by Alan Sokal
We would respond, first of all, that when concepts from mathematics or physics are invoked in another domain of study, some argument ought to be given to justify their relevance. In all the cases cited here, we have checked that no such argument is provided, whether next to the excerpt we quote or elsewhere in the article or book.
Moreover, there are some ‘rules of thumb’ that can be used to decide whether mathematics are being introduced with some real intellectual goal in mind, or merely to impress the reader. First of all, in cases of legitimate use, the author needs to have a good understanding of the mathematics he/she is purporting to apply – in particular, there should be no gross mistakes – and he/she should explain the requisite technical notions, as clearly as possible, in terms that will be understandable to the intended reader (who is presumably a non-scientist). Secondly, because mathematical concepts have precise meanings, mathematics is useful primarily when applied to fields in which the concepts likewise have more-or-less precise meanings. It is difficult to see how the mathematical notion of compact space can be applied fruitfully to something as ill-defined as the ‘space of jouissance’ in psychoanalysis. Thirdly, one should be particularly suspicious when abstruse mathematical concepts (like the axiom of choice in set theory) that are used rarely, if at all, in physics – and certainly never in chemistry or biology – miraculously become relevant in the humanities or the social sciences.
3. Poetic licence
If a poet uses words like ‘black hole’ or ‘degree of freedom’ out of context and without really understanding their scientific meaning, it doesn’t bother us. Likewise, if a science-fiction writer uses secret passageways in space-time in order to send her characters back to the era of the Crusades, it is purely a question of taste whether one likes or dislikes the technique.
By contrast, we insist that the examples cited in this book have nothing to do with poetic licence. These authors are holding forth, in utter seriousness, on philosophy, psychoanalysis, semiotics or sociology. Their works are the subject of innumerable analyses, exegeses, seminars and doctoral theses.10 Their intention is clearly to produce theory, and it is on this ground that we criticize them. Moreover, their style is usually heavy and pompous, so it is highly unlikely that their goal is principally literary or poetic.
4. The role of metaphors
Some people will no doubt think that we are interpreting these authors too literally and that the passages we quote should be read as metaphors rather than as precise logical arguments. Indeed, in certain cases the ‘science’ is undoubtedly intended metaphorically; but what is the purpose of these metaphors? After all, a metaphor is usually employed to clarify an unfamiliar concept by relating it to a more familiar one, not the reverse. Suppose, for example, that in a theoretical physics seminar we were to explain a very technical concept in quantum field theory by comparing it to the concept of aporia in Derridean literary theory. Our audience of physicists would wonder, quite reasonably, what is the goal of such a metaphor – whether or not it is apposite – apart from displaying our own erudition. In the same way, we fail to see the advantage of invoking, even metaphorically, scientific concepts that one oneself understands only shakily when addressing a readership composed almost entirely of non-scientists. Might the goal be to pass off as profound a rather banal philosophical or sociological observation, by dressing it up in fancy scientific jargon?
5. The role of analogies
Many authors, including some of those discussed here, try to argue by analogy. We are by no means opposed to the effort to establish analogies between diverse domains of human thought; indeed, the observation of a valid analogy between two existing theories can often be very useful for the subsequent development of both. Here, however, we think that the analogies are between well-established theories (in the natural sciences) and theories too vague to be tested empirically (for example, Lacanian psychoanalysis). One cannot help but suspect that the function of these analogies is to hide the weaknesses of the vaguer theory.
Let us emphasize that a half-formulated theory – be it in physics, biology or the social sciences – cannot be redeemed simply by wrapping it in symbols or formulae. The sociologist Stanislav Andreski has expressed this idea with his habitual irony:
The recipe for authorship in this line of business is as simple as it is rewarding: just get hold of a textbook of mathematics, copy the less complicated parts, put in some references to the literature in one or two branches of the social studies without worrying unduly about whether the formulae which you wrote down have any bearing on the real human actions, and give your product a good-sounding title, which suggests that you have found a key to an exact science of collective behaviour.
(Andreski 1972, pp. 129–30)
Andreski’s critique was originally aimed at American quantitative sociology, but it is equally applicable to some of the texts cited here, notably those of Lacan and Kristeva.
6. Who is competent?
We have frequently been asked the following question: You want to prevent philosophers from speaking about science because they don’t have the requisite formal training; but what qualifications do you have to speak of philosophy? This question betrays a number of misunderstandings. First, we have no desire to prevent anyone from speaking about anything. Second, the intellectual value of an intervention is determined by its content, not by the identity of the speaker, much less by his or her diplomas.11 Third, there is an asymmetry: we do not purport to judge Lacan’s psychoanalysis, Deleuze’s philosophy or Latour’s concrete work in sociology. We limit ourselves to their statements about the mathematical and physical sciences or about elementary problems in the philosophy of science.
7. Don’t you too rely on argument from authority?
For if we assert that Lacan’s mathematics are nonsense, how is the non-scientist reader to judge? Mustn’t he or she take our word for it?
