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  • "Infinitely Finite"Jean-Luc Nancy on History and Thinking
  • Rodolphe Gasché (bio)

"The true infinite," Hegel writes in the Encyclopedia, is the "fundamental concept of philosophy" (2010, 152). The direct article suggests that true infinity is that concept on which philosophy as such is grounded, and, therefore, it is of essential importance "not to take that as the infinite what is at once made into something particular and finite in the determination of it," in short, "the abstract, one-sided infinite of the understanding"; the bad, or spurious infinite, that is (152). Let us remind ourselves here that for Hegel the true infinite is not something that transcends the finite, an other of the finite, over against it. Rather than a qualitative other of the finite, as is the case with spurious infinity, the true infinite is a result of the finite's development; of its self-transcendence through self-negation and the self-relation operative in this self-negation.1 By virtue of relating to itself, true infinity is the truth, as Hegel expresses himself, of the finite—its very ideality. Now "the ideality of the finite," its immanent infinity, is, Hegel continues, "the chief [End Page 1] proposition of philosophy" (152). In short, for Hegel, philosophy as such is intrinsically connected to the concept of true infinity as that which within the finite itself articulates its relation to self. In Nancy's thought, however, the "infinitely finite"—not simply the finite but a finite that is said to be infinitely finite—becomes the keystone of philosophical thought today, in the aftermath of Hegel, in particular. Hereafter, I will attempt to tease out how this expression of the infinitely finite contrasts to the infinite of understanding, that is, from a finite infinite. At stake in this comparison is the possibility of philosophy itself. Hegel's statement that true infinity is the fundamental concept of philosophy requires us to inquire into whether a finite, however "infinitely" finite, can claim to be the foundation stone of philosophy to begin with, and if the answer is affirmative, what kind of philosophy this could still be in the wake of Hegel's understanding of philosophical thought.

The expression "infinitely finite" resonates, no doubt, with Lévinas's talk of "the infinitely other," where the reference to the infinite concerns the responsibility for the other and thus has a primarily ethical meaning.2 By contrast, the adjective "infinitely" in "infinitely finite" is a hyperbolic emphasis on the ontological nature of the finite. Hence, any further exploration of the semantic and philosophical breadth of the expression would require a clarification of Nancy's conception of the finite. However, for reasons of time I cannot do this here. I will have to limit myself to a commentary on the exact place and moment at which he introduces (perhaps for the first time?) the notion of the "infinitely finite" in his discussion of finitude in the essay "Finite History," originally published in 1990. But before I turn to this text, it is certainly appropriate to reflect for just a moment, while still abstracting from the philosophical overdetermination of the terms that constitute the expression, on what it means in ordinary language to say of something that it is infinitely finite. In the expression, the term "infinitely" in relation to "finite" is in the position of an adverb modalizing an adjective that qualifies something: in our case, history and community, but elsewhere in Nancy's work also sense and thinking. The infinite and the finite are not nouns. Compared to a finitude that is just finite, the infinitely finite suggests a tremendous, inexhaustible, unending finiteness, one that it is impossible to arrest; in short, with which one will never come to a term. In ordinary French, one can also hear an [End Page 2] affirmation of what is said to be "infinitely" finite. Now, in French, fini also means finished, over, and terminated. La fin is not only the goal, the purpose, but also the end in which the goal might have been realized. Infiniment fini can thus also mean that something has come to an end for good; that it has ended once and...

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