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There would not even be the possibility of getting from zero to one unless there were some means of counting the zero first. To get from zero to one, the set must start with nothing, the empty set Ø. In order to reach one, another empty set must be counted in addition to this—the first empty set becomes

counted as one {Ø}. What sutures the set is not an “other” to its members:

insofar as its members are founded upon the absence of the subject, they can only be equal to something else. This element which is not equal to itself is what allows the set’s members to be exchanged for other elements without a loss of truth. Ergo: not being equal to itself, it can always equal another.

Consequently, the difference between Ø and {Ø} is the difference between zero and one—one is the set of the empty set. It is even more difficult to get Hegel Unsutured to two: one must add another set on top of this, the set of the set of the empty

set. By the time 2 is reached, three sets have already been counted. As for 3:

0=Ø 1= {Ø} = {0} 2 = {Ø}, {Ø}} = {0, 1} 3= {Ø}, {Ø}, {Ø}, {Ø}}} = {0, 1, 2} Getting to four is still more arduous since 1 is the counting, in fact, of a nothing which must come first. One is not primary, it is preceded by what engenders lack in the set—it accounts for the inclusive element which does not belong (the missing subject). Or, as the counting of one (to use Badiou’s terms), the subject as one must seek to find its other half in the empty set which it is counted as.5 This, in a sense, is why Lacan’s subject () cannot be written without an objet a.

Now, where, in Hegel, does one encounter the need to produce, or include, an external object to render exceptional closure? Does the dialectic not in fact depend on the exact opposite—the exclusion of externality? Our “answer” is unclear. Perhaps this is not the question to be asked; it is well enough to suggest that Hegel excludes the Other, but this claim is not so easily made when considering that the other, in Hegel, is not really excluded as much as it is revealed in its nullity. The Hegelian knows very well that this nullity has a generative function nonetheless. In the Science of Logic, Hegel begins with the most basic of his categories which, of course, are being and nothing. The immediate goal is to unite the two in the “moment” of being’s emergence out of nothing, but matters are confounded once Hegel speaks of determinate being—a being which is distinguished from mere being (where non-being is taken up in a simple unity with being). As determinate, as something, a posited being no longer simply has non-being as its other, it must also relate to another being, determine itself as the negative of that something.

To this other being, it is equally an other. The former unity of the becoming of being had being and becoming as its moments: here, dialectical thought must grapple with something and other (“something else”). Each “something” is equally its other: “there is no determinate being which is determined only as such, which is not outside a determinate being and therefore is not itself an other.”6 Yet beyond this vicious circle of each being other to its other, Hegel states that a determinate being is an other to itself on its own account: “The other simply by itself is the other in its own self, hence the other of itself and so the other of the other—it is, therefore, that which is absolutely dissimilar within itself, that which negates itself, alters itself.”7 Not being a substantial other, this other is a being’s own non-being.

Hegel here seems intent to unite being with non-being—to sublate otherness into a unity of self and other. In other words, the “dissimilarity” 24 Penumbra mentioned above apparently introduces a positive otherness into Hegel’s system. Being would not be equal to itself since it must share equivalence with its other as well. Difference, it would seem, is not yet eradicated from Hegel’s system. But Hegel insists that the dissimilarity of being with itself does not result from the immanence of otherness, but from the lack of consistency in the other’s being. One could state this logic otherwise: being is not equal to itself because it is not not-equal to its other—it cannot posit, or distinguish itself from, its other. This would be the true logic of the empty set: if zero were equal to nothing, it would no longer function as the empty set, for that nothing, as equal, would then have to be marked as something. To be truly unequal to itself, the empty set must have no equal. For Hegelian non-being then,

something becomes dissimilar to itself when its other does not possess being:

Hence, being-in-itself is, first, a negative relation to the negative determinate being, it has the otherness outside it and is opposed to it; insofar as something is in itself it is withdrawn from otherness and being-for-other.

But secondly it has also present in its own being itself, for it is itself the nonbeing of the being for other.8 This can be better understood when we consider Hegel’s critique of the Kantian thing-in-itself. We believe we are saying something profound when we speak of it, when we refer to something outside the imperfections in human consciousness. But to refer to something in itself is to refer to something apart from that reference; as divorced from all being-for-another, it is stripped of determination, which of course means that it is nothing—that it is impossible to know what it is. Hegel then suggests that by this very realization, we know quite well what a thing-in-itself is: a truthless abstraction. But, in truth, for Hegel, the thing is knowable in the Notion where its determinate content is united with the lack of being in its other (i.e. its positing, which is purely empty being). The limit which separates being-in-itself from being-for-another is superceded once the split itself becomes internally constitutive for the Notion.

What a thing is “in-itself ” can only be externally determined through a being’s own reflection upon its position. So while Hegel may refuse the limit which separates human consciousness from the thing-in-itself, he reaffirms it in the formation of the Notion, where the sensible conditions which affirm the content of a being are supplemented by the “sensuously unfulfilled,” internal limitations of the remaining void of determination.9 It could be assumed that at this moment in the Logic, a sublation of sorts has occurred: that this determined being, in revealing the “other” for the nothing that it is, has become realized, or determinate, in itself as Notion.

