The Science Wars—didn’t they blow over like the bird flu crisis and global cooling? In the 1990s, several books such as Paul Gross and Norman Levitt’s The Higher Superstition and Alan Sokal and Jean Bricmont’s Intellectual Impostures exposed some exceptionally crazy claims about science that were rampant in the humanities circles loosely called “postmodernist.” Science, the postmodernists claimed, was “socially constructed,” in the sense that its claims were the outcome of political pressures rather than the result of rational evaluation of evidence. The critics of the postmodernists demonstrated how badly they had understood science and predicted grave consequences if nothing was done about the threat. The postmodernists ignored the challenge and kept producing the same dense academese as before, while occupying the same tenured chairs. Scientists remained blissfully unaware of the dispute and publish the same research as always.

Now Richard Brown, a mathematician of mature years at the University of Alabama, has looked over the wall at what the humanities “experts” are saying about science and mathematics and is shocked all over again. Quite rightly, and he has produced a readable, well-argued, and often funny (though shockingly proofread) book about the horrors over the way. But should we care enough to pack our bags for another dispiriting traipse through the twists and turns of this intellectual hall of mirrors?

It depends what we care about. If our main interest is the health of science, then there is probably no need to waste our time. The postmodernists’ attacks have washed off science like water off a duck’s back, as they should have, and funding to science does not appear to have been noticeably affected. Science can look after itself. So can professional disciplines like engineering, medicine, business studies, and law, which saw attacks in a similar vein but have not changed noticeably in response to them. If we care about the state of the humanities, things are otherwise. The humanities are where civilization reflects on itself and where it is going, so what happens there sets the tone of thought for the present and even more for the future. It is crucial how young people are inducted into the tradition of culture, so rottenness at the core of what the young encounter in the humanities at universities is of grave concern.

What they encounter is, all too often, something like “Privilege, Possibility, and Perversion: Rethinking the Study of Early Modern Sexuality,” a 2006 paper in the Journal of Modern History which Brown chooses for its typicality. That is, it is a very standard work on a typical humanities topic, unrelated to science. In the course of setting the scene, however, the fifth sentence on the first page says “[the variability in the study of sex], combined with the poststructuralist efforts of Jacques Derrida, Michel Foucault, and others, further undermined claims for scientific truth and objective reality.” The text immediately moves on to other matters. The author plainly believes that the audience will take the demise of scientific truth and objective reality to be a truism, long established and without need of further justification. (There is a footnote to the sentence, which merely lists several whole books by Derrida and Foucault.) The very smugness and casualness of the reference indicates the depth of corruption in the humanities, and reveals the plight of any countersuggestible student who begins to wonder, “Might there be something in claims for scientific truth and objective reality after all?”

Brown’s analysis of postmodern interpretations of science resembles its predecessors—as it should, since their analysis was correct. He does have some new perspectives to add, based on the unique life story that he outlines in his opening chapter, “Rip van Winkle Awakes.” As a student at Berkeley, he was briefly research assistant to Thomas Kuhn around 1962, the year that saw the publication of Kuhn’s The Structure of Scientific Revolutions. That book proved to be the most influential work on the history and philosophy of science in the twentieth century, convincing many in the humanities that scientific research was a political war between “paradigms” rather than a search for the truth based on evidence. From 1967, Brown turned to the serious study of mathematics and pursued a successful research career. In the early 1970s, he worked in the Mathematics Research Centre at the University of Wisconsin, Madison, which had military funding and was the target of a 1970 bombing that killed a postdoctoral researcher. He remained ignorant, like most scientists, of the developments in the sociological deconstruction of science associated with such names as Foucault, Derrida, Latour, and the Edinburgh Strong Program.

Then, in 1996, Brown heard of Sokal’s hoax in Social Text and, after seeing a splenetic review of The Higher Superstition, read it. He nobly embarked on a punishing reading course of the anti-science authors themselves:

After a nearly thirty year nap I had awakened to a new and strange intellectual world. . . . The writers I examined had attitudes that were polar opposites of mine. Most shared a common stance that science is just another from of socially constructed “discourse” divorced from an independently existing natural world (which itself is a social construction).

While a number of scientists (of the few who had read about the matter) felt the same way about the attack on science, Brown is well-qualified to analyze it, for two reasons. The first is his expertise as a mathematician, since mathematics is the area of science where objectivity and certainty are most evident (and so the object of some of the postmodernists’ most ambitious and most deluded attacks, such as Paul Ernest’s Social Constructivism as a Philosophy of Mathematics). The second is his misspent youth in the history and philosophy of science at Berkeley, which gave him the ability to recognize the logical errors and rhetorical strategies deployed against science.

