In the field most commonly known as “postmodern science studies” or, more specifically, “postmodern philosophy of science,” scholars attempt to critique science and mathematics from a high-level perspective. Two of these writers, Karl Popper and Thomas Kuhn, in the view of the present bloggers and many other working scientists, have significant and lasting merit and are worth taking seriously; for a mathematical perspective see, for example, our 2011 article [Exploratory Experimentation and Computation] and [Borwein2012]. Both Popper and Kuhn brought out their most influential books roughly fifty years ago.
Karl Popper (1902-1994), the Austrian born British philosopher, declared in his book The Logic of Scientific Discovery [Popper1959, pg. 40-41]:
I shall certainly admit a system as empirical or scientific only if it is capable of being tested by experience. These considerations suggest that not the verifiability but the falsifiability of a system is to be taken as the criterion of demarcation. … It must be possible for an empirical scientific system to be refuted by experience.
Popper’s ideas on falsifiability appropriately remain highly influential in scientific research to the present day. For example, various prominent scientists have recently expressed concern about whether it is prudent to continue pursuing string theory, given that practitioners have not yet been able to derive empirically testable consequences even after 25 years of effort [Smolin2006, pg. 352]. Or if pursued, it should be justified as a mathematically worthwhile subject.
What Popper was articulating is now quite a orthodox view. Science is an inductive process and, unlike deductive mathematical proofs, no level of observation can ever prove anything. That said, some theories like relativity have been very convincingly tested. Nonetheless, new experiments are being designed to probe and test the theory, and if it is found wanting (as the famous 19th century Michelson-and-Morley experiment did with the idea of ether and eventually Newtonian physics) then relativity will need to be replaced.
However, Popper’s ideas do have limitations, some of which were pointed out by Popper himself. In most modern-day scientific research, major theories are seldom falsified by a single experimental result. There are always questions regarding the underlying experimental design, measurement procedures, data analysis and error statistics. Often multiple follow-on studies, over many years, are necessary to conclusively decide the hypothesis one way or the other. The recent “faster than light” neutrino measurements at CERN provide an illuminating case study.
It must also be kept in mind that in most cases, modern “falsified” theories continue to be extremely accurate models of reality within appropriate domains. Even today, over 100 years after Newton’s mechanics and Maxwell’s electromagnetic equations were “falsified” and supplanted by new theories of physics, they remain the basis of almost all practical engineering and scientific computations, giving results virtually indistinguishable from modern theories.
Relativity is used in GPS systems, and quantum mechanics is employed in electronics, materials science and chemistry. But otherwise it is hard to identify any instances in the modern world where classical theories of physics don’t suffice.
Another hugely influential postmodernist author is Thomas Kuhn (1922-1996). His seminal 1962 The Structure of Scientific Revolutions analyzed numerous historical cases of scientific advancements, and argued compelling that periods of normal science were interrupted by key paradigm shifts in which old ideas were abandoned [Kuhn1970]. He likened shifts to “religious conversions” which do not come easily.
Elsewhere Kuhn has compared paradigm shifts to religious experiences.
Kuhn was originally trained as a scientist, receiving his Ph.D. in physics from Harvard in 1949, and so was especially able to bring significant technical insight into his analyses of historical scientific revolutions.
One difficulty is that Kuhn’s “paradigm shift” model has not worked as well in explaining advances of recent years as it did in the historical examples he cited. He famously quoted Einstein on page 151 of The Structure of Scientific Revolutions:
And Max Planck, surveying his own career in his Scientific Autobiography, sadly remarked that ‘a new scientific truth [quantum theory] does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.’
By contrast, the “standard model” of physics, the currently reigning fundamental theory of elementary particles and forces, was completed in essentially its current form in 1974. Yet by just 1980 it had completely displaced previous theories of particle physics, after a very orderly transition. This may in part reflect on the fact that the shift had to take place within a relatively small group of specialists as opposed to the case of quantum theory. Four centuries ago, Napier’s logarithms were adopted within a few years — at much same the speed they were abandoned for the digital calculator in the 1970s.
Sadly, the term “paradigm shift” is vastly over-used in the modern world, and Kuhn’s writings, much as Popper’s writings before him, have been badly misused by a host of eager amateurs thinking that they can smash the reigning orthodoxy of modern science.
