At the end of his prologue to Chapter 1 of DR, Deleuze asks, "Must difference have been 'mediated' in order to render it both livable and thinkable?" (30). We might add a few questions: is it possible to go back to the beginning and think difference differently? To see it outside of the system of representation? To understand it as something other than a feature of conceptual architecture? Once we expose the philosophical constraints put on difference—i.e., identity, analogy, opposition, resemblance—then what? "[W]e can answer these questions," Deleuze concludes, "only once we have more precisely determined the supposed nature of the propitious moment" in which differences are selected, tested, and deemed essential for our conceptions of things in the world (30). Though Deleuze does not make it all the way back to the beginning of philosophy in this chapter (who could?), he does spend the next few pages with one of the giants of ancient philosophy—the imposing Aristotle. The next two paragraphs may seem a bit strange to regular readers of Deleuze, since it is rare for him to spend so much time summarizing the writings of philosophers and even stranger for him to be spending time on Aristotle. Even his monographs on Nietzsche, Leibniz, and others tend more toward idiosyncratic synthesis or collage—where it is difficult to demarcate, as Roland Barthes puts it, "Who is speaking thus?"—rather than summary or analysis. At the very least, these pages on Aristotle evince the fact that DR is part of Deleuze's doctoral project, the outcome, that is, of decades of research, study, and intellectual development that one can track through his previous books and essays on Hume, Kant, Proust, Bergson, Nietzsche, Sacher-Masoch, and others. As a doctoral thesis, then, DR must portray (as all such documents "must") the scholarly credentials of the one composing it. What better way to establish these credentials than to include a section that directly addresses Aristotle's writings on difference? (We will encounter something similar in the section on Martin Heidegger later in the chapter [pp. 64-66]. I'll get to those pages in about fifteen years...)
Deleuze: Difference in general is distinguished from diversity or otherness. (DR 30)
Aristotle: [. . .] difference is not the same as otherness. (Bk X, Pt 3, 1054b)
Deleuze: For two terms differ when they are other, not in themselves, but in something else; thus when they also agree in something else: in genus when there are differences in species, in species for differences in number [and so on.] (DR 30)
Aristotle: [T]hat which is different is different from some particular thing in some particular respect, so that there must be something identical whereby they differ. And this identical thing is genus or species. (Bk X, Pt 3, 1054b)
Okay, good. For Aristotle, things that are different from one another—and not merely other than each other—must, in some sense, also be the same. They must have, as he puts it, some "way to one another" in order to be "different" from each other at all (Bk X Pt 4, 1055a). It might be worth noting that this is also the logic—though stretched, obscured, and nuanced—of poetic figures like metaphor, simile, and symbol. Figures of speech establish an intriguing way between things that are other, deforming that otherness into the poetic expression of an alluring difference.
I've already indicated that this is a scholarly section of DR, but one might still ask, "Why is Deleuze rehearsing Aristotle, specifically?" Perhaps because—in a pertinent section of The Metaphyics devoted to the problem of oneness or unity—Aristotle identifies and defines "a greatest" or maximal "difference" (Bk X, Pt 4). If Aristotle has already developed a concept of difference and if he has done so from a starting point of mediation ("difference [. . .] must be between two things" [1055a]), then there is no point to move on with Deleuze's chapter, is there? If Aristotle can construct a robust notion of "Difference in Itself" as a matter that must concern two things—rather than a matter of singularities, as Deleuze has already insisted—then perhaps I'm wasting and have wasted my time with this slow reading.
As readers of Categories already know, Aristotle proposes four modes of opposition: [a] relation between correlatives, [b] contrariety between contrarieties, [c] deprivation of a possession / possession of a deprivation, and [d] contradiction. In Metaphysics, Aristotle defines the greatest and most perfect difference with only one of these particular kinds of opposition (Bk X, Pt 4, 1055a-1055b). Deleuze summarizes:
The greatest difference is always an opposition, but of all the forms of opposition, which is the most perfect [. . .]? Related terms belong to one another; contradiction already belongs to a subject, but only in order to make its subsistence impossible and to qualify the change by which it begins or ceases to be; privation again expresses a determinate incapacity on behalf of an existing subject. Contrariety alone expresses the capacity of a subject to bear opposites while remaining substantially the same (in matter or in genus). (DR 30)
Relation is the least considered mode of opposition in Bk X, Part 4. Aristotle mentions it only once, so I have to surmise why relation is not the greatest difference. While relation—unlike contradiction, as we will see—does form some sort of route between two terms, these two terms are opposed only in the most literal sense that they are set against one another. Thomas Aquinas offers a nice example: "child" belongs with the term "parent" and vice versa, not just empirically or morally but conceptually. One term involves and requires the other in order to be conceptually sound. Indeed, our notions of child and parent belong together in a way that other examples of opposition—I sit/I stand, hot/cold, sight/blindness, etc.—do not and cannot. It is this immediate sense of mutual belonging that keeps relation from being the greatest possible difference, for it signifies and evinces an affinity with minimal difference. In an even simpler case, when I refer to "a half" or to a "double" amount of something, it is the "of" that indicates the mode of relation. I cannot understand "half' or "double" without "of something." I cannot understand "child" without "of parent."
