Are Science and Mathematics Socially Constructed?

The following sections are included:

• Contents

• Preface

• Acknowledgments

In the early summer of 1996 my wife and I were spending a few weeks in Brighton where I was visiting a colleague at the University of Sussex and writing a now nearly forgotten paper on weighted Sobolev embeddings. Each morning it was my habit to gratify the local Pakistani newsagent by purchasing the three major British newspapers, the Guardian, Times, and Telegraph, supplemented if I were in a raffish mood by the Sun. I enjoyed savoring the various ideological wars conducted in these newspapers, or to use postmodernist language the “incommensurable discourses” found in them. On a particular June morning a large photograph of Thomas Kuhn was on the front page of each newspaper with the announcement that he had passed away at age 73. Multi-column obituaries followed…

To appreciate what a tremendous change PIS has brought in the intellectual climate it is useful to recall that for around two decades after World War II many, perhaps most, humanistic intellectuals in the US seem to have had a healthy respect for (and perhaps also a salutary fear of) science and mathematics. In the context of the period, this was a natural attitude. After all, had not scientific advances in the form of radar, the atomic bomb, sonar, proximity fuses, operations research, etc., been a decisive factor in winning the war and saving democracy from the threats of fascism and Japanese militarism? And during the Cold War were not these same advances, especially in the form of nuclear weapons, protecting the Free World from the menace of totalitarian communism? By 1960 some intellectuals had also been intimidated by C. P. Snow's fashionable 1959 Rede lecture The Two Cultures and the Scientific Revolution which asserted that ignorance of the Second Law of Thermodynamics was equivalent to ignorance of Shakespeare and ignorance of the concepts of mass and acceleration was the equivalent of illiteracy in one's native language. Science according to Snow was more rigorous and at a “higher conceptual level” than literary argument. Scientists, he said, “have the future in their bones” while literary intellectuals are “natural Luddites” who wish “the future did not exist” and “have never tried, wanted, or been able to understand the industrial revolution, much less accept it.” Scientists, moreover, while sensitive to the tragic aspects of human existence want to improve the human social condition while reactionary literary intellectuals such as Yeats, Pound or Wyndham Lewis have brought “Auschwitz that much nearer.” Certainly, in comparison to the tremendous progress made by science in the twentieth century, achievements in the humanities seemed paltry indeed. Quite a few of the literati were pessimistic. The initially politically radical poet and literary critic Max Eastman, for instance, wondered if science might soon answer every human problem and that literature would have “no place in such a world.” In 1970 Eugene Ionesco seconded this opinion speculating that, in comparison with the “enormous progress that scientists were making, art may have reached a “dead-end.”¹ Michael Yudkin, himself a research chemist with humanistic inclinations, warned in an article critical of Snow…

To give a complete analysis of the intellectual origins of PIS we should have to probe deeply into the history of philosophy. Postmodernists are opportunists and use weapons wherever they can find them. Many of their arguments contain elements that are borrowed from the vast necropolis of past philosophic doctrines. However, the task of exhibiting them is made more difficult because the ideas influencing PIS are seldom clearly stated; they are often presented in a fragmented form—sometimes as if they are the cloudy memories of a long past Philosophy 101 class. It would be inaccurate and unfair to view all of PIS as the intellectual equivalent of the contents of the author's 1957 septic tank; but one can reconstruct the bouillabaisse of ideas PIS has consumed (with some idea of their relative importance) from the residue present in its texts, just as one can reconstruct the diet of the early patrons of the actual septic tank from analysis of the seeds, fruit pits, rinds, and bone fragments found in its contents. Less offensively, we could simply seek the recipe of the steaming intellectual mess set before us. But however we think of it, let us don protective garments and get on with the task…

