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The Emergence of Space in Hellenistic and Neoplatonic Thought
All that is is place.
—Lucretius, De rerum natura
All there is is place.
—Richard Sorabji, Matter, Space, and Motion
I
The nature of the universe is bodies and void [to pan esti sōmata kai kenon].
—Epicurus, Peri phuseōs (On Nature)
One’s thought of the void does not give out anywhere.
—attributed to Cleomedes
Part of the perennial appeal of Aristotle’s conception of place as something confining and confined is doubtless the philosophical support it offers to human beings’ longing for cozy quarters—not merely for adequate shelter but for boundaries that embrace, whether these boundaries belong to decorated rooms in the home or to indecorous glades in the forest primeval. But human beings (and doubtless other animals) also long for wide open spaces and thus for lack of containment, perhaps even for limitlessness. The cozy can be too confining, and just to peer out beyond thick walls or through dense treetops into the sky is to discover the inviting and intriguing presence of empty spaces and unoccupied places.
One way to sanction this different longing is to posit a cosmological model radically divergent from that of Aristotle—or, indeed, from those of Plato and Anaximander, the thinker of the Boundless, to apeiron.1 The ancient Greek world knew such a model: put in crude but compelling terms, the Atomists held that there is nothing but “atoms and the void.” Atoms are incredibly condensed and indivisible bits of matter (a-tomos means “uncuttable”), and the void is the open space, the free leeway, required for their random motions. Consider the cosmogony of Leucippus, the earliest Atomist and the presumed mentor of Democritus (both lived in the fifth century B.C., approximately two generations before Plato).
The coming to be of the worlds (cosmoi) is thus: (1) In severance from the infinite, many bodies, of all varieties of shape, move into a great void. (2) These, being assembled, create a single vortex, in which they collide, gyrate in every way, and are sorted like to like. (3) When because of the number they are no longer able to move round in equilibrium, then the fine ones move into the void outside, as if sifted, while the remainder stay together, become intertwined, join courses with each other, and bring about a first system, in the shape of a sphere.2
This cosmogony is said to proceed by “necessity” (anankē). Unlike Plato’s account in the Timaeus, however, this likely story includes no formative Demiurge, since “all varieties of shape” are present from the start. Also present are “the infinite” (again to apeiron, but now construed not just as boundless but as a positive being), “the great void,” and “many bodies.” These three crucial constituents of the universe—that is, of to pan—are uncreated and pregiven. From them, everything else ensues: regions of “like” things as well as the earth, the sun, the moon, the stars, and all other celestial bodies. The great void is the gathering area for those bodies that will form “a first system,” that system being our own cosmos.3 Other cosmoi will form in what Leucippus calls “the void outside.” Taken together, the great void and the void outside constitute the infinite void, and this all-encompassing void is differentially populated throughout by those compact indivisible material bodies called “atoms.”
The Atomist model entails a double infinity: the infinity of space and the infinity of the atoms that populate this space. Just as there can be no end to space in the universe, so there is no end to the number of atoms (and thus, as a corollary, to the number of worlds to which atomic combinations in turn give rise). As Epicurus (341–270 B.C.) put it, “The totality is infinite both in the quantity of atomic bodies and in spatial magnitude.”4 Instead of there being a fixed number of elements that make up material bodies—as Empedocles, Plato, and Aristotle all believed—the elements and bodies themselves are constituted from an unlimited number of atoms in diverse configurations. In fact, the two Atomist infinities here in question are closely related. On the one hand, an infinite number of atoms requires an infinite space in which to move; anything less would curtail their motions. (Also required is that this infinite space be essentially empty [kenon] or at least “porous” [manon].)5 On the other hand, an infinite space calls for an infinite number of bodies within it; otherwise, it would be merely the region for a few, or even many, bodies—but not for all possible bodies.6
The Atomists would agree with their archrival Parmenides that what is real is a plenum, adding only that what is real is plural and not singular. Since the void per se is empty of any material body, this means that the void in any of its three basic guises is necessarily “unreal” or “not real” (mē on). Yet the void exists (einai); indeed, as we have just seen, it must exist—exist as providing space—if the motion of the atoms is to be possible.7 As Aristotle is reported to have said concerning this double ontology: “The real exists not a whit more than the not real, empty space no less than body.”8 Atoms and the void, the ultimate constituents of the physical universe, both exist, although only one is real in any strict sense. Even if one has “being” (to on) and the other does not, they rejoin each other in the co-necessity of their common existence.
The ingrained wholism of Aristotle and Plato—their passionate desire for perfection, especially of a teleologically ordered sort—ends in a cosmographic picture of a closed and finite world with no further universe around it. In contrast, the Atomists seek, beyond minuscule atoms, that which is infinitely large—a universe of empty space. In the first case, an overriding concern with formal, rational order (an order that, if not found initially, has to be added to the precosmic matrix) eventuates in a world of discrete places, whereas in the second case a commitment to “saving the appearances” (and especially the appearances of particular perceptual objects) calls for a vision of an infinite spatial universe, populated by sporadic and endlessly varying combinations of atomic units—both universe and atoms sharing in a like imperceptibility.9 This difference of vision suggests that a radical departure from the primacy of place (first evident in Hesiod) occurred in the thought of the inaugural Atomists. For does not classical Atomism—a thousand years before Philoponus and two thousand years before Newton—plunge us into an unaccommodating, placeless space? Is there any place for place within the Atomistic void?