Not entirely. First of all, we have tried hard to provide detailed explanations of the scientific background, so that the non-specialist reader can appreciate why a particular assertion is erroneous or meaningless. We may not have succeeded in all cases: space is limited, and scientific pedagogy is difficult. The reader is perfectly entitled to reserve judgment in those cases where our explanation is inadequate. But, most importantly, it should be remembered that our criticism does not deal primarily with errors, but with the manifest irrelevance of the scientific terminology to the subject supposedly under investigation. In all the reviews, debates and private correspondence that have followed the publication of our book in France, no one has given even the slightest argument explaining how that relevance could be established.
8. But these authors are not ‘postmodernist’
It is true that the French authors discussed in this book do not all regard themselves as ‘postmodernist’ or ‘poststructuralist’. Some of these texts were published prior to the emergence of these intellectual currents, and some of these authors reject any link with these currents. Moreover, the intellectual abuses criticized in this book are not homogeneous; they can be classified, very roughly, into two distinct categories, corresponding roughly to two distinct phases in French intellectual life. The first phase is that of extreme structuralism, extending through the early 1970s: the authors try desperately to give vague discourses in the human sciences a veneer of ‘scientificity’ by invoking the trappings of mathematics. Lacan’s work and the early writings of Kristeva fall into this category. The second phase is that of poststructuralism, beginning in the mid-1970s: here any pretense at ‘scientificity’ is abandoned, and the underlying philosophy (to the extent one can be discerned) tends toward irrationalism or nihilism. The texts of Baudrillard, Deleuze and Guattari exemplify this attitude.
Furthermore, the very idea that there exists a distinctive category of thought called ‘postmodernist’ is much less widespread in France than in the English-speaking world. If we nevertheless employ this term for convenience, it is because all the authors analysed here
are utilized as fundamental points of reference in English-language postmodernist discourse, and because some aspects of their writings (obscure jargon, implicit rejection of rational thought, abuse of science as metaphor) are common traits of Anglo-American postmodernism. In any case, the validity of our critiques can in no way depend on our use of one word; our arguments must be judged, for each author, independently of his or her link – be it conceptually justified or merely sociological – with the broader ‘postmodernist’ current.
9. Why do you criticize these authors and not others?
A long list of ‘others’ has been suggested, both in print and in private correspondence: these include virtually all applications of mathematics to the social sciences (e.g. economics), physicists’ speculations in popular books (e.g. Hawking, Penrose), sociobiology, cognitive science, information theory, the Copenhagen interpretation of quantum mechanics, and the use of scientific concepts and formulae by Hume, La Mettrie, D’Holbach, Helvetius, Condillac, Comte, Durkheim, Pareto, Engels and sundry others.12
Let us begin by observing that this question is irrelevant to the validity or invalidity of our arguments; at best it can be used to cast aspersions on our intentions. Suppose there are other abuses as bad as those of Lacan or Deleuze; how would that justify the latter?
However, since the question of the grounds for our ‘selection’ is so often asked, let us try to answer it briefly. First of all, we have no desire to write a ten-volume encyclopedia on ‘nonsense since Plato’, nor do we have the competence to do so. Our scope is limited, first, to abuses in those scientific fields in which we can claim some expertise, namely mathematics and physics13; second, to abuses that are currently fashionable in influential intellectual circles; and third, to abuses that have not previously been analysed in detail. However, even within these constraints, we do not claim that our set of targets is exhaustive or that they constitute a ‘natural kind’. Quite simply, Sokal stumbled on most of these texts in the course of writing his parody, and we decided, after reflection, that it was worth making them public.
Furthermore, we contend that there is a profound difference between the texts analysed here and most of the other examples that have been suggested to us. The authors quoted in this book clearly do not have more than the vaguest understanding of the scientific concepts they invoke and, most importantly, they fail to give any argument justifying the relevance of these scientific concepts to the subjects allegedly under study. They are engaged in name-dropping, not just faulty reasoning. Thus, while it is very important to evaluate critically the uses of mathematics in the social sciences and the philosophical or speculative assertions made by natural scientists, these projects are different from – and considerably more subtle than – our own.14
A related question is:
10. Why do you write a book on this and not on more serious issues? Is postmodernism such a great danger to civilization?
First of all, this is an odd question. Suppose someone discovers documents relevant to the history of Napoleon and writes a book about it. Would anyone ask him whether he thinks this is a more important topic than the Second World War? His answer, and ours, would be that an author writes on a subject under two conditions: that he is competent and that he is able to contribute something original. His subject will not, unless he is particularly lucky, coincide with the most important problem in the world.
Of course we do not think that postmodernism is a great danger to civilization. Viewed on a global scale, it is a rather marginal phenomenon, and there are far more dangerous forms of irrationalism – religious fundamentalism, for instance. But we do think that the critique of postmodernism is worthwhile for intellectual, pedagogical, cultural and political reasons; we shall return to these themes in the Epilogue.
