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Introduction

Karl Popper

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 notion of falsifiability is now a cornerstone of what is known as the "demarcation" of science. As philosopher of science Michael Ruse explains, science is a discipline that (1) is guided by natural law, (2) is explanatory by reference to natural law, (3) is testable against the empirical world, (4) reaches conclusions that are tentative, and (5) is falsifiable [Pennock1999, pg. 5]. Such considerations were key in various court cases that determined creationism and intelligent design do not qualify, for purposes of U.S. legal code, to be taught in public schools as science -- see Court cases.

Popper's ideas remain highly influential in scientific research even to the present day. For example, several 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. Physicist Lee Smolin, for example, writes, "A scientific theory that makes no predictions and therefore is not subject to experiment can never fail, but such a theory can never succeed either, as long as science stands for knowledge gained from rational argument borne out by evidence." [Smolin2006, pg. 352].

However, Popper's ideas do have some limitations, some of which were pointed out by Popper himself in his earliest works. To begin with, in most real 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, and data analysis techniques, not to mention statistical uncertainties. Often multiple follow-on studies, in some cases extending over many years, are necessary to conclusively decide the hypothesis one way or the other. For example, 13 years elapsed between 1998, when two teams of researchers discovered that the expansion of the universe is accelerating, and 2011, when the lead scientists of the two teams (Saul Perlmutter of the Lawrence Berkeley National Laboratory and Brian Schmidt of the Australian national University) were awarded the Nobel Prize in physics, allowing time for these startling results to be very carefully scrutinized in reams of follow-on studies by researchers worldwide. In this sense, scientists are more like detectives, in that they must follow leads and hunches, examine evidence, and tentatively proceed with the most likely scenario. Seldom, if ever, are scientific results black-and-white from day one.

For that matter, if we were to strictly apply Popper's principle, Copernicus' heliocentric theory was falsified from the start and should not have been further considered, because it could not predict planetary motions as accurately as the traditional Ptolemaic system. It only gained acceptance when Kepler modified the theory to include elliptical orbits with time-varying speeds, and when Newton showed that this behavior could be mathematically derived from his laws of motion. In a similar way, Newton's theory was arguably falsified in the mid-19th century, when certain anomalies were noted in the orbit of Mercury. But it would have been irresponsible to have discarded Newtonian mechanics at that time, because of its overwhelming success in accurately explaining a vast array of phenomena, and because there was no better alternative until Einstein's relativity.

It must also be kept in mind that in most cases, "falsified" theories continue to be extremely accurate models of reality within appropriate domains. For example, even today, over 100 years after Newton's mechanics and Maxwell's electromagnetic equations were falsified and replaced by new theories of physics, they remain the basis of almost all practical engineering and scientific computations, giving results virtually indistinguishable from those of more modern theories. Relativity corrections are used in the GPS systems now incorporated into many automobiles, and quantum mechanics is employed in semiconductor device design, materials science and chemistry. But beyond these examples it is hard to identify any instances in everyday life where the classical theories don't suffice.

Thomas Kuhn

One difficulty with Kuhn's writings is that there are really two Kuhns: a moderate Kuhn and an immoderate Kuhn [Sokal1988a, pg. 75]. Unfortunately, many scholars like to quote only the immoderate Kuhn, such as when he denies that paradigm shifts carry scientists closer to fundamental truth [Kuhn1970, pg. 170], or when he argues that paradigm shifts often occur due to non-experimental factors [Kuhn1970, pg. 135].

Another difficulty is that Kuhn's "paradigm shift" model has not worked as well in recent years as it did in the historical examples he cited. For example, the "standard model" of physics, the currently reigning fundamental theory of elementary particles and forces, was developed in the 1960s and early 1970s, and 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 -- even initial skeptics quickly recognized the new theory's power, elegance and precision, and soon threw their support behind it [Tipler1994, pg. 88-89].

The status of modern science

Theoretical: 1.001159652201 (plus or minus 30 in the last two digits)
Experimental: 1.001159652188 (plus or minus 4 in the last two digits)

Is this astonishing level of agreement -- to better than one part in one billion -- just a coincidence?

More recent postmodern writings

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; Gross1996; Koertge1998]. In other words, these writers are guilty of the "forest" fallacy: pointing out flaws in the bark of a few trees, then trying to claim that the forest doesn't exist.

More importantly, observers of the postmodern science literature have also noted: (a) serious confusion on various concepts of science; (b) an emphasis on politically correct conclusions over sound scholarship; (c) engaging in lengthy discussions of mathematical or scientific principles about which the author has only a hazy familiarity; (d) applying highly sophisticated concepts from mathematics or physics into the humanities or social sciences, without justification; (e) displaying superficial erudition by peppering the text with sophisticated technical terms or mathematical formulas; and (f) employing lengthy technical passages that are essentially meaningless [Sokal1998, pg 4-5].

