Against all odds, I had been hoping that  Impostures Intellectuelles, published by physicists Alan Sokal and Jean Bricmont in France in the fall of 1997, was a hoax.  I had enjoyed the hoax that made Sokal famous outside his area of quantum field theory [1], and my motivations were much the same as his.  Like Sokal, I had worked with science departments in Nicaraguan universities.[2]  That experience had left me skeptical of the facile view of objectivity in science as an ideological smokescreen for domination and oppression, a position apparently exemplified by the following quotation from Andrew Ross, co-editor of the special issue of Social Text that published Sokal's parody:

 

"While the original story of science is still being told in opposition to the humanist tradition of rhetoric, in recent years critics have come to see science itself as just another form of rhetoric; one with particularly aggressive claims on objectivity." (Strange Weather, p. 113)[3]

 

To Stanley FishÕs complaint about SokalÕs Òbad joke,Ó[4] one might respond that academia takes itself far too seriously, some universities going so far as to charge upwards of $100,000 for a four-year education.  And Ken HirschkopÕs characterization of the hoax as a Òchildish gestureÓ[5] presupposes that academics, including science warriors, are models of adult behavior, a claim I would find hard to defend.

 

If Impostures Intellectuelles had been a hoax, its target would have been those scientists who, in recent years, have set out to condemn apparently disturbing attitudes toward science on the part of social scientists and philosophers, in the process displaying an often irritating

misunderstanding of the texts they criticize.  Unfortunately, with the publication of Fashionable Nonsense  (FN), the North American translation of Impostures Intellectuelles, it appears Sokal and Bricmont are on the level.  But then, by selecting ten French authors[6] influential in literary and artistic circles in the U.S., assembling a series of lengthy quotations in which these authors discuss science, and annotating  them with the invariable comment  Òmeaningless,Ó what have they accomplished?  Certainly not what sympathetic critics have claimed. Sokal and Bricmont have not established, nor even coherently argued, T. NagelÕs suggestion that  "Clearly all this name-dropping is intended to bolster [the] reputations [of the French authors] as deep thinkers."[7]  Nor have they exhibited sufficient scholarship to justify R. DawkinsÕ assertion that "As for the harder task of reclaiming US literary departments for genuine scholars, Sokal and Bricmont have joined Gross and Levitt[8] in giving a friendly and sympathetic lead from the world of scienceÓ[9].   In fact, FN fails to justify its principal accusations by giving a clear characterization of the phenomenon it purports to study, or even to establish its existence.   Much less does FN shed light on the questions their selected authors address, or the contexts in which they are being addressed.  The book is rather less than an intellectual imposture; it is an intellectual non-event.[10]

 

It's important to insist on this point, because most of the book's supporters — including the reviewers quoted above — have used its appearance as an excuse to call into question the legitimacy of the book's targets, following Sokal and Bricmont's explicit invitation to do so[11].  In the name of science, as we will see, much has been said about mathematics — in particular a facile assimilation of mathematics to the sciences — that many mathematicians would find hard to swallow.   But mathematicians do share with experimental scientists the sense that what we do should be directed to a precise object.  Instead of trying to determine what their object might be, Sokal and Bricmont present a list of silly things some famous French authors have written, or appear to have written, about science and mathematics.   Absent a serious attempt to find these quotationsÕ least common denominator[12], this list is no more edifying or consequential than "NFL Football's Funniest Moments," or "The collected Errata of Michael Harris.Ó[13]  The preface to the American edition admits that FN has two distinct targets:  ÒabuseÓ of scientific concepts and terminology — i.e., the silly quotations — and Òepistemic relativism,Ó the notion that science is just one version of the truth among many.  Among the French authors only Irigaray and (in part) Latour are criticized for relativism, but they are joined by Quine, Kuhn, and Feyerabend, as well as the Edinburgh school of Social Studies of Science in an ÒIntermezzoÓ on the philosophy of science.  ItÕs all just ÒFashionable NonsenseÓ as far as the authors, their publisher, and their sympathetic critics are concerned.  Since the first target is unmotivated and the second target belongs to an extensive philosophical tradition which FN — as the authors admit — addresses only superficially, the book is inevitably shallow as well as incoherent.[14] 

 

  But it has certainly been some kind of event.  A year before publication, when it was still just a manuscript on a random walk among publishers and colleagues, this book was already a Paris scandal.  Bruno Latour launched a preemptive strike in Le Monde, accusing the authors of anti-French protectionism and nostalgia for cold war research budgets. The scandal gained momentum in the weeks before the book hit the stands.  ÒAre our intellectuals  impostors?" screamed Le Nouvel Observateur's headline. The answer was not very encouraging.  Julia Kristeva called the authors Òfrancophobes" and diagnosed the book as a symptom of Òeconomic and diplomatic competition between Europe and America..."; in an interview with Corriere della Sera she prescribed psychoanalysis. Physicist Jean-Marc Levy-Leblond compared Sokal to a cowboy who is Òundoubtedly" fond of Engels (and Bricmont to...a druggist!).  It wasn't even necessary to read anything:  LibŽration published a vicious attack by Vincent Fleury and Yun Sun Limet entitled ÒThe Sokal-Bricmont Swindle," accusing the authors of intellectual dishonesty on the basis of quotations which were nowhere to be found in the book. [15] By contrast, most reviewers of the British and U.S. editions were happy to laugh along with the authors— the reviews by Dawkins and Nagel quoted above were typical — feeding the suspicion that the science wars, like the wider culture wars, are in large part a continuation of the Hundred YearsÕ War by other means.[16]

 

  The arrogance and offensiveness of certain French intellectuals, recalling the defensiveness of Social TextÕs editors in the wake of the initial hoax, is perhaps the strongest argument in favor of the book, just as the arrogance of the book's supporters [17] is the best caution against joining the bandwagon.  The best conclusion is that the science wars are being driven by the mass media — not a hospitable place for careful argument.  Those in the U.S. who have celebrated the revival of the tradition of the public intellectual should bear this in mind, since the result is generally not more enlightening than the science wars. 

 

  Among the mass media I include blockbuster books like the original French edition of the Sokal-Bricmont book, a major media event of the fall 1997 literary season, with a massive press campaign orchestrated by publisher Odile Jacob.[18]  Almost exactly one year later, two responses were published to the general indifference of the media[19] — testimony to the affair's short half-life and to the publishers' relative lack of resources for promotion.  Jeanneret's book  "L'affaire Sokal ou la querelle des impostures" is an extended analysis of the "affaire" in its rhetorical and mass media dimensions or, more properly, what he calls its "trivial dimension", "the way various ideas circulate, legitimate, meet, or avoid one another..." [p. 10].  Whether or not one share's the author's perspective, Jeanneret's book makes for interesting intellectual history, and has the additional merit of avoiding the cycle of accusations of imposture and stupidity that make the Science Wars so tiresome and predictable.  The disadvantage of such an approach is that it sheds little light on the substantial matters at issue.  For these, one has to turn to Impostures Scientifiques  (IS), a collection of articles compiled or commissioned by Baudouin Jurdant and published simultaneously as an issue of the journal Alliage  and as a book by La DŽcouverte press.  Jurdant presents IS as a Òvery broad defense of thought, in natural sciences as well as the humanitiesÉinsofar as [that thought] is at the origin of an original vision of the world that surrounds us and the manner in which that world can have a sense.Ó[20] As we will see, the articles in IS are at their strongest when they explain how Sokal and Bricmont — and their supporters in the press — failed to address the Òoriginal vision[s]Ó of the authors they criticize.  But IS also contains more than its share of distortion, settling of scores, and appeal to crude stereotypes.  In particular, the authors are too often content to criticize FN's weakest points -- to play the sort of fool's game best exemplified by FN  itself -- and, having failed to engage the deeper concerns on the part of the scientific community, can do no better than question Sokal's and Bricmont's motives — again, just as FN Ôs supporters do with the authors it criticizes.  In the end, IS is too contaminated by the science wars agenda, as defined by the media, to help bring about the rigorous and critical dialogue between the polarized camps that alone can replace the science wars by something more constructive.[21] 

 

 

A FOOL'S GAME

 

The most appropriate way to explain what I mean by "a fool's game" is to play it

myself.  To illustrate the technique I have chosen three weak points in FN  for criticism.  I am aware that Sokal and Bricmont have addressed some of these issues more carefully elsewhere, even elsewhere in the book, but since they never really manage a synthesis of their purpose, and since they have frequently complained (with some justice) that their critics impute to them attentions that go beyond what they have written, their actual text is as good a place to start as any.  Readers who object to the tone can treat this section as a parody of a traditional foolÕs game mathematicians play at the expense of physicists.

 

 

Sokal and Bricmont have not ceased to complain that

 

 

"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 [of the scientific terminology to the subject supposedly under investigation] could be established."  [FN, p. 13]

 

Taken literally, this claim is simply false.  Several articles in IS take pains to defend some of the cited quotations from Lacan, Latour, and Deleuze, in particular.[22] At least two of these articles — physicist David Mermin's attempt at a generous interpretation of Latour and the first version of Jean-Michel Salanskis' discussion of Lacan and Deleuze — were published in 1997, well before the appearance of FN, which even contains a brief response to MerminÕs arguments (pp. 131-133).  What Sokal and Bricmont mean, presumably, is that no one has ever given an argument they find convincing.  Rather than try to refute such circular reasoning, I will concentrate on Salanskis' alternative reading of what at first sight is a bizarre and obsessive rehash of basic differential calculus in Deleuze's "Difference et Repetition," and leave it to the reader to decide who is guilty of imposture.[23]

 

The case of Deleuze is crucial for Sokal and Bricmont.  His quotations in FN, alone and with Guattari, are particularly  extensive, and he comes across as the most apparently consistent abuser of mathematics after Lacan.   Let me say at the outset that I havenÕt read Deleuze closely and donÕt pretend to understand the overall purpose of his books — a necessary starting point, one would think, for understanding the importance of the details.  But at least some of the passages quoted in FN are not meaningless abuses of science.  Salanskis argues in IS that the chapter ÒSynth�se idŽelle de la diff�renceÓ in DeleuzeÕs DiffŽrence et RŽpŽtition, the source of the quotations on pp. 163-164 of FN, is concerned with how the Platonic idea, in its Kantian reinterpretation, Òshould and must be reinterpreted as a game of the difference with itself in the virtual, from which all individual things are supposed to ariseÓ (p. 171).  This kind of philosophy is not in favor in English-speaking countries, but one can recognize its affinity with stages in the Western tradition; Deleuze is particularly close to Spinoza and Leibniz, who are still taught in universities, even in the United States.  Once the question of difference is introduced, it seems to me perfectly natural to consider the philosophical bases of the mathematical treatment of difference, not least because Leibniz was a philosopher as well as developer of differential calculus, and Salanskis develops this theme with regard to DeleuzeÕs entire chapter.[24]  But one doesnÕt have to be a philosopher to spot an inexcusable omission in FN.  The first quotation on p. 163 of FN contains an ellipsis.  If you go to the source you will find that Deleuze writes ÒÉin the old interpretations of differential calculus, called barbarian or prescientific, there is a treasure that needs to be released from its infinitesimal straitjacket.Ó  He then refers to three texts from the 18th and early 19th centuries — one by Ho‘nŽ Wronski, whose name should be familiar to readers — which draw philosophical conclusions from calculus, and the ellipsis concludes ÒMany philosophical riches, here, should not be sacrified to modern scientific technique:  a Leibniz, a Kant, a Plato of the calculus.Ó[25] 

 

            This omission is already enough to disqualify Sokal and Bricmont as intellectual historians.  I interpret this to mean that the philosophical questions raised by these texts are of interest independently of the subsequent development of the calculus.  If this interpretation is correct, the comment in FN that "It is hard to see why a philosopher would choose to ignore [a rigorous exposition of differential calculus, based on limits rather than infinitesimals]," [26] is completely irrelevant.  Besides, Deleuze makes it clear on p. 229 that he knows the modern definition of limits, and says explicitly that ÒWhen one speaks of the ÔmetaphysicsÕ of calculus, it is precisely this alternative between the infinite representation and the finite representation.Ó  Here infinite presumably refers to Leibniz and finite refers to the modern definition using limits.   The IS authors are particularly sensitive to this kind of weakness in FN;  J.-L. Gautero makes the point about DeleuzeÕs reading of Leibniz quite clearly in IS (p. 61).   But take another look at these remarks.  How can Sokal and Bricmont claim that Cauchy's theory of limits placed the definition of the derivative on firm foundations when an acceptable definition of real numbers -- the set to which the limit belongs -- was not proposed until 50 years later?  The two physicists seem to be more "realist" about real numbers than most mathematicians.  We will return to this point. 