Democritus and Leucippus will not help us directly with these questions. Not only is the surviving evidence of their full-scale systems—called intriguingly the Great World System and the Little World System—extremely scanty, but these founding figures were not alive to answer Aristotle’s scathing critique of the void. Epicurus, who visited Athens at the time of Aristotle’s death in 322 B.C, was in a better position to answer this critique. This latter-day Atomist conceded to Aristotle that void is indeed placelike in certain basic respects. The concession was so striking that modern editors of Epicurus have been tempted to alter the standard Atomistic phrase “bodies and space” (sōmata kai chōra)” or “bodies and void” (sōmata kai kenon) to “bodies and place” (sōmata kai topos). However controversial this emendation has proven to be,10 the temptation is based on a substantive point. For the more Epicurus pondered Aristotle’s objections to the void as superfluous—superfluous precisely insofar as it duplicates what is already accomplished by place qua topos—the more he came to conceive of the void as locatory in nature. Void is that “in which” (hopou) atoms are located and that “through which” (di’ hou) they move.11 Precisely as such, it is what immediately situates any given atom. Does this mean that void surrounds the atoms it situates? One recent commentator draws our attention to
the striking similarity of Epicurean void, [regarded] as place, to Aristotle’s fluid, immediate place for moving objects. . . . [This void] is not a sort of extension that could be filled or not filled. It was simply an anaphēs phusis (“intangible substance”) surrounding the distinct, constantly moving atoms. . . . Void is accepted as the absence of body, but not, on that account, as the unoccupied part of an extended space. . . . For Epicurus, an atom did not strictly speaking occupy space; it was simply surrounded by the absence of body.12
If this characterization of Epicurus is right, then the mere existence of atoms does not, after all, entail the existence of open and empty, much less infinite, space. No such amplitude, no such vacuity, is required. To each atom there corresponds only a quite particular place in which it is located at any given moment. The fact that atoms are always moving means only that their places are continually changing. On this view atomic motion does not demand an abiding space that is “a continuous entity subsisting everywhere in the same degree and manner, both where bodies are and where they are not.”13 In short, we can retain the basic Atomist cosmologic that says “if there were no void, there would be no motion; but there is motion; therefore, there is void”14—without having to interpret such a void as continuous or empty, not to say infinite. The void is finite; it is the very place of each and every atom.
Epicurus rejoins Democritus and Leucippus by maintaining that a distinction is to be made between genuinely empty space or “void proper” (as we can call the original sense of void in the phrase “atoms and the void”) and what ought to be termed “vacuum,” that is, an empty part or portion of a compound entity constructed of atoms, for example, an empty stomach in a hungry human being. A vacuum is a form of nonbeing, even a nothing, but it exists within the compound—which in turn exists within the void proper. This is why we can speak intelligibly and not merely oxymoronically of a vacuum as a nonbeing that exists: here the ancient paradox is seen to apply to a more discrete entity. The vacuum exists precisely as a “space-filler” in the apt term of David Sedley, who remarks that a vacuum “occupies some parts of space just as effectively as body occupies others.”15 The Archytian axiom is undisturbed by this claim: for a vacuum exists just to the extent that it has a place in which to exist.16 Void proper—redescribed as “intangible substance” by Epicurus—is what provides such a place, its source as it were. Yet neither void nor vacuum is place in Aristotle’s strict sense of an always already occupied locus for fully formed material objects.17
Nevertheless, Epicurus, unlike Leucippus and Democritus, explicitly identifies void proper with what we must begin to call space. The best account of this momentous step is given by Sextus Empiricus.
Therefore one must grasp that, according to Epicurus, of “intangible substance,” as he calls it, one kind is named “void” (kenon), another “place” (topos), and another “room” (chōra), the names varying according to the different ways of looking at it, since the same substance (phusis) when empty of all body is called “void,” when occupied by a body is named “place,” and when bodies roam through it becomes “room.” But generically it is called “intangible substance” in Epicurus’ school, since it lacks resistant touch.18
This remarkable passage supports the contention that Epicurus was “the first ancient thinker to isolate space in the broadest sense.”19 If Sextus is right, Epicurus does so by positing a generic space—that is, what is coextensive with intangible substance (anaphēs phusis)—and then recognizing at least three roles or functions of such space. “Void” (kenon), true to its sense as “empty,” names the circumstance of unoccupied space; it is tantamount to what I have just called “vacuum.” “Place” (topos) names the situation of occupied space; it refers to the location of a sensible thing in space. The thing thus located in a topos is so far stationary, and to account for the different sense of localization possessed by a moving thing Epicurus posits a third avatar of space: “room” for something to move in. “Room” translates chōra, one of whose affiliated verbs is chōrein, “to go,” especially in the sense of “to roam.”20 From its initial role as matrix in the Timaeus, chōra here becomes a much more delimited power—yet a critical one, since for all the Atomists the primary bodies are in constant motion, a motion that requires room in which to move. Such room, affording leeway to solid objects (atoms, even if imperceptible, are “impassible” magnitudes), is literally voluminous. Aristotle’s confining two-dimensional model of place—two-dimensional insofar as it limits itself to the surfaces of things—is surpassed in a three-dimensional roominess.
Thanks to its considerable dynamism, Epicurean space is the Spielraum of atomic bodies, the very medium of their situatedness and movement, the scene of their multiple occupation. Such space “provides these bodies with location, with the gaps between them, and with room to move.”21 Expansive as such space is—giving place and room for everything—it does not pertain to parts of atoms (assuming that atoms have parts), nor does it exist as intervals among atoms of a given body, nor does it even furnish the very position of a given atom.22 Epicurus might respond that this triple limitation follows from the basic premise that atoms “have no share in the void.”23 Yet if atoms have parts and intervals and positions and if they do indeed exist—and if to exist is to exist in space—then these three aspects of atomic existence will have to be spatially specified. One suspects that Epicurus has not thought through the full implications of his own idea of a sheerly intangible space. If space construed as anaphēs phusis is to be taken seriously, its scope will encompass both the utterly large (the infinite) as well as the utterly small (the infinitesimal), including the most diminutive parts, intervals, and positions.
Lucretius (ca. 99–55 B.C.), Epicurus’s devoted and eloquent disciple, adds this thought: “Whatever will exist will have to be in itself something with extension (augmen), whether large or small, so long as it exists.”24 Here Lucretius is drawing on an entire heritage of thought concerning “extension,” a notion of critical importance in the Hellenistic period. Diastēma, the Greek word for “extension,” implies standing!through (dia- signifies “through,” and stēma derives from the Indo-European root sta-, “stand”) and, more particularly, threading/through (stēmōn means “thread”). To be in space is to stand through it, to stretch through it as a thread might stretch over a surface—except that more than surface is at stake here. The “through” is not only entailed by motion in a void but also is implied in all ways of being spatial.
