Structure, Sign, and Play and the Discourse of the Natural Sciences: After the Hyppolite-Derrida Exchange

Introduction

Jacques Derrida's "Structure, Sign, and Play in the Discourse of the Human Sciences" offered a radical rethinking of structuralism and of structure itself. According to Derrida:

Structure—or rather the structurality of structure—although it has always been at work, has always been neutralized or reduced, by a process of giving it a center or of referring to a point of presence, a fixed origin. The function of this center is not only to orient, balance, and organize the structure—one cannot in fact conceive of an unorganized structure—but above all to make sure that the organizing principle of the structure would limit what we might call the play of the structure. By orienting and organizing the coherence of the system, the center of the structure permits the play of its elements inside the total form. And even today the notion of a structure lacking any center represents the unthinkable [l'impensable] itself.

(Derrida, Writing and Difference 278–79)

Both the French "impensable" and the English "unthinkable" may refer to something only previously unthinkable, also as something terrifying or monstrous, invoked in Derrida in closing (Derrida Writing and Difference 293). It is also possible, however, to give it, as I shall do here (even if Derrida does not), its direct sense of something that is beyond thought altogether, rather than only being something as yet unthought and possibly to be thought one day. Derrida locates two interpretations of the play of structure. The first interpretation, as exemplified by that of Claude Lévi-Strauss, is defined by experiencing this absence nostalgically, as a loss. The second is a "Nietzschean affirmation … of the play of the world and of the innocence of becoming, the affirmation of the world of signs without fault, without truth, and without origin, which is offered to an active interpretation … and [which] determined the noncenter otherwise than as loss of center" (Writing and Difference 292). Rather than adopting the second, more radical interpretation, Derrida, while acknowledging the (irreducible) difference between them, argues for the necessity of considering the différance of these two interpretations—their common ground and efficacity.

I shall be primarily concerned here with this problematic in the discourse of mathematics and the natural sciences or that concerning them, as in the history or philosophy of science. The subject, not considered in Derrida's essay, was brought up by Jean Hyppolite in their exchange following Derrida's presentation at the "Structuralist Controversy" conference at Johns Hopkins in 1966. Hyppolite's comments show a sophisticated understanding of mathematics and science. This is not surprising given Hyppolite's background and his directorship of Ecolé Normale Supérieure and his presidency of Collége de France, which brought him in close contact with leading mathematicians and scientists, including those working in relativity, such as Elié Cartan and André Lichnerowitz, and genetics, such as Jacques Monod and François Jacob. I shall argue that twentieth-century mathematics and natural science not only brought into center stage the concept of structure but also, with quantum mechanics, confronted the play of a structure in Derrida's sense. While the concept of structure in twentieth-century mathematics and science and its influence on structuralism in the human sciences have been addressed, the role of quantum mechanics in bringing into play the play of structure has not been. Considering the latter is one of the main contributions of this essay.

The circumstances of the exchange merit a brief commentary in view of the attention and mistreatments it had received during the Science Wars in the late 1990s.¹ Replete as they were with misconceptions, absurdities, and abuses when it came to poststructuralist ("French") thought, the Science Wars had legitimate arguments mostly found, however, in those debates that concerned the history, philosophy, and sociology of science. These debates, conducted in such peer-reviewed journals as Nature and Science, also involved scientists that held much more responsible views than the likes of Alan Sokal and Jean Bricmont, or Paul Gross and Norman Levitt, who had the most notoriety...