Tuesday, January 10, 2017

The Void and Its Dis-Contents: Aristotle's Nature at the Limit

(Here's another seminar paper, this time about Aristotle and... well, Badiou and Zizek, who always crop up in all my academic work no matter how hard I try to escape!)


The Void and Its Dis-Contents:
Aristotle’s Nature at the Limit

I. Introduction
In Physics IV, chapters 6-9,1 Aristotle deals with the question of the void. It would not be too great a stretch to claim that Aristotle is here at his most dense and difficult, but also at his most sophisticated. After spending those several chapters providing myriad arguments against the existence of the void, he makes a statement that is frankly shocking: “From what has been said it is clear that there is no distinct void, neither simply, nor in what is rarefied, nor potentially, unless one wants to call the cause of being moved in general ‘void’” (Phys. IV.9, 217b23; emphasis mine). This odd conclusion is not unprecedented, for earlier in the same book Aristotle writes: “For this reason, some say that the void is the material of body (these also say that place is this same thing), but they do not speak well, for the material is not separable from the thing, but they inquire after the void as separable” (Phys. IV.7, 214a16). And yet Aristotle himself does not treat this question directly or in a thorough-going way, instead being content with the above-cited “unless,” with an off-handed post-conclusion remark.
What are we to make of this strange state of affairs? In order to see the significance of this “unless,” and thereby to understand and resolve the issue, we must have a clear understanding of the function and possible implications of the void within Aristotle’s broader project of physics, that is, his own unique brand of natural philosophy. Then, we must understand Aristotle’s reasoning for rejecting the void within this context. After that, we will be in a position to evaluate the meaning and significance of the “unless.” This will necessarily bring us adjacent to contemporary materialisms of the void, as well as necessitate a look at Plato’s unwritten doctrines.