For Epicurus and Lucretius alike there is an intimate link between the noun “extension,” the preposition “through,” and the concept “space.”25 If placial being is mainly a matter of the “in”—this much we may grant to Aristotle—spatial being is a matter of the “through,” that is, a matter of being “extended,” stretched out such that something exists through the interval or gap that space provides. Instead of being something turned in, en-closed, as in the case of Aristotelian place, space is something turned out; it is something that exists throughout whatever interval is at stake—an interval that can be infinitely large or infinitely small. Atoms may well have a different “order of being,” a different way of existing, than the void proper; the former are essentially plenary, the latter is essentially unoccupied.26 Even so, both atoms and the void must meet certain requirements of existing spatially. These are the requirements of diastemic space as first clearly glimpsed in the Atomism of Epicurus.
II
Some say that chōra is the place of the larger body.
—Sextus Empiricus, Against the Professors
One ancient thinker—not an Atomist but an Aristotelian—thought long and hard about the microphysics of space. I refer to Strato of Lampsacus, the third head of the Peripatetic school, who died ca. 269 B.C. and thus was an exact contemporary of Epicurus. Ancient tradition credits Strato with being the first thinker to proclaim space to be extended in three dimensions, also holding that any part of it always in fact contains a body—even though, in principle, it might not.27 Stobaeus attributes to Strato the following definition: “Place (topos) is the interval in the middle of the container and the contained.”28 At first glance this appears quite Aristotelian, but on closer inspection it turns out that Strato takes place to be something that Aristotle explicitly rejects: the empty pockets found in the interstices of material bodies. These pockets riddle such bodies: “Strato of Lampsacus tries to show that the void exists interspersed in every body so that it is not continuous.”29 Places are thus void spaces: “microvoids,” as we might call them. Even if microvoids are never actually vacuous—Atomists’ claims notwithstanding—they are instances of extension at the most elementary level. Microvoids exist not only between container and contained (which for Strato are far less snugly fitting than Aristotle had imagined) but also within a given material body. Hence they pertain to two of the three aspects of atomic extension neglected by Epicurus: interiors and parts of primary bodies. In fact, they are coextensive and isometric with the interiors and parts of actual bodies that fill them. At the limit, the totality of microvoids may even be coextensive with the “cosmic body” that is equivalent to the complete physical universe.30 It is not certain that Strato espoused this extreme position, but he did maintain that any given microvoid is an integral part of cosmic extension and not a mere lacuna in this extension. Hence he managed to put together what Epicurus failed to combine: the extension of the infinitely large and the extension of the infinitesimally small.
Strato also was known in the classical world for having devised the most convincing denial of Aristotle’s notion of natural places, that is, places proper to given elements. According to Strato, every element is heavy and thus falls downward by its sheer weight. If fire and air escape upward, this movement is due to a process of ekthlipsis, that is, being “squeezed” up by the compression of other more forceful elements. By thinking this way, Strato agreed with Epicurus and the earlier Atomists in rejecting the idea of preexisting places in the void. There is indeed differential direction in the void, but this is determined by chance collisions of atoms and not by the power of extant cosmic places.31 And if there are no places carved out of the cosmos in advance, then it is all the more likely that the universe lying beyond the world is something infinitely extended: and this universe is more aptly characterized in spatial rather than placial terms. Just as for Aristotle there is no space apart from place, for Strato there is no place apart from space—no place that is not merely a portion of a much more encompassing whole whose spatiality is both incredibly large and unimaginably small.
If the unimaginably small is a distinctive concern of the Atomists and of Strato, the incredibly large is what increasingly preoccupies ancient philosophers in the wake of Aristotle and Epicurus. One exemplary form of this preoccupation is found in the Stoic proposal that an endless empty void surrounds the finite and place-bound cosmos. The explicit reason for this proposal—which continued to be widely influential in the Middle Ages and the Renaissance—is that the excess fire generated in periodic cosmic conflagrations has to go somewhere, since the volume of this fire is greater than the finite cosmos can contain. This “somewhere to go” is termed “room” (chōra), where “room” connotes spaciousness, that is, unoccupied space to which to flee.32 The extramundane void is what provides room for world-destructive conflagratory fires.33 Does this mean that such a room-giving void is a place? Cleomedes, writing in the first century A.D., claimed that the void must be “capable of receiving body.”34 This would seem to make it some kind of place. Yet the Stoics took seriously Aristotle’s admonition that the void is “that in which there is no body,”35 and such a void would be a very tenuous place indeed. Perhaps we may say that something (e.g., the cosmic fire) can be received by the extramundane void but cannot occupy it in any strict sense, that is, cannot be implaced there. It can enter the void yet cannot remain there—cannot find therein its own place.
It is an axiom of Stoic cosmology that the void is infinite and place finite.36 With no bodies strictly occupying it—in contrast with the ancient Atomist “void outside”—the Stoic void is neither bounding nor bounded. According to Chrysippus (280–206 B.C.), “the void beyond the cosmos is infinite, unbounded (apeiron) in the literal sense of the word; it has neither beginning nor middle nor end.”37 In fact, the Stoic void lacks both bodies and boundaries: it is “an interval empty of body, or an interval unoccupied by body,”38 where to be an “interval” (diastēma) is precisely not to be a place for a body. Cleomedes characterizes such a void as something “very simple, since it is incorporeal and without contact, neither has shape nor takes on shape, neither is acted upon in any respect, nor acts.”39 In other words, void is an empty extension that has taken the place of place itself: it has (de)voided place. If this is beginning to sound like “negative cosmology”—as is already indicated in the very word “in-finite” (and in a-peiron)—we can at least say, in a more positive vein, that the Stoic void is infinitely large, infinitely absorptive, and altogether external to the cosmos. It gives room, if not place proper, to an expanding cosmos. It is a macrovoid outside the cosmos—the very converse of a microvoid internal to the cosmos and to bodies in that cosmos.
Such an extramundane void is a negatité (to borrow a useful term from Sartre): even if not (a) nothing, it is also not an entity, neither a thing nor a place. It stands in stark contrast with the packed and plenary character of the cosmos, which for the Stoics does not possess void of any kind—neither in the form of microvoids nor as the tiny interstices between polygons that are mentioned in the Timaeus. The cosmos has everything the void lacks; it is full of places and bodies, and full of one in being full of the other—double plenitude.