In Metaphysics, Aristotle calls contradiction "the first" form of opposition because it "admits of no intermediate" (1055b). Indeed, we might say that contradiction is primary because it is the simplest and strictest mode of opposition. Contradictory statements like "I am sitting" and "I am standing" or "I can see" and "I cannot see" admit of no gray area. They are, for Aristotle, either true or false. Even in an example that seems to have more to do with privation/possession, we can learn something about contradiction. Blindness and sight, for instance, already contain—as Aquinas again points out—the respective facts of not-seeing and not-being-blind in our respective notions of them, and each constitutes the point at which, in Deleuze's words, the other "begins or ceases to be" (DR 30). Taking the simpler example, as soon as I begin to stand, I cease to sit. As I begin to sit, I cease to stand. While in the real world, creatures have varying capacities of sight and there may be empirically intermediate stages between sitting and standing, there is no conceptual co-existence, no harmony, no admixture, and no subsistence of sight in the activation of blindness; no blindness in the activation of sight; no sitting in standing; no standing in sitting. The question, "Can I see?" is not the same as the question, "How well do I see?" Indeed, the statement, I am blind, is either true or false and admits (without any additional context) of no intermediate. For Aristotle, difference cannot be in play here because there is no route between contradictories, and difference must—after all—be between two things (1055a). According to the law of non-contradiction, no subject can see and be blind—or sit and stand—at the same time.
Privation is the trickiest of the four because it demonstrates the porousness of the lines dividing Aristotle's oppositional modes. In the example of a being who has a natural incapacity to be or to do something in a certain way (e.g., wood does not see [Aquinas again]), the privation of sight is a contradiction. There is no intermediate between a piece of wood that does not see and one that sees. Wood, quite plainly, cannot see and thus the reason given for why contradiction does not occasion the greatest difference now applies to privation as well. There is no route between sight and blindness in the case of natural incapacity or what Deleuze calls "determinate incapacity on behalf of an existing subject."
Yet there are occasions of privation that do admit of intermediaries, that is, of a potential co-existence of opposites. As Aristotle claims, though "privation is a kind of contradiction" in the case of a natural incapacity, there are instances in which the possession of a natural capacity suffers temporary or permanent privation at a determinate moment in time and space (1055b). Some creatures, for instance, are blind immediately after being born only later developing the sense of sight; aging creatures eventually become blind if they live long enough; if there is no source of light, I am temporarily blind until some source appears and restores my sight to me. In these cases, blindness and sight can co-exist in a relation between natural capacity and particular situation. We understand a kind of simultaneity of natural possession and empirical privation. (Note: While the first sort of privation is a kind of contradiction, the second sort of privation is a contrariety. Indeed, Aristotle calls the contrariety between possession and privation "[t]he primary contrariety" (1055b). In this sense, the greatest difference is actually a privation, though "not all privation is contrariety" (1055b). Thus not all privation signals an occasion of greatest difference, but an occasion of greatest difference and contrariety will always be an occasion of non-contradictory privation that admits of mediation between opposites.)
It is contrariety, according to Aristotle, that occasions the greatest, most complete, and perfect difference. And why? When Deleuze writes, "Contrariety alone expresses the capacity of a subject to bear opposites while remaining substantially the same," he's skipping quite a few of Aristotle's steps, and he acknowledges this when he asks in follow-up, "Under what conditions, however, does contrariety impart its perfection to difference?" (DR 30). Initially, Aristotle's reasoning is quite simple. If things can be more or less different from one another (1055a)—as we see in the case of relation and correlatives—then we can think of difference as a scale of gradations or degrees between extreme end points. Since there is no point of comparison beyond end points (Aristotle: "beyond the end there is nothing"), the difference between extremes must be the greatest, most complete, and perfect difference. Imagine, to give a crude example, a numerical system that only had values 1-100. In this system, the greatest difference would be 100 minus 1, which would equal 99. There be never be a difference greater than 99 in this numerical system, since it would equal the distance between end points.
But, of course, things are more complicated in Aristotle. In the rest of this paragraph, Deleuze summarizes Aristotle's remaining qualifications for defining contrariety as the greatest difference:
So long as we consider the concrete being with respect to its matter, the contrarieties which affect it are corporeal modifications which give us only the empirical, accidental concept of a still extrinsic difference [extra quidditatem]. Accidents may be separable from the subject, as 'white' and 'black' are from 'man'; or inseparable, as 'male' and 'female' are from 'animal': accordingly, the difference will be called either communis or propria [terms Deleuze draws from Porphyry (308n2)], but in so far as it pertains to matter, it will always be accidental. Thus, only a contrariety in the essence or in the form gives us the concept of a difference that is essential [differentia essentialis aut propriissima]. Contraries in this case are modifications which affect a subject with respect to its genus. Genera are in effect divided by differences in essence which take the form of contraries, such as 'with feet' and 'with wings'. In short, contrariety in the genus is the perfect and maximal difference, and contariety in the genus is specific difference. Above and below that, difference tends to become simple otherness and almost to escape the identity of the concept: generic difference is too large, being established between uncombinable objects which do not enter into relations of contrariety; while individual difference is too small, being between indivisible objects which have no contrariety either. (DR 30-31)
How do we make sense of Aristotle's additional qualifications?