 

Salanskis also points out a blunder in FNÕs reading of Deleuze.  Sokal and Bricmont give the ÒcorrectÓ translation of DeleuzeÕs phrase ÒLa limite est la puissance du continuÓ as Òthe limit is the power [i.e., the cardinality] of the continuumÓ, and call this Òexceedingly confused.Ó  Salanskis argues, plausibly, that ÒpuissanceÓ here is the (standard) translation of AristotleÕs dunamis, and that the whole phrase says something like Òindividuals are generated in the continuous [i.e., the flow of experience] by specification of their bordersÓ.  An alternative reading might be that Òthe concept of the continuous [central to metaphysics from Aristotle to Kant] is actualized in the concept of the [mathematical] limit.Ó  Both readings are, at worst, ÒbanalÓ, to use FNÕs favored term for the residual truth value in the texts criticized, after the nonsense has been leached away; the last reading has the added advantage of being compatible with FNÕs correction.[27]  Again, IÕm not particularly a fan of DeleuzeÕs writing, but at least FNÕs reading doesnÕt prove he was a dunce.[28]  One wonders how retrofitting concepts from 19th century mathematics to the metaphysical tradition resolves the question of whether the class of differentiable functions is an adequate representation of physical reality.  University teaching would be an entirely different experience if calculus students were in the habit of raising this question.[29]

 

            Does DeleuzeÕs reputation as a deep thinker really depend on the Òsuperficial eruditionÓ (FN, p. 155) displayed in these and other quotations cited by Sokal and Bricmont?  Whatever his intentions may have been, Deleuze disarmed the implicit accusation of bad faith long before Sokal showed up: ÒHow can write otherwise than about what one doesnÕt know, or knows poorly?  ItÕs necessarily on that subject that one thinks one has something to sayÉ We have thus spoken about science in a way of which we are well aware, unfortunately, that it is not scientific.Ó[30]   If DeleuzeÕs intention was nevertheless to shore up a shaky reputation with pseudo-scientific quotations, it was apparently unnecessary: Deleuze:  une vie philosophique, a collection of articles on his work published shortly after his death, had very little to say about his theory of calculus and still managed to fill 568 pages.[31]

 

Sokal and Bricmont do not claim  any grand philosophical ambitions:  ÒWe are aware that we will be dealing with difficult problems concerning the nature of knowledge and objectivity, which have worried philosophers for centuries" (FN, p. 50).  Their intermezzo on philosophy and Òcognitive relativism,Ó the longest chapter in the book, is just long enough to establish that the authors' are not guilty of the most naive errors (of which they have been accused nevertheless, this being much easier than reading what they actually write).  From a scientistÕs standpoint, it is predictably ÒbanalÓ in the Sokal-Bricmont sense:  they agree with skeptics that PopperÕs epistemology does not capture the fundamental rationality of science, see much that is valid in Kuhn and Feyerabend, and quote approvingly EinsteinÕs remark that ÒThe scientistÉmust appear to the systematic epistemologist as an unscrupulous opportunist.Ó  Hints of a more problematic philosophy emerge nonetheless.  Their philosophy of mathematics, for instance, is summarized in the sentence ÒA mathematical constant like p doesn't change, even if the idea one has about it may change." ( p. 263).  This claim, referring to a Òcrescendo of absurdity" in Sokal's original hoax in  Social Text, is criticized by anthropologist Joan Fujimura, in an article translated for IS. Most of FujimuraÕs article consists of an astonishingly bland account of the history of non-euclidean geometry, in which she points out that the ratio of the circumference to the diameter depends on the metric.   Sokal and Bricmont  know this, and Fujimura's remarks are about as helpful as FN's referral of Quine's readers to Hume (p. 70).  Anyway, Sokal explicitly referred to "Euclid's pi", presumably to avoid trivial objections like Fujimura's -- wasted effort on both sides.[32]  If one insists on making trivial objections, one might recall that the theorem that p is transcendental can be stated as follows:  the homomorphism Q[X] --> R taking X to p is injective.  In other words, ¹ can be identified algebraically with X, the variable par excellence.[33]

 

More interestingly, one can ask what kind of object ¹ was before the formal definition of real numbers.  To assume the real numbers were there all along, waiting to be defined, is to adhere to a form of Platonism.[34]  Dedekind wouldnÕt have agreed.[35]  In a debate marked by the accusation that postmodern writers deny the reality of the external world, it is a peculiar move, to say the least, to make mathematical Platonism a litmus test for rationality.[36]  Not that it makes any more sense simply to declare Platonism out of bounds, like LŽvy-Leblond, who calls Stephen Weinberg's gloss on Sokal's comment Òune absurditŽ, tant il est clair que la signification d'un concept quelconque est Žvidemment affectŽe par sa mise en Ïuvre dans un contexte nouveau!"[37]  Now I find it hard to defend Platonism with a straight face, and I prefer to regard formula ¹2 =  6z(2) as a creation rather than a discovery.  But Platonism does correspond to the familiar experience that there is something about mathematics, and not just about other mathematicians, that precisely doesn't let us get away with saying ÒŽvidemment"![38]  This experience is clearly captured by Alain Connes, a self-avowed Platonist, in his dialogue with neurobiologist J.-P. Changeux, who (to oversimplify) expects to find mathematical structures in the brain.[39]  I don't think Connes (or Roger Penrose, another prominent Platonist) is confused about reality, and I have a hard time imagining a neuronal representation that does justice to the concept of ¹.  But the ontological issues are far from settled, and while there is no reason to assume they will ever be settled, the important point is that this situation is not an obstacle to mathematics, much less to rationality.[40]  The real absurdity is to claim otherwise.

 

FN devotes a separate Intermezzo to ÒSome abuses of Gšdel's theorem and set theory.Ó  Even without having read RŽgis DebrayÕs attempt to use GšdelÕs incompleteness theorem to show that self-government is logically inconsistent (what Michel Serres calls Òthe Gšdel-Debray principleÓ), we know what this chapter is about.  Nothing particularly French is going on here.  Use of Gšdel as a cipher for undecidability has long been a staple of general, not to say popular, culture, especially for my generation, which grew up with HofstadterÕs Gšdel, Escher, Bach..  The temptation to draw worrisome conclusions is irresistible[41], and Sokal and Bricmont should have asked themselves why this is so, rather than attempting to squeeze GšdelÕs theorem back into its logical straitjacket. 

 

Historically, the theorem symbolizes the failure of a program to ground knowledge unshakably on the model of mathematical reason.  Postwar analytic philosophy was born from the ashes of this program, whose sources include that very Enlightenment Sokal and Bricmont claim to be defending.[42]  Writers may be unaware of the content of the theorem, not to mention its proof, and yet understand it perfectly as a watershed in western culture.[43]  The obsession with Gšdel's theorem is proof that the culture cares about  mathematics.  What is incomprehensible is that anyone concerned with the status of mathematics should complain about this.

 

But Sokal and Bricmont make a curious claim:  Òmetatheorems in mathematical logic, like GšdelÕs theoremÉ are rarefied branches of the foundations of mathematics [that] have very little impact on the bulk of mathematical research and almost no impact on the natural sciences.Ó  Ignore the abusive metaphor, absent in the French original, that likens metatheorems to billiard balls.  Ignore the surprising suggestion that the Turing machine has been of little importance for the natural sciences (in theory and practice), or the historical importance of GšdelÕs theorem in paving the way for present-day agnosticism regarding foundations.[44] Morris Kline devoted an entire book to the thesis that GšdelÕs theorem was a ÒdisasterÓ, and called Òthe loss of truthÉ a tragedy of the first magnitude.Ó  ÒThe present state of mathematics is a mockery of the hitherto deep-rooted and widely reputed truth and logical perfection of mathematics.Ó[45] Sokal and Bricmont are observing, correctly, that there was no tragedy; that mathematics, not to mention the natural sciences, have lost none of their creative force in spite of the failure of the foundationalist program.  In this sense perhaps it's true, as a graduate student in Performance Studies once tried to convince me, that mathematics was the first field to go postmodern.[46]

 

 

MATHEMATICS

 

            Attempting to capture the scope of the Science Wars, one soon realizes that it practically coincides with academia as a whole.  Proceeding by a sort of Brownian motion, I discovered abelian groups of exponent 2, popularized among structuralists by AndrŽ WeilÕs appendix to LŽvi-StraussÕ Elementary Structures of Kinship, used as an organizing principle in articles by Rosalind Krauss and James Clifford on Òpost-modernÓ sculpture or the boundary between ethnography and art.[47]  This unorthodox use of technical mathematics, while non-standard, seems perfectly unobjectionable as well as intellectually fruitful; there is no reason to assume its purpose is Òno doubt, to impress and, above all, to intimidate the non-scientist readerÓ (FN, p. 5).  By the same token, Nathalie CharraudÕs article in (IS, p. 243 ff.) makes it at least plausible that Lacanian psychoanalysts found non-orientable surfaces a helpful representation of the structures they claim to have discovered.[48]

 

            Sokal and Bricmont are troubled by the apparent willingness of Roger Anyon, a British anthropologist interviewed by the New York Times, to grant the same epistemic status to scientific theories of Native American migration from Asia and Zuni claims to have originated in the spirit world beneath America:  ÒWe are faced with two theories that contradict  each other.  How can they both be equally valid?Ó[49]  FN wisely allows for the possibility that Anyon was misquoted, but the question is better answered by looking at the incident in its proper context, that of contemporary relations between anthropology and the belief systems of the groups being studied.  A grant proposal to the National Endowment for the Humanities, regarding the reinstallation of Native American objects in an art museum, promised that  Òthe reinstallation Ôwill present both the academic interpretation of an object or objects and the interpretation of the same material as viewed and understood by Native elders and artists ÔÓ.[50]  Rather than accuse anthropologists of attempting to repeal the law of the excluded middle,[51] Sokal and Bricmont need to recognize that Anyon is taking part in a [dialogue], in which truth is only one issue among many.