But there is none. What has actually transpired is that this being, in reflecting inwards on itself, has moved beyond being determined through an external limit; it now contains an internal limitation. That is, this being is now a finite

being. Two consequences follow:

Hegel Unsutured

1. Limitation defines what something is, as opposed to the limit which determines what that being is not. Thus, for Hegel, this limitation is no longer separated from a finite being’s being; as a term, limitation paradoxically suggests that any being is something other than the limit— that a being could “be” more than what it is were it not for its limitation. This “more” is brought to bear upon a finite being in the form of the ought. Something, in itself, ought to be more than what it is. “The ought as such contains the limitation and the limitation contains the ought.”10 Part of its being, what it ought to be, inheres elsewhere. Yet this elsewhere, while being opposed to the limitation, is implanted by that limitation.

2. Through its limitation, the determinate being encounters its ought.

There is a vicious circle between the two: beyond the limitation is the ought, yet this ought is expressed by the limitation. “Limitation is determined as the negative of the ought and the ought is likewise the negative of the limitation.”11 There is thus a double negation at work when a finite being goes beyond itself: the ought, once realized, is now what the being is, yet the limitation remains nonetheless. A first negation is necessary, where the finite becomes determinate, and a second negation of this determination, where the finite becomes another finite (hence, Hegel’s famous “negation of negation”). Herein lies the first emergence of the infinite: it depends on the negation of the finite. The infinite is the beyond of the finite. Of course, this is where Hegel’s reader encounters the “bad infinity,” where the infinite is revealed as the empty

beyond of a finite being:

In this void beyond the finite, what arises? What is the positive element in it? Owing to the inseparability of the infinite and the finite—or because this infinite remaining aloof on its own side is itself limited—there arises a limit, the infinite has vanished and its other, the finite, has entered. But this entrance of the finite appears as happening external to the infinite, and the new limit as something that does not arise from the infinite itself but is likewise found as given. And so we are faced with a relapse into the previous determination which has been sublated in vain.12 The infinite has no other determination than to be the empty negation of the finite. Yet when the finite being transcends its limitation, it finds that it has become another finite in turn. This would constitute infinity in the second stage, where it becomes the alternate term between two successive finites. Hegel’s reader is faced with the dimension of the “tedious repetition of bad infinity.” The empty infinite, {...}, becomes nothing less than the void of determination, the empty limit of the finite. Hegel does however realize a third moment of the infinite, when it is no longer pushed forwards from the one, but is realized within the infinite generation of the one with itself. Infinity 26 Penumbra would be the realization of the infinite return of the one to another one.

Reflection is required—and it does of course come into play in the Logic. But the reader should ask, in what manner?

For Hegel, it is important to remember that each polarity realizes itself through limitation. The infinite (empty beyond of the finite) is itself finite by virtue of what it excludes. Similarly, the finite, while limited, would be doomed to perish were it not for the perennial ought which posits the finite over and against itself in the beyond. The mutual sliding into opposition of either term is what, no doubt, provides for the circularity of the infinite judgment, for the “good” infinity. The infinite is what is drawn from the repetition of either term—or better yet, from the emptiness of the other which either term oscillates towards. Going towards its other, it returns to itself, the One is the infinite that is coextensive with its other in the reproduction of itself. This is Hegel’s thesis.

Over and against the image of a linear progression, the Hegelian infinite is the circle drawn within repetition. “What arises is the same as that from which the movement began, that is, the finite is restored; it has therefore united with itself, has in its beyond found itself again.”13 But even if this reflective circle is composed of two terms, it is not a disjunctive process. This is no unity of difference. In the first place, it is from the limitation of the One, which is indifferent to difference, that the infinite is drawn. The very fact that two opposed terms could become their opposites attests to the very nullity of differences, to the fact that they differ only by virtue of limitation. In other words, it is not that a limit is necessary because of the immanence of otherness, since otherness only follows from the necessity of limitation. As Hegel later writes in the Logic, it is only when the limitation becomes constitutive that the Notion is achieved.

If any of this exegesis on indifference, on the “bad infinity” of alterity and externality leaves something to be desired in contemporary repudiations of Hegel, I will nonetheless stop short of Hegel’s critics. I will only draw two

conclusions at this point:

a. That the repetition of the One, the continual reemergence of the same, does not sufficiently offer a closure onto a Notion. Jacques Lacan observed as much when he distinguished himself from Hegel: the false infinity is linked to a metonymy of recurrence, a metonymy which can luckily be drawn from the function of the repetitive One. But, as Lacan adds, “what experience shows us, is that the different fields that are proposed in it—specifically, the neurotic, perverse, and indeed the psychotic—is that the One which is reduced to the successions of signifying elements, the fact that they are distinct and successive does not exhaust the function of the Other.”14 It is not insignificant that Lacan calls it the function of the Other, for even if the Other is impossible, it still possesses a function in the object that repetition generates. It is even from the repetition of the One, from its recurrence, that the question from the other arises: “che vuoi?” What is it that I, the Other, demand of you? Don’t Hegel Unsutured get me wrong: there is not a lot of bad infinity in Lacan, this is not a radical alterity of otherness, yet there is a remainder of the Other which is buttressed through jouissance. And the trouble, as Lacan said in Television, is that this latter term cannot be inscribed in a repetitive quantum. Jouissance does not have a numerical constant, it does not register “in” a given repetition. A repetitive quantum is not guided by the “energy” of a human constituent: it is guided forwards by a demand that must be deciphered. To speak directly to Hegel on this count, recurrence does not exhaust, much less explain, the determination of a singular being’s ought.

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