Chrysippus declared place to be “what is occupied through and through by an existent, or what can be occupied by an existent and is through and through occupied whether by one thing or by several things.”40 Nothing empty, nothing a lacking, nothing tenuous here! Place is a dense fabric in the even denser place-world it composes. Guaranteeing coherence and connection in this cosmic plenum is the pneuma, the cosmic breath or spirit that circulates throughout the plenary world. Composed of fire and air, the pneuma is an active force that transmutes Plato’s and Aristotle’s geometric continuum of discrete bodies-in-places into a dynamic network of implaced and interpenetrating bodies.41 Proceeding by a combination of habit (hexis) and tension (tonos), connection (sunecheia) and sympathy (sumpatheia), the pneuma constitutes “the physical field which is the carrier of all specific properties of material bodies.”42 This field is a close concinnation of places; it is as place-full as the void is sheerly space-rich.
“Under Chrysippus’s guidance,” writes David Hahm, “the Aristotelian cosmos of elements, each moving by nature to its own concentric sphere, is finally given a comfortable home in the infinite void.”43 Yet there is a darker side to Stoic physics: isolation, not comfort, looms. The cosmos, the physical world as we know it, is “an island embedded in an infinite void.”44 To be an island, however replete with places and bodies, is to be sequestered in an ocean of indifference. Moreover, if the only void is the void “outside the world,”45 this leaves precious little leeway for maneuver in this world.
The Stoics were not insensitive to the problems inherent in the bifurcation of the universe into empty and full, void and place, the incorporeal and the corporeal, with material bodies brought forcibly into place by inescapable pneumatic forces. To address this dilemma, some Stoics speculated that a third entity is required to break the gridlock of their fiercely dichotomous universe. Thus Chrysippus “distinguishes an unnamed entity, different from void or place, that is capable of being occupied by being, but is only partly occupied.”46 This third thing is none other than “room.” Room is not just space for roaming—as it was for Epicurus—but extension allowing for possible occupation. Extension and room, diastēma and chōra, come together in a single complex, or more exactly a duplex, entity: cosmos-cum-void.47 The duplexity is evident in Sextus Empiricus’s assertion that for the Stoics the universe is “the external void together with the world.”48 Or we might say that void and place merge in space, and they do so in the room space furnishes.
Yet this leaves us wondering if “room” and “space”—both terms being translations of chōra—are not merely terms of compromise, posited to conceal the abyss opened up by the diremptive difference between place (topos) and the void (kenon) that lies at the heart of Stoic cosmology. This is not to say that the compromise in question represents an admixture of equal parts of place (or world) and of void. Void is given the major emphasis insofar as its infinity is presupposed by the very room that promises to heal the cosmologically troublesome dichotomy of void and world: “The ‘whole’ [i.e., to holon] is finite, since the world is finite, but the ‘all’ [i.e., to pan] is infinite (apeiron), since the void outside the world is such.”49 For room or space to combine place and void, it must be at least as capacious as void; hence it must be as infinite as the void it coadunates with place. With the Stoics, therefore, we take a concerted step toward the view that space, affording room and as modeled on the void, is—properly and primarily—infinite.
III
Place is animated through the primal soul and has a divine life.
—Proclus, cited by Simplicius
It is likely that place first enjoyed the divine illumination, especially the place of more complete and perpetual things.
—Simplicius, with reference to Damascius
Neoplatonic notions of place and space take account of Stoic, Epicurean, and earlier Atomist conceptions—while always addressing themselves explicitly to Plato and even more especially to Aristotle. In many respects, then, Neoplatonists confirm ideas and distinctions that we have already encountered. Iamblichus (A.D. ca. 250–ca. 325), for example, distinguishes “limit” and “boundary” in a manner reminiscent of the distinction to which my discussion of Aristotle progressed in the last chapter.50 Syrianus (active in the fifth century A.D.) speaks of “room” in a sense that directly recalls Chrysippus: “Extension goes through the whole cosmos and receives into itself the whole nature of body . . . conferring room (chōra) and receptacle and boundary and outline and all suchlike upon all things that fill up the visible cosmos.”51 The extension that gives room is designated by the same term (diastēma) as that used by many previous thinkers, but here its meaning is not restricted to mere “interval” construed as a span or gap or interstice between or within determinate entities (whether atoms or bodies). For a Neoplatonist such as Syrianus, diastēma refers to the boundless and immobile and (usually) incorporeal spread-outness that “goes through the whole cosmos,” a cosmos no longer distinguished from the universe. Such extreme expansiveness is coextensive with what Syrianus calls intriguingly “a different body, the more universal one.”52 This body is in turn identified with “broad, shared place”—place so broad as to have no effective limits.53 The more we push the roomfulness of extension, however, the closer we come to the quite modern idea of a space that in its uncompromised infinity is considered “absolute.”
Thus far we find ourselves on more or less familiar terrain. What do the Neoplatonists introduce that is novel? At least two basic lines of thought.
(1) The first is that there are more kinds of place, each with more sorts of power, than Aristotle dreamed of. Plotinus strikes the opening note in his Enneads: “The place of the intelligible world is the place of life and the very principle and source of the soul and the Intellect.”54 Both kinds of place here mentioned—that of the “intelligible world” and that of “life”—are unreducible to the physical surrounder made paradigmatic by Aristotle in the Physics. Once Pandora’s box is opened in this fashion, there is no limit to the sorts of place one can consider as fully valid instances. When Aristotle spoke of the mind as “the place of forms” in the De Anima, he was speaking metaphorically. But when Iamblichus talks of “formal place,” he is not ascribing place to forms by means of a trope. He means straightforwardly that forms—in the Platonic sense—possess their own proper sort of place, to be distinguished from physical place as well as from the place of life and from what Iamblichus calls “intrinsic place.”55 The claim of variety comes paired with a claim concerning the plurality of the powers of place. As Richard Sorabji remarks, “It is because the concept of place has so many other applications [than simply surrounding] that a dynamic conception is required to fit all the cases.”56 When Aristotle said that place “has some power,” he meant the particular power of encompassing the physical things it contains. Iamblichus does not deny this power—especially if it is not merely an external delimiting function but one that bestows boundary (horizein)—yet he insists that place possesses a set of distinctive strengths beyond that of surrounding (periechein).
