LITMIR.BIZ

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used the word stigmē for “point.” Stigmē connotes a puncturing point,⁶⁶ a point that includes the arrows of Marduk, punctuation points, and the insistent isolation of separated geometric points. Becalming the ambition and hostility of the stigmatic point—embedding stigmatism within the ambience of place—Aristotle inaugurates an astigmatic era in which a more irenic relation between dot and matrix will become possible.⁶⁷

      VI

      Yet how can there be a motion of void or a place for void? That into which void moves comes to be void of void.

      —Physics 217a3–5

      Aristotle repeatedly assimilates theories of void to theories of place.

      —Edward Hussey, Aristotle’s Physics, Books III and IV

      It is a striking structural fact that Aristotle, having disposed of infinity in the opening chapters of book 4 of the Physics, treats the void in between place and time in the same book. Void, then, exists between place and time: as if to say that to get out of place is to get into the void and to get into time is to get out of the void. Time is therefore one way of avoiding, indeed of devoiding the void—emptying its emptiness by introducing measured cadences and reliable rhythms into its abyss. These cadences and rhythms are dependent on motions and magnitudes that belong in turn to place.⁶⁸ Thus to go from place to void to time is in the end to return to place; it is to travel in a topoteleological trajectory that keeps coming back to place even as it departs from it.

      In view of this circular topology it is hardly surprising that Aristotle argues for the indissociability of place and void.⁶⁹ He does so at two levels. First, at the level of endoxa, or common belief, “those who say there is a void suppose it to be a kind of place” (213a16). They do so because of a seemingly commonsensical (but in fact paralogical) line of reasoning: “People think that what is, is body, and that every body is in a place, and that void is place in which there is no body; so that, if anywhere there is no body, then there is nothing there” (213b32–34). Second, at the level of conceptual analysis, Aristotle takes over this paralogic of ordinary belief for his own purposes. He assumes the possible truth of this belief in order to discern its implications for place: void, were it to exist, would be placelike. As placelike, however, it cannot exist as “separated,” that is, in its own right: for a place is always inseparable from its occupant. And yet an unseparated void—a void dependent on its contents—is no void at all. In short, to the extent that void is placelike, it cannot be a true void; conversely, insofar as a place is vacuous, it cannot be a true place. Referring to his own discussion of place in the immediately preceding chapters of the Physics, Aristotle concludes that “since an analysis of place has been made, and void, if it is, must be place deprived of body, and [as] it has been stated in what sense there is and is not place, it is manifest that in this sense there is no void” (214a16–18). Even when we regard void merely as “extension between bodies”—that is, as the interval (diastēma) posited by the Atomists—we find that it remains placelike, for such an extension is a place of possible occupancy by bodies.⁷⁰

      Consider the leading argument for the void as set forth by the Atomists: the void is “responsible for” change in that it provides the setting for all change (including motion), being “that in which change occurs.”⁷¹ But, given that the void is nondifferentially structured, it cannot explain the inherent directedness or the differential speed of natural motion—indeed, it cannot explain why anything moves to begin with—and its invocation in physics is otiose: “For what then will the void be responsible? It is thought to be responsible for change in respect of place, but for this it is not.”⁷² Place, on the other hand, explains any change—including velocity and direction—that involves locomotion. Thanks to its stationariness, it also explains rest. While the void renders motion as well as rest incoherent, for Aristotle place qua container accounts for both of these phenomena economically and effectively.⁷³ Similarly, if we consider condensation or rarefaction, or the displacement of substances, the void will explain nothing: worse, if it were in fact to exist, it would render such changes senseless.⁷⁴

      For all of these reasons, the void as a concept (and not merely as a belief) is regarded as dispensable by Aristotle. Fascinating as its idea may be and compelling to the Atomists as it doubtless was, it is finally a gratuitous fiction—a ghostly double of that which is not gratuitous at all, namely, place. Place suffices to account for all that the vaunted void purports to illuminate. As Edward Hussey comments, “The implication of the argument is that a void which is not an explanatory factor of anything is pointless and therefore cannot exist.”⁷⁵

      Pointless as well is any effort to associate the point with the void—an effort stemming from the Pythagorean association between the point and the Unlimited.⁷⁶ As Aristotle says brusquely, “It is absurd, if a point is to be void; for [void] must be [place] in which there is an extension [within] tangible body” (214a4–6). Just as we can neither imagine nor think a void that is unplacelike, so we cannot imagine or think point as void—or, for that matter, void as point. Therefore, not only does Aristotle deconstruct the point as a candidate for place, but he ends by eliminating both point and void as competitors with place in the determination of location. In such determination, place takes first place; and in this privileged position it takes care of itself, needing neither the point nor the void as explanation or support. If everything is fully placed—if nothing, at least nothing sensible, is without a place of its own—then no void need exist, actually or potentially, and things do not require points to specify their status.⁷⁷ Otherwise put: to be a physical body is to occupy a determinate topos, a place-pocket as it were, that is filled by this very body and that (at another time) can be reoccupied by another body of the same dimensions. To Freud’s dictum that “the finding of an object is in fact a refinding of it,” we can add Aristotle’s rule that every implacement is in effect a reimplacement.⁷⁸ And if everything in the physical world is not only placed but also displaceable and replaceable, then we have to do with a world in plenary session—a lococentric world-whole. This is a world in which points and the void are not so much absent (particular points and discrete vacua may still occur) as superfluous. As Bergson says, “All is full in Aristotle’s world.”⁷⁹

      Aristotle conceives this place-world not by expanding but by restricting his field of inquiry. In contrast with the logical and rhetorical excesses of Zeno, Parmenides, and Gorgias—each of whom extols the ubiquity of place without ever telling us anything specific about place itself—Aristotle’s nuanced descriptions attempt to say just what place is and how it differs from other constituents of the physical world. And in contrast with Plato, Aristotle confines his efforts to describing the exact characteristics of just one of the three sorts of spatial entities distinguished in the Timaeus. The Physics concerns itself only with the most particular such entity, that is, topos, while general regions and chōra are made marginal. The amplitude of the Receptacle gives way to the stringency of the container; and within place-as-container, concrete issues bearing on boundary and limit, line and surface, point and void, are addressed in scrupulous detail.

      VII

      It is obvious that one has to grant priority to place.

      —Archytas

      This is not to claim that Aristotle’s idea of place is without complications and difficulties. To begin with, there is the fact that he changed his model of place in a major way in the period between the early composition of the Categories—where place qua chōra is construed as equivalent to empty “interval” (diastēma)—and the text of the Physics, where this very model is decisively rejected.⁸⁰ More important, there are at least four serious problems in Aristotle’s mature view of place as the immobile inner surface of a container, (1) By its emphasis on surface (epiphaneia), this view is confined to a two-dimensional model of place, despite the fact that place itself is manifestly three-dimensional inasmuch as it surrounds solid objects. (In comparison, Aristotle’s fascination with the point can be taken as an incursion into one-dimensional or even zero-dimensional space and, for all its interest, is foredoomed as a fitting model for volumetric containment.) (2) There is an unresolved tension between the localism of the container model—which points to physical things as “place tight” in their immediate environs—and

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