 

            Sokal and Bricmont have a hard time imagining that anthropologists have anything more interesting to discuss than the truth.  It will therefore come as a surprise to them, and to many philosophers, that truth is also a secondary issue in mathematics.  Of course we want to prove true theorems, but this is hardly an adequate or even useful description of our objective. Mathematicians, and scientists for that matter, judge our peers not by the truth of their work but by how interesting it is[52].  The difference between the true and the interesting even has a market value.  Professor Ed Fredkin of Carnegie-Mellon will give you $100,000 — almost enough to buy a bachelorÕs degree — if you are the first to make a computer prove an interesting theorem in mathematics.[53]  Whereas any beginner can program the computer to prove a true theorem after a single lesson.

 

      This point is hardly novel; LŽvy-Leblond says something similar in IS  (p. 39), and DieudonnŽ distinguishes further between ÒmathŽmatiques videsÓ and ÒmathŽmatiques significatives.Ó[54]   But it is surprising to see just how little we seem to be concerned with ÒtruthÓ these days.  Mathematicians rarely discuss foundational issues any more[55], so it was significant that an article by Arthur Jaffe and Frank Quinn, reaffirming the importance of rigorous proof in the current context of strong interaction between physics and mathematics, provoked no fewer than 16 responses by eminent mathematicians, physicists, and historians.   No two of the positions expressed were identical, which already should suggest caution in laying down the law on rationality, as Sokal and Bricmont (and LŽvy-Leblond, see note *) seem inclined to do. But for our purposes here, what is remarkable is that almost none of the responses had much to say about Òtruth.Ó[56]  ÒTruthÓ was central, predictably, only to the responses of Chaitin and Glimm.  ChaitinÕs branch of mathematics treats ÒtruthÓ as a technical term, without metaphysical connotations, and ChaitinÕs claim to have Òfound mathematical truths that are true for no reason at allÓ suggests that it may be harder than Fredkin suspects to know just when to award his prize. GlimmÕs brand of truth is quite the opposite:  it Òlies not in the eye of the beholder, but in objective realityÉ  It is thus reproducible across barriers of  distance, political boundaries and time.Ó[57]  Turning to the introduction to the book Quantum Physics, by Glimm and Jaffe, one finds the unusual assertion that Òmathematical analysis must be included in the list of appropriate methods in the search for truth in theoretical physics.Ó  Generally speaking, the mathematics department may be the only spot on campus where belief in the reality of the external world is not only optional but frequently an annoying distraction.  But this patently does not apply to mathematical physicists, and I canÕt help thinking itÕs not a coincidence that both Bricmont and Sokal are amply represented in the Glimm-Jaffe bibliography.

 

Philosophers and philosophically-minded sociologists concerned with mathematics seem to think their job is to explain mathematical truth.  Edinburgh sociologist David Bloor and philosopher Philip Kitcher, cast for science wars purposes as an irresponsible relativist and a moderate realist, respectively,[58]  have both attempted to develop empiricist accounts of mathematical knowledge[59].  (Knowledge and truth are not synonyms but they are on the same wavelength. [60])  They have their own (very different) reasons, but in so doing IÕm convinced they have missed the point of mathematics.  As is typical in such discussions, their examples are drawn either from mathematical logic or from mathematics no more recent than the 19th century.  If the sociologist, at least, had done some field work, he couldnÕt have helped observing that what mathematicians seem to value most are ÒideasÓ (not necessarily of the Platonic variety); the most respected mathematicians are those with strong Òintuition.Ó  Now intuition, the philosopher assures us, is philosophically indefensible; Sokal and Bricmont add that Òintuition cannot play an explicit role in the reasoning leading to the verification  (or falsification) of these theories, since this process must remain independent of the subjectivity of individual scientists.Ó[61]  FredkinÕs theorem-proving machine may see things that way, but what are we do make of ThurstonÕs emphasis on the Òcontinuing desire for human understanding  of a proof, in addition to knowledge that the theorem is trueÓ?[62]  We know what he means, as we know what Robert Coleman means, when, having discovered a gap in ManinÕs proof of MordellÕs conjecture over function fields, he nevertheless writes ÒI believe that all this is testimony to the power and depth of ManinÕs intuition.Ó[63]  Is Coleman trying to slip a counterfeit coin between the context of discovery and the context of justification?  Do these offhand comments touch on something genuine and profound about mathematics?  Or is it just my indoctrination that makes me think so? 

 

 

LetÕs try a thought experiment.   How do we know WilesÕ proof of FermatÕs Last Theorem, completed by Taylor and Wiles, is correct? Although this particular theorem, better publicized than any in history, has been treated with unusual care by the mathematical community, whose ÒverdictÓ is developed at length in a graduate textbook of exceptionally high quality,  IÕd guess that no more than 5% of mathematicians have made a real effort to work through the proof[64].  Some scientists (and some mathematicians as well) apparently view Wiles and his proof as an Òanachronism.Ó[65]  The general public is not entirely convinced.  Why are we?  Can a sociologist study this question without knowing the proof?  Can mathematicians pose the question in terms sociologists would find meaningful?  Knowing the truth of the matter is obviously of no help, and relativism is not the issue:  itÕs not clear what kind of ÒrealityÓ would be relevant to settling the question, but the fact that no one has found a counterexample is certainly not a good candidate.  The question is rather more subtle than the example Sokal and Bricmont propose in their philosophical intermezzo, how to decide whether a herd of elephants is stampeding inside a lecture room.[66]  We will conclude the thought experiment at the end of the essay. 

 

CONTEXT

 

As an occasional geometer, I was delighted to read recently that ÒLa gŽomŽtrie nous enseigne la toute-puissance de la forme.  Dans sa logique, la mati�re importe peu, nÕexiste pas.  DÕailleurs, il nÕy a pas de mati�re dans lÕUnivers.  La physique ne reconna”t que des formes et des masses.Ó  The source of this information was the December/January issue of Paris Vogue magazine entitled ÒFashion and Science,Ó which featured 100 pages of highlights from the history of science, from Euclid and Archimedes to cloning and wormholes.  SchršdingerÕs cat, the Mandelbrot set, and the butterfly effect make their expected appearances, as do Galileo, Darwin, Einstein, Heisenberg, and the rest of the gang, in a running series of captions below fashion photos vaguely arranged by scientific themes. 

 

At about the same time, Givenchy introduced a new menÕs cologne called ¹; the ads showed a cosmonaut and the slogan Òun peu plus loin que lÕinfini.Ó  A few months earlier, at the seventh annual ÒCitŽ de la rŽussiteÓ at the Sorbonne, 100 assorted big names from all fields — Nobel prize winners, a Cardinal, three former prime ministers and a constellation of ministers, Yehudi Menuhin, fashion designer Sonia Rykiel, Jean-Marc LŽvy-Leblond — gathered to talk about time.  The program looked like something straight out of Virilio:  Boutros Boutros-Ghali and Javier Solana talked about ÒHuman rights beyond time and spaceÓ while (former Mitterand adviser) Jacques Attali and communications professor Daniel Bougnoux spoke on Òinfinite spaceÓ and the global village. 

 

Has nothing changed in Paris since the Ô60s, when LacanÕs Ecrits  and books about philosophy of mathematics were best-sellers, available in drugstores.[67]  Does intellectual imposture on scientific themes really sell cologne and haute couture[68] and public policy[69]?   These are the wrong questions.  Science plays a peculiar role in every culture, and maybe the peculiarities are more visible in France than elsewhere.  Picador, Sokal and BricmontÕs U.S. publisher,  finds this an occasion for levity; hence the titleÕs allusion to the sterotypically Parisian industry and the picture of the Eiffel Tower on the cover.  The original title in France and Britain was sterner:  somebody is guilty of imposture.    The reader is offered the implausible choice:  the French authors are either fools or frauds, and finally someone is willing to say so.  This explains the recurring reference to The EmperorÕs New Clothes.  But why did these authors turn to science?  Why these particular branches of science?  And why have their readers been so dumb for so long?  

 

The failure of FN as an intellectual event is its authors' failure to ask these questions, the ones that should naturally occur to a scientist.  Sokal and Bricmont write: 

 

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. (FN, p. 17)

 

This may satisfy those who imagine that the context of page 50 is pages 48-52, say, but if the context is an ongoing literary debate or an entire cultureÕs orientation to mathematics and science, then the length of the quotations is irrelevant.  To paraphrase remarks made by David Bloor, Sokal and Bricmont are Òas it were, coming into the middle of a conversation that has been going on for some time.Ó[70]  In what is perhaps the most cogent observation in IS, Dahan-Dalmedico and Pestre point out that, while they are prepared to laugh along with Sokal and Bricmont at the Òextraordinary scientistic mimicry that overcame most intellectuals in France in the 1960Õs,Ó the two physicistsÕ reading of the French authors concentrates on Òwhat is badly expressed or ridiculous — while never  asking what is at stake intellectually, never  speaking of the manner in which these authorsÉwork and propose to think the world.Ó[71]

 

Perhaps the biggest scandal is that the answers to the questions Sokal and Bricmont neglected to ask are probably not that hard to find.  From Oulipo to Althusser, postwar France was obsessed with the search for scientific  regularity, preferably mathematical, of the Bourbaki variety.[72] Dahan-Dalmedico and Pestre assert that this ÒscientismÓ was Òdesired and sustained by the scientists themselves[73]Ó  Unfortunately, the examples they cite are too special, and much more historical work needs to be done to reconstruct all the interactions between philosophers and scientists of the Òpost May Ô68Ó generation.[74]   WhatÕs certain is that some of the variables hidden from Sokal and Bricmont can be found literally around the corner from the offices of Odile Jacob, at the Ecole Normale Superieure, where scientists in good standing were among those attending Lacan's and Althusser's seminars.  Some credentialed mathematicians talked topology with Lacan; others worked with Althusserian philosophers on some of the same texts of Leibniz and Hegel discussed by Deleuze[75]; still others tried to develop mathematics adequate to structuralism and post-structuralism.  Salanskis refers to his own experience as well as that of Gilles Ch‰telet and Jean Petitot, both of whom found inspiration in DeleuzeÕs DiffŽrence et RŽpŽtition..[76] Sokal and Bricmont replace this history by an H.C. Andersen fairy tale.[77]

 

            Interactions between the most famous French mathematicians and literary intellectuals of the Ô60s and Ô70s have not been documented, as far as I know, and perhaps Sokal and Bricmont fault the latter for learning their mathematics from unrepresentative figures.  They certainly expect the intellectuals to make the distinction between mainstream physics and Òthe most subjectivist writings of Heisenberg and Bohr.Ó[78]   The collaboration between scientists and philosophers initiated by Althusser was paralleled by the continuing seminar on philosophy and mathematics, where Jean Bricmont spoke in December 1997, on the problem of hidden variables in quantum mechanics.  This topic is by no means irrelevant to the science wars.  Hidden variables theories as an alternative to Òquantum orthodoxyÓ are defended by Gross and Levitt in Higher Superstition,  by S. Goldstein in an article in The Flight from Science and Reason,  and by Bricmont in a separate publication.[79]   As a mathematician I can only be cheered by the news that DŸrr, Goldstein, et al. may have constructed a consistent deterministic account of quantum mechanics, and the fact that it comes at the cost of adding variables that can never be measured is the least of my concerns.  As a mathematician, furthermore, the question is strictly none of my business, but it does seem to me that (1) sociologists of science are going to be hard-pressed to figure out who is the mainstream and who is the margin in this debate and (2) that the primary motivation for hidden variables theories seems to be the desire to preserve determinism at all costs is probably the strongest argument IÕve yet seen in favor of the social constructivist view of science.

