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One Divides into Two


One divides into two, two doesn’t merge into one. This was an old Maoist slogan from the 1960s. Despite its air of universal truth it has become dated, and I fully realize the danger of appearing dated myself by starting in this way. Nowadays, one can recite this slogan in front of a class full of students and none will have ever heard it or have any inkling as to its bearing or its author—it’s almost like speaking Chinese. The slogan combines an ontological statement, a mathematical theorem, and a political battle-cry. So why does one split into two in mathematics, ontology, and politics? And why, once we arrive at two, can we never get back to the supposed unity of one?

I will try to speak about something very minimal and basic, something extremely simple and at the same time very enigmatic: namely, how to get from one to two. This movement suggests ways to conceive difference and, more precisely, how to conceive the difference between two kinds of difference. The first kind of difference can be seen as the difference of numerical count. What accounts for counting, for getting from one to two? What pushes the count in its forward thrust? For if we have successfully managed this heroic feat of addition, assuming that one plus one makes two, then there seems to be no stopping this process, we can reproduce this step again and again, and thus count to infinity. To be sure, what seems to be a simple operation, the most elementary of all, the one acquired with the first lesson in mathematics, is itself full of pitfalls and hidden traps, and we only need to mention Frege, set theory, the suture, or Badiou’s intricate theory of numbers to remind ourselves of the complexity of the operations involved. But I will not follow this path. I will simply point out that in this way one hasn’t really arrived at two, first because the two that has been thereby produced is still hostage to one, is its extrapolation and extension, its replication, one splitting itself and reproducing itself; and second, one hasn’t arrived at two but at more than two, the two of many, the whole host of numbers, since the process that one has instigated cannot stop at two, it is endowed with the forward thrust to multiply itself, so that “two” is merely a provisional stopover, a halt from which we must hurry on.

The other side of this question of the two is precisely the side of the other, the Other, its capital letter signifying the “big Other,” underscoring the implication of drama. The question of the Other brings forth not merely the numerical two, the second following the first, but the question of something of a different order, something that is not a mere extension of the first, but rather something that would really present two, count for two, the two heterogeneous to the one and recalcitrant to the progression of ones into infinity. However much we count, however many ones we add to the first one, we cannot count to the two of the Other. The progression of counting extends the initial one into a homogeneous and uniform process, while the Other presents a dimension that would be precisely “other” in relation to this uniformity. In a nutshell, the otherness of the Other, if it can be conceived, is a dimension that cannot be accounted for in terms of One. If the Other exists, then we have some hope of escaping from the circle, or the ban, of One. The dimension of the Other might present a two that would really make a difference, not merely a difference between one and another, that is, ultimately, between the one and itself, the count based on the internal splitting of one, but rather another difference altogether, beyond the delightful oxymoronic phrase “same difference.”

One can immediately appreciate the high philosophical stakes here. A large part of modern philosophy, if not all of it, has aligned under the banner of the Other, in one way or another, whatever particular names have been used to designate it, and if philosophy has thus espoused the slogan of the Other it has done so in order to establish a dimension that would be able to break the spell of One, in particular its complicity with totality, with forming a whole. There is a hidden propensity of One to form a whole, to encompass multiplicity and heterogeneity within a single first principle. That program was pronounced at the dawn of philosophy, spelled out by Parmenides in three simple words, the slogan hen kai pan, one and all—to conceive the all as one, to encompass the whole in its unity, and to take the one as the simple clue to the whole and whatever multiplicity it may present; to take the whole under the auspices of One. “One and all” served as the blueprint for philosophy, holding in check its whole history; it spelled out philosophy’s mission, its grand overarching chart, its task and its calling, in whatever particulars one conceived it. So if the Other exists, if it can be conceived in terms other than the terms of one, it would permit us to get out of this ban and this circle. Indeed, the task of modern philosophy, if I may take the liberty of using this grossly simplified and massive language, was to think the Other that would not be complicit in collusion with the One of hen kai pan, and thus, ultimately, the task to think the two, to conceive the Other that wouldn’t fall into the register of the One. And if I content myself to mention just three great names, I will invoke Nietzsche with a single line from the end of Beyond Good and Evil: “Am Mittag wars da wurde eins zu zwei” [It was at noon that one turned into two]—the noon as the time of the shortest shadow and the minimal difference, the time of the suspension of time, the division of time—and the title of Alenka Zupančič’s book The Shortest Shadow: Nietzsche’s Philosophy of the Two. I will invoke Marx and the two of antagonism—Mao’s slogan was designed to spell out its political and ontological impact in a simple adage, transposing it into terms of counting. I will invoke Freud—and now I will take the tricky path of conceiving the two in terms of the Other in psychoanalysis, the Other being a key psychoanalytic term.]. To contradict this is a duty [Y contredire est un devoir]].” To contradict the synonymy of One—but with what?]

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