 The greatest difference is in essence or what Aristotle also calls "nature" and "definition" (Book X, Pts 8 and 9, 1058a). Though white/black and male/female are contraries of a sort, they do not factor into an account of a difference, say, between bird and horse. A black bird and a white horse certainly differ in color, but it is in the features included in their respective definitions of birdness and horseness (both of which include the possibility of being different colors and male or female) that the greatest differences and the essential contraries emerge. Taking a simple example, Aristotle writes, "[A] brazen and a wooden circle, then, [do not] differ in" their nature, definition, essence, or "species; and if a brazen triangle and a wooden circle differ in species, it is not because of the matter, but because of a contrariety in definition" (Book X, Pt 9, 1058b). The extreme difference between triangle and circle, in other words, does not depend on accidental material features. It is not essential for a circle to be wooden or brazen, but it is essential that it be round, that it encompass a full rotation instead of only half of one (as a triangle does). Likewise for male and female birds and horses. The sexes of these creatures are mere "modifications" of individual, material bodies and do not belong to the "essence[s]" that unite these bodies into either a bird or a horse—though the determinations "with feet" and "with wings" are modifications "in virtue of [their] essence[s]" (1058b).
 Contraries that pertain to essence or definition or nature, then, "affect a subject with respect to its genus" (DR 30). A circle and a triangle are distinct species of geometric shape; they are "the same in genus," as Aristotle puts it, but "other in species" (1055a) and are "differentiated in no merely accidental way" (1057b-1058a). Therefore, some contraries "make things different in species" while others "do not" (1058a). Only contrariety within a genus—a difference between and among species understood as complete and distinct but ultimately comparable essences/unities—constitutes the greatest difference. Here, then, we get a sense of the correct range of the greatest difference. Big generic differences—that between a geometric shape, for instance and an animal—are "too large, being established between uncombinable objects" (DR 30). As Aristotle puts it, "things which differ in genus have no way [or route] to one another, but are too far distant and are not comparable" (1055a). Within a certain species, individuals certainly differ but they only do so in small, accidental ways. "And so paleness in man," Aristotle writes in Part 9, "or darkness, does not make" a difference in species and does not make one "human" rather than "horse"; "nor is there," he continues, "a difference in species between the pale man and the dark man, not even if each of them be denoted by one word" (1058b).
At last I finally understand Deleuze's reference to the test of the Large and Small. Large differences between objects that are completed noncomparable—circles and horses, for instance—do not create contrarieties but, rather, generic differences that are not useful in accounting for the essence of either object. Small differences might create contraries (male/female, white/black), though Deleuze claims that they do not. Regardless, these differences in material or matter are accidental rather than essential and are not part of the concept of a thing's oneness or unity. Therefore, the test of the Large and Small, for Aristotle, enables one to develop an account or a definition of a thing's unity by attending to its specific difference from things within its genus.
"It seems," Deleuze continues in his next paragraph, "that specific difference meets all the requirements of a harmonious concept [of difference?] and an organic representation" (DR 31). But does it really? Aristotle appears to have developed an impressive concept of difference, one that is "pure," "intrinsic," "qualitative," "synthetic," "mediated," and "productive" (31). This account of difference is attractive because it accounts for the ways in which difference participates in the "comprehension" and "composition" of species, mediating particular actualizations of a genus. What picture of genera appear in Aristotle's account? Specific difference, Deleuze writes,
is a predicate of a peculiar type, since it is attributed to the species [anchoring a sense of its unity, we might say] but at the same time attributes the genus to it and constitutes the species to which it is attributed. Such a synthetic and constitutive predicate, attributive [something that gives or is determining] rather than attributed [something given or determined], a veritable rule of production, has one final property: that of carrying with itself that which it attributes. In effect, the quality of the essence [of a species] is sufficiently special to make the genus something other, and not simply of another quality. It is thus in the nature of genera to remain the same in themselves while becoming other in the [specific] differences which divide them. (DR 31)
In my next installment, I will try to unpack Deleuze's interpretation of his summary of Aristotle and continue reading into his critique of Aristotle's equation of contrariety and the greatest difference. Ultimately, he will argue that Aristotle's Metaphysics does not provide a concept of difference at all and that his presupposition that difference be intrinsically conceptual as well as a matter of two things leads to philosophical confusion.
Reading on . . .