 

 

ETHICS

 

            The publication of IS in France was celebrated by a discussion in a small bookstore near Jussieu, in which one author after another expressed regret at the distortions and bitterness that make real dialogue impossible in the shadow of the science wars.  Fran�ois G�ze, the director of La DŽcouverte, made clear his sincere hope that publishing IS would contribute to raising the intellectual and ethical level of the debate.  More than one of the IS authors expresses a similar concern for ethics; SalanskisÕ call for an Òepistemology of readingÓ is equally a plea for an ethics of reading.   Toward the end of IS, Isabelle Stengers makes the point, which someone surely ought to have made before, that the negative reaction of many scientists to science studies is not necessarily a sign that the sociologists are on the right track; that the feeling of scientists that their work is being treated with contempt should be taken seriously.[80] 

StengersÕ article proposes to imagine a possible ÒpeaceÓ in place of the science wars, and she writes of ethics explicitly.  There are reasons to be skeptical:  her article is often rather nasty in its description of the reaction of scientists, who Òhave never read [Lacan, Kristeva, Deleuze, or Bergson] and certainly never plan to read them.Ó[81]  And in a September 1998 meeting organized by the association ÒFemmes et mathŽmatiques,Ó Stengers announced baldly that, Òof course,Ó Sokal is being ÒpilotedÓ by Weinberg.  This is not only offensive; it also shows a profound ignorance of and contempt for SokalÕs political motivations, with which the North American left broadly identified, for reasons having nothing to do with Weinberg or the superconducting supercollider.  Disregard for the U.S. political context is all too frequent in the French reaction to Sokal, among supporters as well as critics.  At the bookstore meeting near Jussieu, LŽvy-Leblond saw the Gross-Levitt book (see note **) as an expression of the extreme right (!), and even Fran�ois G�ze, whose good faith seems beyond question, read the Sokal affair as part of the campaign against political correctness.  More subtly, Patrick PetitjeanÕs generally excellent article in IS  on the historical tendency of the French left to identify science uncritically with social progress (and socialism) slips into the error of suggesting that Sokal and Bricmont want to restore this identification[82]; if FN  makes anything clear, it is that this is not the case. 

There is no intellectual excuse for these mistakes.  IS  itself contains an accurate account by Michel Pierssens of some elements of the political background of cultural studies and the academic scene in North America.[83]  But this is a war.   Thus Michel Callon, echoing LatourÕs comments about cultural protectionism, writes Òthere is an increasingly strong and direct link between forms of competition in the markets and strategies of cooperation and rivalry in the academic worldÓ[84]; Jon Henley wrote in the Guardian that Òmodern French philosophy is a load of old tosh[85]Ó; and, inevitably, someone (in this case Gautero) talked about MacDonaldÕs and Coca-Cola.[86]

                  

The martial mood is based on a perception of the urgency of mounting a defense of oneÕs epistemic perspective in the face of an enemy with whom negotiation is impossible.  Ethical considerations go by the board; as in the Balkans, yesterday's aggrieved becomes today's aggressor.[87]  Paul Gross, speaking of the 1995 New York meeting on which The Flight from Science and Reason   was based, claimed that "The strong constructivists have been in charge, in control of departments of sociology, anthropology, and, to a very significant extent, history of science nationwide [in the U.S.] and in Western Europe for 15 yearsÉWe are the oppressed. We have to find a voice, and so this meeting is our voice."[88]   It is unsettling to compare this with quotations from the other side.  Jon Agar, expressing misgivings about the prospects of scientists adopting the STS perspective, wrote ÒThe resources open to scientists to construct their authority are greater than those open to science studies - and they will do so to reproduce science.Ó[89]  And in IS, Jurdant reports some scientistsÕ second thoughts about SokalÕs hoax: ÒIl nÕest pas toujours facile dÕ�tre du c™tŽ des plus forts quand il sÕagit de rire avec eux aux dŽpens des plus faiblesÓ[90].

 

            The sense of urgency can only be proportional[91] to the danger, which has been described in outlandish terms on both sides.  Once you accuse your opponent of being a charlatan, or an idiot, or a power-hungry authoritarian, or a dupe, the usual rules of argument no longer apply.  The prize has to go to Mario Bunge, whose call to Òexpel the charlatans from the universityÓ warns that the alternative is to Òput modern culture at riskÉundermine modern civilizationÉprepare for a new Dark Age.Ó[92]  On the other side, my (least) favorite is Bruce RobbinsÕ claim that Òwhat is really expressed by the angry tirades against cultural politics that have accompanied the Sokal affair is a longing for the days when women were back in the kitchen and it was respectable to joke about faggots and other natural objects of humor.Ó[93] 

 

Most science warriors express themselves more moderately, but the distrust of their colleagues at the other end of campus is palpable.  Speculations as to why this may be the case have ranged from the pop psychology of Gross and LevittÕs Higher Superstition [94] to Dorothy NelkinÕs unsubstantiated claim that the science wars are Òreally aboutÓ declining government funding.[95]    It seems most scientists — the ones too busy to look into the matter — have swallowed the notion that French philosophy (or cultural studies, or science studies) really is the work of cretins and poseurs on the one hand and their intimidated acolytes on the other.  The symmetric bad faith accusation — for instance, that the scientists in the science wars are acting to defend their undeserved authority or their military budgets or their secular religion — apparently circulates equally unchallenged.   

 

In the introduction, Sokal and Bricmont claim that they Òdo not findÉof very great interestÓ the question whether the abuses they believe they have identified Òarise from conscious fraud, self-deception, or perhaps a combination of the two.Ó [p. 6].  Apart from a few remarks of this kind, and rather to their credit, the two physicists do not speculate much about ulterior motives.[96]   The same cannot be said for IS.  Dahan-Dalmedico and Pestre ask whether Sokal and Bricmont are not motivated by Òa more irrepressible desire to control the proliferation [foisonnement] of the social and of thought at work, a desire, exhorbitant in its pretention that would like to see ÒscienceÓ (?) control words and their proliferationÉÓ  FujimuraÕs article is entitled ÒThe authority of knowledge in questionÓ and summarizes SokalÕs hoax as Òa tool of social control, a form of discipline.Ó[97]  Treating motivations at this level wouldnÕt work as a plot device in a grade B thriller. But because a warÕs on, a number of IS authors, like Robbins and Nelkin, favor explanations that place Sokal and Bricmont and their supporters in a bad light.  Thus, FNÕs explicit distancing itself from the Òboundary transgressingÓ of sociobiology and neurobiology is passed over in silence.[98]  Indeed, if it werenÕt for the war, the scientistsÕ ulterior motives in the science wars might more charitably be sought in WeinbergÕs commitment, shared with Stephen Jay Gould, to keeping creationism out of the schools; in GouldÕs work on the IQ controversy, in Richard LewontinÕs exposure of the role of the Ògenetico-industrial complexÓ in the most recent developments in agriculture, and in Serge LangÕs successful campaign, largely based on Neal KoblitzÕ research, to keep Samuel P. Huntington out of the National Academy of Sciences.[99]

 

 

 

HOPEFUL SIGNS

 

Sokal and Bricmont express the sincere wish to create Òa real dialogue between the ÔTwo CulturesÕÓ (p. 183), to Òput aside the Ôscience warÕÓ (p. 185).  ISÕs dust jacket concludes in almost identical terms:  Òpour en finir enfin avec la Ôguerre des sciencesÕÓ.  And yet both books are pure science wars products.  The reason is not hard to find:  FNÕs goal is to discredit a certain list of authors, at least insofar as they use the vocabulary of science; ISÕs goal is to discredit FN.  Here and there both books give the occasional nod to the legitimate concerns of the other side, and AndrŽe Bergeron admits in IS  to having some sympathy, as a scientist, with FNÕs goals.  But, StengersÕ talk of peace notwithstanding, negotiation is not on either bookÕs agenda.  A House Built on Sand, another recent entry on the pro-reality side, edited by Noretta Koertge, and featuring articles by Sokal, Gross, Levitt, and Kitcher, among many others, is in some ways even more disappointing.  Though many (by no means all) of the contributions are substantial, as a whole the collection reads like a monologue, like ÒScience Wars Minus One.Ó  As in The Flight from Science and Reason, only one camp gets to present its position, and an open-minded reader canÕt help thinking this is a distortion of the debate, that the other side canÕt possibly be guilty of such gross errors.   Indeed, Kitcher objects to the bookÕs title and calls his contribution ÒA Plea for Science Studies,Ó making himself the advocate for the position that ÒThe work done in [certain branches of science studies is] an important part of scientific activity and often continuous with science itself.Ó  And Sokal adds, ÒI agree with nearly everything inÓ KitcherÕs article.[100]  But the practitioners of science studies were not invited, and one gets no real sense of what the debate is about. 

 

 

Fortunately, there are venues, far from the noise of the science wars, where real differences in perspective as well as problems stemming from the difficulty of translation,  particularly between disciplines, are being discussed civilly.  At the very least, the simultaneous presence of specialists holding different perspectives is a guarantee against the crudest distortions.  If you have learned about science studies from Gross and LevittÕsHigher Superstition , I urge you to look at the recent collection The Disunity of Science, edited by Peter Galison and David J. Stump.   The first thing you will notice is that the debate over relativism and realism is a central theme within science studies, which in no way resembles the abridged version criticized in FNÕs philosophical intermezzo.[101]    StumpÕs article is largely a call to Òend the tiresome battles over realism and relativism.Ó  The second thing you will notice is that science studies is by no means monolithic, that there really are differences of opinion.    Arthur Fine, a philosopher sympathetic to constructivist sociology of science, nevertheless asserts that Òconstructivists write a great deal of nonsenseÓ on the question of relativism, and attributes this in part to their Òromantic and apocalypticÉrhetorical styleÓ.  StumpÕs Afterword calls for Òa continuing debate on [realism, the rationality of science, and relativism], but a positive and consensus-building debate, not a hostile and divisive debate such as has occurred in the past.Ó[102]

 

ÒRomantic rhetoricÓ serves better than Òhigher superstitionÓ or Òfashionable nonsenseÓ to describe the sentiment expressed in the Andrew Ross quotation with which this article began, and unlike the other two is compatible with dialogue, of which The Disunity of Science  provides a prime example.  Stump notes that ÒPhilosophers, historians, and sociologists all have something to add to the new science-studies philosophy, and what has been a hostile debate is being replaced by signs of cooperation.Ó [p. 256] All three disciplines were well represented in the 1991 workship on whichThe Disunity of Science   was based but, with the hindsight provided by the science wars, the absence of scientists seems, or should seem, a gross oversight.  Neither scientists nor sociologists were invited to the discussion recently published in Le DŽbat   under the heading, ÒHow to write the History of Science?.Ó  But historian Dominique Pestre represented sociologists in explaining the new approaches in the history of science, while philosophers Catherine Chevalley, Pierre Jacob, and GŽrard Jorland raised objections similar to those expressed by scientists in the wake of the Sokal affair. 