One has to conceive place not only as encompassing and establishing in itself the things existing in place, but as sustaining them by one single power. Regarded thus, place will not only encompass bodies from outside, but will fill them totally with a power which raises them up. And the bodies sustained by this power, falling down by their proper nature, but being raised up by the superiority of place, will thus exist in it.57
Iamblichus’s own list of the plenipotentiary powers of place includes, then, supporting, elevating, and filling up. Underwriting this list is the basic twofold action of
•raising up bodies that would otherwise fall into the degradation of prime matter, filling them with a power that elevates them;
•drawing together bodies and parts of bodies that are already dissipated from their contact with prime matter, the lowest form of existence in the Neoplatonic universe: “gathering together the scattered ones.”58
“Up” and “together” are thus to be added to the “around” and “in” of the repertoire of placial powers. To be implaced is not just to be cozily contained by an encircling surface but to be sustained by powers that ensure that what is in place will be inherently stronger for having been there. If the Aristotelian model of containment makes possible definition and location, the Iamblichean model of sustaining engrafts the dynamism of implacement onto what exists in place. This is why Iamblichus says expressly that “place is naturally united with things in place”59—instead of just surrounding them or offering them “bare extension” (diastēma psilon), much less (as the Stoics are held to assert) merely “supervening upon them” (paruphistasthai). To be “united with” (sumphuēs) is to be dynamically linked with something—to make a difference not just in its shape or form but in its very being or reality (ousia). Place is thus “never separate from [a body’s] first entrance into existing things and from the principal reality.”60 Through place, reality is reached. Through reality, place is maintained.
Indeed, place has its own being, on the basis of which it is a “cause” (aitia) and not something merely inert or passive (argos, adranēs)—something caused by something else in turn. As Simplicius points out in the sixth century A.D., the essence of something and its place are difficult to distinguish, driving him to posit an “essential place” that is “naturally united with substance [i.e., the substance of what is in place].”61 For Iamblichus and Simplicius alike, a place “has reality in itself and “has an active power as well as an incorporeal and definitive reality.”62 In attributing such power and reality to place, these authors contest Aristotle’s denial of place’s intinsic causal power. Not only does place have such a power, it is a causal power: it is “a power that acts” (drastērios dunamis).63
(2) The second new line of thought is that the less material place is, the more powerful it becomes. This notion derives from the basic premise that “everywhere the incorporeal reality ranks as prior to the corporeal one.”64 It follows that places incorporeal in nature will be superior in effective power to material places. Another corollary is that incorporeal places will be more powerful than anything physical they can be said to contain: as Iamblichus says, “Place, being incorporeal, is superior to the things that exist in it; and as something more independent it is superior to those things which are in need of and wanting to be in place.”65 The power of incorporeal place is even exerted over extension itself: instead of being dependent on a pregiven cosmic or universal extendedness, place generates the very spread-outness of the things it serves to situate.66 Iamblichus explicitly contrasts this view with that of the Stoics—who are said to hold that “place subsists upon bodies”67—and claims to have rejoined Archytas: “Clearly he assumes place to be of a higher rank than things that act or are acted upon.”68
In Iamblichus—that exemplary Neoplatonic thinker of place—we see the “intellective theory” (noētē theōria) of implacement in its full-blown expression. The place something is in is not only more real than the implaced thing; it is itself situated in increasingly intellective and ever more elevated kinds of place: material things are in the world’s body (i.e., the cosmos), which is in the World Soul, which is in the Intellect, and so on. There is a virtual shell game of steadily improving implacement in which each place-level is at once sustained and surpassed in the next until we reach the ultimate level of the One that provides (again in Plotinus’s phrase) “the place of the intelligible world.” This escalating model of implacement can be regarded as an attempt to reconcile Aristotelian encasement with Platonic ascension to the final forms of things.69
The intellective or noetic nature of place was a theme throughout the history of Neoplatonic thought, for which place was a central theme for four continuous centuries—from Plotinus (A.D. ca. 205–260) to Simplicius (who flourished after A.D. 529). The two thinkers who pursued this particular theme furthest, however, were Damascius and Proclus. For Damascius, who served in the sixth century as the last head of the Athenian branch of the Neoplatonic school, place in general exhibits its power and superiority by its ability to measure what is in place. The positioning of the parts of something as well as the size of that something are measured by the place it is in. The measure (metron) is conceived as a mold or outline into which the implaced thing is set: “Place is as it were a sort of outline (proüpographē) of the whole position (thesis) and of its parts, and so to say a mould (tupos) into which the thing must fit, if it is to lie properly and not be diffused, or in an unnatural state.”70 As the idea of mold indicates, far from being a measure that proceeds in terms of numbers, placial measure is more like a shaping force that acts to hold off the diffusion inherent in prime matter. Such measuring resembles measuring through more than measuring out: it is through the configuration of a given place that the measure of a thing-in-place is taken.71 Rather than giving exact quantitative assessments—which require a rigid ruler of some sort—place as metron is more plastic than it is rigid, with the result that, as Sorabji comments, “it can allow for a variety of positionings, as it does in the case of the moving heavens.”72 Aristotle’s obsessive question as to what kind of place the heavens occupy is here answered by the view that they occupy a nonrigid, molded place—not entirely unlike the receptive regions proffered by primordial chōra, which is also characterized by Plato as acting like a mold. Such a place, precisely by virtue of its measuring power, ranks as superior to all the particular places it encompasses. Simplicius, commenting on Damascius, brings out the assumption at stake here: “The nature of the measure is superior to the nature of the measured and is not in need of the same things as [the measured] is.”73 Given this assumption, it is clear why Neoplatonists tend to give priority to places that are noetic in nature.
