downwards, towards our mobile world, why should it lack limits upwards? Third, though it cannot be denied that there can be many stars which, either because of their minuteness or because of their very great distance, are not seen, nevertheless you cannot because of them assert an infinite space. For if they are, individually, of a finite size, they must, all of them, be of a finite number. Otherwise, if they were of an infinite number, then, be they as small as you like, provided they are not infinitely so, they


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would be able to constitute one infinite [star] and thus there would be a body, of three dimensions, and nevertheless infinite, which implies a contradiction. For we call infinite what lacks limit and end, and therefore also dimension. Thus all number of things is actually finite for the very reason that it is a number; consequently a finite number of finite bodies does not imply an infinite space, as if engendered by the multiplication of a multitude of finite spaces.


Kepler's objection against infinity is, of course, not new: it is essentially that of Aristotle. Yet it is by no means negligible, and modern science seems rather to have discarded than to have solved the problem.37 Now, even if we deny that there is an infinite number of stars in space, there still remains, for the infinitist, a last possibility: that of asserting a finite world immersed in an infinite space.38 Kepler does not accept this, either, and his reasons for rejecting it reveal the ultimate metaphysical background of his thinking:39


If you are speaking of void space, that is, of what is nothing, what neither is, nor is created, and cannot oppose a resistance to anything being there, you are dealing with quite another question. It is clear that [this void space], which is obviously nothing, cannot have an actual existence. If, however, space exists because of the bodies located in it [it will not be infinite as] it is already demonstrated that no body that can be located is actually infinite, and that bodies of finite magnitude cannot be infinite in number. It is therefore by no means necessary that space be infinite on account of the bodies located in it. And it is also impossible that between two bodies there be an actually infinite line. For it is incompatible to be infinite and to have limits in the two individual bodies or points that constitute the ends of the line.


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Space, void space, is just "nothing," a non-ens. Space, as such, neither is—how, indeed, could it be if it is nothing?—nor has it been created by God, who assuredly has created the world out of nothing, but did not start by creating "nothing."40 Space exists on account of the bodies; if there were no bodies, there would not be space. And if God should destroy the world, there would be no void space left behind. There would be simply nothing, just as there was nothing at all before God created the world.

All that is not new, nor specific to Kepler: it is the traditional teaching of Aristotelian scholasticism. Thus we have to admit that Johannes Kepler, the great and truly revolutionary thinker, was, nevertheless, bound by tradition. In his conception of being, of motion, though not of science, Kepler, in the last analysis, remains an Aristotelian.