In a newly-published but posthumous fiftieth-anniversary interview of Kuhn by Scientific American writer John Horgan, Kuhn was deeply upset that he had become a patron saint to this type of would-be scientific revolutionaries: “I get a lot of letters saying, ‘I’ve just read your book, and it’s transformed my life. I’m trying to start a revolution. Please help me,’ and accompanied by a book-length manuscript.” [Horgan2012].
Many social scientists and humanists, who should know better, have also misused these ideas and continue to do so. Geoffrey Wheatcroft, in historian Tony Judt’s 2010 Guardian Obituary, approvingly quoted Judt’s remarkable 2005 book Postwar on the sogginess of much current social science:
On the other, his judgments could be pointed: the 1970s was intellectually the bleakest decade of the century: structuralism and deconstructionism came to the fore because their “inherently difficult vocabulary had achieved a level of expressive opacity that proved irresistibly appealing to a new generation of students and their teachers.”
More recent postmodern writings
More recent writings in post-modern science studies have over-zealously extended the scope of their critiques, declaring that much of modern science, like literary and historical analysis, is “socially constructed,” dependent on the social and political environment of the researchers, with no claim to fundamental truth. Collins and Pinch, for instance, after examining a handful of case studies, assert that “scientists at the research front cannot settle their disagreements through better experimentation, more knowledge, more advanced theories, or clearer thinking” [Collins1993, pg. 143-145; Koertge1998, pg. 258].
Scientists counter that these scholars have distorted a few historical controversies, and then have parlayed these isolated claims to a global condemnation of the scientific enterprise [Gross1998]. What’s more, scientists have noted, in several instances of the postmodern science literature: (a) serious confusion on technical concepts; (b) politically charged rhetoric; (c) lengthy discussions of mathematical or scientific principles about which the author has only hazy familiarity; (d) applications of highly sophisticated concepts from mathematics or physics where they don’t apply; (e) text peppered with sophisticated technical terms or mathematical formulas; and (f) technical passages that are essentially meaningless [Sokal1998, pg 4-5; SkepticalTeacher].
The Sokal hoax
The tension between the scientific and postmodernist communities came to a head in 1996, when Alan Sokal, a physicist at New York University, wrote a parody of a postmodern science article, entitled “Transgressing the Boundaries: Toward a Transformative Hermeneutics of Quantum Gravity,” and submitted it to Social Text, a prominent journal in the postmodern studies field [Sokal1996a].
The article was filled with page after page of erudite-sounding nonsense, political rhetoric, irrelevant references to arcane scientific concepts and approving quotations from leading postmodern science scholars.
In spite of its seemingly apparent flaws, the article was not only accepted for the journal, but it appeared in a special issue devoted to defending the legitimacy of the postmodern science studies field against its detractors. As Sokal later noted, “I intentionally wrote the article so that any competent physicist or mathematician (or undergraduate physics or math major) would realize that it is a spoof.” [Sokal1996b, pg. 50].
He resorted to the hoax out of a deeply felt concern that the postmodern science world has taken a complete about-face from its roots in the Enlightenment, which identified with science and rationalism and rejected obscurantism.
“Theorizing about ‘the social construction of reality’ won’t help us find an effective treatment for AIDS or devise strategies for preventing global warming. Nor can we combat false ideas in history, sociology, economics, and politics if we reject the notions of truth and falsity.” [Lingua2000, pg. 52].
Other prominent postmodern science writers
In the same journal issue as Sokal’s piece, a prominent postmodern writer (in a serious article) wrote:
Once it is acknowledged that the West does not have a monopoly on all the good scientific ideas in the world, or that reason, divorced from value, is not everywhere and always a productive human principle, then we should expect to see some self-modification of the universalist claims maintained on behalf of empirical rationality. Only then can we begin to talk about different ways of doing science, ways that downgrade methodology, experiment, and manufacturing in favor of local environments, cultural values, and principles of social justice. [Ross1996, pg. 3-4].
It is easy to imagine the consequences if this extreme cultural relativism were widely adopted in modern science. As a single example, a few years ago the Mexican government encouraged potters, for their own safety, to use lead-free glazes, but the local potters were convinced that this was only a foreign conspiracy. Unfortunately, as Michael Sullivan has noted, “lead does not care who believes what.” [Sullivan1996]. South Africa’s experience with AIDS also shows how destructive of human life ill-educated views of “imperialist scientific plots” can be. Tea party politics in the USA drinks unknowingly from the same stream.