To what intellectual chef then do we owe the beginning of PIS? One answer has been given and relentlessly defended¹ by David Stove: He locates culinary guilt in the philosophy of Karl Popper (1902—1994). For Stove, Popper was the unconscious fons et origo of the sickening flavor of the PIS bouillabaisse—that is, of all the fashionable irrationalism that was to come in the philosophy of science. More precisely, in relation to these later currents, Stove compares Popper's role to that of the liberal, westernized Stepan Verkhovensky who played with “advanced ideas” and whose son Peter as a result became a terrorist in Dostoyevsky's novel The Possessed.² Popper's philosophy, according to Stove, reflected the chaos of post-World War I Vienna, the city where he resided until his emigration to New Zealand in 1937 because of the Anschluss.³ It was a typical product of the Jazz Age which was characterized by the desire to overturn all established opinion in every field, and, concerning science, was the philosophic embodiment of Cole Porter's “anything goes” and “day's night today,” “good's bad today.”⁴…

A common characteristic of many of the intellectual movements sketched in Chapter 3, especially as they developed after around 1850, is a progressive narrowing of the scope of human reason together with a destruction of belief in its integrity and autonomy. As Max Horkheimer observed this “end of Reason” followed inexorably from the very triumph of the power of reason since the Enlightenment.¹ In a process of self-immolation similar to that which we have argued was instrumental in the transition from modernism to postmodernism, Reason, via its ruthless critique of all existing institutions, ultimately also undermined itself. This suicidal course, a nearly precise but negative parallelism to the process celebrated by Auguste Comte, went through three stages of which Horkheimer identifies two. The first was already evident in the rationally founded skepticism of Hume and can even be traced back to the sophistic opposition to Plato and Ockham's or Siger of Brabant's destructive criticism of Thomas Aquinas' scholastic rationalism.² By the Renaissance Reason had effectively lost its role as an arbiter of religious truth. Also, the problem of the relationship of the Self to the external world raised by Descartes which bedeviled seventeenth century philosophers—and especially the solution to it given by Kant—along with the corrosive effects of Hume's skepicism seemed to destroy the Platonic vision that Reason could be either “the herald of eternal ideas which were only dimly shadowed in the material world” or the belief that it could “discover the immutable forms of reality in which eternal reason was expressed.”³ But if Reason could not give comforting answers to ultimate religious, metaphysical, or epistemological problems, perhaps it still could by contemplating the ultimate structure of reality, so the thinkers of the Enlightenment thought, construct a rational society and dissolve the archaic structures of the Old Regime. But by the nineteenth century this hope was also being undermined as a result of critical self-examination. Reason was no longer the neutral and infallible arbiter of the social world. Reason was increasingly revealed to be the slave of hidden factors of which the reasoner was unaware, an immediate consequence being that it could no longer be taken at face value. Apparently rational argument need not be either defended or refuted; only the “unmasking” of its origins and hidden purposes counted. For Hegel Reason was the work of the World Spirit, not the individual, which caused the reasoner to fulfill purposes and goals that could contradict his conscious intentions. For Wilhelm Dilthey (1833–1911) and German historicism generally what passed for Reason was completely relative to the historical situation.⁴ For Marx the political applications of Reason by the ruling class was mere ideology, reflecting (often unconscious) class interests and the constraints imposed on the social order by the means of production; it was usually a form of what Engels and later Marxists called “false consciousness” which systematically misled the proletariat as to its true position. For Vilfredo Pareto (1848-1923) the motivation behind human actions are deep nonrational perhaps unconscious drives of various sorts which he called “residues.” Reason functions merely as a rationalization or “derivation” of these actions. Still later for Freud “Reason” was a rationalization of neurotic complexes. By the twentieth century, according to Max Horkheimer, it seemed that Reason was now limited to the technical and scientific spheres where it served as a tool or means to achieve various ends, but not as an authority to judge them. Social goals were now beyond Reason.⁵…