Finally, to avoid useless polemics and facile ‘refutations’, let us emphasize that this book is not a right-wing pamphlet against left-wing intellectuals, or an American imperialist attack against the Parisian intelligentsia, or a simple know-nothing appeal to ‘common sense’. In fact, the scientific rigour we are advocating often leads to results at odds with ‘common sense’; obscurantism, confused thinking, anti-scientific attitudes and the quasi-religious veneration of ‘great intellectuals’ are in no way left-wing; and the attachment of part of the American intelligentsia to postmodernism demonstrates that the phenomenon is international. In particular, our critique is in no way motivated by the ‘theoretical nationalism and protectionism’ that French writer Didier Eribon claims to detect in the work of some American critics.15 Our aim is, quite simply, to denounce intellectual posturing and dishonesty, from wherever they come. If a significant part of the postmodernist ‘discourse’ in contemporary American and British academia is of French origin, it is equally true that English-language intellectuals have long since given it an authentic home-grown flavour.16
Plan of this book
The bulk of this book consists of an analysis of texts, author by author. For the convenience of non-specialist readers, we have provided, in footnotes, brief explanations of the relevant scientific concepts as well as references to good popular and semi-popular explanatory texts.
Some readers will no doubt think that we are taking these texts too seriously. That is true, in some sense. But since these texts are taken seriously by many people, we think that they deserve to be analysed with the greatest rigour. In some cases we have quoted rather long passages, at the risk of boring the reader, in order to show that we have not misrepresented the meaning of the text by pulling sentences out of context.
In addition to abuses in the strict sense, we have also analysed certain scientific and philosophical confusions that underlie much postmodernist thinking. First, we shall consider the problem of cognitive relativism, and show that a series of ideas coming from the history and philosophy of science do not have the radical implications that are often attributed to them (Chapter 4). Next we shall address several misunderstandings concerning chaos theory and so-called ‘postmodern science’ (Chapter 7). Finally, in the Epilogue, we shall situate our critique in a wider cultural context.
Many of the texts quoted in this book originally appeared in French. Where a published English translation exists, we have most often used it (sometimes noting our corrections); it is cited in the bibliography, along with the original French source in brackets. In other cases, the translation is ours. We have endeavoured to remain as faithful as possible to the original French, and in case of doubt we have reproduced the latter in brackets or even in toto. We assure the reader that if the passage seems incomprehensible in English, it is because the original French is likewise.
2
JACQUES LACAN
Lacan finally gives Freud’s thought the scientific concepts it requires.
(Louis Althusser, Écrits sur la psychanalyse, 1993, p. 50)
Lacan is, as he himself says, a crystal-clear author.
(Jean-Claude Milner, L’œuvre claire, 1995, p. 7)
Jacques Lacan was one of the most famous and influential psychoanalysts of this century. Each year, dozens of books and articles are devoted to the analysis of his work. According to his disciples, he revolutionized the theory and practice of psychoanalysis; according to his critics, he is a charlatan and his writings are pure verbiage. We shall not enter here into the debate concerning the purely psychoanalytic part of Lacan’s work. Rather, we shall limit ourselves to an analysis of his frequent references to mathematics, and show that Lacan illustrates perfectly, in different parts of his œuvre, the abuses listed in our introduction.
‘Psychoanalytic Topology’
Lacan’s mathematical interests centered primarily on topology, the branch of mathematics dealing (among other things) with the properties of geometrical objects – surfaces, solids and so forth – that remain unchanged when the object is deformed without being torn. (According to the classic joke, a topologist is unable to tell a doughnut from a coffee cup, as both are solid objects with a single hole.) Lacan’s wr
itings contained some references to topology already in the 1950s; but the first extended (and publicly available) discussion goes back to a celebrated conference on The Languages of Criticism and the Sciences of Man, held at Johns Hopkins University in 1966. Here is an excerpt from Lacan’s lecture:
This diagram [the Möbius strip17] can be considered the basis of a sort of essential inscription at the origin, in the knot which constitutes the subject. This goes much further than you may think at first, because you can search for the sort of surface able to receive such inscriptions. You can perhaps see that the sphere, that old symbol for totality, is unsuitable. A torus, a Klein bottle, a cross-cut surface,18 are able to receive such a cut. And this diversity is very important as it explains many things about the structure of mental disease. If one can symbolize the subject by this fundamental cut, in the same way one can show that a cut on a torus corresponds to the neurotic subject, and on a cross-cut surface to another sort of mental disease.
(Lacan 1970, pp. 192–3)
Perhaps the reader is wondering what these different topological objects have to do with the structure of mental disease. Well, so are we; and the rest of Lacan’s text does nothing to clarify the matter. Nevertheless, Lacan insists that his topology ‘explains many things’. In the discussion following his lecture, one finds the following dialogue: