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- Herausgeber: John Wiley & Sons
- Kategorie: Geisteswissenschaft
- Sprache: Englisch
- Veröffentlichungsjahr: 2016
Why bother to praise mathematics when you claim, as Alain Badiou does, that philosophy is first and foremost a metaphysics of happiness, or else it's not worth an hour of trouble? What possible relationship can there be between mathematics and happiness? That is precisely the issue at stake in this dialogue, which serves as a very accessible introduction to what mathematics is and an exploration of the crucial influence it has always exerted on the greatest philosophers. Far from the thankless, pointless exercises they are often thought to be, mathematics and logic are indispensable guides to ridding ourselves of dominant opinions and making possible an access to truths, or to a human experience of the utmost value. That is why mathematics may well be the shortest path to the true life, which, when it exists, is characterized by an incomparable happiness.
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Contents
Cover
Title Page
Copyright
I Mathematics Must Be Saved
II Philosophy and Mathematics, or the Story of an Old Couple
III What is Mathematics About?
IV An Attempt at a Mathematics-based Metaphysics
V Does Mathematics Bring Happiness?
Conclusion
End User License Agreement
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In Praise of Mathematics
Alain Badiou with Gilles Haéri
Translated by Susan Spitzer
polity
First published in French as Éloge des mathématiques © Flammarion, Paris, 2015
This English edition © Polity Press, 2016
Polity Press65 Bridge StreetCambridge CB2 1UR, UK
Polity Press350 Main StreetMalden, MA 02148, USA
All rights reserved. Except for the quotation of short passages for the purpose of criticism and review, no part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior permission of the publisher.
ISBN-13: 978-1-5095-1206-5
A catalogue record for this book is available from the British Library. Library of Congress Cataloging-in-Publication Data
Names: Badiou, Alain, author. | Haéri, Gilles, author.Title: In praise of mathematics / Alain Badiou, Gilles Haéri.Other titles: Éloge des mathématiques. EnglishDescription: Malden, MA : Polity Press, 2016. | Includes bibliographical references and index.Identifiers: LCCN 2016012538| ISBN 9781509512027 (hardback : alk. paper) | ISBN 9781509512034 (pbk. : alk. paper)Subjects: LCSH: Mathematics--Philosophy. | Badiou, Alain--Interviews. | Haéri, Gilles--Interviews.Classification: LCC QA8.4 .B33713 2016 | DDC 510.1--dc23 LC record available at https://lccn.loc.gov/2016012538
The publisher has used its best endeavours to ensure that the URLs for external websites referred to in this book are correct and active at the time of going to press. However, the publisher has no responsibility for the websites and can make no guarantee that a site will remain live or that the content is or will remain appropriate.
Every effort has been made to trace all copyright holders, but if any have been inadvertently overlooked the publisher will be pleased to include any necessary credits in any subsequent reprint or edition.
For further information on Polity, visit our website: politybooks.com
Many years ago – a little before and a little after my first philosophical “opus,” Being and Event (1988) – I introduced the concept of the conditions of philosophy, which you’ll encounter later in this book. The aim was to identify precisely the real types of creative activity of which humanity is capable and on whose existence philosophy depends. Indeed, it is clear that philosophy was born in Greece because in that country, beginning, at any rate, in the fifth century BCE, there were some totally new ideas about mathematics (deductive geometry and arithmetic), artistic activity (humanized sculpture, painting, dance, music, tragedy, and comedy), politics (the invention of democracy), and the status of the emotions (transference-love, lyric poetry, and so on). So I suggested that philosophy really only develops when new advances emerge in a set of “truths” (that’s the name I give them for philosophical reasons) of four different types: science, art, politics, and love. That’s why I responded positively to Nicolas Truong’s invitation to have a dialogue with him in praise of love, and then in praise of theater, in Avignon. Likewise, I accepted Gilles Haéri’s proposal of a dialogue in praise of mathematics in the setting of the Villa Gillet in Lyon. The first two conversations resulted in books published in Flammarion’s “Café Voltaire” series. [English translations: In Praise of Love, New Press, 2012, and In Praise of Theatre, Polity, 2015.] The same is true of the third, which is the subject of this book. All that remains to be done is to write a book in praise of politics, and I’m considering it.
IMathematics Must Be Saved
Alain Badiou, you are what I would call, to use a mathematical term, a singularity in the French intellectual landscape.
There’s your political commitment, of course, which the general public has been aware of since 2006, with the success of De quoi Sarkozy est-il le nom? [translated as The Meaning of Sarkozy, Verso, 2010]. You represent one of the last great figures of the politically-engaged intellectual today, one of the fiercest critics of our liberal democracies, and the tireless defender of the communist Idea, which you refuse to throw out with the bathwater of History.
But from a more specifically philosophical point of view, the body of work you have produced isalso very singular. At a time when philosophy has retreated into specialization, and, in so doing, has renounced its original ambitions, you have consistently attempted to restore meaning to metaphysics by building a system that can be described as a great synthesis on the world and on being. Now, this philosophy, set out mainly in Being and Event, and later in Logics of Worlds, is based to a very large extent on mathematics. You are in this regard one of the rare contemporary philosophers to take mathematics really seriously, and you do not just speak about it as a philosopher but practice it almost on a daily basis.
