From the Closed World to the Infinite Universe: II. The New Astronomy and the New Metaphysics

From the Closed World to the Infinite Universe, by Alexander Koyré, [1957], at sacred-texts.com

II. The New Astronomy and the New Metaphysics

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

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

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

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.

[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

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

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,

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

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

[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:

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
FIGURE 2
Thomas Digges's diagram of the infinite Copernican universe
(from A Perfit Description of the Caelestiall Orbes, 1576)

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

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

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

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

[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.

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

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

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,

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,

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

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

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

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

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

[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.

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

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

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.

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.

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

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

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

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

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