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5

The Ascent of Infinite Space

Medieval and Renaissance Speculations

God, however, is infused into the world He makes, which is placed wherever He makes it.

—Thomas Bradwardine, De causa Dei contra Pelagium

Physical objects are not in space, but these objects are spatially extended. In this way the concept of “empty space” loses its meaning.

—Albert Einstein, Relativity, the Special and the General Theory, A Popular Exposition

I

From Archytas’s challenging conundrum we can derive a more momentous question: not whether an outstretched hand or staff can reach out into something (or nothing) but whether the whole world (i.e., the physical cosmos as one entity) can move. And if the world moves, in what, into what, does it move? These questions vexed philosophers and theologians of the Middle Ages—construing this period as the entire era stretching between A.D. 600 (a date that marks the demise of Hellenistic and Neoplatonic philosophy) and A.D. 1500 (when the Renaissance was fully alive in Italy). Whichever way you answer such questions, the stakes are high. For if the world cannot move—if it is bound forever to occupy the same place, that place being coextensive with the outermost sphere, as Aristotle and Aristotelians assumed—then a surrounding space that exceeds the place of the cosmos, were such space to exist, would be idle. But if the world does move (i.e., laterally by displacement, rather than spinning in place like a top), then there must be an encompassing space in and through which to move, a space that extends beyond the discernible heavens. Once more, the issue is that of place versus space, only now on the grandest scale. Theologically considered (and everything in the Middle Ages was eventually, if not always immediately, so considered), this issue amounts to whether God has the power to create and occupy space sufficient to surpass the place of the cosmos—in short, space unbounded by any particular cosmic constraints and thus ultimately infinite in extent.

One form this discussion took was whether God could create something possessing infinite magnitude. Aristotle, predictably, denied any such ability, since for him there was only a finite amount of matter in the universe to begin with and this could not be increased; he could entertain the idea of the indefinitely small (though only in potentia), but the infinitely large was out of the question.¹ Far from taking this restriction as problematic, Aristotle regarded it as a sign of the perfection of the universe: its very delimitation in size, like the confinement of the places within it, was a matter for admiration. (Of course, for Aristotle the two delimitations are closely related, given that place is quantitatively determined on his own analysis: questions of place are matters of magnitude, and vice versa.) But Aristotle’s espousal of this double finitude left a particularly puzzling question: Does the outermost sphere (which, as encompassing all lesser spheres, provides a place for them) itself have a place! Or is it an unplaced placer, not entirely unlike the Unmoved Mover posited at its periphery? Aristotle himself hinted at—and his Hellenistic commentator Themistius developed in the fourth century A.D.—the idea that the moving parts of this super-sphere have places, for these parts change place as they move in a perfectly circular fashion. But what of the final sphere itself? Does it have its own proper place? Aristotle was inclined to think not: “The heavens,” he maintained, “are not, as a whole, somewhere or in some place.”² Is this to say that the heavens are nowhere? Averroës (ca. 1126—ca. 1198) gave an ingenious analysis of this paradoxical situation. According to “the Commentator,” the outermost sphere has a place, not in relation to anything more encompassing (there is not anything more encompassing than this sphere), but in relation to the earth as the fixed center of all the celestial spheres. The earth is the immobile body at the center that provides place to the otherwise unplaced outer sphere. Roger Bacon (ca. 1220-1292), building on Averroes, distinguished between “place per se”—this is what the final sphere lacks—and place per accidens: place that is parasitic on another, altogether fixed place. As Bacon put it pithily, “Heaven has a place per accidens because its center has a place per se.”³

The Averroesan-Baconian solution to the dilemma inherited from the Stagirite accounts for the world’s place by turning inward to its very center—to what, existing at this center (indeed as this center) is most immobile. Moreover, this inward/downward turn teases apart the two main Aristotelian criteria of place, containment and immobility, since, conceding that the final sphere is not contained in any surrounder, it relies exclusively on the second criterion, exemplified uniquely in the unmoving earth. But the earth is precisely what is contained and thus implaced, via intermediate spheres, by the outer heaven itself. Strange indeed to think that the place of this heaven is dependent on that to which it itself gives place. One place calls for another: celestial and sublunar entities are codependent in their very difference.

Thomas Aquinas (ca. 1224-1274) thought this solution strange enough to remark, “It seems ridiculous to me to maintain that the final sphere is accidentally in a place by the mere fact that its center is in a place.”⁴ Given the choice, the Angelic Doctor preferred to return to the Themistian model whereby the final sphere is in place thanks to its own constitution: “It is much more suitable to say that the ultimate sphere is in place because of its own intrinsic parts than because of the center which is altogether outside of its substance.”⁵ But despite adopting this expressly Aristotelian model for the implacement of the outer sphere, Aquinas came to espouse a quite different model for the implacement of everything else. The true immobility that is required if a place is to be more than a sheer container is not to be found in the centrated earth but in a set of relations to the celestial spheres that surround earth itself. Hence the place of something subcelestial is determined by these relations or, more exactly, by the “order and situation” (prdo et situ) they offer.

Although the container is moved insofar as it is a body, nevertheless, considered according to the order it has to the whole body of heaven, it is not moved. For the other body that succeeds it has the same order and site in comparison to all of heaven that the body which previously left had.⁶

In other words, the place of anything other than the outermost sphere is determined by its position vis-a-vis the celestial spheres (i.e., “heaven” or “the heavens”)—a position that can also be occupied by other bodies. The heavens, taken as a whole to which all other parts of the cosmos relate, furnish the very fixity or stable reference required by any given place in the cosmos. This radically relational view echoes Theophrastus’s paradigm of place as a matter of the way the parts of a quasi-organic body relate to the whole of that body. It anticipates Leibniz, the most systematic Western thinker of place as relational and someone whose theory also depends on the substitutability of objects located “in the same place” considered in relation to fixed external referents. In between, and in the immediate wake of Aquinas, others were to take up a comparably cosmic relational model: for example, Giles of Rome (who said that “what is formal in place is its location with respect to the universe”),⁷ John of Jandun (for whom it is the heavens that determine the very centrality of the earth),⁸ and Duns Scotus (who held that formal or rational place, ratio loci, “is a relation with respect to the whole universe”).⁹

Although they often go hand in hand, an absolutist model of space is not necessarily a model of infinite space. For if this world system is the only cosmos, it will be at once absolute and self-enclosed. But a relational model such as that proposed by Aquinas and the other theorists just cited is not self-contained; it leads beyond itself, beckoning toward spatial infinity. For it calls for a fixed referent located somewhere external to an implaced item: a stable point on the shore when at sea, a permanent object, an everlasting celestial sphere. In proposing that place is a matter of ordo et situ in regard to something immobile, Aquinas is driven to extend the scene of place itself to “the whole body of heaven.” Refusing to rely exclusively on the earth’s centrality and immobility as had Averroes and Bacon, Aquinas finds the more pertinent fixity to reside in the larger arena of the planets and stars—that is to say, an expansive domain that increasingly demands the term “spatial” rather than “placial.” Where this latter term implies something strictly contained, the heavens, taken as a spatial whole, are uncontained. Regular and steady enough in their appearance and motions to provide a stable region of reference for everything here below, as unbounded they lead outward beyond themselves into what can be regarded only as unending space.

In this way we rejoin the second question raised above: In (or into) what would the cosmos move if it were to move at all? Where would the system of fixed reference be if it were itself to be displaced? If it is anywhere, it is in space. Moreover, in infinite space: if the world can be moved even once, it can be moved an indefinite number of times and will thus require an endless amount of space in which to move.

It follows that God’s creative force, if it is to be truly omnipotent, must not be limited to constituting finite regions of the known universe, such as the earth or the planets or even the stars. This force must be equal to the task of creating infinite space—and not just of shaping an already existing space, as befits the Demiurge in the Timaeus. World-constitution is not enough when space-creation is called for.

II

The infinite is an imperative necessity.

—Giordano Bruno, On the Infinite Universe and Worlds

This brings us to the fateful year 1277, just three years after Aquinas’s death. It is only fitting that shortly after the death of the very thinker who had so ingeniously pointed to the need for infinite space—if Thomas did not explicitly endorse such space, his relational model certainly entails it¹⁰—Etienne Tempier, Bishop of Paris, at Pope John XXI’s request and after consulting with theologians of the Sorbonne, issued a series of 219 condemnations of doctrines that denied or limited the power of God, including the power to move the world into a different place than it currently occupies. These momentous condemnations were driven by a desire to make the intellectual world safe for Christian doctrine, its teaching and its theology. But in fact they marked a decisive turning point in medieval thought concerning place and especially space. Until then, the primary efforts had been to shore up Aristotle with the aid of sympathetic commentators such as Themistius and Averroes—in short, to patch up the system of the world first outlined in Physics, book 4, a text preserved in Arabic during the Dark Ages and then translated into Latin in the twelfth century A.D. by Gerard of Cremona. The massive translation of many texts authored by Aristotle and Averroes at this same time sparked a renewed passion for discussing questions of place and space that was to continue for four more centuries and that rivaled the Hellenistic and Neoplatonic preoccupation with many of the same questions.¹¹

The availability of these translations also led to the incorporation of Aristotle into the official curriculum of the University of Paris by the middle of the thirteenth century. So successful was this revival of Aristotle that local theologians in Paris became disturbed: Did not the Aristotelian cosmology hamper God’s powers unduly? Is the extent of God’s creative force limited to this admittedly finite world? Are not other worlds possible? Could not God jostle our world sideways in space, moving it into a new place and leaving an empty place behind? These and affiliated questions fueled the Condemnations, which attempted to reinstate the omnipotence of God in the physical world—a world whose final description was not to be left to the hands of a pagan philosopher, like Aristotle, no matter how important he had been for Thomas Aquinas (who was at least indirectly indicted by the Condemnations: their retraction in 1325 was motivated mainly by an effort to effect his redemption).

For our purposes, the primary importance of the documents of 1277 lies in their reopening the vista of the possible infinity of space. For the Condemnations give virtual carte blanche to explorations of spatial infinity—so long as this infinity remains linked to God’s omnipotence. But the explorations themselves soon exceeded their theological origins; directly or indirectly, they inspired the bold thought experiments of thinkers in the fourteenth and fifteenth centuries, engendering the conceptual ventures that laid down the foundations of modern physics, above all its commitment to the infinity of the physical universe. Pierre Duhem has termed 1277 “the birthdate of modern science.”¹² Whatever may be the truth of this claim, there can be little doubt that one of the most fateful things condemned by the Condemnations was the primacy of place, thereby making room for the apotheosis of space that occurred in the seventeenth century. Yet place was not condemned outright—any more than it had been by Philoponus or Simplicius. As in the case of the Neoplatonists, space was allowed to triumph gradually over place by a steadily increasing affirmation of its supremacy.

