Place, too, not less than time, pervades everything; for everything that happens is in a place.
—Simplicius, In Aristotelis categorias commentarium
Philoponus—born in A.D. 490, five years after Proclus was buried with Syrianus in a conjoint tomb—sought to refine the idea of extension (diastēma), whose full significance had become overshadowed by the more speculative ideas of his immediate Neoplatonic predecessors. For Philoponus, extension and not body, not even immaterial body, is the very essence of place: place is “a certain extension in three dimensions, different from the bodies that come to be in it, bodiless in its own definition—dimensions alone, empty of body.”82 The tie between extension (diastēma) and dimensions (diastaseis) is close, not just linguistically but conceptually: dimensions are what open out extension, delineating its outreach, giving bodies room through which to move. This is why Philoponus can define extension as “room (chōra) for body, and [for] dimensions alone, empty and apart from all substance and matter.”83 Extension is what provides room for things, and the fact that chōra signifies either “room” or “space” allows Philoponus to make a crucial move, namely, to distinguish “spatial extension” from “bodily extension.” Bodily extension is equivalent to the particular place occupied by a given physical body. It is the room taken up by the matter of that body.84 Spatial extension, in contrast, is the extension that need not, in principle, be occupied by any given body or group of bodies: rather than being the room of a body, it gives room for a body. Thus it is a matter of “dimensions alone” and as such is “empty and apart from all substance and matter.” This is so even though such extension is always actually occupied by bodies. Both sorts of extension are alike in being three-dimensional, but bodily extension is filled both in principle and in fact, whereas spatial extension is empty in principle but full in fact.85
Furthermore, bodily extension fits into spatial extension but not vice versa.86 There is always more spatial extension than bodily extension, and spatial extension can be said to consist precisely in this “more,” in fact so much more that Philoponus is tempted to regard spatial extension as tantamount to void. Where void can be defined as “spatial extension extended in three dimensions,” spatial extension is “bodiless and matterless—space without body.”87 Both void and spatial extension are incorporeal and immaterial. In making this quasi-equation, Philoponus is concerned to wipe the slate clean of any such suspicious hybrid entities as immaterial bodies. He replaces Proclus ‘s idea of such bodies—or, for that matter, the quasi-material plenum of Stoic pneuma—with something genuinely “empty by its own definition,”88 that is to say, with the conceptual equivalent of the void. To carry out this radical cleansing operation, Philoponus will even say that “in itself place is void” and that “void and place are in reality the same in substance.”89 Nevertheless, in the end, there is no actual void—void does not exist—and, rather than being the counterpart of place, void is Philoponus’s “name for space.”90
Philoponus here effects a genuine tour de force. He proposes a theory of place or space—the ambiguity is inescapable, given the distinction between bodily and spatial extension—that obviates Aristotle’s most important criterion for being in place: to be enclosed by the surface of a surrounding substance. Philoponus argues persuasively that no surface can contain a solid body: “for the surface is extended in two dimensions and so could not receive in itself what is extended in three dimensions.”91 It follows that any adequate theory of place and/or space must include three-dimensional extension as a minimum requirement. Yet precisely such a requirement is met in the idea of a spatial extension that situates bodily extension. Furthermore, spatial extension satisfies all of Aristotle’s other criteria for being in place: it encompasses what is in place just as much as a boundary (peras), is (at least) equal to the thing in place, is not part of this thing, and is itself immobile.92
From this point—and from his virtual equation of void with spatial extension—one might have expected Philoponus to move to a theory of infinite space. Indeed, the very immobility of spatial extension would seem to entail an unending spatial expanse.
We conceive the [spatial] extension to be different from all body and empty in its own definition, but various bodies are always coming to be in it, now this one, now that, while it remains unmoved both as a whole and in its parts—as a whole, because the cosmic extension which receives the body of the whole cosmos can never move, and in its parts, because it is impossible for an extension that is bodiless and empty in its own definition to move.93
What is this “cosmical extension” (cosmikon diastēma) but the extension of the ultimately unbounded, thus of a universe that can no longer be set over against the world? Nevertheless, just at the point when Philoponus is most tempted to join his Neoplatonic predecessors in a common step toward the infinite, he draws back from the abyss. Admitting the allure of thinking that cosmical extension, “void by its own definition and capable of receiving bodies, must be infinite,” since it does not have any effective boundary or delimiting surface of its own, he proceeds to argue that (i) you still might be able to imagine such a surface; (ii) even if you could not, cosmical extension “would not necessarily be extended to infinity for this reason,” that is, just because one could not succeed in this thought experiment.94 A principle of parsimony is also invoked: only so much of spatial extension need subsist as is coextensive with the outer boundaries of the bodies that actually occupy it.95 Philoponus’s ultimate motive for denying the infinity of space is doubtless theological—as a believing Christian Neoplatonist, he may have wished to restrict infinity to God—but his argumentation remains unconvincing, especially for someone whose own idea of cosmical extension seems to entail spatial infinity by its very nature.96
Not only is such infinity repudiated, but likewise the powers of place. Despite his endorsement of the Damascian position that place is “a measure of things in place,”97 Philoponus is unwilling to admit any other power intrinsic to place. Sarcasm surfaces when he says that “it is quite ridiculous to say that place has any power in its own right.”98 No longer sustaining or upholding, gathering or supporting, spatial extension is void indeed in its lack of inherent dynamism. Gone as well is the basic Neoplatonic premise that place is superior in status to what is in place.99 The disappearance of placial dynamism is paired with the demise of the noetic nature of place. Although spatial extension is neither bodily nor material, it is also not intellective. It is something sheerly spatial, where “spatial” connotes what is true of the physical universe even if not itself physicalistic in constitution.
We are left with the paradox that despite Philoponus’s outright rejection of infinite space, he is decidedly protomodern in his notion of a spatial (and ultimately cosmical) extension that is three-dimensional, empty in principle, and incorporeal, and that “gives room for body” while remaining independent of any particular material substance. In their expansive and extending character, these aspects of a distinctively diastemic space open up the prospect of a spatiality that is positively infinite and not just in-finite by negation (e.g., bound-less, end-less, empty, etc.). The same aspects will continue to be rediscovered, often piecemeal, during the next millennium in the West, sometimes as influenced by Philoponus himself.100 The space they collectively characterize is perhaps most properly termed “absolute space,” a term I have already invoked in discussing Syrianus and Proclus and that will be employed explicitly by Newton in his Mathematical Principles of Natural Philosophy.
Not only was Philoponus on the verge of espousing an infinite space that he felt impelled to repudiate, but the spatial absolutism entailed by the idea of a purely dimensional spatial extension was accompanied by a concomitant relativism of place. This latter is evident in his concern for the proper arrangement of things in space: “It is not through desire for a surface that things move each to its proper place, but through desire for that station in the order which they have