 

Pestre,  a contributor to IS,   restates some of the themes developed in his article with Dahan-Dalmedico.  Away from the Science Wars, though, the arguments have much more room to develop. The exchange in Le dŽbat  makes it clear that, once one gets past the Òromantic rhetoricÓ and the rather arbitrary assignment of political labels on the basis of philosophical positions, the intellectual conflict underlying the science wars hinges on the fact that historians and philosophers (and sociologists and scientists) simply donÕt choose to Òcut upÓ [dŽcouper] the phenomena in the same way (Pestre, p. 100).  The philosophers want to know, as Chevalley asks, ÒPeut-on dire que la [nouvelle historiographie scientifique] dŽcrit correctement lÕactivitŽ scientifique en gŽnŽral?Ó  Jorland asserts that  ÒCÕest parce que les propositions scientifiques sÕaffirment universelles quÕelles intŽressent la philosophie.Ó   And for Jacob:  Òla question  soulevŽe par le dŽveloppement scientifique nÕest pas tant de comprendre les dŽsaccords entre les spŽcialistes que leurs convergences.Ó[103]  As it happens, this is the question I find most interesting, but itÕs certainly not the only interesting question, itÕs not a question to which anyone has ever proposed a credible answer[104] , and I would never dream of assigning it to the sociologists or historians as their sole legitimate task.[105]  In his response to the philosophers, Pestre defends the historiansÕ perspective in the following terms:  ÒLe choix de ne pas placer comme prŽalable la question ŽpistŽmologique (qui, du social ou de la nature, dŽtermine le savoir?) ou, plus exactement, de la juger indŽcidable, est une renonciation ˆ lÕabsolu et vaut acceptation que lÕhomme est ˆ jamais un �tre limitŽ.Ó[106]  

 

            There are even signs of dialogue between scientists and sociologists of the SSK perspective.  Physicist David Mermin, a contributor to IS, was invited by  Social Studies of Science  (SSS) to reviewScientific Knowledge  by Barnes, Bloor, and Henry (abbreviated BBH), the most recent general expression of the Edinburgh school.  Mermin took this invitation as an opportunity Òto set out, as a basis for subsequent discussion, several examples where I find [the BBH] picture of scientific knowledge or the process of creation to be deficient or misleading.Ó  Bloor and Barnes were given the chance to respond to MerminÕs criticisms, and this was followed by MerminÕs reply to their response.[107]  As in Le Debat,  the exchange is cordial and respectful; Mermin and Bloor go out of their way to adapt their arguments to each otherÕs languages.   The resulting dialogue is deeply frustrating, in that it reveals how difficult it is to elminate misunderstanding — somehow questions of methodology or disciplinary perspective keep being mistaken for questions of truth claims, in spite of the best efforts on both sides to avoid such slippage.  Bloor writes that Òwhen ideas are expressed in a slightly unfamiliar idiom the can becomeÉ completely unrecognizable.Ó  But the very existence of the dialogue, despite the science warsÕ distortions, is an immensely hopeful sign, and Bloor continues, ÒPerhaps this is the strongest testimony possible to the importance, in the present circumstances, of learning to switch back and forth between the different perspectives of the natural and social scientist.Ó[108]

 

            The BBH book begins by regretting that Òsome scientists and philosophers have assumed that since we neither praise nor defend science our objective must be to subvert it,Ó an implicit acknowledgment the need for more dialogue of the kind described in the last paragraph.  Nevertheless, there has been rhetorical backsliding by members of the SSK community.  In a second review of BBH published in the same issue of SSS, Jon Agar, criticizing what he perceives as the bookÕs defensiveness, claims Òtheir stance of disinterestedness makes the authors very shy of suggesting that their arguments could be used to criticize science.É The idea that theory is neutral is reminiscent of the American gun lobby slogan: Ôguns donÕt kill people, people do.ÕÓ  Why would anyone want to criticize ÒscienceÓ as such, if not out of a taste for romantic and apocalyptic rhetoric?   And Bloor himself, reviewing Barbara Herrnstein SmithÕs Belief and Resistance, wonders ÒWhat if scientists need to believe a mythical and false ideology, because they would lose motivation without it?Ó  He then goes on to praise Herrnstein Smith as an example Òof persons who can reason cogently and clearly without the prop of myth.Ó[109]  Here we see how adherence to a specific epistemological position is elevated to the level of a moral imperative.  Much science wars rhetoric on both sides is really about conflicting views of the good, giving the lie to Sokal and BricmontÕs a priori  isolation of ÒcognitiveÓ from moral and aesthetic factors.[110]  Though I wouldnÕt go so far as to write a book about it, I happen to find rationalism much more ethically compelling than skepticism.  This is why I do not secretly loathe myself for doing mathematics.  When Borel expresses a core belief of mathematicians, writing ÒI do believe in the self-correcting power of mathematicsÓ in the BAMS exchange, it would not only be crude and condescending (from what privileged vantage point?) to treat this as an instance of ÒmythÓ or Òfalse ideology;Ó a sociology that feels the need to do so is suspect on intellectual as well as moral grounds.

 

Few of us would choose to treat our belief that Wiles proved FermatÕs last theorem as Òa mythical and false ideology,Ó but is it possible that our attempts to justify this belief always involve an element of self-delusion?  And how are we to convince a skeptical outsider that this is not the case?  The only reasonable answers that come to mind are empirical in nature, and specifically historical and sociological, rather than philosophical.[111]  We would have to pay attention to the question of how knowledge is transmitted among mathematicians.   FermatÕs last theorem provides a particularly good test case.  WilesÕ proof generated an unprecedented[112] number of reports, survey articles, colloquium talks, working seminars, graduate courses, and mini-conferences, as well as books, newspaper and magazine articles, television reports, and other forms of communication with non-mathematicians.  Not to mention the spate of announcements, designed to impress public policy-makers and the public at large, citing WilesÕ work as proof that mathematics Òhas never been healthier.**Ó Has anyone been keeping track of all these incitements to belief formation, checking them for contamination by myth and false ideology?   

 

Studying questions like these provides a second answer to the thought experiment proposed above, complementary to the answer we would naturally provide based on our experience as mathematicians, and potentially just as interesting.  Leaving aside romantic rhetoric, these two answers are not in competition, much less on opposite sides of a battlefield.  Arriving at the second answer would be the work of sociologists.  For this, full cooperation with mathematicians would be necessary.  The examples just cited provide hope that such cooperation may be possible.

 

With this in mind, and in the spirit of Paul Erdšs rather than Professor Fredkin, I offer $100[113] to the first person who programs a computer to compose recognizable contributions to the Science Wars.  The genre is now sufficiently extensive that this should be scarcely more difficult than the Postmodernism Generator so often cited by science warriors,[114] and should provide at least as much fun.  Human combatants will be less tempted to take up arms when the battlefield is fully automated.  Our energies will then be free for more interesting matters.

 



[1] In 1996, Sokal published an article entitled ÒTransgressing the Boundaries:  Toward a Transformative Hermeneutics of Quantum Gravity,Ó in a special issue of the journal Social Text  entitled ÒScience Wars.Ó  A few weeks later, Sokal reveealed that the article was a parody of an intellectual style he and others call Òpostmodernism.Ó 

[2] Unlike Sokal, most of my work was based in the U.S.

[3] Given the media distortions surrounding the so-called Science Wars, it is difficult to gauge the prevalence of this position among practitioners of Science Studies, or even whether Andrew Ross takes it seriously. Compare this to an earlier statement by Cornel West:  ÒIf science is, as Rorty notes, a 'value-laden enterprise,'  is there an ideological character intrinsic to the very methods of the natural sciences owing to an agreed-upon conception of and disposition toward nature which may promote the domination not only of our environment but also those people subsumed under the rubric 'nature' such as women, non-Europeans, and even 'earthy' workers?"   (J. Rajchman and C. West, "Post-Analytic Philosophy," 1985, p. 268).  Nicaraguan educators in the mid 1980s answered this question with a sophisticated pragmatic approach to basic science as a means to escape

dependence on expensive imported technology. Some of their debates were recorded in Nexo, a theoretical journal published by the Universidad Nacional de Ingenier’a, with the support of Italian NGOs.  As far as I know, Nexo has never been cited in the science wars debate, not even by those claiming a Òpost-colonialÓ perspective.

[4] New York Times, 5/21/96.

[5] K. Hirschkop, ÒCultural Studies and Its Discontents, in Social Text , 50, 131-133 (1997).

[6] Lacan, Kristeva, Irigaray, Latour, Baudrillard, Deleuze, Guattari, Virilio, and secondarily Lyotard and Debray.

[7]  (Nagel, New Republic)

[8] Authors most notably of Higher Superstition, the locus classicus of science wars confusion on the science side, published in 1994.

[9] ." (Dawkins, Nature, 7/9/98)

[10] This dubious categorical judgment has been placed near the beginning of the article for the convenience of journalists too lazy to read through to the end.  Not that I really expect any journalists to read this article, on a topic whose time may have passed.

[11] Ò[I]f these writers have become international stars primarily for sociological rather than intellectual reasons, and in part because they are masters of language and can impress their audience with a clever abuse of sophisticated terminology--non-scientific as well as scientific—then the revelations contained in this essay may indeed havesignificant repercussions.Ó  FN, p. 8.   Elsewhere in FN  and in published interviews, Sokal and Bricmont insist that their objective is the more modest one of pointing out abuses of science, and claim not to judge the substantial works of the authors in question.  As Yves Jeanneret points out in LÕaffaire Sokal ou la querelle des impostures, (PUF, 1998), discussed below, this only adds to the confusion (pp. 133-136).   JeanneretÕs book also contains the most sustained attempt to theorize the unity of the Sokal affair, including FN.  It should be obvious to everyone that the book would not have attracted such attention on the basis of the more modest goal alone.

[12] Sokal and Bricmont actually Òwarn the reader against the temptation to lump [the authors] together in a single category.Ó  Of course, the bookÕs success is largely conditioned on the readerÕs ignoring the warning, and indeed calling into question the whole of ÒFrench thought.Ó   

[13] A prolific contributor to the genre, unfortunately.

[14] Incredibly, the only explanation offered for combining these two targets in a single book is that ÒSokal stumbled on most of these texts in the course of writing his parodyÓ (p. 15).

[15]Latour:  Le Monde, 18 janvier 1997.  Kristeva:  RŽponse ˆ Alan Sokal et Jean Bricmont:  Une dŽsinformation, Le Nouvel Observateur, 23 septembre 1997 (the issue with the screaming cover); Ocrriere della Sera [date].  LŽvy-Leblond:  Le Cow-boy et lÕapothicaire:  LÕalliance du revolver ŽpistŽmologique et du discours scientiste, La Recherche, dŽcembre 1997.  Fleury and Limet:  LibŽration,

[16] Of course the ÒaffaireÓ doesnÕt break down neatly along national lines:  the French reaction to SokalÕs initial hoax was evenly divided, and a few intellectuels, most notably J. Bouveresse and J.-F. Revel, were pleased at the opportunity Sokal and Bricmont provided to denounce what they saw as the ÒimposturesÓ of certain of their compatriots.  And the London Review of Books published a quite hostile review of the British edition, provoking an unusually angry reaction on the part of readers.

