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