Article 34 of the Condemnations states: “That the first cause [i.e., God] could not make several worlds.”¹³ But if God is truly omnipotent, reasoned Tempier, then there is no reason why He cannot make other worlds than this world. As Nicholas Oresme (ca. 1325-1382) put it straightforwardly in the fourteenth century: “God can and could in his omnipotence make another world besides this one or several like or unlike it.”¹⁴ Of most interest to us is not the question of world plurality as such; rather, it is the implication of such plurality: if there are several worlds that coexist with each other, then they must share a space larger than the place taken up by any one of them. If, moreover, there are an infinite number of such worlds—as the Atomists first speculated, and as ensues from God’s omnipotence (for why should He stop at the creation of one or even a few worlds?)—then the space shared must be infinite in extent. Such intercosmic space is empty, a void, except where occupied by given worlds, as Oresme concludes: “Outside the heavens, then, is an empty incorporeal space quite different from any other plenum or corporeal space.”¹⁵ The indefinite plurality of worlds calls for such a space; thanks to its coherent imaginability, its real—its plausible—possibility (though not its actuality) is assured.

A second path to spatial infinity arises from article 49: “That God could not move the heavens [i.e., the world] with rectilinear motion; and the reason is that a vacuum would remain.”¹⁶ At stake here is the question, what would happen if the world were moved, even ever so slightly, in a lateral direction along an imaginary line? In moving from position A to position B, would it not vacate position A, leaving it strictly empty? Would it not move into position B, which must have been empty for it to be occupied by this movement? Extending the stakes further—as theologians are wont to do, given their desire to do justice to God’s unlimited powers—are we not driven to ask, is not such emptiness endless in principle, if it is true that God could move the world anywhere! Oresme is again apt.

But perhaps someone will say that to move with respect to place is to change one’s position in relation to some other body which may, or may not, be in motion itself. Yet I say that this is not valid primarily because there is an imagined infinite and immobile space outside the world . . . and it is possible without contradiction that the whole world could be moved in that space with rectilinear motion. To say the contrary is an article condemned at Paris. Now assuming such a motion, there would be no other body to which the world could be related with respect to place.¹⁷

This is a particularly revealing statement. Not only does it posit “space” (spatium)—immobile, infinite, and extracosmic—as what is required for worldtranslation, but it does so in express contrast with “place” (locus). As the last sentence suggests, place is at stake in a delimited relational model wherein one body is situated vis-a-vis another body. But this model does not obtain in the case of article 49: at issue here is the movement of the world in and by itself without reference to anything else, including any fixed marker. It is a question of an isolated motu recto, a motion taken with reference to the moving thing alone. Such a sheer motion is a motion in an absolute space—a space in which locations are not relative to each other but intrinsic to the preestablished parts of that space itself. Which is to say: a literally absolute space. Oresme’s espousal of such a model of space, occurring exactly a century after the Condemnations, looks forward to Newton—including his defender, Samuel Clarke, who argued against Leibniz that a relativist model of space could not explain world-translation: “If space were nothing but the order of things coexisting [as Leibniz holds], it would follow that if God should remove the whole material world entire, with any swiftness whatever, yet it would still always continue in the same place.”¹⁸ The world would stay in the same place, since its relations with its own constituents would remain the same. If the world is to move into another place than the one it presently occupies, it must be with a motion that moves across the steady structure of an absolute space.

This last discussion makes it even more apparent that “absolute space” and “infinite space,” though closely allied in thinkers such as Oresme and Newton, are not to be confused. “Absolute” implies something self-sufficient, “freed from” any dependency on its own parts, much less any relation to other things elsewhere; whatever is absolute stands apart—thus the ab-, ‘away’, ‘off—from any immersion (i.e., any “solution”) in these extraneous factors, being genuinely independent of them. “Infinite” entails unending extent; here sheer quantity is at stake: what John Locke calls “expansion.” Unlikely as it may seem to the modern mind—indebted as it is to Newton, who brought absolute and infinite space together in one consistent theory—it is perfectly possible to posit an absolute, finite space. This is precisely the space of Plato’s chōra, of Aristotle’s heavens with the earth at the center, of almost every other ancient model of a closed world, and of Philoponean “spatial extension.”¹⁹ It is also perfectly possible to think of an absolute and finite world set in an open sea of infinite space: such is the standard Stoic model.

Further evidence for the inherent dissociability of absolute and infinite space is found in the fact that medieval thought arrived at the infinity of space in two distinctly different ways. In the first, a relational model, pushed to an extreme in the manner I have discussed, yields spatial infinity: such is the way of Aquinas (and of Bacon, Scotus, and others). In the second, an absolutist model ends equally in infinity: such is the way of Oresme (and of Robert Holkot, Richard of Middleton, and others).²⁰ It is striking that articles 34 and 49 of the Condemnations point respectively to these two primary avenues to the infinity of space. On the one hand, the plurality of worlds at issue in article 34 encourages a relational model of infinite space inasmuch as these various worlds serve as reference points—that is, cosmic places—for each other’s positions in a vast intercosmic void. On the other hand, the movement of a single world (and in particular our world), which is at stake in article 49, induces the spectacle of an endless space in which locations are not determined by reference to the positions of other entities.

Two problems of cosmological/theological scope; two solutions of physical/philosophical import. The result is two paths to infinite space: one keeps a role for place; the other dispenses with place altogether.

