An artist’s representation of superstrings. Illustration by Mehau Kuylyk/Science Photo Library

Philosophy of science

An artist’s representation of superstrings. Illustration by Mehau Kuylyk/Science Photo Library

How science fails

For the émigré philosopher Imre Lakatos, science degenerates unless it is theoretically and experimentally progressive

Jim Baggott

An artist’s representation of superstrings. Illustration by Mehau Kuylyk/Science Photo Library

Jim Baggott

is an awardwinning British popular-science author, with more than 25 years’ experience writing on topics in science, philosophy and history. He is the author of Quantum Space: Loop Quantum Gravity and the Search for the Structure of Space, Time, and the Universe (2018) and Quantum Reality: The Quest for the Real Meaning of Quantum Mechanics – A Game of Theories (forthcoming, 2020) He lives in Reading, UK.

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If you ask a scientist a question about the philosophy of science, there’s a good chance the answer will feature just one or two philosophers. The name of the Austrian-born British philosopher Karl Popper (1902-94) will likely arise in the context of his principle of falsifiability, the ‘demarcation criterion’ that many scientists still use to distinguish science from non-science. A theory is considered scientific only if it makes predictions that can – in principle – be proved wrong. So astrology is not a science because its predictions are typically so vague that they can’t be falsified: they are irrefutable. This is the basis for Popper’s take on the scientific method. Scientists make a series of creative conjectures which they then attempt to refute. They make progress by refining their hypotheses in light of these refutations, and the process begins again.

Meanwhile, the name of the American philosopher Thomas Kuhn (1922-96) will likely be mentioned in the context of his theory of scientific revolutions. In the normal science of every day, puzzles are solved and discoveries are made within a network of accepted foundational theories, or what Kuhn called a paradigm, which is accepted to be irrefutable. Logically, if scientists stopped what they were doing every five minutes, and sought to falsify the basis on which they make their predictions and devise and perform tests, then they wouldn’t get much done. Contrast this with revolutionary science, in which all bets are off and paradigms shift, in a process that Kuhn likened to religious conversion or political revolution. Kuhn argued that such revolutionary scientific change involves not just a change in laws, entities and their mathematical descriptions, but also in the standards by which scientists judge the adequacy of theoretical explanations.

According to Kuhn, what makes astrology different from astronomy is not the irrefutability of the former, but rather the research tradition of the latter and its role in resolving the puzzles of normal science. Confronted with a failed prediction, the astronomer sets to work, checking the data, re-running the calculations, or re-designing and improving instruments. The astrologer has no such tradition, and resorts to arm-waving. Astrology is not science because astrologers don’t do science.

The average scientist’s acquaintance with philosophy tends to be of the passing variety. This is a great pity. Deep-rooted, seemingly intractable problems in foundational theoretical physics – the physics of matter and radiation, space, time and the Universe – have now frustrated progress for 50 years or more. We’re living through a period in the history of foundational physics in which ideas about nature are cheap, but gathering the empirical facts needed to show that these ideas have anything at all to do with the real world has become extraordinarily expensive, protracted and time-consuming, and without guarantee of success. It turns out that this is a period in which Popper and Kuhn can’t really help us. We need to look further afield.

This is particularly true for those foundational theoretical physicists who favour string theory as the new paradigm-in-waiting. In the string theory programme, begun in the late 1970s, the elementary constituents of nature and the forces between them are imagined to be formed from strings or loops of energy. This picture was quickly complicated by the need to assume a fundamental symmetry – called supersymmetry – between matter and force particles, and the need to hide away six extra spatial dimensions in a mathematical structure called a Calabi-Yau shape. Things got considerably more complicated when it became apparent that there are at least five varieties of string theory and an extraordinary number of possible Calabi-Yau shapes, with no means to identify the one relevant to the particles and the forces that make up our universe. The response of some string theorists has been to invoke the anthropic principle: in a multiverse of all possible shapes, we shouldn’t be too surprised to find ourselves in a ‘Goldilocks’ universe constructed from a shape perfectly suited to the evolution of intelligent life.

Other than vaguely ‘predict’ the possible existence of so-called supersymmetric particles (which, to date, have not been found), string theory appears quite incapable of predicting anything at all. It is irrefutable.