II. Nature & the Void
Aristotle’s account of physics is not merely that of a pre-modern scientist, as if he were a less-developed form of a modern physicist. He belongs, rather, to a different paradigm that is neither reducible to modern physics nor intelligible by the same criteria as the modern scientific method. While Aristotle is also investigating “nature,” he is using that term in a rather different way. This section will explore the paradigmatic context of Aristotle’s thinking of the void by reference to the concepts of nature and place, and by way of contrast to the common contemporary meanings of some of his key terms. While necessary, this section will be brief, since discussion of the void itself will take up the bulk of this paper.
Near the beginning of his exposition, Aristotle rejects the Parmenidean way of approaching the question of what is; the method of proceeding advocated by Parmenides and his followers is “not according to nature” (Phys. I.2, 185a1). Why is this? They begin not in the phenomenon of what they aim to explain, but in abstract logical principles, in the end completely contradicting appearances. Nature, in the first instance, is motion, since it appears as motion, or as moving things (Phys. I.2, 185a15). There is for Aristotle a fundamental connection between nature and motion that can never be severed, based on a proto-phenomenological attitude toward philosophical investigation; in fact, the Physics is entirely concerned with motion and its causes, as well as the aporias and corollaries that accompany such theories and phenomena).
An important category relating to that of motion is place, especially natural place; it is the conception of place that lays the groundwork for the problem of the void. Place, according to Aristotle, is not at all like our modern conception of homogeneous three-dimensional space; rather, it is akin to a surface or container; it is “the first motionless boundary of what surrounds” (Phys. IV.4, 212a21). Expanding on this a little, we can say that already in the definition of place, Aristotle has defined it with regard to the being of which it is the boundary: “Further, the place coincides with the thing, for the boundaries coincide with the bounded” (Phys. IV.4, 212a29). This in itself will complicate the interpretation of the void, which seems to already be foreclosed by this very definition, and yet Aristotle still spends several chapters arguing against it; this will be examined in more detail in section IV.
What then is a natural place? Aristotle seems to think that different things have different natural places, places towards which they tend. A heavy body tends downward, and this is why earth is “down”; a lighter body tends upwards, and that is why above the earth is water, above water is air, and above air is fire; Aristotle calls this “[…] some change of place of each of the simple bodies by nature, as with fire up and with earth down and toward the center [...]” (Phys. IV.8, 214b15). Aristotle seems to be attempting to account for the kind of general ordering that we now account for with the law of gravity (and of density, and so on). The notion of natural place will play an important part in Aristotle’s arguments against the void.
So what exactly is the void, and why would its existence or non-existence be an issue for Aristotle? According to the relevant endoxa, the void would be “a place in which nothing is” (Phys. IV.7, 213b30). That is, the void is generally understood to be an empty place, “that in which there is nothing heavy or light” (Phys. IV.7, 214a5). According to some, the void is necessary for movement to take place, “since it would be impossible for what is full to accept anything” (Phys. IV.6, 213b5). Now, Aristotle will go on to argue that, far from enabling motion, the existence of the void would make motion impossible, since it would make motion unintelligible, but clearly motion appears to us as intelligible: “And to those who say there must be a void if there is to be motion, it turns out rather to be the other way around when one examines it, that it is not possible for even one single thing to be moved if there is a void” (Phys. IV.8, 214b30). Before turning to these arguments, we would do well to consider Aristotle’s methodology as it relates to this question.
The void cannot be proven to exist using modern scientific methods. It is quite possible to produce a vacuum with modern equipment, but this would then not be physics as Aristotle understands it. Physics is connected intimately with presentation, that is, with motion. Two good pieces of evidence for this are available in the text: first, Aristotle’s already-cited rejection of dealing with the void as the Parmenideans have, that is, merely defining the void as non-being and thereby excluding it entirely by logic (in other words, by treating it as disconnected from nature and motion); and second, Aristotle’s rejection of conceiving of the void as a point, writing “it would be absurd if a point were said to be a void, for it must be a place in which there is extension for a tangible body” (Phys. IV.7, 214a8). If the void were a point, it could not be presented to us in the appearance of movement; Aristotle’s immediate rejection of this possibility indicates his commitments to thinking even the void in these terms. Furthermore, the void must be connected not merely to motion and presentation (that is, to appearance), but to natural motion. To construct an experiment is to expressly violate nature, to produce unnatural motion; experiments in general appear to be inapplicable to the Aristotelian paradigm. To this effect, he writes, “[…] for what is forced is contrary to nature, and what is contrary to nature is secondary to what is by nature” (Phys. IV.8, 215a5). Following the reading of Aristotle as a proto-phenomenologist, if we want to prove the existence of the void, we must use the appearance of nature, that is, the motion of natural beings and of the cosmos in general, without our artificial and violent interventions.