But the matter is more complicated than this. Proclus (ca. 411–485), a quintessential Neoplatonist, considered place to be a body and not just something around a body (or through which a body moves, or in which it is located). Yet, despite its corporeality, place is at the same time immobile, indivisible, and above all immaterial. Place an immaterial body? Proclus is driven to this intriguing idea in an effort to imagine an adequate vehicle for the World Soul. Such a vehicle must be immaterial—that is, must lack the dissipative effects of prime matter—if it is to escort anything as pure as the World Soul. Indeed, the place of the World Soul “must be the most immaterial of all bodies, of those that move as well as of the immaterial ones among those that move.”74 The only candidate for such a sheerly immaterial place is light and, more especially, supracelestial light. This latter, hinted at in Plato’s Myth of Er, is luminous without being literal illumination. Proclus appropriates this most diaphanous of media as a model for place of all kinds and in particular for that place which is “the luminous vehicle of the World Soul.”75 This is not sheer spiritualism, for there is a distinctive geocosmic specificity in Proclus’s model of the universe.
Let us then conceive two spheres, one made of a single light, the other of many bodies, the two equal to each other in volume. But seat one concentrically with the other, and on implanting (embibazein) the other in it, you will see the whole cosmos residing in its place, moving in the immobile light.76
Instead of thinking of the cosmos as an isolated island in an empty universe, Proclus contends that the physical world is coextensive with the luminous supracelestial sphere. As a form of light, this sphere is bodily and elemental; but as a place, it is immaterial. To be immaterial in this manner, however, is to be quite dynamic: the sphere of light is “called place (topos) as being a certain shape (tupos) of the whole cosmic body, causing unextended things to be extended. . . . [Such a] place is animated through the primal soul and has a divine life, being stationary, self-moving intrinsically, [even if it is not] externally active.”77 The sphere of supracelestial light is a Place of places, for it is the vehicle of the World Soul as well as the very place of the cosmos—at once its center and periphery, situating everything in between. Nowhere is there not such light; wherever there is something, it is there in the light—there somewhere, there in a particular place within the absolute Place of the universe. I capitalize this Proclean Place to suggest that it is an adumbration of infinite space. As “supracelestial,” the ultimate sphere of light has a peculiar standing: as bodily, it has sufficient density to count as a place (thus is able to mold, measure, etc.), and yet, as immaterial, it is not the positive infinity of the physical universe that will be the obsession of seventeenth-century speculation. If not yet strictly infinite, however, the supracelestial sphere can be considered absolute: it “forms a kind of absolute place against which the cosmos can rotate and other things move.”78
What Proclus teaches us is that in Neoplatonic thinking there is no contradiction between the bodily and the noetic character of place. A place like the supracelestial sphere is composed of light—it is corporeal—and yet it ranks high in the ascending noetic scale of being. This vision is in many ways the exact converse of the Atomist view of place. Where place for the Atomists is mechanical and physical, that is, bodily and material (and nothing else), place for the Neoplatonists is dynamic and intellective—and one thanks to the other. Moreover, indivisibility now pertains to place, not to atoms: as Proclus puts it bluntly, “Place is an indivisible body.”79 The immateriality of place also allows Neoplatonists to escape the confines of the Aristotelian container model, whose resolute physicalism dictates that the encompassing surface of place has to be material if this surface is to secure sensible bodies in place. Once it is agreed that place need not be physical, place can effect more than delimitation and location: it can preserve and order, support and sustain, raise up and gather. The singular inertia of a material surface is replaced by the plural dynamics of an immaterial presence. The dynamics can be forceful—even holding up bodies from a quasi-gravitational downward pull—as well as subtle. The subtlety is evident both in the nonnumerical measuring power of place and in such ideas as the situatedness of all things in “the luminous vehicle of the World Soul.”
A Neoplatonic approach to place vindicates the common conviction that place always implies some sort of quantity (i.e., some amount of “room”) while also always involving a set of distinctive qualities (as is indicated in such expressions as a “pleasant place,” a “dangerous place”). Just as it is advantageous not to have to tie the quantum of place to arithmetical determination (or else we find ourselves in the midst of land surveys, property lines, and the like), so it is helpful not to limit the qualitative aspects of place to literally sensible properties. Thus Proclus’s idea of a preternatural “light above the Empyrean”80 enables us to draw on the panoply of properties of a natural phenomenon such as light while not enclosing ourselves in the straitjacket of a reductive physics. The immateriality of the noetic notion of place also rejoins Epicurus’s idea of “intangible substance”—without, however, exacting a commitment to a macro- or microvoid. As corporeal, the universe is plenary and not vacuous; but as immaterial, it enjoys the flexibility required for the empowerment and determination of things in place. This conception also artfully avoids the awkward dichotomy inherent in the Stoic view that the world is plenary whereas what lies beyond the world is vacuous. Moreover, when place is recognized as immobile as well as indivisible and immaterial, place can assume an absolute status: as when Syrianus, Proclus’s master, proclaims that “an extension goes through the whole world and receives into itself the whole of corporeal nature.”81
IV
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 been given by the Creator.”101 “Station in the order” translates taxis—the very word that Theophrastus, the first theorist of the essential relativity of place, used in departing from Aristotle. I cite from a celebrated statement of Theophrastus.
Perhaps place is not a substance in itself, but is predicated in relation to the order (taxis) and position (thesis) of bodies, according to their natures and powers, equally in the case of animals and plants and, generally, of things composed of different elements, whether animate or inanimate, that have a natural shape. For the order and position of these parts is relative to the whole being. Therefore each is said to be in its own space (chōra) through having its proper order, since each of the parts of a body would desire and demand its own space (chōra) and position (thesis).102
Theophrastus, Aristotle’s immediate successor in the Lyceum, opened the Hellenistic period in Greek philosophy; Philoponus is often considered the last great thinker of the same period. In between, Stoicism, Epicureanism, Skepticism, and Neoplatonism flourished. Yet Philoponus, the primary advocate of a purely empty extensiveness, was widely regarded as “a true upholder of Theophrastus”103—given that both thinkers attribute power to things in place rather than to place itself, and both believe that the ordering of things in place is the most important single effect of implacement.
