capacity of vessels: their power to hold (things) in. By carefully describing this capacity of holding-in, Aristotle is able to determine the exact definition, the “what-is-it” (211a8: ti estin) of place. The definition itself is set forth in two stages. In the first, Aristotle concentrates on the factor of containment as such by observing that we are located in the celestial system by virtue of being surrounded by air, which is in turn surrounded by the heavens. We are placed in this system by being located “in the air—not the whole air, but it is because of the limit of it that surrounds us that we say that we are in the air.”18 Place in its “primary” sense is thus “the first thing surrounding each body.”19 It is this immediately environing thing taken as a limit. But the limit here belongs to the surrounder, not to the body surrounded (the limit of the latter is determined by its form, i.e., its outer shape: see 209b3–6). As a vessel, such as a glass or a jug, surrounds its content—say, air or water—so place surrounds the body or group of bodies located within it. “Surround” translates periechein, which means “to circumscribe without including as a component part” literally, it signifies to “hold” (echein) “around” (peri-, as in perimeter). As a vessel holds water or air within it, so a place holds a body or bodies within it in a snug fit.
But Aristotle does not rest content with this first definition of place. For one thing, the analogy with a vessel is imperfect. While a vessel can be transported, a place cannot: “Just as the vessel is a place which can be carried around, so place is a vessel which cannot be moved around” (212a14–15). Still more serious, there is the problematic fact that a river is a place for a boat and yet the content of the water immediately surrounding a boat continually changes. Hence the inner surface of the surrounding water, that which delimits the boat’s place, is not selfsame from moment to moment. Since a minimal requirement of place is to be selfsame—to be the same place for different things located in it—Aristotle must add to the first definition the rider that a place cannot itself be changing or moving: it must be “unchangeable” (akinēton). This allows him to move to his most definitive formulation: “That is what place is: the first unchangeable limit (peras) of that which surrounds” (212a20–21). In the case of the river, it is thus “the whole river” that is the place: a phrase that Simplicius and others interpret to mean the banks and bed of the river, its fixed inner surrounding surface.20
Place thus construed is “the inner surface of the innermost unmoved container of a body.”21 As such, it contains-and-surrounds the body by furnishing to it an environment that, if not always stable (the immediate “spot” of a boat in the river is only a momentary locale, not a lasting locus), is nevertheless a defining locatory presence. Thanks to this presence, place is actively circumambient rather than merely receptive.22 It is just here that Aristotle’s departure from Plato becomes most manifest. In the Timaeus, space qua chōra—including both regions and particular places—is held to be receptive: indeed, it is “omnirecipient.” Precisely as such, it can be qualified by sensible qualities and can serve as the medium in which physical bodies will appear. But these bodies receive their definition, that is, their limit or shape, from geometric figures. Hence the limiting factor comes from the active infusion of forms by the Demiurge.
On Aristotle’s account, the limiting power is already in place; it is of the essence of place itself to provide this delimitation by its capacity to contain and to surround: to contain by surrounding. Where Plato’s interest lay in the shaping of the outer surface of physical bodies, Aristotle’s concern is with the fixed contour of the inner surface of environing places. For Aristotle, the limit is found within place, indeed as part of place itself. Limit is ingredient in place from the beginning—indeed, as the beginning of an ordered natural world—and is not imposed by an external ordering agent. Hence there is no need to invoke a deific regulator, a divine inseminator possessing a logos spermatikos. Places have their own independent potency. As Aristotle puts it in a characteristic understatement, place “has some power” (208b11). But the result of this modest proposal is quite sweeping: the world is always already fully implaced; it is never without those determinate topoi whose limits circumlocate particular things within their immediate environments.
III
Given the choice between Whitehead’s two models of creation—“Immanence” versus “Imposition”—Aristotle, in revealing contrast to Plato, opts unambiguously for a model of immanence. This is to be expected, for the Aristotelian scheme of things does not contain anything even remotely resembling chaos (the word itself appears in the Physics only as a vestigial term). Only by a process of conceptual prescinding does Aristotle reach the level of “prime matter” (prōtē hulē), which is as close as he allows himself to come to chaos. But prime matter is too indefinite in status to exist by itself. Instead, in the physical world—and that means effectively everywhere, since “everything is in [this] world” (212b18)—we encounter only matter that is already informed. In this world, material bodies have their own integrity thanks to their indissociably hylomorphic character. There is thus no need to explain the infusion of form into matter, much less the generation of an entire well-formed cosmos. The invocation of the Demiurge may have been essential in a situation in which sheer sensible qualities had to be transformed into full-fledged material bodies with stereometric shapes, but any such invocation is now pointless. Since the physical world takes care of itself by appearing from the start as fully formed, the only pertinent deity is an utterly stationary Mover who is (despite the appellation) eternally at rest outside the world and thus in effect nowhere at all. All places belong to the world, but the world-all itself has no place of its own.23 We have come a long way from the temptation to posit a primordial no-place: now the only philosophically legitimate null place is located neither before creation (as in ex nihilo accounts) nor between bits of created matter (as in the infinite void of the Atomists) but in the very being of the Unmoved Mover. If it is indeed true that there is “no place or void or time outside the heaven” (De Caelo 279a12–13), then the Mover itself is placeless.
A crucial paradox emerges from this situation.24 In a text such as the Ti-maeus, a quasi-diachronic account of creation leads both to the positing of a preexisting Space (along with its various regions and places) and to the need for demiurgic intercession in order to give regular shape to formless sensible qualities. Space is thematized in an account whose narrative nature entails Time. In the Physics, a nonnarrative account plays down place at the origin: placelessness obtains “outside the universe” (212b18). The paradox is thus double-sided: where a time-bound tale such as that told in the Timaeus requires deity to interpose itself literally in place—to give shape to qualities in particular places so that “the ordered whole consisting of them [can come] to be” (Timaeus 53a)—the timeless tale told in the Physics gives to its deity no place to intervene, given that this deity exists outside the world-whole of perceptible bodies in a metaphysical Erewhon of its own. In the one case, time and place conspire to draw deity into the world—at least during the critical event of creation. In the other, deity remains out of the world in a timeless and placeless state. The conception of a richly regionalized and still unordered world, spatially inchoate even if not strictly chaotic, gives way to the idea of a world at once coherently placed and formally shaped—a world having an immanent order that is the rigorous counterpart of the independence of the Unmoved Mover.
One important corollary of this shift in outlook concerns the role of mathematics and of geometry in particular. If the created world of the Timaeus involves what might be called an “ingrafted geometrism”—that is, the introduction of plane triangular figures as the primary structures of the surfaces of solids—there is no trace of any such externally infused geometrization of material things in the Physics. What had been essential to Platonic cosmology (creation necessarily includes geometrization in the Timaean account) is viewed with deep skepticism by Aristotle, who might well have applied to this cosmology Eugène Minkowski’s sardonic pathognomonic label “morbid geometrism.”25 If the world already possesses an inherent ordering that includes form or shape as well as place, to call for a separate act of geometrizing is an otiose gesture.26
I dwell thus on the disparity between Plato and Aristotle—especially