III. Aristotle Against the Void
We now turn to Aristotle’s arguments against the void as defined in the previous section. As it turns out, this definition of the void (as empty place) leaves two possibilities: first, the separable or separate void, which exists on its own, so to speak, outside of any bodies; or second, the inseparable void, conceived as that whose presence inside bodies makes them light. Aristotle goes on to argue against both of these conceptions. The general gist of his arguments has been explicated and classified by Alain Badiou, who writes:
The demonstration, which is very effective, employs, one after the other, the concepts of difference, unlimitedness (or infinity), and incommensurability. There is great profundity in positing the void in this manner; as in-difference, as in-finite, and as un-measured. This triple determination specifies the errancy of the void, its subtractive ontological function and its inconsistency with regard to any presented multiple.2
This analysis will deal with each of the three types of argument Aristotle brings to bear against the void (in-difference, in-finite, and un-measured), before briefly touching on the significance of the “errancy” of the void that is pointed to in the last sentence of the Badiou passage above.
Aristotle’s first argument against the void is based on the lack of difference within the void, which implies its subversion of motion in various ways. Paradigmatic of this line of argumentation is the following passage: “For just as people say that the earth is at rest because of being evenly balanced, so also is it necessary to be at rest in the void: for there is nowhere that a thing will be moved more or less than anywhere else, since insofar as it is a void it has no differences” (Phys. IV.8, 214b33). Particularly with regard to natural motion, this will be entirely incoherent, since a being tends towards its natural place presumably because its natural place is different from its current place: “But change of place by nature is differentiated, so there is a difference by nature. Then either there is no change of place by nature anywhere for anything, or if there is, there is no void” (Phys. IV.8, 215a15). But it seems obvious that there is such a phenomenon of natural motion, so therefore there must be no void.
This argument leads directly to the second one regarding the in-finite, which in many ways is an extension of the point about in-difference. Aristotle argues that, since there is no difference in the void, a being moved into it “will either stand still or it must be carried into infinity, unless something stronger gets in the way” (Phys. IV.8, 215a23). In addition to this endless motion, there is also an infinity of possible directions to this motion, since no one direction can be favored over any other (due to in-difference): “[…] so the thing will have been carried in every direction” (Phys. IV.8, 215a25). The main point is that in-difference leads to the in-finite proliferation of possibilities; there is no longer a single reason why any object in a void should do one thing as opposed to any other, so therefore an infinity of things seems possible. This is obviously not what we experience in the phenomenon of motion, so Aristotle takes it as another argument against the existence of the void.
Finally, there is the argument about un-measure, which is quite an imaginative point. The idea seems to be that motion through a dense medium is slower than that through a rare medium, and that the void, as an infinitely rare medium, destroys the ratio whereby we can describe this difference in speed. Aristotle goes through several possibilities (everything will move at the same speed, or everything will move infinitely fast), indicating the primary reason for this as a lack of ratio: “And to state the main point, the cause of this result is clear, that of every motion to any other motion there is a ratio (for they are in time, and of every time there is a ratio to any other time, if both are finite), but of a void to the full there is none” (Phys. IV.8, 216a9). Once again, the existence of the void would seem to make motion unintelligible, and since motion seems clearly to be intelligible, regulated, and even relatively predictable (we know what to expect when we throw a rock; it won’t move at infinite speed in all directions at once), this is yet another argument for the void’s non-existence.
While these three arguments would seem to clearly do away with the void once and for all, there is one last possibility Aristotle considers: the inseparable void. As opposed to an empty place existing independently outside of beings, the inseparable void is conceived as an internal cause of density and rarefaction, which is supposed to explain the possibility that things have “to contract or be compressed” (Phys. IV.9, 216b24). A rare thing, under this understanding, would have many voids inside of it, but if it was compressed (made denser), it would have less voids. The presence of internal voids, then, would be the reason for light things to move upward: “[…] the void would be a cause of motion not as that in which it happens, but just as wineskins, by being carried upward themselves, carry what is connected to them, so would the void carry things up” (Phys. IV.9, 217a3). According to Aristotle, this conception suffers from just the same problems as the separate void did (Phys. IV.9, 217a9). However, it also suffers from a kind of reduplication problem: how can the void itself have a change of place? The void (and the being in which it exists) would move upward, towards the void, but “a void then comes to have a void, into which it is carried” (Phys. IV.9, 217a5). Voids inside of voids seem to Aristotle an unnecessary complication, since according to him once can positively describe change and motion, even of the heavy and the light, without resort to the void; however, these arguments do not concern us here and would take us too far afield from our question of the void as name of matter.
Now, what all these arguments against the void do is establish its errancy, according to Badiou. Without getting into Badiou’s specific and highly unique system, we can nonetheless interpret this errancy with regard to Aristotle’s physics. The void cannot, anywhere, appear in motion, and it cannot be implied by a phenomenological analysis of motion. It is a strictly unintelligible concept, leading to contradiction and paradox, whenever it is interpreted or conceived within the bounds of possible experience (as that experience is always given to us as an experience of motion). No, if there is to be a void, according to Aristotle, it must not by an empty place. Might there, then, be an understanding of the void that does not succumb to these problems? Aristotle seems to indicate just as much in the passages that were quoted in the introduction to this paper. The possibility is, in a word: the void as name of matter. It is to this problem that we now turn.