Could you begin by telling us where this very strong relationship with mathematics comes from?
It’s something that goes back to before I was even born! Simply because my father was a math teacher. So there was the mark of the name of the father, as Lacan would say. Actually, it had a profound effect on me, because I heard mathematics spoken about in my family – by my father and my older brother, by my father and colleagues of his, etc. – in a sort of early imprinting, without my understanding at first what it was all about but sensing that it was at once keenly and obscurely interesting. So much for the first, prenatal stage, so to speak.
Later, as a high-school student, I was fascinated by mathematics as soon as we started doing a few really complex proofs. I must say that what really captivated me was the feeling that, when you do math, it’s a bit like following an incredibly twisted, convoluted path through a forest of ideas and concepts, and yet, at a given moment, the path leads to a sort of beautiful clearing. I was struck early on by this quasi-esthetic feeling about mathematics. I think I could mention a few theorems of plane geometry here, in particular theorems of the inexhaustible geometry of the triangle, which we were taught in grades 9 and 10. I’m thinking of Euler’s line. First we were shown that the three altitudes of a triangle are concurrent in a point H, which was already great. And then that the three perpendicular bisectors were also concurrent, in a point O – it kept getting better and better! And finally that the three medians were concurrent, too, in a point G! Wonderful. But then the teacher mysteriously told us that it could be proved, as the mathematical genius Euler had done, that these points H, O, and G were moreover all on the same line, which is obviously called “the Euler line”! This alignment of three fundamental points, as the behavior of the characteristics of a triangle, was so unexpected, so elegant! We weren’t given the proof, because it was considered too difficult for 10th grade, but our interest in it was piqued. I was thrilled that such a thing could be proved. There’s this idea of a real discovery, of an unexpected solution, even if it means you have to make your way along a path that’s sometimes a little hard to follow but where you’re ultimately rewarded. Later, I often compared mathematics to a walk in the mountains: the approach is long and hard, with lots of twists and turns and steep climbs. You think you’re finally there, but there’s still one more turn … You sweat and strain, but when you reach the summit of the pass, the reward is truly beyond compare: that amazement, that ultimate beauty of mathematics, that hard-won, utterly unique beauty. That’s why I continue to promote mathematics from this esthetic perspective, too, noting that it’s a very ancient perspective, since Aristotle in fact regarded mathematics as a discipline, not so much of truth as of beauty. He claimed that the greatness of mathematics was esthetic, far more than ontological or metaphysical.
Next, I studied contemporary mathematics in greater depth by taking the first two years of university math. This was from 1956 to 1958, my first two years at the École normale supérieure. I combined significant philosophical discoveries I made there (Hyppolite, Althusser, and Canguilhem were my professors at the time) with the math courses at the Sorbonne and substantive discussions with the math students at the École. It was then, probably also because of the atmosphere of structuralism and the 1960s, when there was a lot of buzz about formal disciplines, that I became really convinced that mathematics was in a very close dialectical relationship with philosophy – at least my conception of it, because mathematics was at the heart of my concerns. Structures are first and foremost the business of mathematicians. At the very end of his seminal book, The Elementary Structures of Kinship, the great anthropologist Lévi-Strauss, whom I was reading with passionate interest at the time, referred to the mathematician Weil to show that the exchange of women could be understood by using the algebraic theory of groups. Now, at that time, my philosophical approach required mastering enormous conceptual constructions. What’s more, because of its esthetic force and the creativity it calls for, mathematics requires you to become a Subject whose freedom, far from being opposed to discipline, demands it. Indeed, when you work on a mathematical problem, the discovery of the solution – and therefore the creative freedom of the mind – is not some sort of blind wandering but rather the determination of a path that’s always lined, as it were, by the obligations of overall consistency and demonstrative rules. You fulfill your desire to find the solution not in spite of the law of reason but thanks to both its prohibitions and its assistance. Now, this is what I had begun to think, first in conjunction with Lacan: desire and the law are not opposites but dialectically identical. And finally, mathematics combines intuition and proof in a unique way, which the philosophical text must also do, as far as possible.
I’ll conclude by saying that this back-and-forth movement between philosophy and mathematics produced a sort of split in me … and all my work may be nothing but the attempt to overcome this split. This is because my master in philosophy, the one who revealed philosophy to me, was Sartre. I was a convinced Sartrian. But frankly, mathematics and Sartre, as you know, weren’t exactly compatible … He even had a vulgar phrase that he used to trot out all the time when he was young, at the École normale supérieure: “Science is zilch; morality’s an asshole.”1 To be sure, he didn’t stick to this simplistic maxim, but he never really returned to the sciences, and in particular to the formal sciences. So the conviction grew in me that philosophy should be able to preserve the dimension of the subject, the dimension of the politically committed subject, that sort of historical drama that subjectivity is capable of being, and yet to integrate mathematics in all its rational force and splendor, particularly as regards the doctrine of being.
I could almost sum everything up by saying that it is the overcoming of this split that still constitutes my relationship to mathematics today.
Why do you think it’s necessary to praise mathematics today? After all, that discipline is still central to our educational system; it’s even one of its primary selection tools. And if one were to judge by the recent French Fields Medalist – bringing to 11 the numberof our winners in the field, right after the United States – one might even think that mathematics has pride of place in France. Do you have the contrary feeling that it is under threat?