It did not take long for Mannheim's refusal to apply SK to the content of science to be challenged. Among the first to do so was Ludwig Fleck (1896–1961), a little known Polish physician and medical researcher who specialized in serology and bacteriology.¹ Fleck's most fundamental work Entstehung und Entwicklung einer wissenschaftlichen Tatsache: Einführung in die Lehr vom Denkstil und Denkkollective² was published in 1935, a year after Karl Popper's Logik der Forschung. The two books encountered very different fortunes. Popper's book was noticed and caused quite a stir. While many in the Vienna Circle as well as Werner Heisenberg disliked it, Einstein, Carnap, and other philosophers praised it lavishly. The work was reviewed by leading journals and via the potent idea of falsifiability began to make Popper's reputation as a serious philosopher of science. Fleck's book, on the other hand, was almost ignored. Except for a few reviews in German journals it dropped “dead-born from the press” as David Hume described the fate of his Treatise on Human Nature in 1739. While Popper's book was translated into English in 1958, Fleck's had to wait nearly another forty years before an English language version was available…

Ludwik Fleck was certainly a precursor of SSK and the postmodernist turn of mind generally, and would have probably agreed with many of the PIS-like theses (i)—(xv) we have listed. But he was nearly invisible, having as we have remarked no initial influence. An effective rebuttal to Mannheim and Merton's separation of the substance of science and mathematics from SK by their intellectual descendants had to await the 1970s when it was conjoined with a much broader attack on the entire Enlightenment project which privileged science as the only reliable source of knowledge. The process by which this happened and eventually triumphed in many humanistic disciplines is our central theme. It was certainly foreshadowed by Berger and Luckmann's influential 1966 book The Social Construction of Reality which implied that all knowledge including the most fundamental conceptions of reality was the product of human social interactions. Berger and Luckman, however, like other contemporary sociologists were following the tradition of Mannheim and Merton; unlike Ludwik Fleck they did not apply their ideas to explain the content of science. The primary (but quite unintentional) catalyst which changed the situation and opened the door to a total sociological interpretation of science was supplied not by a sociologist, but by a mathematical physicist turned historian of science. The physicist was Thomas Kuhn and the work was his famous The Structure of Scientific Revolutions. This book written in 1962 has almost certainly had more influence on the historiography and philosophy of science than any other individual work in the history of these disciplines; in fact, it appears to have been the single most cited book on any subject in the twentieth century.¹ By the time of Kuhn's death in 1996, sales had exceeded a million copies,² and the book had been translated into at least nineteen languages including Korean and Serbo-Croatian.³ Unlike many historians and philosophers of science Thomas Kuhn (1922–1996) had a solid training in a scientific discipline. In 1949 he was awarded a Harvard Ph.D. in Physics under John H. van Vleck, who later (1977) shared a Nobel Prize. In 1947, while a graduate student, Kuhn was asked by the President of Harvard James B. Conant (1893–1978), who had been the director of the National Defense Research Council during the war and who was soon to become High Commissioner to occupied Germany, to assist in the teaching and organization of a science appreciation course for undergraduates in the humanities which Conant had wished to establish…

Kuhn still, however, had a high regard for science. He admired the power of increasingly sophisticated paradigms to solve puzzles, and I have found no evidence that he questioned the prominence and prestige of science in modern western societies. Paradigm choice may not be a completely logically determined process like proof in mathematics; but Kuhn, as we have seen, came to believe in the virtue of rational argument and stressed the importance of “internal” factors in scientific change. In none of his published writings does he express the view that a legitimate scientific theory mirrors in any simple fashion a political ideology or originates in the class interest of a certain group, although he probably would have admitted that nonscientific aspects especially connected with philosophy may be present.¹ From his student days at Harvard until his death, he was also a man deeply committed to finding what he conceived to be the truth, and not merely to winning arguments.² These barriers would have to be demolished before the sociological deconstruction of science could proceed further…

The final stage in the process of scientific deconstruction inadvertently begun by by Thomas Kuhn and continued by Paul Feyerabend was the achievement of Barry Barnes, David Bloor, Steve Shapin,¹ and John Henry² at the University of Edinburgh's Science Studies Unit³ who, beginning in the early 1970s, created the so-called “Edinburgh Strong Program.” Over the next twenty years closely related ideas were advanced by Harry Collins and Trevor Pinch⁴ in Bath (“The Bath School”), Michael Mulkay⁵ at York, Simon Schaffer,⁶ Karin Knorr-Cetina⁷ at the University of Pennsylvania, Steve Woolgar⁸ at Brunel, Michel Callon and Bruno Latour⁹ in Paris, and several others. Their collective approach became a new and fashionable academic discipline, usually called “sociology of scientific knowledge” (SSK), some form of which is now extremely influential in the historiography of science and in STS generally. SSK is not monolithic; as in any academic field there are discordant points of view and disputes, sometimes vicious, among its practitioners. We will briefly discuss some of these and attempt to point out some of the differences among the major figures in the movement. But an exhaustive discussion of SSK and its various strands is beyond our scope, requiring at the very least a much larger book than the present one…