IV. ‘Void’ as Name of Matter
We now seek to explicate the possibilities opened up by Aristotle’s pointing to “void” as a possible name of matter. There are three primary passages that open up this possibility: first, the remark about void as material of body (Phys. IV.7, 214a15); second, the strange and difficult passage about the wooden cube (the entire paragraph beginning around Phys. IV.8, 216a,28); and finally, the previously-indicated “[…] unless one wants to call the cause of being moved in general ‘void’” (Phys. IV.9, 217b23). Unfortunately, the first mention does not give us anything to work with beyond a mere possibility that is immediately rejected. So we turn to the passage about the wooden cube, and then to the final passage of chapter 9, finally connecting these to the question of the void in contemporary materialism.
The paragraph about the wooden cube is extraordinarily dense, and rightly so, for it is a feat of stupendous and dazzling abstraction. The argument seems to go something like this. When a cube is moved into an area containing air, it displaces a quantity of air equal to the bulk of the cube (if it does not instead compress it). If a cube is moved into a void, on the other hand, it cannot displace the void, since the void is not a thing that could be moved around. Insofar as our cube is a being that has extension, Aristotle concludes that the void is precisely equivalent to the cube: “So even if it were separated from all the other things, and were neither heavy nor light, it would occupy the equal void and be in the same place as that part of the place or of the void equal to itself. In what way, then, will the body of the cube differ from the equal void or place?” (Phys. IV.8, 216b8). Pure extension, body-ness as such, distinct from all its different qualifiers (hot, cold, heavy, light, &c.) is equivalent to void.
Aristotle takes this argument to disprove void in that it seems to him to make the notion of void incoherent, since it makes it possible for two things to occupy the same place (namely, the cube and the void). However, this argument can also be taken not as a reductio ad absurdum, but as a positive argument in favor of the identification of matter and void. But this is strange; is there a precedent for such a conception?
According to the Tübingen School of Plato interpretation, Plato’s unwritten doctrines contain two principles that supposedly ground the Theory of Forms: the One and the Indefinite Dyad.3 The One gives things unity, presses them into forms, and so on, while the Dyad is the principle of multiplicity and of indefiniteness and unlimitedness. What Aristotle may have in mind with his tentative suggestion of void as matter is something like this. The void-as-matter is the matter as such, as distinct and separate from form and unity. This matter is wholly indefinite, containing contraries within itself and not resting in either one or the other pole of difference.4 It may be called “void” for this fundamental unintelligibility, this primordial lack with regard to definiteness and unity.
We are now in a position to better interpret Aristotle’s final paragraph on the void, where he presents us with his shocking suggestion, “[…] unless one wants to call the cause of being moved in general ‘void’” (Phys. IV.9, 217b23). This “cause of being moved in general” is nothing other than matter. Things must be made of matter to move, since motion in its most general sense is a change, a being-otherwise, and matter just is this open potency of being otherwise (Metaphysics Θ.8, 1050b8-28).5 Void can therefore be conceived as a kind of fundamental indeterminacy, the name of matter as such.
What are the implications of such a position? In particular, since Aristotle seems to reject this possibility as unintuitive or at least as not primary, exploring its implications affords us an important view of the road not taken, so to speak. First, as Badiou notes, Aristotle’s need to think void as a modification of “place” makes him unable to conceive the nothingness or emptiness of the void as a necessary point (more generally, non-place):
The in-extension of a point does not make any place for a void. It is precisely here that Aristotle’s acute thought encounters its own point of impossibility: that it is necessary to think, under the name of the void, the outside-place on the basis of which any place—any situation—maintains itself with respect to its being.6
We can understand this critique generally without embarking on an explication of Badiou’s philosophy. What Badiou is getting at is the importance of the void for a thinking of materialism, as the point necessarily excluded that allows for the possibility of inclusion (the thing outside of presentation, itself unpresentable, that makes presentation possible in the first place). This is materialist because it insists on the foundation of appearance lying outside of appearance, a fundamental limit to intelligibility and phenomenal access, without necessarily invoking the idealist implications of the Kantian transcendental (it is the void as outside, not a particular thing-in-itself).7 As Slavoj Žižek puts it:
The ultimate divide between idealism and materialism does not concern the materiality of existence (‘only material things really exist’), but the ‘existence’ of nothingness/the void: the fundamental axiom of materialism is that the void/nothingness is (the only ultimate) real, i.e., there is an indistinction of being and the void.8
This is precisely what Aristotle touches on in his passage about the wooden cube, and what he points to in the final paragraph of his discussion of the void. While it would be unreasonable to propose any of this as strictly internal to Aristotle in the way it is meant here, this possibility nonetheless coincides with the limit to Aristotle’s thought, and the limit is certainly there in Aristotle. The limit of the “natural” thought of Aristotle (his necessary connection of void and place) is here reached.9 Furthermore, it is due to Aristotle’s rigorous honesty as a thinker that such a possibility is even pointed to, especially in such an open gesture. Though he does not take it as the primary meaning of the term “void,” he nonetheless addresses it as a real possibility not reduced to utter meaninglessness—such a rejection by definition is precisely what he accuses the Eleatics of doing. So, paradoxically, for Aristotle his thinking by nature is both what enables him to reject the Eleatic mode of thought as well as what constrains him to think the void merely as empty place. This is the limit to which I have referred.

