Mathematics and the Roots of Postmodern Thought This page intentionally left blank Mathematics and the Roots of Postmodern Thought Vladimir Tasic OXFORD UNIVERSITY PRESS 2001 OXTORD UNIVERSITY PRESS Oxford New York Athens Auckland Bangkok Bogota Buenos Aires Cape Town Chennai Dar es Salaam Delhi Florence Hong Kong Istanbul Karachi Kolkata Kuala Lumpur Madrid Melbourne Mexico City Mumbai Nairobi Paris Sao Paulo Shanghai Singapore Taipei Tokyo Toronto Warsaw and associated companies in Berlin Ibadan Copyright © 2001 by Oxford University Press, Inc. Published by Oxford University Press, Inc. 198 Madison Avenue. New York, New York 10016 Oxford is a registered trademark of Oxford University Press All rights reserved. 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 Oxford University Press. Library of Congress Cataloging-in-Publication Data Tasic, Vladimir, 1965- Mathematics and the roots of postmodern thought / Vladimir Tasic. p. cm. Includes bibliographical references and index. ISBN 0-19-513967-4 1. Mathematics—Philosophy. 2. Postmodernism. I. Title. QA8.4.T35 2001 510M—dc21 2001021846 987654321 Printed in the United States of America on acid-free paper For Maja This page intentionally left blank ACKNOWLEDGMENTS As much as I would like to share the responsibility for my oversimplifications, misreadings or misinterpretations with all the people and texts that have in- fluenced my thinking, I must bear that burden alone. For valuable discussions and critiques, I am indebted to Hart Caplan, Gre- gory Chaitin, Sinisa Crvenkovic, Guillermo Martinez, Lianne McTavish, Maja Padrov, Shauna Pomerantz, Goran Stanivukovic, Marija and Milos Tasic, Jon Thompson, and Steven Turner. I also thank a number of anonymous re- viewers at Oxford University Press, and acknowledge the patient guidance of executive editor Kirk Jensen. Their thoughtful and critical comments led me to rethink the text many times over, and helped me improve it considerably. Last, but certainly not least, I express my deepest love and gratitude to Maja, to whom I am fortunate to be married. This page intentionally left blank CONTENTS 1. Introduction, 3 2. Around the Cartesian Circuit, 7 2.1. Imagination, 7 2.2. Intuition, 10 2.3. Counting to One, 14 3. Space Oddity and Linguistic Turn, 20 4. Wound of Language, 32 4.1. Being and Time Continuum, 36 4.2. Language and Will, 45 5. Beyond the Code, 50 5.1. Medium of Free Becoming, 53 5.2. Nonpresence of Identity, 58 6. The Expired Subject, 67 6.1. Empire of Signs, 67 6.2. Mechanical Bride, 77 7. The Vanishing Author, 84 8. Say Hello to the Structure Bubble, 100 8.1. Algebra of Language, 101 8.2. Functionalism Chic, 114 9. Don't Think, Look, 119 9.1. Interpolating the Self, 123 9.2. Language Games, 127 9.3. Thermostats "H" Us, 132 10. Postmodern Enigmas, 138 10.1. Unspeakable Differance, 139 10.2. Dysfunctionalism Chic, 154 Notes, 159 Select Bibliography, 177 Index, 183 x Contents Mathematics and the Roots of Postmodern Thought This page intentionally left blank 1 INTRODUCTION To know the world, one must construct it. —Cesare Pavese he antagonism between two vaguely conceived entities, collo- T,quially labeled "science" and "postmodernism," seems to have become part of public life. In the past few years, pages filled with entertain- ing invective have sprung up both on the Internet and in print, attracting the attention of such mainstream media as The New York Times, The Guardian, and Liberation. These exchanges come under the heading "science wars." This passionate debate—which revolves around the problem of how sci- ence in general and mathematics in particular are read or misread—raises a number of social, historical, and even political questions. I am primarily in- terested in the following one: Why would various postmodern intellectuals bother invoking mathematics in their theories at all? It could, of course, be a matter of "fashion," as is sometimes claimed. But let us imagine, if only as a counterfactual, that these theorists are try- ing to convey something that may not be entirely disconnected from mathe- matics and its history. Can one divine what that is, and how would one go about it? Whatever it is, it seems unlikely that it would reveal its secret if we restrict ourselves to considering the quasi-mathematical content of assorted post- modern texts. This was fairly clearly demonstrated in Alan Sokal and Jean Bricmont's Fashionable Nonsense: Postmodern Intellectuals' Abuse of Science (1998). On the other hand, it could perhaps be recovered by tracing the con- nections between mathematics and continental philosophy, by searching for 3 historical ties that go deeper than today's tedious incantations of chaos, fractals, and fuzziness.1 Perhaps. But there is a small obstacle standing in the way of realizing this idea: No one knows what postmodernism is supposed to be. Attempts to make sense of this elusive concept threaten to outnumber attempts to square the circle. The confusion seems to have reached a