Concept and Form:
The Cahiers pour l’Analyse
and Contemporary French Thought

Ontology is the study of being in itself, abstracted or subtracted from the particular properties attendant on any particular beings or kinds of being. One of the most ancient discourses in philosophy, ontology underwent a resurgence in twentieth-century philosophy, as a result of several distinct developments. In the philosophy of logic, Frege, Meinong and Russell had renewed the logical analysis of fundamental ontological concepts such as ‘being’, ‘existence’ and ‘non-being’. In Being and Time (1927), and subsequent works, Martin Heidegger developed what he called a ‘fundamental ontology’. Finally, in mathematics, ontological questions had also gained renewed significance in the wake of Georg Cantor’s set theory, which raised old questions concerning the nature and reality of mathematical objects in newly challenging ways. The debate concerning the ontological remit of mathematics would be one of the guiding concerns of the Cahiers pour l’Analyse, and the theories presented range from the Platonism affirmed by e.g. Kurt Gödel and Alain Badiou to Ludwig Wittgenstein’s conception of mathematics as a kind of language game with no direct purchase on a reality that might exist independently of mathematical discourse.

These three contexts combine in the Cahiers pour l’Analyse to produce novel approaches to the key ontological concepts of ‘being’ and ‘non-being’. Developing a critique of metaphysical categories of substance or presence, Heidegger had identified what he termed an ‘ontological difference’ between Being as such and extant beings or entities. Fundamental ontology was to be the discourse devoted to the question of the meaning and unity of the concept of Being as such. Against discourses that would objectify or reify being in abstraction, through representationalist or correspondence theories of truth, Heidegger conceived of the truth of being as a matter of ‘disclosure’, coming in his later writings to see poetic language as its essential medium. The work on ontology in the Cahiers goes in a different direction. As in Heidegger, a return to the Greek sources of ontology is undertaken. Xavier Audouard, Jean-Claude Milner and François Regnault each return to the key sources for Plato’s ontology, the late works The Sophist and Parmenides, interrogating anew the significance of the concepts of ‘being’, ‘non-being’ and ‘unity’. But their methods and results are quite different to those of Heidegger, and revolve around questions arising within epistemology and the theory of science. In his articles in the Cahiers, Alain Badiou has yet to arrive at the alternative ontology he will elaborate in his Being and Event (1988), which breaks decisively with Heidegger by affirming post-Cantorian mathematics as the discourse of being-qua-being. Badiou’s later work integrates many of the distinctive interests of the Cahiers pour l’Analyse into a single philosophical project, e.g. the concern for Greek ontology, the ontology of mathematics, and the ramifications of the Heideggerian legacy.

The ontological concerns of the Cahiers pour l’Analyse themselves are prefigured in a key moment in Jacques Lacan’s seminar in the spring of 1964, when Jacques-Alain Miller asked Lacan if his theory of the subject, grounded in an account of lack and its structuring function of the unconscious, presupposed an ontology.¹ In the seminar, Lacan answered this question with the suggestion that the constitutive gap of the unconscious was essentially ‘pre-ontological’. The Cahiers pursue Miller’s original question along multiple lines, identifying points of contact between Lacan’s theory of subjectivity and the ontological concerns to be found in recent and contemporary developments in logic and the sciences.

In the Cahiers pour l’Analyse

Ontological questions are specifically addressed in a dossier concerning Plato’s Sophist in Volume 3 of the Cahiers, comprised of two articles: Xavier Audouard’s ‘Le Simulacre’ (CpA 3.4) and Jean-Claude Milner’s ‘Le Point du signifiant’ (CpA 3.5). Following Lacan’s suggestion that this Platonic dialogue, concerning the relation of being to non-being, holds a special significance for the psychoanalytic investigation of language and logic, Audouard pursues the status of non-being as the domain of semblance and falsehood, linking it to the perspectival nature of the subject. He argues that Plato masters the concept of non-being by transforming it into the concept of ‘otherness’ or ‘difference’. Approaching the same Platonic dialogue, Milner emphasizes the vacillating nature of ‘being’, as at once function and term, in the dialogue, reading it in light of Miller’s arguments in ‘La Suture’ (CpA 1.3). The generative quality of ‘being’, that is its capacity to generate ‘non-being’, does not depend merely on the latter’s being a semblance or simulacrum, but rather on the alternating sequence whereby, in the extension of the category of ‘being’, new genera of inclusion are established and ultimately found to be lacking.

In the segment of his seminar reproduced in Volume 8, Serge Leclaire pursues the ontological significance of jouissance in the Lacanian framework, relating it to the ‘exaltation and dissolution of being’ (CpA 8.6:94).

Along with the dossier on the Sophist in Volume 3, François Regnault’s reading of the Parmenides in ‘Dialectique d’épistémologies’ (CpA 9.4) is the most extensive engagement with Platonist ontology in the Cahiers. Regnault analyses the relation between the One and its others, in either absolute or relative terms, in the light of a concern for the relation between science and epistemology, with the latter conceived as the former’s discourse. There is a generative movement to Regnault’s dialectical procedure that is evocative of Milner’s more narrow argument in Volume 3 and that likewise inscribes a Lacanian concern for lack and the logic of the signifier at the heart of ontology itself.

Select bibliography

• Badiou, Alain. L’Être et l’événement. Paris: Seuil, 1988. Being and Event (1988), trans. Oliver Feltham. London: Continuum, 2005.
• Cornford, Francis MacDonald. Plato’s Theory of Knowledge. The Theaetetus and the Sophist of Plato, translated with a running commentary. London: Routledge, 1935.
• ---. Plato and Parmenides: Parmenides’ Way of Truth and Plato’s Parmenides, translated with a running commentary. New York: Harcourt, Brace, and Company, 1939.
• Heidegger, Martin. Being and Time (1927), trans. John Macquarrie and Edward M. Robinson. New York: Harper Row, 1962.
• Lacan, Jacques. Écrits. Paris: Seuil, 1966. Écrits, trans. Bruce Fink, in collaboration with Héloïse Fink and Russell Grigg. New York: W.W. Norton, 2006.
• ---. Le Séminaire, livre XI: Les quatre concepts fondamentaux de la psychanalyse, ed. Jacques-Alain Miller. Paris: Seuil, 1973. Seminar IX: The Four Fundamental Concepts of Psychoanalysis, ed. Jacques-Alain Miller, trans. Alan Sheridan. London: Penguin, 1977.
• Plato. Sophist, trans. Harold North Fowler. Cambridge, MA: Harvard, Loeb Classical Library, 1921.