In other postmodern science writing, researchers have attempted to apply arcane scientific and mathematical concepts into the social sciences and the humanities, often with disastrous results. Here is one pathetic example. The reader need not feel bad that he/she does not understand this text. It is nonsense:
We can clearly see that there is no bi-univocal correspondence between linear signifying links archi-writing, depending on the author, and this multireferential, multidimensional machinic catalysis. The symmetry of scale, the transversality, the pathic non-discursive character of their expansion: all these dimensions re-move us from the logic of the excluded middle and reinforce us in our dismissal of the ontological binarism we criticised previously. A machinic assemblage, through its diverse components, extracts its consistency by crossing ontological thresholds, non-linear thresholds of irreversibility, ontological and phylogenetic thresholds, creative thresholds of heterogenesis and autopoiesis. The notion of scale needs to be expanded to consider fractal symmetries in ontological terms. [Guattari1995, pg. 50; Sokal1998, pg. 166].
So where are we fifty years on?
In summary, the works of Kuhn and Popper have provided valuable insights into the process of scientific research. In particular, their observations on falsifiability and paradigm shifts have been largely incorporated into the fabric of modern science. But beyond these two authors, what is generally termed the “postmodern science studies” literature has not been very useful in advancing scientific research. And even the writings of Kuhn and Popper have often been misused.
As biologist Paul Gross and mathematician Norman Levitt wrote [Gross1996, pg. 50]:
The dictum that everything that people do is ‘cultural’ … licenses the idea that every cultural critic can meaningfully analyze even the most intricate accomplishments of art and science. … It is distinctly weird to listen to pronouncements on the nature of mathematics from the lips of someone who cannot tell you what a complex number is!
One criticism that applies rather broadly to this literature at the present time is that these scholars work almost entirely from outside the realm of real scientific research. Unlike predecessors such as Kuhn and Popper, most of these writers do not have substantial scientific training and/or credentials; they do not address state-of-the-art scientific theories or methods in significant technical depth; and they do not participate with scientific research teams in performing peer-reviewed scientific research.
Their approach is best exemplified by a comment made by a leading postmodern writer in the introduction to one of his published works: “This book is dedicated to all of the science teachers I never had. It could only have been written without them.” [Ross1991]. Such is the width of the gulf between C.P. Snow’s Two Cultures half a century on. Lucretius would be turning in his grave were he to have one.
According to an ancient account, when Pharaoh Ptolemy I of Egypt grew frustrated at the degree of effort required to master geometry, he asked Euclid whether there was some easier path. Euclid is said to have replied, “There is no royal road to geometry.” [Durant1975, vol. 2, pg. 501]. Indeed. And there is no royal road to modern science either.
After all, state-of-the-art scientific research is all about the details: underlying physical theories; mathematical derivations; crisp, testable hypotheses; experimental design; data collection; data reduction; statistical techniques; computer simulations; numerical methods; and, of course, cautiously inferred conclusions.
Thus, to the extent that the postmodern science studies community avoids delving into the technical details of leading-edge scientific research, these writers cannot possibly hope to have tangible impact in the scientific enterprise. And, needless to say, when leading figures in this community openly express their contempt for day-to-day scientific work, they are not building bridges that will lead to productive collaborations with real scientists in the future.
Maybe one way the tide will turn, opening the way for a more respectful dialogue between the two disciplines. As physicist Carlos Rovelli recently wrote, “I believe [we] can teach one another enormously.” Philosopher Tim Maudlin’s 2007 book The Metaphysics within Physics is as Rovellian would wish. It offers a thoughtful physically-centered set of essays on topics — time, causality, ontology — we mostly still find as puzzling as did Plato or Kant. In the preface [pg. 4] he writes:
The concepts of the laws of nature and of the passage of time play central roles in our picture of the world, and the arguments that these can, or need to, be reduced to something else [epistomology] strike me as flimsy.