[17] To be fair, Sokal and Bricmont do distance themselves from their Òmore enthusiastic supportersÓ on the very first page of their preface.  But DawkinsÕ review appears on the dust jacket and the publisher sent NagelÕs article along with my review copy.

[18] SokalÕs hoax had already taken on national political significance the previous spring, with an article by RŽgis Debray using it as a pretext for attacking Pierre BourdieuÕs book Sur la tŽlŽvision  (Le Monde,   March 18, 1997).  Kristina ZarlengoÕs review of FN in Salon (November 2, 1998) indicates that the publishers had run out of galleys four months ahead of publication.

[19] The major daily newspapers and a few magazines reviewed these books, but the Sokal-Bricmont book generated a press packet is easily 20 times thicker than the competition.  WhatÕs more, the reviews of the responses were mostly taken up with a review of the Sokal affair and the Sokal-Bricmont book; hardly any space was devoted to the new books.

                  A third response, Marc RichelleÕs DŽfense des Sciences Humaines, was largely favorable to Sokal and Bricmont. 

[20] IS, p. 13.

[21] As Jeanneret puts it, Òla provocation se vend bien, en Ždition et en recherche.Ó (p. 32).  JeanneretÕs suggestion for a constructive alternative is worth quoting in full: "Il faut demander ˆ cette querelle ce qu'elle peut nous donner.  Le proc�s en culpabilitŽ, de part et d'autre, ne donnera mati�re qu'ˆ esquives et paradoxes; mal engagŽ, il ne saurait dŽboucher sur aucune certitude. En revanche, le d\'ebat qu'il provoque concerne des enjeux tr�s importants, d�s qu'on accepte de considŽrer les accusations mutuelles entre les protagonistes successifs, non comme des cas ˆ trancher, mais comme des points de vue ˆ comprendre.  Car, discutant du sens de la pseudo-expŽrience, les uns et les autres Žcrivent, ou dŽfont, une conception de ce que sont des influences intellectuelles.  Les centaines de pages Žcrites au fil de cette querelle pourraient ainsi ne pas avoir \'et\'e produites en pure perte."  Jeanneret, p. 65.  Other hopeful avenues of dialogue will be discussed at the end of the article.

                  Jurdant also refers to the media Òphenomenon that makes all intelligent reflection improbable or, at any rate, difficultÓ (p. 11), which he identifies as one of the main obstacles to putting IS together.  The collection concludes on an interesting article by Allain Glykos, comparing the Sokal affair (as media event) with a rather different media scandal called ÒThe crisis of contemporary art,Ó which goes back to the early Ô90s.  In the process, Glykos asks whether the media Òare able to found normatively the validity and legitimacy of debates in our modern democracies?Ó  The reviewer in Sciences et Avenir  (October 1998) didnÕt much care for this question, and attacked Glykos with a paragraph of self-righteous and irrelevant abuse, in the process proving GlykosÕ point.

 

[22] By contrast, Baudrillard, Virilio, Irigaray, and Kristeva are all but ignored in IS.  Michel Pierssens, in his contribution to IS on the North American context of Sokal's hoax, sees Baudrillard as more influential in the U.S. than in France, "his articles in  LibŽration having a perfect predictability that removes all their surprise and impact." (p. 107)  When I spoke with Sokal in 1997 I tried to convince him that Baudrillard's scientific metaphors

are seen as purely stylistic devices; this is presumably why I am listed among the 60-odd names on the acknowledgment page.

[23]  I find Nathalie Charraud's explanation of Lacanian topology in "MathŽmatiques avec Lacan" less convincing; more on this below.

[24] Referring to Leibniz, G. Ch‰telet wrote ÒcÕest bien le concept mŽtaphysique de ÔmonadeÕ qui permet de comprendre le calcul diffŽrentiel.Ó   Les Enjeux du Mobile  , p. 24.

[25] DiffŽrence et RŽpŽtition, p. 221, my translation. 

[26]  Footnote 184, p. 148. Several colleagues have pointed out that the same comments applies to Abraham Robinson's non-standard analysis.

[27] Deleuze, DiffŽrence et rŽpŽtition, p. 67; FN, note 211, p. 162; Salanskis, op. Cit., p. 176.    

[28] Nor a ÒmixtureÓ of ÒcharlatanÓ and ÒidiotÓ, according to Nagel; see note 7.  I donÕt pretend to know the correct reading of this sentence; I freely admit to being out of my depth here, being unfamiliar with the history of the concept of continuity in the western tradition even in translation, much less in the Greek and Latin originals.   As for puissance, this is at worst Érelatively technical; dunamis is the 12th entry in the glossary of AristotleÕs Metaphysics.  Of course, the word has other meanings, and even granting SalanskisÕ reading one might find DeleuzeÕs casual tossing around of such terms tiresome, or snobbish; but these objections would be on literary, not intellectual grounds.    

[29] The philosophical reductionism for which Weinberg gives Òtwo cheersÓ , in Dreams of a Final Theory, begs precisely this question, insofar as reducing molecular biology to physics, say, depends on heuristic extrapolations from the existence and uniqueness theorems of ordinary differential equations.  [**Quote Ch‰telet??]

[30] Deleuze, op. Cit., p. 4.  Needless to say, these remarks are not  quoted in FN. 

[31] Several contributors to this volume refer to DeleuzeÕs use of the term Òsingularity,Ó  which they seem to read as a metaphor.  See also note **, below.

[32] There are many circles in Euclid, but no pi, so I canÕt think of any other reason for Sokal to have written ÒEuclidÕs pi,Ó unless this anachronism was an intentional part of the hoax.  SokalÕs full quotation was Òthe ¹ of Euclid and the G of Newton, formerly thought to be constant and universal, are now perceived in their ineluctable historicity. Ò  But there is no need to invoke non-Euclidean geometry to perceive the historicity of the circle, or of pi:  see Catherine GoldsteinÕs ÒLÕun est lÕautre:  pour une histoire du cercle,Ó  in M. Serres, Elements d'histoire des sciences, Bordas, 1989, pp. 129-149. 

[33] This is not mere sophistry:  the construction of models over number fields actually uses arguments of this kind.  A careless construction of the equations defining modular curves may make it appear that pi is included in their field of scalars.

[34] Unless you claim, like the present French Minister of Education, that real numbers exist in nature, while imaginary numbers were invented by mathematicians.  Thus ¹ would be a physical constant, like the mass of the electron, that can be determined experimentally with increasing accuracy, say by measuring physical circles with ever more sensitive rulers.  This sort of position has not been welcomed by most French mathematicians.

[35] Cf. M. Kline, Mathematics The Loss of Certainty, p. 324.

[36] Compare Morris HirschÕs remarks in BAMS April 94.

[37] IS, p. 38, footnote 26.   WeinbergÕs remarks are contained in his article ÒSokalÕs Hoax,Ó  in the New York Review of Books,  August 8, 1996.

[38]Metaphors from virtual reality may help here.

NOTE ADDED JANUARY 2008:    Barry Mazur's forthcoming "Mathematical Platonism and its Opposites" was written this year and should henceforth be considered the classic account of this question.

[39] Mati�re ˆ penser .  Odile Jacob, 1989. For example, Connes writes, ÒJe pense que le mathŽmaticien dŽveloppe un ÒsensÓ, irrŽductible ˆ la vue, ˆ lÕou•e et au toucher, qui lui permet de percevoir une rŽalitŽ tout aussi contraignante mais beaucoup plus stable que la rŽalitŽ physique, car non localisŽe dans lÕespace-tempsÓ (p. 49).  In fact, the debate is even more complex, because Changeux often comes across as a social constructivist, though one who see society as materialized in the human brain; thus he sees mathematical objects as ÒÕreprŽsentations culturellesÕ susceptibles de se propager, se fructifier et de prolifŽrer et dÕ�tre transmises de cerveau ˆ cerveau.

[40] See Barry MazurÕs astonishing ÒImagining Numbers (particularly …-15)Ó for (among other things) an attempt to get beyond sterile ontological debates.

[41] A recent example:  ÒÉas the mathematician Gšdel showed, inconsistency is an inevitable trait of any self-sustaining system built up out of consistent parts.Ó   K. Kelly, Out of Control, (1994), p. 394.  Kevin Kelly, executive editor of Wired, presumably has understood GšdelÕs proof, as did molecular biologist Fran�ois Jacob, when he used GšdelÕs theorem to argue that the human mind will always resist science (La logique du vivant , 1970, quoted in Mati�re ˆ Penser, p. 205).   ÒGšdelizing,Ó as a repentant Debray puts it, may legitimately be criticized as a clichŽ, but this is primarily a literary judgment.

[42] This point is made by Amy Dahan-Dalmedico and Dominique Pestre in their contribution to IS, p. 87.

[43] See SalanskisÕ comments on this point, IS, p. 184 ff.

[44] I recently made explicit use of the axiom of choice for the first time in my professional life, in an article with Richard Taylor in which we identify C with .  In ÒLa Conjecture de Weil. II,Ó Deligne writes ÒJe ne prŽtends pas croire ˆ lÕexistence dÕisomorphismes entre  et C, et ceux-ci ne sont quÕune commoditŽ dÕexpression.Ó  (Publ. Math. IHES, 52, (1981)  p. 332).  I suspect DeligneÕs position is widely shared, but not being a sociologist I wouldnÕt know how to go about determining whether this is the case.

[45] Kline, op. Cit., pp. 5, 278, 6.

[46] There is no room here to discussFN Ôs third intermezzo, on ÒChaos Theory and ÔPostmodern ScienceÕÓ  — again, the reader can probably guess its contents from the title — except to say that, if the philosophical significance of chaos theory has been exaggerated, this is largely the fault of (parts of) the scientific community itself.  This point is made clearly by Dahan-Dalmedico and Pestre in IS,  pp. 95-96.  See also Note **, below.

[47] R. Krauss, ÒSculpture in the Expanded Field,Ó in H. Foster, ed. The Anti-Aesthetic (1983), p. 37; J. Clifford, ÒCollecting Art and Culture,Ó in R. Ferguson et al., eds., Out There (1990), p. 146 ff.  From KraussÕs article I learned that the Klein group is also called the Piaget group. 

[48] In other words, if there is a problem with LacanÕs work, itÕs pointless to look for it in his topology.

[49] FN, p. 195.  See also P. Boghossian, ÒWhat the Sokal Hoax Ought to Teach Us,Ó in N. Koertge, ed., A House Built on Sand, (1998), p. 27 ff.  Sokal mentioned this example in a debate with Andrew Ross, who (according to Boghossian) didnÕt help matters by using it as an excuse for demagogically  accusing Sokal of putting Native Americans Òon trial.Ó

[50] Clifford, loc. cit., p. 169, footnote 69.