I do not mean to imply that there ever existed a perfect equilibrium between the two approaches to space in its infinity. The first approach, significantly inaugurated by Aquinas before the Condemnations, was not to be fully pursued again until Locke took it up in 1690 in his Essay Concerning Human Understanding. The second approach, which stemmed more directly from the Condemnations themselves, was more favored and influential during the next few centuries, culminating in the publication of Newton’s Mathematical Principles of Natural Philosophy just three years before Locke’s Essay. Despite the predominance of the second direction, both tendencies share one important thing in common: they both were conceived as ways in which infinite space can be imagined.

For philosophers and theologians alike in the wake of 1277, what had been liberated was not so much a revised picture of the physical world as the freedom to project purely possible cosmological scenarios: what the world and the universe would be like if God were to choose to alter things as they are radically. Concerning things as they are, Aristotelian cosmology and physics were still regarded as the most reliable modes of explanation; but suddenly there was occasion, indeed active solicitation, to imagine things differently. Even if God is unlikely to reverse course—He has, after all, quite an investment in a world He has already created—it is conceptually salutary to think how He might have proceeded otherwise. When one begins to think this “otherwise,” one is approaching things secundum imaginationem, “according to imagination”—not according to how things in fact are, have been, or will presumably be. Pondering the imagined situation in which God might destroy everything within “the arch of the heavens or within the sphere of the moon”—thereby leaving “a great expanse and empty space”—Oresme remarks that “such a situation can surely be imagined and is definitely possible although it could not arise from pure natural causes, as Aristotle shows in his arguments in the fourth book of the Physics.”²¹ By extension, infinite space is a matter of what can be imagined, of what could be; finite space is a matter of what is the case. Thus for Oresme’s near-contemporary John Buridan (ca. 1295-1356), “although God could indeed create corporeal spaces and substances beyond the world, and to any degree he pleased, it did not follow that he had actually done so.”²² Buridan’s statement makes it clear that, in the end, post-1277 thinkers wanted to have it both ways: what is possible and what is so are both valorized, albeit on drastically different grounds. Edward Grant concludes that “because of the Condemnations, it became a characteristic feature of fourteenth-century scholastic discussion for authors to declare that although something was naturally impossible, it was supernaturally possible.”²³

The move to infinite space, whether it takes the “relativist” or the “absolutist” route, was thus a move to a posited or supposed space—not to an actual space, as occurred later on in the Renaissance and in the seventeenth century. But the move remains immensely significant, since it accustomed medieval minds to think in terms of a space without end, whatever they held to be in fact the case concerning the given material universe. Even if the Condemnations of 1277 do not represent the literal birth of modern science, they certainly prepared the way for a science significantly committed to the actual infinity of physical space. And they did so by the promotion of pure possibilities projected by a cosmologically informed theological imagination.

The valorization of secundum imaginationem also prepared the way for an important new development in the advancing conceptualization of infinite space. Precisely because such space had been freely projected by the intense discussions that followed the publication of the Condemnations, it could be recharacterized in terms of divinity rather than sheer physicality. Oresme, for instance, says expressly that “this space of which we are talking is infinite and indivisible, and is the immensity of God and God Himself.”²⁴ The converse also holds: God’s immensity is “necessarily all in every extension or space or place which exists or can be imagined.” ²⁵ This is so even though God Himself is “without any quantity”²⁶ and thus dimensionless and unextended. Unlike Philo of Alexandria (for whom God is Place) and such seventeenth-century thinkers as More, Raphson, and Newton—all of whom consider God to be identical with infinite physical space—Oresme makes God immanent to infinite space without being identical with such space in every respect, especially not in its dimensional, extended character.

It is a remarkable fact that no medieval thinker, not even those who basked in the euphoria unleashed by the Bishop of Paris, claimed that God creates an infinite void space separate from Himself. The reason is that such a space, existing apart from God, would be a rival and limit to God’s own infinite spatiality.²⁷ It is more plausible to maintain that if there is an infinite empty space, it is at one with God, pervaded by Him (and He by it), and finally not distinguishable from His own immensity. A crucial step in this direction had already been taken by Hermes Trismegistus, that apocryphal Egyptian vatic figure who was a numinous presence for the Middle Ages and the Renaissance alike. Trismegistus was held to proclaim in the widely read Asclepius that the extramundane space outside the cosmos is not filled with anything material or even quasi-material (e.g., pneuma) but is packed with “things apprehensible by thought alone, that is, with things of like nature with its own [i.e., thought’s] divine being.”²⁸ Thinking is divine, and it is this internal divinity that allows “thought alone” to be akin to the noetic content of an imagined infinite space. But the divinity of human thought—an Aristotelian theme—was bypassed in the High Middle Ages in favor of God’s much superior divinity. Hence it is God’s divine presence, not human “active intellect,” that was believed to fill any possible extramundane, unmoving infinite space.

This last, momentous step was first made by Thomas Bradwardine (ca. 1290-1349) in his De causa Dei contra Pelagium. In this text, Bradwardine sets forth five crucial corollaries.

1 First, that essentially and in presence, God is necessarily everywhere in the world and all its parts;

2 And also beyond the real world in a place, or in an imaginary infinite void.

3 And so truly can He be called immense and unlimited.

4 And so a reply seems to emerge to the old questions of the gentiles and heretics—”Where is your God?” And, “Where was God before the [creation of the] world?”

5 And it also seems obvious that a void can exist without body, but in no manner can it exist without God.29

Bradwardine presents us with a pure panentheism of the void. God’s “presence . . . necessarily everywhere” converts the void from what had been a purely negative and imaginary entity for other thinkers into something at once positive and real: positive insofar as it is not simply a form of nonbeing (e.g., void as sheer nothing), real insofar as it is filled with God’s being (which is not only real but most real). Where Oresme had attributed reality to the void solely on the basis that it is an object of reason or understanding (as opposed to sensation or perception), Bradwardine is unhesitating in his conviction that the reality of any extramundane void stems exclusively from God’s ulterior reality.³⁰ It does not stem from any quasi-physical attributes such as extendedness or dimensionality. Indeed, the void in question may even lack extension or dimension—unacceptable as this thought would be to Philoponus or Descartes. In this regard, it is nonphysical and “imaginary.” But in the regard that matters most—that is, God’s immanence in this space—it is altogether real.

By the same token, however, we can ask: Is such a void “empty of everything except God”?³¹ Perhaps this vast void is not dimensional or extended precisely because nothing else is there but God, who was considered dimensionless and unextended by Bradwardine, Oresme, and other fourteenth-century theologians. But if so, perhaps this new void is literally a deus ex machina, invoked only in order to ensure that God has a proper place in which to exist. The void would then be a “place” that, precisely in accommodating God as “immense and unlimited,” must be an infinite “space.” Its existence would be merely tautological in status, a conceptual redundancy, part of God’s definition. This much seems implied by Bradwardine’s fifth corollary: if the void can “in no manner exist without God,” by the same token it need not have (perhaps it cannot have) any other occupants in it. This is hardly a suitable model for the known universe, filled as it is with innumerable and diverse things.

As if anticipating this skeptical line of questioning, Bradwardine singles out three respects in which the void is more than a scene for God’s residence. First, the void has parts, which are not necessarily identical with God’s parts and which can thus belong to things other than God. I take this to be the purport of the first corollary: “God is necessarily everywhere in the world and all its parts.” Second, the void has places, which once again are not necessarily those of God Himself; as Bradwardine adds, “God persists essentially by Himself in every place, eternally and immovably everywhere.”³² Indeed, as if to drive the point home, he remarks that “it is more perfect to be everywhere in some place, and simultaneously in many places, than in a unique place only.”³³ Thus God does not restrict his occupation of the universe to His own place (assuming that this place is somehow delimited)—any more than to one part of space. Third, and most convincing, is Bradwardine’s explication of his second corollary. To say that God is “beyond the real world in a place, or in an imaginary infinite void,” is coded language for a return engagement with the continuing issue of whether God can move the world motu recto. The place beyond the world is the place to which God moves this world; since God can move the world to an infinite number of such extramundane places, he moves it in an “imaginary infinite void” that is the whole of space in which such motions are possible. Indefinite displacing entails unending spacing. As Bradwardine is wont to put it, if God moves the world from place A to place B, then either He was already in B or not. If he was not, then his omnipresence is compromised. If he was, then he is necessarily everywhere—in A and B, but also in C, D, E, and so on, ad infinitum. “If he was there [in B], then, by the same reasoning, He was there before and can now be imagined as everywhere outside the world.”³⁴

Bradwardine’s views, though forgotten in detail until the belated publication of his De causa Dei contra Pelagium in 1618, nevertheless spelled out an entire way of thinking about the void and infinite space—a way that was deeply persuasive in its general outlines. It was pursued not only by John of Ripa and Nicole Oresme in the fourteenth century but by subsequent generations of philosophers and theologians. As Grant observes, “It was some version of Bradwardine’s conception of the relationship between God and infinite space that was adopted and explicated by numerous scholastics during the next few centuries.”³⁵ Bradwardine’s adventuresome view was also explored by the great Jewish thinker Crescas (1340-1410), though with a distinctly Stoic emphasis on the infinite deific void as surrounding the plenary finite world.³⁶ More momentous, this same view “helped shape nonscholastic spatial interpretations in the seventeenth century.”³⁷

The point is not that everyone shared the Bradwardinian vision. Some, like Albert of Saxony (d. 1390) and John of Jandun (d. 1328), decidedly did not, denying any significant sense of a vacuum separatum. Others, like Richard of Middleton (a contemporary of Bradwardine), vacillated by divorcing God’s immensity from infinite void space. Still others were preoccupied with the ancient question as to whether there was voidlike space within the world (even Bradwardine conceded that “by means of His absolute power, God could make a void anywhere that he wishes, inside or outside of the world”).³⁸ Certain thinkers, like Nicholas of Autrecourt (active in the first half of the fourteenth century), even attempted to revive an Atomist notion of internal, interstitial vacua. But it remains the case that the freedom of speculation first tasted on the issuance of the 219 condemnations by the Bishop of Paris in 1277 was not only satisfying theologically (since it acted to restore faith in God’s uninhibited powers, hemmed in as they were by Aristotelian cosmology) but also intoxicating philosophically (since it allowed numerous thought experiments concerning infinite space as a situs imaginarius).³⁹ Most important, it led to a fresh vision of what infinite space might be like were it to be identical with God—and God with it. It was a vision, befitting the Middle Ages, that was nothing short of “the divinization of space.”⁴⁰

We can say, in fact, that the Middle Ages contributed two new senses of infinite space to the gathering field of forces that were gradually granting primacy to space over place. Beyond the distinctive spatial infinites already posited in the ancient world by Atomism, Epicureanism, Stoicism, and Neoplatonism, we must now take into account a sense of infinite space as (a) imaginal-hypothetico-speculative, a space projected in a series of bold Gedankenexperimente that were not idle excursions but disciplined and serious efforts to grasp what space would be like if it had no imaginable limits; (b) divine, that is, an attribute of God or, more strongly still, identical with God’s very being as immense beyond measure. These two emerging senses of the spatially infinite are deeply coimplicated: the divinization of space makes what is otherwise merely imaginal and negative into something real and positive, while imagined projections of such space furnish a limitless scope to the divine that is lacking on Aristotle’s model of God as a Unmoved Mover who has no choice but to deal with a self-contained cosmos.

Along with this extended foray into a divinized-imaginified space came a related effort to overcome the confinement of place—at least as this latter was conceived on the model of Physics, book 4. Place itself (locus) was conceived in three distinctive senses in the medieval period. The first of these senses remains at least partly Aristotelian, while the other two senses depart ever more radically from the paradigm of place as an immobile container:

•place in the cosmos: this is specified by the immediate surrounder of an object; it is termed “material” or “mobile” (this latter inasmuch as what surrounds the object may give way to another environing medium);

•place of the cosmos: this is the position of the world-whole itself; and the burning issue, as we have seen, is whether this place can be exchanged for another place—whether in particular the world can be moved from position A to position B; this is what is at stake in article 49 of the Condemnations, which concerns whether God can move the existing world from its apparently “immobile” position;

•place between worlds: here the issue is how one existing cosmos is related spatially to another also-existing cosmos—and to still others as well, ultimately to the entire universe; the debate is over article 34, that is, whether there can be plural worlds.

If the first conception keeps place securely in the wraps in which Aristotle and the Peripatetic school had left it—literally a wraparound position that the medievals euphemistically called “lodging”—the second and third conceptions begin to break away from this tight tethering. In both of these latter cases, we witness place becoming space under our very eyes. In the second case, this happens in the form of a concern with the absolute locus of the world: if this locus can be displaced, then there must already exist an encompassing scene of diverse possible loci, each such place preestablished in an absolute space that embraces them all and each an unchanging part of that all-embracing space. In the third case, the transformation occurs on a relativist paradigm in which the crucial connection is not with a single Space but with other worlds in other places: what matters most is what lies between these worlds, that is, their interplace.

Whether by the second or by the third route, the adventurous avenue toward infinite space opened up decisively after the thirteenth century in the West. The closely confining circuit of place-as-perimeter dissolved and the vista of a New World of Space began to captivate the ablest minds of the succeeding period. It seems hardly accidental that the great Age of Discovery in the fifteenth and sixteenth centuries—an age that set out expressly to explore a terra incognita of interconnected places within the larger space of the earth itself as well as the still larger space of the heavens—immediately followed upon the bold speculations of philosophers and theologians in the thirteenth and fourteenth centuries. From an entirely imagined and divine status that was fully gained by A.D. 1400, such spaces became actual in the form of an earth and a sky that lay ready for discovery and possession not only by thought and faith but also by arms and men. And with the advent of an endlessly challenging space of exploration, we have reached the threshold of the Renaissance.

III

All things are in all things.

—Nicholas of Cusa, On Learned Ignorance

Henceforth I spread confident wings to space; I fear no barrier of crystal or of glass; I cleave the heavens and soar to the infinite.

—Giordano Bruno, Dedicatory Poem to On the Infinite Universe and Worlds

“Renaissance” does not mean something entirely new but, instead, renewed, new again. The New World of Renaissance thinking about place and space, more often than not, carries forward an Old World of previous conceptions. Just as the Middle Ages—and before that, the Hellenistic period—looked back at Aristotle most insistently, so the Renaissance will return to Plato for comparable inspiration. It will also go back to other sources, for example, the Neo-platonists (especially Plotinus, Iamblichus, and Philoponus) and the unknown authors of the Hermetica. As Frances Yates, who has made the strongest case for the Hermetic origins of Renaissance thought, puts it,

The great forward movements of the Renaissance all derive their vigour, their emotional impulse, from looking backwards. . . . [For the Renaissance] history was not an evolution from primitive animal origins through ever growing complexity and progress; the past was always better than the present, and progress was revival, rebirth, renaissance of antiquity.⁴¹

A primary case in point is the very idea of spatial infinity, sometimes assumed to have been a product of late Renaissance thinking. We have seen, however, that this idea, at once alarming and attractive, first arose in ancient Atomism, and was pursued vigorously by Epicurus and the Stoics, explicitly formulated by Lucretius and Sextus Empiricus, investigated with subtle fervor by many generations of philosophers in the wake of Aristotle (from Theophrastus and Strato to Philoponus and Simplicius), examined in Arabic commentaries on Aristotle, and forcefully revived after 1277 in medieval thought. It is a paradox of the history of ideas that a book as insightful and scrupulous as Alexandre Koyre’s From the Closed World to the Infinite Universe contributes by its title, if not always by its explicit claims, to the mistaken view that spatial infinity was a belated invention of the fifteenth and sixteenth centuries in the West.⁴²

Also quite fateful in its consequences was the famous claim that the universe has its center “everywhere” (ubique) and its circumference “nowhere” (nullibi). Although often attributed to Nicholas of Cusa (1401-1464), in fact the claim derives from a pseudo-Hermetic text of the twelfth century, “The Book of the XXIV Philosophers.”⁴³ This statement of early medieval origin was destined to become a mot celebre: not only Cusa but Giordano Bruno and Blaise Pascal (in the sixteenth and seventeenth centuries, respectively) cite it without attribution, each as if he had composed it himself.

Bruno’s version is unusually instructive: “Surely we can affirm that the universe is all center, or that the center of the universe is everywhere, and that the circumference is not in any part, although it is different from the center; or that the circumference is throughout all, but the center is not to be found inasmuch as it is different from that.”⁴⁴ Considered as a challenge to Aristotle—to his closed and centered world—this complex proposition has two parts: (i) In saying that the center is everywhere, it proposes that there is no single privileged center such as the earth—or any other heavenly body, not even the sun (Copernicus’s efforts, known to Bruno, notwithstanding). The Arisotelian cosmographic model of a hierarchical universe with an immobile earth situated at the still center gives way to the idea that any part of the universe can be considered a fully valid center: the universe is “all center.” This in turn implies that every place is a center—a center of perspectival viewing from which all other places can (at least in principle) be seen. As Cusa was the first to insist, the perception of the universe is relative to the place of the observer.⁴⁵ In other words, place is anywhere you choose to take up a point of view, and the universe yields an indefinite number of such places, (ii) In holding that the circumference is “throughout all”—that is, not in any single region, not even at the delimiting edge of the universe—Bruno maintains that it is in effect nowhere, “not in any [single] part.” The circumference is all over the place, which is tantamount to saying that it is located in pure space and not in a particular place or set of places. Nor is such space a mere composite of places that are parts of the whole. It is a radically open field that is coextensive with the universe in its totality. In terms of Archytas’s conundrum, we would have to say that no one could ever get to the edge of the world in the first place: nothing is at the edge since nothing can serve as the edge, as a simple circumference. There is no outer limit, no end to space. As Bruno himself comments, “Outside and beyond the infinite being, there exists nothing that is, because [such being] has no outside and no beyond.”⁴⁶

What is remarkable, then, about the claim in question—whether in its initial or its Cusan version—is that it manages to combine recognition of the importance of place with an equal acknowledgment of the value of infinite space. In this respect, it reflects its historical origin at the beginning of the Middle Ages: at the very moment when Aristotle was being rediscovered, yet also when burgeoning interest in the possible infinity of space was colluding with theological speculation as to God’s uncontainable immensity. That the Renaissance took up the pseudo-Hermetic saying so enthusiastically indicates that the tension between place and space was still very much alive centuries after its first formulation in the twelfth century. Aristotle’s celebrated utterance retained its relevance: place still “has some power.” And it was just because it continued to have this power that the triumph of space was so slow in coming and so hard won during this same period. A considerable part of the struggle was due to the sheer fact that the looking-back was to place in its confinement (perspective is as confining as surface), just as the looking-forward was to a space unencumbered by such confinement. The situation was Januslike, exhibiting all the tension that looking in two opposed directions always brings with it. Instead of being surprised, we should ask instead: How could it be otherwise?

Nevertheless, the finally “triumphant beast” of Renaissance cosmology and theology is, indisputably, infinite space.⁴⁷ This becomes evident in Cusa’s conception of space as modeled on the Absolute Maximum (absoluta maximitas), that is, the unqualifiedly great, that than which there can be no greater. Earlier medieval notions of absolute magnitude and of God’s perfection (especially as invoked in the ontological argument) are detectable in the Cusan idea of the absolutely maximal, but what is new in this idea is that it makes infinity and the finite radically incommensurate. For Cusa, whatever is finite is subject to degrees of greatness—thus to comparison—but what is infinite is incomparably great: “Where we find comparative degrees of greatness, we do not arrive at the unqualifiedly Maximum; for things which are comparatively greater and lesser are finite; but, necessarily, such a Maximum is infinite.”⁴⁸ It follows that we can never get to the infinite from any addition or compilation of the finite, no matter how massive or prolonged our efforts may be.⁴⁹ “The absolutely Maximum is all that which can be, it is altogether actual.”⁵⁰ It also follows that the Absolute Maximum is equivalent to the Absolute Minimum—a palmary instance of Cusa’s celebrated principle of coincidentia oppositorum. (For example, neither extremity can tolerate anything greater or lesser, since each is complete in itself.)⁵¹ Further, the Absolute Maximum is incomprehensible and “beyond all affirmation and all negation.”⁵² Such a Maximum is numerically one (i.e., it is unique) and logically necessary (i.e., cannot not exist) as well as infinite.⁵³ We are thus not surprised to be told that the Absolute Maximum is God—and vice versa. By a very different route, then, we attain the divinization of the infinite first encountered in Bradwardine and Crescas.

Yet the route and the result are very different. This becomes clear when we ask ourselves: Is the Cusan infinite divinity infinite space? With his usual subtlety, Cusa distinguishes between two kinds of infinite, one applicable strictly to God and the other to the universe. God—the absolutely Maximum—is “negatively infinite.” God is infinite in a negative mode insofar as He is not the sheer summation of finite things. The universe, in contrast, is “privately infinite,” by which Cusa means that it is unbounded yet not actually infinite.⁵⁴ We can even say that the universe is “neither finite nor infinite,” but by this Cusa only means that “it cannot be greater than it is.”⁵⁵ Not being able to be greater than it is—and not being as great as God—it is finite; but as it is, it is privately infinite, since it is as great as it can possibly be as something physical. As physical, the universe is the “contraction” (contractio) of divine infinity: it is this infinity in a compressed state. But precisely such a “finite infinity”⁵⁶—another coincidence of opposites—characterizes infinite space.