V. Conclusion
While the discussion of contemporary materialism could itself comprise many papers of this length, the main point should at least by now be clear: the problematic passages in Aristotle’s discussion of the void can be read as an important opening onto materialism and as his admission, at least in some sense, of the limits of his approach. To reject readings wherein physics itself somehow disproves Aristotle, and instead to read him as perfectly consistent so far as he goes—up to the very limit of his thought, the void as name of matter—is to make him our contemporary. This limit may be a place of profound productivity; the connection to contemporary materialism is one that can make the ek-static or temporally-extended reading of Aristotle as proto-phenomenologist just a bit more compelling, as well as complicating the one-sidedness of that phenomenology with regard to what lies beyond.

Works Cited
Aristotle. Aristotle’s Physics: A Guided Study. Trans. Joe Sachs. New Jersey: Rutgers University Press, 1995. Print.
---. Metaphysics. in The Complete Works of Aristotle: Volume 2. Trans. W. D. Ross. Ed. Jonathan Barnes. New Jersey: Princeton University Press, 1995. Print.
Badiou, Alain. Being and Event. Trans. Oliver Feltham. London; New York: Continuum, 2005. Print.
Krämer, Hans Joachim. Plato and the Foundations of Metaphysics: A Work on the Theory of the Principles and Unwritten Doctrines of Plato with a Collection of the Fundamental Documents. Ed. and Trans. John R. Catan. New York: State University of New York Press, 1990. Print.
Žižek, Slavoj. Less Than Nothing: Hegel and the Shadow of Dialectical Materialism. London; New York: Verso, 2012. Print.

1 Hereafter, Aristotle’s Physics will be cited in-line as “Phys.” followed by the book number and chapter, then by an approximation of the beginning line number e.g. “Phys. IV.6, 250a15.”
2 Badiou, Alain. Being and Event, 73.
3 Krämer, Hans Joachim. Plato and the Foundations of Metaphysics, 77-78.
4 It seems highly possible that this has a deeper relation to prime matter; unfortunately, exploring this might take us too far afield, so I leave that explication for another time.
5 This is also the reason why the Unmoved Mover is pure actuality; it is not moved, since as pure actuality it cannot be made of matter, since matter is this opening onto being-otherwise, i.e. potency. Prime matter, on the other hand, is the opposite of the Prime Mover, since it is pure potency. Furthermore, here I am invoking an interpretation of Aristotle wherein en-mattered beings, by their very materiality, are exposed to difference and even non-being, the basis of which can be found, in addition to the above-cited chapter of the Metaphysics, in Aristotle’s discussion of time (Phys. IV.10-14).
6 Badiou, Alain. Being and Event, 77.
7 For more on this difference, the work of Slavoj Žižek is indispensible, in particular Less Than Nothing. See, for example, his reading of Kant and his relation to Hegel in the introduction of that book. Unfortunately, there is no space here to embark on an explication of this difference, even as important as it is.
8 Žižek, Slavoj. Less Than Nothing: Hegel and the Shadow of Dialectical Materialism, 60.
9 This is also Badiou’s argument in his meditation on Aristotle (see Being and Event Meditation 8).

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