The Sokal hoax

Rather, [scientists] cling to the dogma imposed by the long post-Enlightenment hegemony over the Western intellectual outlook, which can be summarized briefly as follows: that there exists an external world, whose properties are independent of any individual human being and indeed of humanity as a whole; that these properties are encoded in "eternal" physical laws; and that human beings can obtain reliable, albeit imperfect and tentative, knowledge of these laws by hewing to the "objective" procedures and epistemological strictures prescribed by the (so-called) scientific method. [Sokal1996a, pg. 217; Sokal2008, pg. 7].

In this way the infinite-dimensional invariance group erodes the distinction between the observer and observed; the pi of Euclid and the G of Newton, formerly thought to be constant and universal, are now perceived in their ineluctable historicity; and the putative observer becomes fatally de-centered, disconnected from any epistemic link to a space-time point that can no longer be defined by geometry alone. [Sokal1996a, pg. 222; Sokal2008, pg. 27].

For, as Bohr noted, "a complete elucidation of one and the same object may require diverse points of view which defy a unique description" -- this is quite simply a fact about the world, much as the self-proclaimed empiricists of modernist science might prefer to deny it. In such a situation, how can a self-perpetuating secular priesthood of credentialed "scientists" purport to maintain a monopoly on the production of scientific knowledge? [Sokal1996a, pg. 229; Sokal2008, pg. 53].

With regards to the first passage, note that it derides the most basic notions of scientific reality and common sense. With regards to the second passage, the fundamental constants Pi and G certainly do not have varying values. With regards to the third passage, quantum mechanics, whose effects are significant only at the atomic level, has absolutely nothing to say about the relative validity of cultural points of view.

In spite of its severe 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

Most theoretical physicists, for example, sincerely believe that however partial our collective knowledge may be, ... one day scientists shall find the necessary correlation between wave and particle; the unified field theory of matter and energy will transcend Heisenberg's uncertainly principle. [Aronowitz1996, pg. 181].

Einstein's relativity theory was subjected to official skepticism twenty years after the publication of his Special Theory article in 1905; and equally passionate partisans of wave and matrix mechanics explanations for the behavior of electrons were unable to reach agreement for decades. [Aronowitz1996, pg. 195].

In the first passage, the author is seriously mistaken about wave-particle duality: this is inherent in quantum physics and cannot be removed by a "unified field theory." In the second passage, even his history is in error: the matrix and wave mechanics formulations of quantum mechanics were resolved within weeks [Gottfried2000]. Also appearing in the same issue with Sokal's article was the following, written by the chief editor of Social Text:

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 potentially serious 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 the lead issue was only a foreign conspiracy. Unfortunately, as Michael Sullivan has noted, "lead does not care who believes what." [Sullivan1996].

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. For example a leading French postmodern scholar wrote:

This diagram [the Mobius strip] can be considered the basis of a sort of essential inscription at the origin, in the knot which constitutes the [human] subject. ... You can perhaps see that the sphere, that old symbol for totality, is unsuitable. A torus, a Klein bottle, a cross-cut surface, are able to receive such a cut. And this diversity is very important as it explains many things about the structure of mental disease. If one can symbolize the subject by this fundamental cut, in the same way one can show that a cut on a torus corresponds to the neurotic subject, and on a cross-cut surface to another sort of mental disease. [Lacan1970, pg. 192-196; Sokal1998, pg. 19-20].

With regards to this passage, "Mobius strips," "toruses," "Klein bottles" and "cross-cut surfaces" are terms from mathematical topology, the theory of continuous functions and continuously deformed surfaces. There is absolutely no connection between this arcane mathematical theory and psychology. Yet this author pressed this absurd connection between psychology and topology further in several other writings, sadly misusing sophisticated mathematical concepts such as compactness, open sets, limit points, subcoverings and countable sets [Lacan1998, pg. 9-10; Sokal1998, pg. 21-22].

Numerous examples of gratuitous and often meaningless scientific jargon can also be cited in the postmodern science literature. Here is one example. The reader need not feel bad that he/she does not understand this text. It is complete nonsense, yet it survived peer review in the postmodern science field:

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].

Conclusions

One difficulty 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 significant scientific training and/or credentials; they do not address state-of-the-art scientific theories or methods in any 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 Andrew Ross, editor of Social Text during the Sokal hoax episode, 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].

But this is a point upon which virtually all practicing research scientists will disagree. 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]. In our age, we might add "there is no royal road to modern science."

Indeed, 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. What's more, the details of the methods underlying a study are often as significant as the 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.

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.