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113 Curvatures: Hegel and the Baroque  Arkady Plotnitsky The Idealist, the Materialist, and the Mathematical Hegel The problem of Hegel has been given many names, idealism and the absolute arguably most prominent (and most often misleadingly applied) among these names. The very name Hegel may be best seen as the name of a problem. The question is whether such a problem, as it is posed each time, places G. W. F. Hegel and his work further out of reach or even makes him a kind of thing-initself , or, conversely, (re)defines the problem as the way toward or even as a solution, in a process that Gilles Deleuze envisions, or whether it would make our, perhaps unavoidable, oscillations between these two poles more productive for our understanding of Hegel and for our thought and culture.1 Could one think, for example, of a materialist or even “materialist-mathematical” Hegel, such as that invoked by Fredric Jameson?2 And how materialist could mathematics , perhaps the most refined form of ideality, if not idealism, be? Jameson may, first of all, be thinking of a Hegel whose genealogy extends from the philosophical and scientific materialism of the Enlightenment , rather than only from post-Kantian philosophical idealism. That scientific materialism develops from that of the natural, mathematical sciences, in particular physics, to that of Adam Smith’s political economy, crucial to the development of Hegel’s thought and then to Karl Marx and Marxism, in relation to which Jameson places his mathematical-materialist Hegel. This Hegel “comes after the Grundrisse; quite unlike the idealist conservative Hegel who preceded the writing of Marx’s first great work, the unpublished commentary of the Philosophy of Right” (LM 241). 114 Arkady Plotnitsky On the other hand, rather than only a philosophy of matter or philosophy grounded in materiality, materialism is for Jameson also a particular philosophical and political anti-idealist strategy or set of strategies—something which, while a product of human, material history, and politics, is not simply (physically) material, although it is not merely phenomenal or merely social either. It would be difficult to find anything ever simply phenomenal in any significant Idealism, in particular that of Immanuel Kant or that of Hegel, as Paul de Man argues.3 In considering de Man’s work, Jacques Derrida speaks of “materiality without matter,” thus also suggesting (differently from Jameson) a certain strategy of intervening in and undermining metaphysical idealism, which could also take the form of a metaphysical materialism, an idealism of matter.4 From this viewpoint, a materialist Hegel is hardly out of place, whether as a precursor of Marx or otherwise. There is, however, plenty of matter and materiality with matter in Hegel. Earlier, in Positions, Derrida speaks of his work as “materialist.” There is a crucial proviso, according to which “matter” is now inscribed, in a certain general economy (in Georges Bataille’s sense), through the radical alterity of différance.5 At the same time, it is still a question of a displacement of Hegel and of the system of the Aufhebung and speculative dialectic, the displacement that is both infinitesimal and radical (P 43–44). Thus, the question of inscription (subject to a material regime of its own) and a conceptuality displacing, infinitesimally and radically, that system is crucial to any rigorous materiality, anyhow impossible without its relationships with phenomenality and conceptuality. It may, thus, be necessary to place the question of materialism in a Hegelian “idealist” regime. Reciprocally, this placement makes materiality, with or (if this is ever possible) without matter, an equally necessary part of this regime. The materialist and the idealist Hegel are ultimately indissociable and must be engaged interactively. This is an argument I shall pursue here. I shall also argue that, in view of this reciprocity of the two Hegels, materialist and idealist, a certain mathematical—reciprocally both, materialistmathematical and idealist-mathematical—Hegel emerges as well, or there emerges something mathematical or mathematical-materialist in Hegel’s philosophy . This mathematical or, one might say, “quasi-mathematical” element may be seen as a form of mathematical materialism, a particular strategy of intervention, which also allows us to emancipate the mathematical in Hegel and in mathematics itself from its idealist appurtenances. One here confronts a conceptuality that works against mathematical idealism and that, while not in itself mathematical, is irreducible in mathematics and ultimately makes it possible. (Accordingly, it may indeed be more accurate to speak of this conceptuality...

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