The analysis of mathematics has from the very beginning represented a more difficult challenge to SSK than mere science. Here is a subject that is universal and which seemingly deals with a transcendental world of mathematical objects and necessary truths. To our minds, according to Wittgenstein, “Logic is a kind of ultra-physics, the description of the ‘logical structure’ of the world.”¹…

Since the dialogue Theaetetus philosophers have argued about what knowledge is, how we know we have it, and whether or not knowledge is possible. Since they have never agreed on any of these issues, it may be too ambitious a goal to demolish all the theses shared in common by SSK and PIS—at least to the satisfaction of all reasonable minds—as decisively as mathematicians have demolished circle squarers. Insofar as epistemological ideas which deny science access to objective knowledge of reality are based on some form of skepticism they cannot be definitively refuted…

Having dealt with the SSK/PIS view of science, how valid is its conception of mathematics? As in the case of science, direct refutation is impossible. There is no universally accepted theory of the origins or foundations of mathematics. Every account that has been offered—whether Plato's view (as revived by Frege) that mathematical objects are in some sense “real,” or the twentieth century doctrines of formalism or logicism—has been shown to have fundamental weaknesses and to offer an unsatisfactory account of mathematics.¹ Our goal will be simply to demonstrate that the same is true of SSK by examining some of its implications and to see whether or not SSK conforms to or can explain the intuitions of practicing mathematicians concerning their subject…

One beautiful spring day in 1973 I had just finished having a bratwurst and beer at a sandwich place on State Street, a few blocks from the Madison campus of the University of Wisconsin. As I walked out I noticed to my left a small mob (about fifteen to twenty individuals) running down State Street from the direction of the Capitol. Evidently the anti-MRC demonstrators were out again! They were headed for a Mathematics Research Center (MRC) Symposium in applied mathematics being held at a conference center on the edge of campus. I was attending the Symposium and was on my lunch break. Although at age 34 I was a bit old to be a recent Ph.D. in mathematics, I was in fairly good shape as I was in the habit of jogging daily a few miles along the shore of Lake Mendota, so it was a simple matter for me to lope at an easy pace in front of the approaching mob and take shelter behind the police lines guarding the entrance to the conference center…

The central aim of this essay has been to critically analyze the doctrines of SSK/PIS as they relate to science and mathematics. We reach conclusions hostile to the more extreme members of the school, and in the particular case of mathematics regard the issue of “fallibility” as a straw man whose significance Paul Ernest and other social constructivists have grossly exaggerated. Many of the individuals discussed in Chapters 3—9 have helped cause at least two fundamental changes in the interpretation of science. In the first place, they have almost destroyed the internalist “conceptual analysis” approach to the history of science pioneered by Alexandre Koyré in such works as Études Galiléennes, so influential at his death in 1964, and replaced it, as we have seen, by the constructivism and contextualism so characteristic of SSK. Secondly, they have ignored traditional philosophy of science and its perennial project of analyzing “scientific method” in order to find prescriptive rules that science should follow and substituted a descriptive historically oriented analysis via case studies of the way science “warts and all” actually has developed. This approach has persuaded them that there are no epistemological differences between science and other historically contingent cultural “discourses.” Both of these revolutionary changes have had similar consequences: Concern over the “truth” of a theory is replaced by an analysis of the sociology of its acceptance. The hagiography accorded “great scientists” is replaced by the kind of treatment reserved for other historical actors, such as politicians. And the view that the history of science shows progression towards truth (i.e., Whig history) is replaced by a view of it as a random process having no particular direction…

The following sections are included:

• Bibliography

• Index