He writes of his research: “The effort to write the book has been immense. It required catching up in a year or two on forty years of unread books and articles. . . . Much of it I found to be junk”—by which he means not that just that he disagrees with it but that “the work is unintelligent and would not have earned a B- in a Berkeley seminar c. 1960.” His efforts have unearthed some remarkable statements deserving of exposure to the plain light of day. Let us take just two.

The first is an argument of Kuhn in support of disbelief in science:

All past beliefs about nature have sooner or later turned out to be false. On the record, therefore, the probability that any proposed belief will fare better must be close to zero.

The first of these two sentences is spectacularly self-refuting, in that present beliefs are also past beliefs—indeed, exactly those past beliefs that have not turned out to be false. Nor is there any shortage of beliefs about nature that have survived since time immemorial (for example, “it’s in spring that the wheat comes up”) or since they were established centuries ago by science (for example, the theory of the circulation of the blood).

The second exhibit is an answer by postmodernists to the question everyone has wanted to ask them, “If you don’t believe in the reality of the scientific laws of nature, why not jump out of a tenth-story window?” Or, as Richard Dawkins put it, “Show me a relativist at 30,000 feet and I will show you a hypocrite.” Postmodernists, especially famous ones, very rarely reply to criticisms, but Brown has found a certain Sarah Franklin (no relation) who tackles this head-on in her article “Making Transparencies: Seeing Through the Science Wars.” She writes:

But what is so self-evident about the fact that planes can fly? This feat could as easily be described as sophisticated tool use instead of as an indicator of epistemological certainty. And as certain as the fact that planes can fly is the fact that their design is constantly evolving, that experiments such as that of the Wright brothers have as much to do with desire as with established scientific principles, that some airlines show prayer films during take-off to invoke the aid of Allah.

Show me a postmodernist at any altitude and I will show you the worst example of wilful unteachability you will ever meet.

On a more theoretical front, Brown draws attention to the ideas of Karl Mannheim, which go some way towards explaining why postmodernists see no need to respond to criticism. Mannheim held that the point of explaining away (alleged) knowledge in sociological terms was not to refute it, but to enforce the

“unmasking turn of mind.” This is a turn of mind which does not seek to refute, negate or call into doubt certain ideas, but rather to disintegrate them . . . when I do not even raise the question . . . whether what the idea asserts is true, but consider it merely in terms of the extra-theoretical function it serves, then, and only then, do I achieve an “unmasking.”

That means, in simple terms, that if an enemy of science can think of some cause of resentment against it, expressing indignation loudly will rule out any possibility of science mounting a defense of truth.

One weakness of Brown’s book, which he admits, is the lack of a satisfactory philosophy of mathematics. If the objectivity of mathematics is to be used as a last line of defense against claims of relativism, then it becomes important to say what mathematics is about. There is no similar problem for science in general, since it is clear that biology is about living things, physics is about physical things, and so on. It is not so clear what mathematics is about. It is implausible to say it is about Numbers and Sets, conceived of as “abstract” entities in some Platonic world, while the alternative of seeing it as about nothing (as just a language) is equally unappetizing and undercuts its vaunted objectivity. Brown is reduced to saying, after a lifetime in mathematics, “Mathematics simply exists; where it comes from and its ontological implications are mysteries which we do not believe it is possible to solve.” That is a sad extreme of mysterianism, which could be remedied by a serious Aristotelian realist philosophy of mathematics that explained what aspects of the world (quantity, ratio, symmetry, continuity, for example) mathematics is about. Unfortunately, there is no such complete philosophy of mathematics on the market.

Like many critics with excellent analyses of what is wrong with something, Brown is less clear what can be done about the problem. He debates the merits of scientists taking up the political methods of their enemies: “mobilize propaganda, rhetoric, and persuasion, seek allies, isolate the opposition, and sow discord among them.” But he is well aware that scientists do not know how to do those things, even if they could be persuaded to notice the problem.

Perhaps a smaller goal would be more achievable. If universities were to refuse to pay for medical insurance for any of their staff who had attacked the objectivity of science, then the problem would at least be on the way to solution. Why would anyone who denied the objectivity of science want medical insurance?