peak when the sociologist of science Bruno Latour, who is sometimes categorized as a "postmodernist," published We Have Never Been Modern.2 The term "post- modernism" has become a signifier burdened with so many signifieds that it may well be sinking toward insignificance. (At the least, it appears that its meaning is undecidable.) It therefore seems best not to rush to judgments and definitions. Rather, I would like to look into the possibility of reconstructing some aspects of postmodern thought, especially its theoretical aspects known as "post- structuralism" and "deconstruction," from a mathematical point of view. (I will use "postmodernism" as a convenient umbrella term and provide neces- sary differentiations on a case-by-case basis.) Mathematics has always been an important testing ground. It is not un- reasonable to say, paraphrasing a famous postmodern proverb, that few things can escape the mathematical "text." Mathematics has been part of the Western tradition, inseparable from its culture and its philosophy. Among other things, it has been a source of metaphors. Plato's Republic, for instance, advises philosophers that they should study mathematics in order to rise above the world of change and grasp "true being." The modern era owes a good deal to this old tenet of Plato's. In the six- teenth century, Galileo said that the Book of Nature is written in the lan- guage of mathematics. Dutch philosopher Benedict Spinoza authored Ethics, Demonstrated in Geometrical Order (1677), whose title, while not self- explanatory, seems telling nevertheless. It has been claimed that the entire project of the Enlightenment had as its goal achieving the clarity of mathe- matics everywhere by employing the method known as "analytic thinking," whose origins are traceable to mathematics. Even Martin Heidegger, a phi- losopher known for his sharp critiques of science, endeavored to explain "in what sense the foundation of modern thought and knowledge is essentially mathematical."3 It would be possible to skip a few details at this point and tell a wonder- fully uplifting story of unstoppable mathematical progress and cultural im- pact of mathematical ideas—the story of how mathematicians started tack- ling difficult problems regarding formal reasoning, infinity, sets, logic, and abstract structures; how a number of influential twentieth-century thinkers (e.g., Edmund Husserl, Ludwig Wittgenstein, and Bertrand Russell) were dili- gent students of mathematics; how mathematics contributed to the con- ceptualization of computability, intelligence, information, randomness, in- 4 Mathematics and the Roots of Postmodern Thought completeness, chaos, and even the conceptualization of the structure of language itself. I intend to tell parts of that narrative in due course. Its im- portance is impossible to disregard even if it has been told many times. But mathematics is as much a science as it is an art. It is a peculiar hybrid that—as Byron wrote, not of mathematics but of humanity in general—is "half dust, half deity, alike unfit to sink or soar."4 Mathematics is practiced by people who are influenced by philosophy and cultural circumstances, by science and poetry, by politics, style, and other passions, by all the traditions to which they belong. Hence, mathematical "accidental tourists" occasionally happen upon places that do not come highly recommended in rationalist guides. These excursions cannot be ignored here, since my project is to reconstruct certain "antirationalist" exercises of contemporary continental philosophy from a mathematical viewpoint. I would therefore like to consider, among other things, an important part of Western heritage that did not rely on mathematically inspired methods, but that nevertheless informed the views of several influential mathematicians at the turn of the twentieth century. I have in mind nineteenth-century romanticism. Its philosophical contri- butions were, for the most part, separate from mathematics and were opposed to the ideal of formal reasoning that mathematics represented. Romanticist rebellion, sometimes called "the counter-enlightenment," is known for its cri- tiques of science and reason. Romanticist "linguistic turn," with its empha- sis on the importance of language and culture, art and myth, on the indis- pensability of imagination and inexhaustibility of the flux of lived experience by means of formal reasoning, played a significant role in placing language and its limits on the philosophical agenda. In this sense, we might regard the early 1800s as the time when the seeds of the conflict that we now call science wars were planted. Yet the story of science wars seems to be more complex. It is more than a mere episode in a two-centuries-old dispute. It appears, for example, that parts of postmodern theory—despite some superficial similarities with romantic anti-rationalism— find themselves applauding the ultimate in all reductionist projects: artifi- cial intelligence.