ψ

874 NOTICES OF THE AMS VOLUME 45, NUMBER 7

Book Review

time no longer ex-ists as an objec-tive physical real-ity. “When eventhe gravitationalfield—geometryi n c a r n a t e —becomes a non-commuting (andhence nonlinear)operator, how canthe classical in-terpretation ofGµν as a geomet-ric entity be sus-tained? Now notonly the observer,but the very con-cept of geometry,

becomes relational and contextual.”

The article might have passed unnoticed in thetorrent of words produced by academics during theyear 1996. Perhaps the heavy use of postmod-ernist jargon should have given it away. In any case,the author soon revealed it as a parody [S2]. Thisprovoked a reaction from the editors of SocialText, followed by articles and exchanges of lettersin the New York Times and the New York Reviewof Books and eventually in Le Monde. The disputealso generated new texts in the ultimate post-modern format, the Web page.

A scientifically alert reader might notice im-mediately that the article is not serious. For in-stance, in quantum mechanics the fundamentalstructure is a noncommutative algebra of opera-tors, but Sokal’s casual equation of noncommuta-tive and nonlinear is ludicrous to a quantum physi-

Impostures intellectuellesReviewed by William G. Faris

Impostures intellectuelles

Alan Sokal and Jean BricmontÉditions Odile Jacob, Paris, 1997Softcover 140 Francs (ISBN 2-7381-0503-3)

Quantized Relativity

In 1996 the mathematical physicist Alan Sokal

published an article [S1] in the cultural studies

journal Social Text. He argued that “deep concep-

tual shifts within twentieth-century science have

undermined [the] Cartesian-Newtonian meta-

physics . . . It has thus become increasingly appar-

ent that physical ‘reality’, no less than social ‘re-

ality’, is at bottom a social and linguistic

construct . . .the truth claims of science are inher-

ently theory-laden and self-referential; and con-

sequently, that the discourse of the scientific com-

munity, for all its undeniable value, cannot assert

a privileged epistemological status with respect to

counter-hegemonic narratives emanating from dis-

sident or marginalized communities.”

Sokal’s professed aim was “to carry these deep

analyses one step farther, by taking account of re-

cent developments in quantum gravity: the emerg-

ing branch of physics in which Heisenberg’s quan-

tum mechanics and Einstein’s general relativity

are at once synthesized and superseded.” Space-

William G. Faris is professor of mathematics at the Uni-versity of Arizona. His e-mail address is faris@math.arizona.edu.

Editor’s Note: The topic of the book under review was alsoexplored in “A mathematician reads Social Text”, byMichael C. Sullivan, and “A report from the front of the‘Science Wars’”, by Evans M. Harrell, both of which ap-peared in the October 1996 issue of the Notices.

AUGUST 1998 NOTICES OF THE AMS 875

cist. One of the strangest features of quantum me-chanics is that it is an entirely linear theory.

Relativistic Science

The book by Sokal and Bricmont—mathematicalphysicists who know the difference between non-commutative and nonlinear—continues the attack,implicit in the Sokal parody, on postmodernistviews of science. It argues that relativistic views ofscience are both prevalent and wrong. It proceedson two fronts. The first is criticism of authors saidto use scientific language and metaphors in a mis-leading way. Those who merit chapter headings areJacques Lacan, Julia Kristeva, Luce Irigaray, BrunoLatour, Jean Baudrillard, Gilles Deleuze, Félix Guat-tari, and Paul Virilio. These are French writerswhom Sokal and Bricmont consider to be influen-tial on postmodern thought in the United States.

Some of these writers produce quite extravagantprose. One author (Virilio) claims that “it seems nec-essary to reconsider the importance of the notionof ACCELERATION and DECELERATION (positiveand negative velocities according to physicists).”(The capitals are in the original text.) Another (Bau-drillard) suggests that “one should perhaps con-sider history itself as a chaotic formation whereacceleration puts an end to linearity.” After read-ing a number of these extracts, it is a pleasure toencounter a quoted paragraph that presents aclear and eloquent explanation of the principle ofrelativity; Galileo wrote it in 1632.