What scientists think
We find that our views on this topic are, if anything, somewhat more reserved that those of many colleagues. We include here some representative commentary by three other eminent scientists and one philosopher:
In a previous Math Drudge blog, we reviewed a book by Richard Brown (an historian turned research mathematician) entitled Are Science and Mathematics Socially Constructed?: A Mathematician Encounters Postmodern Interpretations of Science. He concludes that in spite of postmodern critiques [pg. 239]:
Like Ol’ Man River, mathematics just keeps rolling along and produces at an accelerating rate ’200,000 mathematical theorems of the traditional handcrafted variety … annually’. [quoting Davis and Hersh's book The Mathematical Experience, pg. 24]. Although sometimes proofs can be mistaken — sometimes spectacularly — and it is a matter of contention as to what exactly a ‘proof’ is — there is absolutely no doubt that the bulk of this output is correct (though probably uninteresting) mathematics.
Canadian-American physicist Lawrence Krauss summed up his view of these issues in the following terms [Krauss2012a]:
As both a general reader and as someone who is interested in ideas and culture, I have great respect for and have learned a great deal from a number of individuals who currently classify themselves as philosophers. … What I find common and so stimulating about the philosophical efforts of these intellectual colleagues is the way they thoughtfully reflect on human knowledge, amassed from empirical explorations in areas ranging from science to history, to clarify issues that are relevant to making decisions about how to function more effectively and happily as an individual, and as a member of a society.
As a practicing physicist however, the situation is somewhat different. There, I, and most of the colleagues with whom I have discussed this matter, have found that philosophical speculations about physics and the nature of science are not particularly useful, and have had little or no impact upon progress in my field. Even in several areas associated with what one can rightfully call the philosophy of science I have found the reflections of physicists to be more useful. For example, on the nature of science and the scientific method, I have found the insights offered by scientists who have chosen to write concretely about their experience and reflections, from Jacob Bronowski, to Richard Feynman, to Francis Crick, to Werner Heisenberg, Albert Einstein, and Sir James Jeans, to have provided me with a better practical guide than the work of even the most significant philosophical writers of whom I am aware, such as Karl Popper and Thomas Kuhn.
In the same vein, sparing no feelings, biologist Steven Jones of University College, London wrote:
This is the essence of science. Even though I do not understand quantum mechanics or the nerve cell membrane, I trust those who do. Most scientists are quite ignorant about most sciences but all use a shared grammar that allows them to recognize their craft when they see it. The motto of the Royal Society of London is ‘Nullius in verba’: trust not in words. Observation and experiment are what count, not opinion and introspection. Few working scientists have much respect for those who try to interpret nature in metaphysical terms. For most wearers of white coats, philosophy is to science as pornography is to sex: it is cheaper, easier, and some people seem, bafflingly, to prefer it. Outside of psychology it plays almost no part in the functions of the research machine.
Rhetorical overkill perhaps, but it contains much that most scientists will agree with.
The absurdity of denying a substantial level of objective reality to mathematics and science is made wonderfully clear by writer A. N. Wilson in God’s Funeral, Norton, 1999, p. 178:
In all likelihood, our post-modern habit of viewing science as only a paradigm would evaporate if we developed appendicitis. We should look for a medically trained surgeon who knew what an appendix was, where it was, and how to cut it out without killing us. Likewise, we should be happy to debate the essentially fictive nature of, let us say, Newton’s Laws of Gravity unless and until someone threatened to throw us out of a top-storey window. Then the law of gravity would seem very real indeed.
As cognitive and neuroscientists begin to seriously study consciousness, ethics, qualia (qualitative experience such redness or pain level) and other notions once the domain only of philosophers (see Paul Churchland’s Neurophilosophy at Work, Cambridge University Press 2007), it does behove us to attempt Carlos Rovelli’s reconciliation.
In another very recent blog we reviewed mathematician Brian Davies book Why Beliefs Matter: Reflections on the Nature of Science. Davies makes the case well that while Jones is largely right regarding day-by-day lab science, nonetheless beliefs, at least in the fields we have touch upon, really do matter for seeing the bigger picture.
In any event, the modern scientific method taking its full form after the Enlightenment has been astonishingly successful as anyone who has ever been treated for a major once incurable disease can attest. While no knowledge may be certain, modern science comes remarkably close.
[Added 9 Jun 2012] This topic continues to draw the interest of scientists, philosophers and the public at large. In a New York Times op-ed, Jim Holt laments the conflict that has recently erupted between the two camps, and asks “Why do physicists have to be so churlish toward philosophy? … Physicists expand the circle, and philosophers help clear up the paradoxes. May both camps flourish.”
[This is reprinted from Math Drudge blog.]