The more closely you look at the critical span stretching from Theophrastus to Philoponus—already a first millennium!—the more one becomes convinced that the increasing interest in absolute or infinite space is shadowed at every step by an equal, though often less salient, concern with the importance of order and position in the process of implacement. Damascius’s conception of place as metron, for instance, entails an ordering of the “position” of the “parts” of something: the key words remain Theophrastian. Damascius gives the example of the head being situated above and the feet below in a human body, thereby illustrating that “the order and position of these parts is relative to the whole being.”104 Damascius also extends the relativist model to nonnatural places: “Even among incorporeal things there will be position according to their order.”105 Iamblichus as well, attests Simplicius, is Theophrastian in inspiration: “The divine Iamblichus bears witness to the same position [i.e., as adopted by Theophrastus],”106 namely, in his view that “place is of like nature with things in place.”107 Such likeness both facilitates and reflects the ordering of things in place: the more place is like what is being implaced, the better it can operate as an immanent agency of arrangement, and the more such an arrangement is realized, the more it exhibits a likeness between the things so ordered. (Much the same isomorphism is manifest in the shaking together of like with like that takes place in the primordial regions of the Timaean Receptacle.) Proclus, too, pays close attention to the power of position.
The cardinal points of the whole universe are fixed in it as a unity. For, if the oracles say that the cardinal points of the material universe are fixed in the aether above it, correspondingly we shall say, ascending, that the cardinal points of the highest universe are seated in that light.108
Indeed, not just cardinal points—which are relative to each other and to the directions they serve to specify—but the entire Neoplatonic universe of ascending/descending levels of being betokens a deeply relativist model of place. In this universe, where you are at in the scale of things—your being situated at a material or psychic or noetic level—has everything to do with the kind of being you possess. Position is relative not only to other members of the same level but to other levels in the ontological scale as well.
So powerful is the effect of this scalar model that Simplicius can claim that extension, far from being a universal feature of things, is found only at the lower levels. In the realm of intellective being, there are only unextended and incorporeal items, including the places of noetic items such as ideas and numbers. As descent is made into the realm of matter, extension becomes ever more crucial—an extension that applies to places as well as to things in places. This means that place becomes extended with bodies,109 and is not simply extended on its own and independently of bodies, as is implied on the model of Philoponean spatial and cosmical extension. Extension is thus an acquired attribute of place: “As the body that has position became extended through its decline, so also place that is the measure of position became extended, in the way that is possible for a measure that has declined from the unextended measurer.”110 In this statement of Simplicius, the Damascian idea of place as measure—intrinsically tied to the relativism of internal positions—is set within an emanationism of levels that is no less relativistic in implication. Speaking of place and time alike, Simplicius can comment that “their extension is not like that of other things, seen as they are as a mean between the unextended measurer and the extended objects measured.”111 To be “a mean between” is to have a position in a hierarchy of at least three levels, and thus to have a cosmic position that determines the very character of place and time themselves. Instead of being “God’s infinite sensoria” (Newton) or the universal forms of pure sensible intuition (Kant), place and time are creatures of the level of emanation on which they are situated.
Double positioning is at play, then, in the Neoplatonic universe: first, a structural positioning within the cosmic hierarchy (which determines, in turn, whether place is extended or not) and, second, the pinpointed positioning that is the work of extended place proper (about such place Simplicius says that “everywhere it is the position of bodies and the determination of their position”).112 Moreover, the first positioning makes possible the second: only when place becomes adequately extended at an intermediate level of the emanationist hierarchy can it begin to do its locational work. For only at this level is there a distinction to be made between the immediate, unique, and shared implacements that guarantee a complete positioning for any extended body.113 As a result, the scalar model in its Neoplatonic format allows Simplicius to adopt a relativism that is finally more radical than that of Theophrastus. Where Theophrastus had made “natural shape” (emmorphos phusis) responsible for the “order and position” of bodies, Simplicius attributes this ordering force to place: “Place is a certain arrangement and measure or demarcation of position.”114
V
The signs of the gods are perpetually scattered in places.
—Simplicius, In Aristotelis physicorum libros quattuor priores commentaria
Just as the Neoplatonic proclivity for absolutism in spatial matters harbors an unsuspected underside of place-relativism, so the latter tendency leads, by rebound as it were, to a proposal that encompasses both directions of thought. Only several sentences after the words quoted at the end of the previous paragraph—words that epitomize the relativistic position—Simplicius speculates that when particular positions are not just juxtaposed but “well arranged” (euthetismenoi), that is, “well positioned and well placed” (euthetoi kai eutopoi), they will contribute to the harmony of the whole of which they are parts. Ultimately, all bodies, once they are well arranged, will become inherent parts of the “whole universe,” and this universe itself will have its own place: “so there is, in truth, the whole place of the whole universe (holos topos tou holou kosmou), but it has its supreme position through the good arrangement in respect of its parts and through its whole good arrangement in respect of its parts.”115
This last claim is remarkable. On the one hand, there is a proper place of, or rather for, the entire cosmos. This place must be unique, since there is no other cosmos or anything else of comparable magnitude to which it could be relative. (The idea of multiple worlds, entertained by the Atomists and Epicurus, will not be taken seriously again for another thousand years.) In this regard, the single cosmic Place can be considered the “transcendent measure” of all other places, including those parts and places (and places-as-parts) of which it is composed.116 Concerning such a cosmically distinctive Place, Simplicius can say that “the essential place of the universe has stored up all the varying places and produces from within itself the proper measure of every position.”117 In this monolithic capacity, it is not unlike the Philoponean idea of “cosmical extension.” On the other hand, this same super-place remains relative. Even if the place of the cosmos is not dependent on any of its parts (or on their totality), its “supreme position” does depend on a good arrangement that involves these parts in the following ways.
•The parts must be well arranged among themselves; this is what Simplicius means by the simple phrase “through the good arrangement of its parts.”
•The same parts must be well arranged in relation to the whole they compose—that is, the whole cosmos or universe (terms significantly not distinguished by Simplicius).
•Finally, the cosmos itself must be well arranged in relation to its own parts, both as particular parts and as a whole of parts. This is what Simplicius implies when he speaks of “its whole good arrangement in respect of its parts.”