Sokal and Bricmont’s other front is a more gen-eral attack on relativism in the philosophy andsociology of science. This is the notion that the va-lidity of a scientific assertion is relative to an in-dividual or to a social group. Sokal and Bricmontbegin by a dismissal of radical skepticism, the doc-trine that our sensations are not adequate to giveus access to reality. They consider this to be ageneral philosophical position that applies to allforms of knowledge equally. They do not claim torefute it, but instead argue that a skepticism thisuniversal cannot be relevant to the discussion ofthe reliability of particular forms of knowledge.

The real question is the degree to which scien-tific practice has a rational basis. Sokal and Bric-mont insist on the continuity of scientific ratio-nality with rationality in other areas of humanknowledge and in everyday life. They admit thatthere is no definitive and complete codification ofscientific practice, and they present the exampleof a police investigation as an analog of scientificresearch. In both cases principles of good practicearise through experience.

They also discuss a movement sometimesknown as the “strong program” in the sociology ofscience [BBH]. This is a sociological explanation ofthe conditions that give rise to scientific beliefs.Some proponents maintain that the particular be-liefs a person prefers to hold will generally coin-

cide with those of other persons in the same com-munity, and the words “true” and “false” are thelanguage in which the preferences are expressed.Sokal and Bricmont consider this position am-biguous: either it falls into radical skepticism (thereis no reality beyond our inadequate perceptions),or it itself relies on the external reliability of sci-ence. When Sokal believes that he has taken hismorning coffee, then that is not the expression ofa preference, but an attempt to record a fact. Hemight have broken his pattern and taken morningtea. If he forgot this switch to tea, then his beliefis wrong. The tea bag may remain as evidence, ifit has not gone out with the garbage.

Scientific Truth

Who could doubt such conclusions of commonsense? Even a postmodernist might agree with thefact that Sokal took his morning coffee, or tea. Per-haps language is in some circumstances an inno-cent tool for describing a world of subjects and ob-jects. But is this so common? The use of languagein many spheres of life is as much instrumentalas descriptive. An advertiser wants Sokal to changeto another brand of coffee. A neighbor offers teaand conversation simply to affirm friendship. Anactivist (cited in the Sokal parody) has a politicalpurpose: “to develop strategic theories—not truetheories, not false theories, but strategic theories.”

The concept that there are multiple uses of lan-guage is quite acceptable in philosophy of scienceprovided that there is some way to insulate thetruth-telling function of language from its otheruses. However, this is difficult, precisely for the rea-sons that Sokal and Bricmont describe. In theirview, “historians, detectives, and plumbers—infact, all humans—use the same methods of in-duction, deduction, and evaluation of facts thatphysicists and biochemists use.” Modern scienceis only more systematic and precise. Furthermore,they agree with Feyerabend when he claims that“the idea that science can and should be orga-nized according to fixed and universal rules is atthe same time utopian and pernicious.”

If one judges the epistemological basis of sci-ence by the standards of physical science andmathematics, then the lack of fixed and universalrules is troubling. Can there not be a decent gen-eral theory of truth in science? The idea is not ab-surd. The logical positivists made an attempt tofind such a theory; the fact that it failed does notsay that it was not worth the effort.

Truth in mathematics is a somewhat differentstory. The logician Tarski gave a precise definitionof truth for sentences in a formalized language in-terpreted in a universe of mathematical objects.However, Tarski then proved that the criterion fortruth in a language cannot be formalized in the lan-guage itself. (See Smullyan’s book [Sm] for an ele-mentary but precise treatment.) This seems un-

876 NOTICES OF THE AMS VOLUME 45, NUMBER 7

promising for a general theory of truth, eventhough there have been attempts to supersede theTarski analysis [BE]. Of course, a theorem abouttruth in formalized mathematical languages is notdirectly relevant to other areas of discourse, andlinguists debate the extent to which the semanticsof natural languages resembles that of math-ematical logic [H]. In any case, if it is difficult tocharacterize truth in the limited context of math-ematics, then it may be even more difficult in em-pirical sciences. What if only some principle ofpragmatic functioning is attainable? Is this enoughto ward off relativism? Could there be but oneuniversal truth: universal rules are impossible?

Mathematical practice does not require a com-plete characterization of mathematical truth. Thenotions of axiom system and mathematical proofalready provide a rich and useful system. However,even here the foundations are obscure. In the So-cial Text article [S1] Sokal says, with humorous in-tent, that mathematicians “are often content towork in the hegemonic framework of Zermelo-Fraenkel set theory—but this framework is noto-riously insufficient for a mathematics of liberation.”Indeed, this framework is arbitrary, and somemathematicians have proposed both serious cri-tiques and alternatives. To cite only one example,there are category theorists who do not regardthe category of sets as privileged; it is only one cat-egory among many. In particular, certain cate-gories of “variable sets” provide new settings forconstructions of analysis and geometry [MR]. A re-cent text [LS] promotes the categorical point of viewat the level of the general reader or beginning stu-dent.

Truth in Quantization

The major gap in the Sokal-Bricmont book is thatit avoids dealing with the status of quantum me-chanics. If Sokal had chosen a different area ofphysics, would he have been able to pull off thehoax? Though there are numerous scientific ab-surdities in the Social Text article, its heart is theconfusion over the foundations of quantum me-chanics. This confusion is a major weak point inmodern physical science. Numerous popular writ-ings about science exploit this obscurity, but thebook does not address this issue. Writers who con-fuse velocity and acceleration are comparativelyeasy targets.

When Sokal and Bricmont briefly mention quan-tum mechanics, they recommend the recent bookof Albert [A] as an introduction to nonspecialists.This is an excellent book, but the ideas are hardlycomforting to Sokal and Bricmont’s view that mod-ern science is an extrapolation of common sense.Albert concludes his book with an interpretationof quantum mechanics due to Bohm and with an-other interpretation that he calls the “many-minds”theory. According to Albert, “what a ‘many-minds’

theory takes physics to be ultimately about is whatobservers think; and it entails that there will be fre-

quently not even matters of fact about where thingsgo.” (The italics are in the original.) The Bohm the-

ory and the many-minds theory are incommensu-

rable. Thus, again according to Albert, “questions

about the structure of space and time, and ques-

tions about whether the world is deterministic

(which were supposed to be the two central ques-

tions of the physics of this century, and which

both happen to be questions on which these two

theories radically disagree with one another), are

the kinds of questions which there can’t ever be

scientific answers to. Period.” Is this an extrapo-

lation of common sense? No, it is scientific au-

thority in full retreat. What kind of hegemony is

that?

Clearly quantum mechanics is one of the great-

est successes of science. Yet something remains

to be said before the full truth is known. (See

Wick’s recent book [W] for a fuller account of the

quantum quandary.) One can take Sokal [S1] en-

tirely seriously when he says that “images of the

future mathematics must remain but the haziest

glimmer: for, alongside these . . .young branches

in the tree of science, there will arise new trunks

and branches—entire new theoretical frame-

works—of which we, with our present ideological

blinders, cannot yet even conceive.”

References

[A] DAVID Z. ALBERT, Quantum mechanics and experience,

Harvard Univ. Press, Cambridge, MA, 1992.

[BBH] BARRY BARNES, DAVID BLOOR, and JOHN HENRY, Scien-tific knowledge: A sociological analysis, Univ. of

Chicago Press, Chicago, 1996.

[BE] JON BARWISE and JOHN ETCHEMENDY, The liar: An essayon truth and circularity, Oxford Univ. Press, New

York, 1987.

[H] RANDY ALLEN HARRIS, The linguistics wars, Oxford

Univ. Press, New York, 1993.

[LS] F. WILLIAM LAWVERE and STEPHEN H. SCHANUEL, Con-ceptual mathematics: A first introduction to cate-gories, Cambridge Univ. Press, New York, 1997.

[MR] IEKE MOERDIJK and GONZALO E. REYES, Models for smoothinfinitesimal analysis, Springer, New York, 1991.

[Sm] RAYMOND M. SMULLYAN, Gödel’s incompleteness theo-rems, Oxford Univ. Press, New York, 1992.

[S1] ALAN D. SOKAL, Transgressing the boundaries: To-wards a transformative hermeneutics of quantumgravity, Social Text 46/47 (1996), 217–252.

[S2] ALAN D. SOKAL, A physicist experiments with cul-tural studies, Lingua Franca 6 (4) (1996), 62–64.

[W] DAVID WICK, The infamous boundary: Seven decadesof controversy in quantum physics, Copernicus

(Springer-Verlag), New York, 1996.