NOTE TO USERS This reproduction is the best copy available. ® UMI THIS INFINITE, UNANIMOUS DISSONANCE: A STUDY IN MATHEMATICAL EXISTENTIALISM THROUGH THE WORK OF JEAN-PAUL SARTRE AND ALAIN BADIOU by Zachary Luke Fraser THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS In the Department of Philosophy Supervisor: Dr. Rohit Dalvi Internal Examiner: Dr. Wing-cheuk Chan External Examiner: Dr. Ray Brassier (Middlesex) © Zachary Luke Fraser BROCK UNIVERSITY January 2008 All rights reserved. This work may not be reproduced in whole or in part, by photocopy or other means, without permission of the author. 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Canada This infinite, unanimous dissonance: A Study in Mathematical Existentialism Through the Work of Jean-Paul Sartre and Alain Badiou Zachary Luke Fraser Brock University, 2008 ABSTRACT This thesis seeks to elucidate a motif common to the work both of Jean-Paul Sartre and Alain Badiou (with special attention being given to Being and Nothingness and Being and Event respectively): the thesis that the subject's existence precedes and determines its essence. To this end, the author aims to explicate the structural invariances, common to both philosophies, that allow this thesis to take shape. Their explication requires the construction of an overarching conceptual framework within which it may be possible to embed both the phenomenological ontology elaborated in Being and Event and the mathematical ontology outlined in Being and Event. Within this framework, whose axial concept is that of multiplicity, the precedence of essence by existence becomes intelligible in terms of a priority of extensional over intensional determination. A series of familiar existentialist concepts are reconstructed on this basis, such as lack and value, and these are set to work in the task of fleshing out the more or less skeletal theory of the subject presented in Being and Event. NOTICE The following thesis contains, among other things, an interpretation of Sartre's Being and Nothingness. In the course of this interpretation, the demands of rigour have been such as to force a decisive break with certain, fairly widespread notions bearing upon the content of Sartre's philosophy and the styles of inquiry appropriate to its analysis. The general thrust of these demands is contained in the conviction that, in order to understand the significance and singularity of Sartre's philosophical undertaking, it is not enough to bathe in the light of (what might take itself to be) 'mere description' or 'evidence', nor to meditate roundly on those aphorisms that have become slogans and watchwords of existentialists everywhere. It is necessary, before all else, to unearth the basic theoretical scaffolding that gives his work its very structure, and which polarises and refracts the phenomena that he so brilliantly describes. The product of this excavation is an interpretation that lays emphasis on what could be called Sartre's 'formal ontology', and lends little space to the customary rehearsal of the striking, descriptive vignettes for which Sartre is justly famous. I claim neither that this project is complete, nor that it should not eventually be supplemented by an investigation of the role of 'evidence' in Sartre's philosophy. I do claim that no exegesis of Sartre's thought can be sufficient without having passed through the rigours of his 'formal ontology'. Some Abbreviations Used in the Text BE : Alain Badiou, L 'etre et I'evenement, (Paris: Seuil, 1988). Translated into English by Oliver Feltham as Being and Event (London: Continuum, 2005). Citations will be of the form (BE, m#, ##/##), providing the meditation number followed by the page number in Feltham's translation, and the page number of the French original. Where the translation is my own, an asterisk is placed after the page numbers. BN : Jean-Paul Sartre, L 'etre et le neant: Essai d'ontologie phenomenologique, (Paris: Editions Gallimard, 1943). Translated into English by Hazel E. Barnes as Being and Nothingness: An Essay on Phenomenological Ontology, (New York: Philosophical Library, 1956). Citations will be of the form (BN, #.#.#, ##/##), providing the Part, Chapter and Section number of the text, followed by the English and French page numbers. Where the translation is my own, an asterisk is placed after the page numbers. 2 INTRODUCTION Against all odds, I have always been concerned in a privileged way by the question of how something could still be called 'subject' within the most rigorous conditions possible of the investigation of structures. This question had an echo for me of an even older question, which I had posed at the time that I was fully Sartrean, namely, the question of how to make Sartre compatible with the intelligibility of mathematics. - Alain Badiou1 § 1: Mathematical Existentialism The wager of this thesis is that this question bears more fruit than might be expected, and that, if pursued, it offers valuable insight into the structure and trajectory of Badiou's thought, illuminating the inner workings of Sartre's ontology in the same stroke. One effect of this pursuit is that the rubric 'mathematical existentialism' comes to suggest itself quite strongly as a description of the project undertaken in Badiou's landmark text, Being and Event. The value of this label, though, lies more in forcing a question than in promising an adequate description. It is for this reason I chose it as a title, as the first words of this project rather than the last. It nevertheless threatens to cause some confusion, which I will try to dispel straightaway. To begin with, the title suggests that we might fruitfully place both Sartre and Badiou under this rubric. We cannot. Sartre's ontology and existentialist philosophy radically resist mathematisation, in virtue of the very structure of their concepts. This resistance, however, is as minimal as it is radical. Sartre's concepts—particularly the notions of the for-itself, consciousness and nihilation —resist mathematisation insofar as they elude identity. As Sartre formulates it, the theory of intentionality itself, which is the bedrock of his ontology, implicates an irreducible clinamen of non-self-identity in the very event of consciousness, which makes it a priori recalcitrant to the self-identical literality of anything that can be thought within the formal productions of mathematics. In this respect, the non-mathematicity of Sartrean ontology is radical. Yet, as I will 3 show, Sartre formulates the concept of consciousness in such a way that it comes into startling proximity with the mathematical theory of sets, a proximity that allows the manifold kinships between Being and Nothingness and Being and Event to come closer into view. The reason for this is that Badiou's Being and Event announces, as its first philosophical axiom, the thesis that mathematical set theory is the science of being qua being. The ontology with respect to which Badiou articulates his entire theory of the subject, a theory which Badiou explicitly composes in view of "a determinant 'existential' motif,"2 is mathematical through and through. Even in Badiou's case, however, we must avoid the confusion into which the rubric of 'mathematical existentialism' might lead us if we move too quickly. Between existentialism and mathematics, Badiou's philosophy does not produce any sort of coincidence or identity, but a strict dialectical tension. What is most 'existentialist', or Sartrean, in Being and Event is articulated on the ground of a mathematical ontology, but nevertheless eludes coincidence with the latter. What is most 'existentialist' in that text is Badiou's theory of the subject, which, like Sartre's, has at its core the form of a clinamen by which the subject subtracts itself from being- in-itself and so resists mathematisation and identity, into which it nevertheless comes to inscribe itself.3 Badiou's name for this clinamen is the 'event', and the resulting tension between its deviation from and reinscription in being is finds an expression in the very title of Badiou's major work, just as it does in that of Sartre's: neither Being and Event nor Being and Nothingness describe an insurmountable dualism, but a productive dissonance.