[51] Or their audience of having redefined truth:  FN, p. 195, note 258.

[52] As Barry Mazur reminded me, ÒinterestÓ in this context is generally used as shorthand for an intellectual criterion, such as Òenhancement of understandingÓ (see ThurstonÕs comments, quoted below).  Such a criterion is by nature not well-defined, yet we have the sense that we know what it means.    

[53] Actually a Òmajor mathematical discoveryÓ  [FredkinÕs website]

[54] Quoted in Dominique Lambert, ÒLÕincroyable efficacitŽ des mathŽmatiques,Ó La Recherche, janvier 1999, p. 50.  This article also includes a detailed comparison among various contending theories of the nature of mathematics.  Truth is also not what interests Deleuze and Guattari:  Òce nÕest pas la vŽritŽ qui inspire la philosophie, mais des catŽgories comme celles dÕIntŽressant, de Remarquable ou dÕImportant qui dŽcident de la rŽussite ou de lÕŽchec.Ó  QuÕest-ce que la philosophie, (1991) p. 80.

[55] A course on foundations of mathematics is not a core requirement in any university with which I am familiar.  One would think this fact would be of interest to sociologists of science, but I have not seen it addressed in the literature.  As a graduate student at Harvard, I only saw foundations actively discussed in the graffiti in the menÕs room on the second floor of the science library.

[56] The debate provoked by the Jaffe-Quinn article is taken up in a recent article by Leo Corry, ÒThe Origins of Eternal Truth in Modern Mathematics,Ó Science in Context 10 (1997), 297-342.  Corry is so intent on developing his theme (that Òthe idea of eternal mathematical truthÉhas not itself been eternalÓ) that he completely misses the near absence of the word ÒtruthÓ from the debate, claiming that Òthe eternal character of mathematical truthÓ was Òimplicit[] at the very leastÓ in the Jaffe-Quinn proposal.Ó

[57] Glimm goes on to say that mathematical truth  is to be compared with the stronger standard of truth in science, Òthe agreement between theory and data.Ó  The whole discussion can be found in Bulletin of the AMS, July 1993 and  April 1994.

[58] What they really think hardly matters.  The Òstrong programÓ of Bloor and Barry Barnes is criticized at length in the philosophical ÒintermezzoÓ of FN; but Sokal Òagrees with nearly everythingÓ in KitcherÕs attempt to Òoccupy middle groundÓ in Koertge, op. Cit.  We return to Bloor and Kitcher at the end of this essay.

[59] D. Bloor, Knowledge and Social Imagery  (U. of Chicago press, 1991), chapters 5-8; P. Kitcher, The Nature of Mathematical Knowledge, (Oxford University Press, 1984). 

[60] ThurstonÕs extended response to the Jaffe-Quinn article does refer to truth but he seems more interested in knowledge and especially on understanding; see below.

[61] Chapter 3 of KitcherÕs op. Cit. is devoted to a refutation of Kantian or Platonist intuition as a means to mathematical knowledge, and what we mean when we use the word informally is presumably even less defensible.  The quotation is from FN,  pp. 143-44, note 183.

[62] Thurston, op. Cit., p. **.  ThurstonÕs comment referred to the computer-assisted proof of the Four Color Theorem, and echo DeligneÕs remarks on the same topic, quoted by Ruelle in Chance and Chaos, pp. 3-4.

[63] Coleman, ÒManinÕs proof of the Mordell conjecture over function fields,Ó LÕEnseignement Math., 36 (1990), p. 393.

[64] The text book is G. Cornell, J. H. Silverman, G. Stevens, eds.:  Modular Forms and FermatÕs Last Theorem,  Springer-Verlag (1997).  If I believe, or understand, or have some meaningful relation to the proof, itÕs mainly because I have been collaborating with Richard Taylor to generalize parts of the argument to automorphic forms of higher dimension. 

[65] Horgan, Scientific American.

[66] FN, p. 91.

[67] Fran�ois Vosse, Histoire du Structuralisme, Eds. La DŽcouverte (1992), p. 273.

[68] I called Caroline van der Voort, the Vogue  editor who produced the special issue on science, and asked for an explanation.  The motivations were apparently quite simple and unpretentious:  she needed an original theme, she found the graphic qualities of numbers appealing, etc. 

[69] Some French management theorists do seem to like the work of Latour and his collaborator M. Callon:  see H. Amblard, P. Bernoux, G. Herreros, and Y-F. Livian, Les nouvelles approches sociologiques des organisations, Eds Seuil (1996), pp. 127-185  And the feeling appears to be mutual:  see CallonÕs comments in  IS, pp. 264-266, e.g. Òil existe un couplage de plus en plus fort et direct entre les modalitŽs de la compŽtition sur les marchŽs et les stratŽgies de concurrence et de coopŽration dans le monde acadŽmique.Ó

[70] In ÒChanging AxesÓ, Social Studies of Science, 28/4 (August 1998),  p. 635.

[71] IS, p. 92.

[72] ÒLe rŽflexion ŽpistŽmologique dans le domaine des sciences humaines est tributaire des mutations en cours dans les sciences ÒduresÓ, et sur ce plan on constate la m�me inflexion formaliste.Ó  And Ò[L]ÕidŽologie bourbakiste a certainement fortement contribuŽ ˆ forger la mentalitŽ et lÕactivitŽ structuralisteÉÓ Vosse, op. Cit., p. 111, p. 272.

[73] IS, p. 93.

[74] A reasonable start is made by David Aubin in "The Withering immortality of Nicolas Bourbaki. A cultural connector at the confluence of mathematics, structuralism and the Oulipo in France", Science in Context 10

(1997), 297-342.  Aubin presents a good review of the interaction between Bourbaki and Levi-Strauss, Piaget, and Oulipo, pointedly refusing to claim that the latter were a consequence of the former.  For my taste, Aubin follows too closely Jean-Fran�ois LyotardÕs evaluation  (in La Condition Postmoderne) of fractals, chaos, and ThomÕs catastrophe theory as Òsymptomatic of a Ôpostmodern scienceÕÓ .   It is symptomatic that Aubin thanks no mathematicians in his acknowledgments, though his article is based on a Princeton Ph.D. thesis.  Nevertheless, it is interesting to contrast AubinÕs reading of Lyotard with that of Sokal and Bricmont in their ÒintermezzoÓ on Chaos, and even more interesting to compare AubinÕs account of BourbakiÕs decline (as Òcultural connectorÓ) with CartierÕs reminiscences in the Intelligencer [date??].

[75] Two of my French colleagues, who would probably prefer not to be identified here,  were involved in this project and seem none the worse for the experience.  The project, on the history of the rigorous development of calculus, was published  as Philosophie et calcul de lÕinfini  (Maspero, 1978).  Pierre Raymond, director of the project, wrote, in response to unspecified texts by Deleuze, that "les sciences sont le moyen fondamental et particulier  du combat revolutionnaire", a comment that would Sokal and Bricmont would probably view as an abuse of science.

[76] Cite Ch‰telet, Petitot.  DeleuzeÕs discussion of singularities in DiffŽrence et RŽpŽtition , as well as in the passages from La Logique du Sens  ridiculed in FN, pp. 165-166, is based almost word for word on Albert LautmanÕs Essai sur lÕUnitŽ des MathŽmatiques, as Salanskis points out (and Deleuze gives the reference on p. 230 of DiffŽrence et RŽpŽtition ).  LautmanÕs essays, written in the Ô30s and Ô40s, were reissued in 1977 by the publisher 10/18 with a forward by DieudonnŽ.  LautmanÕs discussion of the role of singularities of systems of differential equations in organizing structure, the point of departure for DeleuzeÕs Òlucubrations,Ó as Sokal and Bricmont call them, should look familiar to readers of RenŽ ThomÕs theory of catastrophes, or for that matter to anyone who has studied Morse theory.  

[77] More precisely, they devote one sentence to the history, on the bottom of p. 191 of FN ,  referring to LyotardÕs postmodernism as a post Õ68 Òreaction against the scientism of certain rather dogmatic strains of structuralism and MarxismÓ (FN, p. 191) but this effectively erases the 1970s.  Incidentally, Levi-Strauss was already criticized for his mathematical ÒimposturesÓ in the late 60s.  See the discussion in Vosse, p. **  In this sense, FN  is nothing new. 

[78] FN, p 261.   Dahan-Dalmedico and Pestre devote several interesting pages to the history of BohrÕs complementarity and the Òfelt necessity of speaking  of atomic phenomena outside of formalism, to speak in the words of ordinary language.Ó  In response to WeinbergÕs rejection of BohrÕs attempt to make complementarity into a general principle, they conclude: ÒÉsaying that things could have happened otherwise never runs the risk of contradictionÓ but for the historian Òit is without interest to take the position of those who know better than their predecessors what they should have done.Ó 

[79] Higher Superstition, p. 261, note 9; Goldstein, ÒQuantum Philosophy:  the Flight from Reason in ScienceÓ in Gross, Levitt, Lewis, op. Cit., pp. 119-125;  Levitt, ÒMonsieur Jourdain and Uncle Vanya,Ó  in Koertge, op. Cit, p. 280.

[80] Stengers, in IS, p. 277.  Explicitly, Stengers wrote ÒJe proposerais aux constructivistes sociaux, sociologuqes, et penseurs postmodernes de ne pas ressentir un sentiment de triomphe facile face aux rŽactions, certes quelques peu stupides, que leur travail a suscitŽes de la part de ceux quÕils dŽcrivaient,Ó p. 288.

[81] IS P. 271.  Though this is completely beside the point, I canÕt resist mentioning that Stengers, taking her inspiration from Stanley Fish, devotes several pages to baseball, in which she seems to have found room for a referee with a whistle (p. 282).  And this in the middle of a long discussion of an article by Stephen Jay Gould!

[82] IS, p. 133.

[83] By contrast, the brief review of this background by Dahan-Dalmedico and Pestre in IS  is mainly useful as an illustration of how misinformed  many French authors are regarding North American cultural politics (pp. 102-104).  Among their many confusions, the most unforgivable is blaming ÒSokalÕs friendsÓ  for the term Òscience wars,Ó which seems to have been coined by Andrew Ross.  PierssensÕ piece, unlike most of IS, is basically sympathetic to Sokal and Bricmont, or at least hostile to much of cultural studies; he even calls Andrew Ross a Òtypical product of the star system.Ó   Jeanneret is also well-informed about the political content of the culture wars.  On the other hand, I have yet to see a French reference to earlier critiques of science coming from within the English-speaking science communities themselves, as in the group Science for the People and its British counterparts.  Three of the contributors to the Science Wars  issue of Social Text  come from this tradition, and at least two of them are respected scientists.  I have seen no mention of this fact anywhere.  This ÒNew LeftÓ critique of science from within was addressed in my remarks, prepared in collaboration with Jim Ritter, at the afternoon meeting mentioned in note *.

[84] IS, p. 264.

[85] The Guardian Weekly, October 1997.

[86] IS, p. 67.  Michel Callon also gets in a dig at Californians on p. 261.

[87] JeanneretÕs analysis of the language used by both sides is one of the best features of his book.  Recurrent motifs identified by Jeanneret include war, religion, (judicial) trials, fashion, and disease. (p. 222 ff.). 