When Cusa remarks that “the world, or universe, is a contracted maximum” and “is, contractedly, that which all things are,”⁵⁷ he means that this world or universe (between which he does not distinguish) is a spatially maximal whole, even if it is not an absolutely maximal whole. As maximal, it is infinite; but as nonabsolute, it is finite: it is this world, a world that “sprang into existence by a simple emanation of the contracted maximum from the Absolute Maximum.”⁵⁸ The finite infinity of the world, we might say, is the world put into its place: its “contracted infinity” is “infinitely lower than what is absolute, so that the infinite and eternal world [i.e., our world] falls dispro-portionally short of Absolute Infinity and Absolute Eternity.”⁵⁹ But the distinctive privative infinity of this world remains unbounded, and in this format it contains, in contracted form, the very “Absolute Infinity” that it does not possess in itself without qualification.⁶⁰ The same special infinity of the cosmos is contained contractedly in the particular things of the world, and in this latter capacity it is irrevocably spatial: What else other than space could be the medium of universal contraction, with the result that “all things are in all things” in “a most wonderful union”?⁶¹ If God is “in the one universe,” the universe itself is “contractedly in all things.”⁶² Double contractio ensures at once the spatial infinity of the world and its failure to be divinely infinite. The world is unbounded yet undivine. Spatial infinity is secured only by the loss of divinization—just the reverse of what Bradwardine and other fourteenth-century theologians had held. The infinitization of space requires its dedivinization.

To be unbounded is to be without circumference. Cusa does not assert the lack of circumference dogmatically, or just to repeat his pseudo-Hermetic source. He argues that insofar as the earth is not a “fixed and immovable center”—it cannot be such a center, since fixity and immobility are always relative to the movement of something else—it cannot have a set boundary: if the world had a settled center in the earth (as Ptolemy notoriously held),⁶³ it would also have an equally settled perimeter. Moreover, it would also have a surrounding space: “It would be bounded in relation to something else, and beyond the world there would be both something else and space.”⁶⁴ A boundary entails something on the other side of itself, and this something in turn requires “space” in which to be located. It is significant that Cusa uses locus, not spatium, in the phrase “and space” just cited. For the kind of space that is at stake in the situation is locatory, not infinite space. Locatory space is tantamount to “place” as this concept had been employed since Aristotle. It is a matter of a place for something—an “in which”—that lies beyond the boundary. But just such a place is lacking, indeed is superfluous, in a circumstance in which there is no effective boundary. To be infinite qua unbounded is to be placeless qua located. Between the full but nonspatial infinity of God and the essentially empty but precisely positional place of physical things lies the unbounded state, the spatial infinity, of the universe. Thanks to the articulation of this infinity, “a new spirit, the spirit of the Renaissance, breathes in the work of Cardinal Nicholas of Cusa.”⁶⁵

Bruno, deeply influenced by Cusa as he was, differed from him on at least two basic matters. For one thing, the infinity of the physical universe was for Bruno not less dignified or worthy than the infinity of God. As Paul Kristeller says, “Whereas Cusanus reserves true infinity for God alone, Bruno uses the relation between the universe and God as an argument for the infinity of the former.”⁶⁶ Then again, Bruno extends spatial infinity from this world to all worlds, worlds that are themselves infinite in number. A third form of infinity, that of worlds in their innumerability, is thus added to the spatial and divine infinities distinguished by Cusa. The proposal of infinite worlds ensues from a principle of sufficient reason: “Insofar as there is a reason why some finite good, some limited perfection, should be, there is a still greater reason why an infinite good should be; for, while the finite good exists because its existence is suitable and reasonable, the infinite good exists with absolute necessity.”⁶⁷ As Arthur Lovejoy puts it, it is “because of the necessity for the realization of the full Scale of Being that there must be an infinity of worlds to afford room for such a complete deployment of the possibles.”⁶⁸ Crucial for the thesis of infinite worlds is thus a principle of plenitude, as is made explicit in Bruno’s On the Infinite Universe and Worlds: “For just as it would be ill were this our space not filled, that is, were our world not to exist, then, since [particular] spaces are [otherwise] indistinguishable, it would be no less ill if the whole of space were not filled.”⁶⁹ It would be ill, indeed, if the whole of space were not filled, for it then would be an utterly indistinct and purposeless void. For Bruno, however, things and the worlds they constitute do not fill in a preexisting void; they remove the need to presume the existence of any such emptiness, since their presence gives to space a distinctive, qualitative heterogeneity otherwise wholly lacking. The only space that exists is fully qualified, plenary space, described by Bruno as “not merely reasonable but inevitable.”⁷⁰ The issue is not that of horror vacui, since nature does not rush to repair any momentary gaps but is always already full, never gappy or vacuous. As Bruno says explicitly, “Where there is no differentiation, there is no distinction of quality.”⁷¹ Worlds and the things they contain differentiate and fill up that which, without their distinguishing presence, would be a merely undifferentiated “undistinguishable inane” (in Locke’s memorable phrase).

Bruno agrees with Cusa that the idea of a strictly bounded world lands us in the Stoic predicament of positing an empty extramundane space that has no other role than that of being occupied by some possible world. But God ensures that every possible world will become an actual one—”the possible and the actual [are] identical in God”⁷²—and thus such space is otiose. Moreover, to believe that a given world occupies a preexisting empty space is to require a reason why it occupies this particular space rather than some other.