LITMIR.BIZ

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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

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