Academic journal article Cosmos and History: The Journal of Natural and Social Philosophy

Mathematics and Revolutionary Theory: Reading Castoriadis after Badiou

Academic journal article Cosmos and History: The Journal of Natural and Social Philosophy

Mathematics and Revolutionary Theory: Reading Castoriadis after Badiou

Article excerpt

The intellectual and political trajectory of Cornelius Castoriadis makes for a narrative of considerable complexity. It involves, to list only a few dramatic points, an early engagement in the communist party and a quick disengagement from it, a turn toward Trotskyism and a turn away from its own orthodoxies, and co-founding of the libertarian socialist group Socialisme ou barbarie, which for a brief time included the almost mythical figure of Guy Debord. All the while Castoriadis continued publishing on a broad range of subjects under several pen-names (Paul Cardan, Pierre Chalieu, Jean-Marc Coudray) in an effort to demonstrate that resistance required new ways of thinking and practical organization: a response to modern forms of capitalism and, at the same time, a critique of Marxism.

Castoriadis's emphasis on the revolutionary potential of diverse social groups, not only the proletariat, resonated well with parts of the student movement in France of the late 1960s. In an article from 1961, he argued that "the crisis of culture" is pushing students and intellectuals toward a radical critique of the system. (1) It was presumably for this reason that Daniel Cohn-Bendit, one of the leaders of the student revolt, regarded himself as a disciple of Castoriadis. (2) On the other hand, Castoriadis's assessment of Marxist theory was severe enough to be perceived as an attack, and could not have endeared him to a younger but later influential generation of philosophers who, for a time, were fascinated with Maoism.

It is not altogether farfetched, then, to imagine that broader political considerations should be reflected in Castoriadis's theoretical writings and in the reception of his work, even when the subject matter is as rarefied as the philosophy of mathematics. If true, this is perhaps especially true of The Imaginary Institution of Society? The book was composed over a period spanning a decade, from 1964 to 1974, and provides a picture of the development of Castoriadis's thought in a politically turbulent but extremely productive historical moment of French philosophy.

The text sweeps with verve and eloquence over the fields of philosophy, politics, psychoanalysis, history, science and--significantly for the purposes of this essay--mathematics. Although by no means the central concern in the book, mathematics plays an important role. Sets and the logic of sets, in particular, are somehow involved with ontology. The "ensemblist" logic, writes Castoriadis, "is equivalent to an ontological decision concerning what is and the manner in which it exists: what is is such that sets exist." (IIS: 227).

Sets, logic, ontological decisions: terms familiar from the work of Alain Badiou, whose Being and Event argues that set theory, in a sense, is ontology. One might expect that Badiou would have taken an interest in the mathematical facet of Castoriadis's argument, as an object of critique or a foil if nothing else. But that may be too naive. As far as I know, Badiou seems to have remained silent on this possibility. The name of Castoriadis does not appear, for example, in Badiou's precis of twentieth-century French philosophy. (4) Indeed, I am aware of only one explicit reference in the vast expanses of Badiou's textual output: a marginal note in the entry on Jean-Francois Lyotard in the Pocket Pantheon, where a split within Socialisme ou barbarie, a break also between Castoriadis and Lyotard, is mentioned in passing. (5)

The article at hand is therefore best viewed an exercise in philosophical fiction; or, perhaps less provocatively, as an attempt at a comparative reading of (parts of) The Imaginary Institution of Society and (aspects of) Being and Event and related but less technical texts. The question I would like to address is not whether Badiou did in fact respond to Castoriadis, but whether the system of Being and Event--in hindsight and with a conscious nod to the speculative--may be seen as a critical reworking of Castoriadis's ideas on the relation of mathematics and ontology. …

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