[88] Quoted by Franklin Hoke in The Scientist, Vol:9, #14, pg.1 , July 10, 1995.  Elsewhere, Gross writes: ÒAmong the best-known science critics are some well-known femininst philosophers, many of the new multiculturists, postmodernists, eco-radicals, and purveyors of identity politics. I stress again that this description applies to a subset of sociologists, historians, anthropologists, and philosophers of science, probably to a minority among them. Nevertheless, their views have risen to dominance.  And within the last five years this has led to a few books and one conference in explicit opposition-a drop in the bucket by the frenetic standard of science studies, which is an international movement well-supported by universities, foundations, and government agencies such as the National Science Foundation.Ó (emphasis added).

 

[89] Posted June 2, 1997 on sts@CCTR.UMKC.EDU, h-sci-med-tech@h-net.msu.edu.   Agar continued: Ò...therefore, underlying their account is the familiar grand narrative of enlightenment emancipation from superstition. There is an unacknowledged contradiction between this narrative and the direction of argument of science studies. And who has the resources and authority to make interpretations of science studies stick?Ó (emphasis added).

[90] IS, p. 13.

[91] This formulation is a typical ordinary language metaphorical abuse of a precise mathematical concept, which gives the lie to Sokal and BricmontÕs much-quoted theory that Òa metaphor is usually employed to clarify an unfamiliar concept by relating it to a more familiar one, not the reverseÓ  (FN , p. 11), a claim that would mystify analysts of Greek tragedy, for example.  At least ten such abusive metaphors have been planted in the present text. 

[92] ÒCharlatanism in AcademiaÓ, in P. R. Gross, N. Levitt, and M.W. Lewis, eds., The Flight from Science and Reason, p. 110.  Charlatans, for Bunge, include radical feminists, ÒscientificÓ racists, Latour-style sociologists, pseudoquantitative economists, phenomenologists, existentialists, and ethnomethodologists. 

[93]ÒAnatomy of a Hoax,Ó Tikkun, September-October 1996.  In a March 1997 interview with a Rutgers newspaper, Robbins, one of the editors of the issue of Social Text  containing SokalÕs hoax, shows how little time he has spent in mathematics departments when he asks ÒWhere does one find the strongest anti-nationalist sentiment: among scientists who are funded by the military and the government, or among multicultural critics?Ó  RobbinsÕs resort to cross-campus stereotypes is particularly disappointing because his book Secular Vocations  (Verso, 1993) shows keen sensitivity to mass media stereotyping of literary intellectuals.

[94] More recently, in  an article entitled ÒMonsieur Jourdain and Uncle Vanya,Ó  Levitt offered this explanation: ÒIf the general culture seems headed into a stagnant slough [he  had previously asked whether there is a contemporary composer we would compare with Brahms or Debussy or Mahler or Strauss, and likewise for novelists, poets, etc.] where irony infuses everything and all values are transient or self-negating, why shouldnÕt science be drawn into the overall disaster?Ó  Levitt, without irony, credits John Searle with this particular insight.  (In Koertge, op. Cit, p. 280).

[95] D. Nelkin, ÒWhat are the science wars really about?Ó  The Chronicle of Higher Education, July 26, 1996.  The claim, already present in NelkinÕs contribution to the Social Text  issue on the Science Wars, may be unsubstantiated, but that doesnÕt mean it wasnÕt repeated , by Latour and Robbins, among others; cf. Jeanneret, op. Cit., p. 157.  The claim is echoed in the article by Dahan-Dalmedico and Pestre in IS, where it is claimed that ÒMathematical and physical sciences [É] contribute more than ever to the cold war (think of President ReaganÕs Strategic Defense Initiative)ÉÓ (p. 103).  At the very least, this statement is tendentious and one-sided; recall that the majority of U.S. physicists and mathematicians voted against  funding for SDI through their professional organizations.

[96] They do have their own theories about the Òintellectual sources of postmodernism and relativism.Ó   Sokal and Bricmont admit the Òconjectural natureÓ of these theories.  One might add that the theories derive from no systematic study, and that moreover the authors suggest no methodology on which such a study might be based.

 

[97] Sokal and Bricmont:  FN, p. 6; Dahan-Dalmedico and Pestre:  IS, p. 98; Fujimura:  IS, p. 233.  It's beyond me how a literature that identifies itself as post-colonial -- Fujimori explicitly compares Sokal to "the missionaries and anthropologists ... who brought back to their home countries information about the 'Others'" [IS, p. 232] -- can identify with Latour and Woolgar when they compare their rejection of "the uncritical acceptance of the concepts and terminology used by some scientists" to "an anthropologist's refusal to bow before the knowledge of a primitive sorcerer." [p. 29]

[98] See FN, p. 184.  Sokal and Bricmont are here in agreement with Bruce Robbins, who, in the Rutgers interview already quoted, saw the science wars deriving in part from Òa backlash against cultural explanations, in favor of explanations of social and cultural phenomena in terms of the physical sciences--a sort of imperialism in which physical science models claimed the right to explain human or sociopolitical phenomena.Ó  See also the comments by J. Treiner, one of SokalÕs most energetic French supporters, in Le Monde, 11 octobre 1997. 

[99] Weinberg, Dreams of a Final Theory, pp. 248-249; Gould, The Mismeasure of Man; J.-P. Berlan  and R. C. Lewontin, ÒLa menace du complexe gŽnŽtico-industriel,Ó  Le Monde Diplomatique, dŽcembre 1998, p. 1; Math. Intelligencer  (Koblitz/Simon).  The value of the distinction between good and bad science is described in similar terms by Peter Galison,  where  in his introduction to The Disunity of Science  he expands on a point made in J. DuprŽÕs article (p. 13; DuprŽÕs comments are on p. 106).

Possibly in a reference to FNÕs French title, and speaking about how the ideology of scientific progress is used to mask private interests, Berlan and Lewontin write that ÒGloser sur le progr�s en gŽnŽral, en ignorant comment les choses se passent en pratique, rel�ve de lÕimposture.Ó 

[100] A House Built on Sand, N. Koertge, ed., Oxford University Press (1998).  Kitcher:  p. 33;  Sokal:  p. 17.

[101] Sokal and Bricmont distinguish between general philosophical relativism and methodological relativism.   The former leads to sentences like Òscience is a social process, not a mode of inquiryÓ (Gross, in The Flight from Science and Reason, op. Cit., p. 6) or even Òphysical ÔrealityÕÉ is at bottom a social and linguistic constructÓ (from SokalÕs parody, reprinted in FN, p. 213), of which Dominique Pestre, responding to accusations of relativism, writes ÒCe genre de propositions est sans intŽr�t et je les pense idiots,Ó (in Le dŽbat,  102, nov.-dŽc. 1998, p. 103) and David Bloor writes ÒEvery sane person knows [that human interaction with the material world] is central to scientific activity.Ó  (in Social Studies of Science, 28/4, 1998, p. 624).  No contributor to The Disunity of Science  defends such a perspective, and the two physicists admit that the symmetry principle in the Òstrong programmeÓ in sociology of science, associated with Bloor and Barry Barnes, is a form of methodological relativism.  But they go on to say Òthis position is untenable if one abandons philosophical relativism, because it ignores an essential element of the desired explanations, namely Nature itself.Ó (FN,  p. 92).  The ÒbecauseÓ in this sentence is misplaced, unless you assume that the goal of sociologists is to produce the kind of explanations physicists ÒdesireÓ.  The selections discussed below demonstrate that sociologists (and some historians) have other motivations entirely, deriving from their own discipline, and the failure of certain scientists and philosophers to understand this point is the main reason the science wars are not going away. 

[102] Stump, p. 286;  Fine, p. 232; Stump, p. 447.   I choose these quotations not because I necessarily endorse them, nor because they are the most interesting material in the book, but for their relevance to FN.    The third thing you will notice, reading The Disunity of Science,  is that there is much more to science studies than the debate on realism vs. relativism.  But the margins of the science wars are not wide enough to explain what else there is.

                  The book Science as Practice and Culture ,  edited by A. Pickering (Chicago, 1992), contains some heated debates on some of these issues, including an exchange between British and French schools in sociology of science.  A low point in the science wars came with Paul GrossÕs description of these debates as Òinternecine wars,Édeadly and amusing.Ó (Gross, loc. cit.).   One might as well ridicule the mathematicians for their disagreements in the BAMS   exchange.

[103] Le DŽbat, op. Cit.  Chevalley, p. 71; Jorland, p. 93; Jacob (emphasis added) , p. 85. 

[104] When I was a graduate student, a distinguished philosopher once confided to me his opinion that philosophy of mathematics was impossible.  He had written many papers on the subject and it would be presumptuous of me to disagree with him.

[105] ***see note (about FN and methodological relativism)

[106] Le DŽbat, op. Cit.  P. 104.  PestreÕs response, entitled ÒScience des philosophes, science des historiens,Ó is an extremely well-written account of the misunderstandings that arise when one discipline (in this case, philosophy) attempts to judge the productions of a second discipline (in this case, history) without understanding its specific goals.  But as the quotation indicates, there is a difference in philosophical perspective, which may really reflect a difference in taste.  Thus when Jacob defends the distinction between the fact that a proof is valid and the fact that the experts consider it to be so, Pestre replies ÒI would not know where to place myself, nor on what authority to base my judgments to hold such a position, and therefore judge it sufficient   to describe how each one comes to the conviction of a fact or a  proof, how a collective governed intersubjectively (É) comes to agree that a representation it defines is true, correct, interesting, or practical and usefulÉwith regard to certain constraints and approximations.  I would then have the impression that my statements are very solid andÉof having attained all that it is honest to say.Ó

                  PestreÕs comments have to be qualified, however, according to one local historian of science, who notes a Ògeneral tendency in science studiesÓ to Òslide irresistably along the philosophical slopeÓ when they attempt to theorize their work [private communication].  This tendency, which overlaps with the Ògreat deal of nonsenseÓ Fine sees in constructivist writings on philosophy, is obviously in direct contradiction with PestreÕs quotation.

[107] N. David Mermin, ÒThe Science of Science:  A Physicist reads Barnes, Bloor, and Henry,Ó  Social Studies of Science, 28/4 (August 1998), 603-623, followed by David Bloor, ÒChanging AxesÓ, pp. 624-635; Barry Barnes, ÒOversimplification and the Desire for Truth,Ó pp. 636-640; N. David Mermin, ÒAbandoning PreconceptionsÓ, pp. 641-647.

[108] Op. Cit., p. 634.  There is no space here to develop any of the questions raised by Mermin, or the sociologistsÕ responses, and I can only encourage those interested to read these articles before tackling the science wars literature.

[109] Agar:  SSS, p. 651.  Bloor:  SSS, p. 658.

[110] FN, p. 52.

[111] As Thurston wrote, WilesÕ proof — still incomplete at the time — Òhelps illustrate how mathematics evolves by rather organic psychological and social processes.Ó  Thurston, op. Cit.

[112] Or so I would assume.

[113] Or my royalties from this article, whichever is greater.

[114] For instance, in Dawkins, Op. Cit., and on Alan SokalÕs web site.  The Postmodernism Generator produces random paragraphs that look like some peopleÕs idea of postmodern literary/cultural criticism