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