Simplicius sums up this line of thought by observing that “in general, we do not only say that the parts have a well-arranged position in relation to each other and to the whole, but also that the whole has it in relation to its parts.”118
I single out this final position of Simplicius—himself the last great pagan Neoplatonist—for its special promise as an answer to a question that will preoccupy the rest of this chapter and the next three chapters: Is place, as well as space, essentially relative or absolute? Are they heteronomous in status, that is, dependent on other entities for their being and character, or autonomous, that is, able to stand on their own no matter what their parts (or constituents) and motions are? Simplicius’s response is that place/space is both absolute and relative. Not just both in the sense of an indifferent mixture, but both in the sense of one through the agency of the other. The place of the universe would not be absolute unless it were also relative—and relative in the particular ways just described. And it would not be relative—relative to the parts of which it is composed—unless these were the parts that, in proper arrangement, make up the cosmic whole. Put otherwise, the place of the universe is absolute in certain respects (e.g., in its transcendent all-measuring role) and relative in certain others (i.e., the three modes of relativity just singled out).
Simplicius’s model, ingenious and satisfying as it is in many respects, leaves us with two major unresolved questions. Is there a place of this world, the cosmos? Is there infinite space beyond the cosmos? Aristotle, of course, would respond negatively to both of these questions. Given that place on his view requires an unmoving and immediate inner boundary, the outer heaven cannot count as a place since it has no such boundary; and it is not set in any subsequent extracosmic space either, since there is “no place or void or time outside the [outer] heaven.”119 It was the audacity of Aristotle’s archrivals, the Atomists, not only to propose an unbounded void but also to argue that precisely because there is such a void the cosmos can be located in it. The void gives room for the world to be found within it—just as the world in turn gives “space for body” (in Philoponus’s phrase). It is clear that any such void is infinite in the sense of unbounded. As Hahm comments with reference to the Stoic void, “If there is any void at all beyond the cosmos, it is necessarily infinite, for there is nothing that can bound it.”120 But the void elicits its own disquieting questions: Is it necessarily empty (as its name, kenon, certainly implies and as the Stoics explicitly posited in the idea of a strictly external void)? If so, the cosmos will float in this void as an anchorless entity adrift in infinite space: “How can the cosmos remain intact though situated in an infinite void?”121 Or is it empty only in principle, being always filled in fact (as Philoponus holds)? But then it threatens to become a redundant entity or, rather, nonentity.
Yet no sooner do we give up on the idea of void—or perhaps just restrict its domain of application, as in Strato’s idea of the microvoid—than we run into other questions, at least equally difficult to resolve. Could the universe be at once infinite and plenary? If it were entirely full of bodies, there would then be no space for motion, and it would become a frozen Parmenidean One. Yet if it were not chock-full, we would need more than microvoids internal to bodies to allow for motion. Perhaps, after all (as the Atomists held), there are empty “intervals” between bodies. But how can we determine just how big such intervals would need to be in order to make motion possible? There seems to be no way of giving a generally satisfactory answer to this last question. Maybe because of this difficulty, the very idea of interval (diastema) was expanded by the Neoplatonists to become extension, ultimately the “spatial extension” posited by Philoponus. Yet this latter idea, especially under the guise of “cosmical extension,” returns us to the deeply perplexing issue of whether the cosmos itself has a place. A place for the cosmos may be asserted—as it is by Simplicius—but then we must ask: a place where? Is its place a place in the universe at large, that is, in a space that exceeds the world-place itself? And is such a space finite or infinite?
By this circuitous route, we return once again to Archytas, who is reported to have posed the following conundrum.
If I came to be at the edge, for example at the heaven of the fixed stars, could I stretch my hand or my staff outside, or not? That I should not stretch it out would be absurd (atopos), but if I do stretch it out, what is outside will be either body or place. . . . If it is always something different into which the staff is stretched, it will clearly be something infinite.122
Alexander of Aphrodisias claimed that this thought experiment comes to naught, since what is outside the cosmos is nothing at all, not even a void.
He will not stretch out his hand; he will be prevented, but prevented not as they say by some obstacle bordering the universe (to pan) on the outside, but rather by there being nothing (to meden einai). For how can anyone stretch something, but stretch it into nothing? How can the thing come to be in what does not even exist?123
Simplicius insists similarly that Archytas’s conundrum is question-begging: “In imagination it assumes in advance what it seeks to prove, that there is something, whether empty or solid, outside the universe.”124
Despite these telling objections, Archytas’s provocative puzzle kept arising in ancient and medieval debates, and it still haunts contemporary cosmological thinking. For it will always occur to the cosmologically curious to ask, what lies beyond the last boundary of the known world? If there is some thing there, then I can (at least in principle) get to this thing and even reach beyond it. If there is no thing, then there might be, not nothing (as Alexander assumes), but empty space. This observation indicates that Archytas’s exclusive alternative of “body or place” needs to be supplemented. If place is always bounded—as it is for Archytas and Aristotle alike—then it is not what we encounter when we stretch out our hand or staff beyond the final frontier of the cosmos. What such extracosmic stretching gets us into is something else, and its increasingly unrefusable name is space. This word (or its equivalent in other languages: spatium, Raum, espace, etc.) is required if we are to designate a domain that, itself unbounded, affords sufficient room for motion of all kinds, including the modest motion of a hand or staff as it reaches out tentatively beyond the world’s outer limit.
But space thus regarded is precisely what “infinite space” means—at least minimally. Infinite space is space for (motion) and space without (bounds). In its twofold character, such space brings together two of the most ancient terms in Greek philosophy, attributable to Plato and Anaximander, respectively: “room” (chōra) and “the boundless” (to apeiron). Their conjunction, which is conceptual as well as historical, suggests that if the cosmos indeed has a place, it is a place in space: space at once endlessly voluminous and boundaryless. Moreover, the world not only has a place, it is in place: it is in the very place of infinite space, occupying particular stations in the regions that make up the spatial universe. Just as Archytas’s conundrum drives us to the idea of infinite space from the known fact of the cosmos, so this same space preserves a place—indeed, innumerably many places—for the world from whose edge we are asked to stretch out our hand or staff, or (in Lucretius’s version) throw a long javelin. The Archytian axiom abides, but only as applicable to a much larger domain than Archytas himself envisioned. To be is still to be in place, but a place that is part of an unending space.