Concern that the string theory programme had lost all contact with reality led in 2006 to the ‘string wars’. Popper’s falsifiability criterion was used in an attempt to bring string theorists to account. String theorists hit back, rejecting the diktat of philosophical principles and the views of the ‘Popperazi’. With hindsight, this was a missed opportunity, as the problems with Popper’s criterion have been known to philosophers for some time, and there is a ready alternative that incorporates aspects of both Popper’s and Kuhn’s philosophies. This is Imre Lakatos’s methodology of scientific research programmes.

Among all the most notable philosophers of science, it is perhaps Lakatos who embodies philosophy as lived experience. Born in the Hungarian city of Debrecen in 1922, he studied mathematics, physics and philosophy at university, but his passion was revolutionary communism. Following the Nazi invasion of Hungary in March 1944, Jews in Debrecen were forced into a ghetto, and some 6,000 were subsequently deported to Auschwitz. Lakatos’s mother and grandmother were among them. They did not survive.

Lakatos escaped to Nagváryad (now Oradea in Romania), where he appointed himself the de facto leader of a radical student study group, over which he cast a strong intellectual spell. These young Stalinists embraced a romantic vision of the revolution: they ‘longed to be … hanged several times a day in the interests of the working class and the great Soviet Union’. The group was joined by 19-year-old Éva Izsák. But as she struggled to find secure lodging, Lakatos worried that she would be captured by the Nazis and forced to betray them. He encouraged her instead to commit suicide, in a singular act of revolutionary self-sacrifice. At his direction, she was escorted to a remote part of the Great Forest, where she took cyanide and died. When her body was later discovered, she was not immediately identified.

Following the Soviet victory in Hungary in late 1944, Lakatos became a somewhat overzealous member of the ruling Communist Party. But his own eagerness eventually put him at odds with the Party leadership, and he was expelled and arrested by the State Protection Authority (the ÁVH) in April 1950. He spent more than two months under ‘interrogation’ at ÁVH headquarters, before eventually being transferred to a prison camp in northeastern Hungary. He was released three years later, six months after Stalin’s death. Remarkably, he remained a Party loyalist, and continued to inform on friends and colleagues to the ÁVH.

Lakatos secured a position at the Mathematical Institute of the Hungarian Academy of Sciences where he read voraciously, in an effort to make up for lost time. It was here that he first encountered the works of Popper, and particularly his criticism of Marxist theory. It completely shattered his worldview. As far as he could tell, the ‘scientific’ predictions of orthodox Marxism had all been systematically falsified. By 1956, Lakatos had transformed from passionate Stalinist to passionate revisionist. Popper changed his life.

When Soviet T-54 tanks rolled into the centre of Budapest to quell the Hungarian uprising in November 1956, Lakatos escaped to Austria. He secured a grant from the Rockefeller Foundation’s Hungarian refugee programme, and arrived in England in January 1957. While studying for a PhD at the University of Cambridge, he took the opportunity to reinvent himself, avoiding émigré politics and drawing a veil over his Stalinist past. In 1960, he was appointed assistant lecturer in Popper’s department at the London School of Economics (LSE). Nine years later, he was installed as the LSE’s Professor of Logic, with an established international reputation. In 1965, he presented a paper titled ‘Falsification and the Methodology of Scientific Research Programmes’ at an international colloquium held in London. It stands as a singular contribution to the philosophy of science.

The problems with Popper’s principle of falsifiability were by this time well-known: this is just not how science works. As Kuhn had observed, strict falsificationist principles, naively applied, rule out much of what passes for normal, everyday scientific practice. For example, we know that the planetary orbits are not exact ellipses, and that each planet’s point of closest approach to the Sun (called the perihelion) shifts slightly, or ‘precesses’. This was thought to be caused by the cumulative gravitational pull of all the other planets in the solar system, and is most marked for the planet Mercury. But Newton’s laws predict a precession, which disagrees with observation. Though small, this difference accumulates and is equivalent to one ‘extra’ orbit every 3 million years or so.

Lakatos saw merits in both Popper’s and Kuhn’s approaches

To understand what such disagreement really means, we need to appreciate how theories are routinely applied. This typically involves some simplification or additional assumptions or hypotheses. Some are inherent in the mathematical formulation of the theory, such as the assumption in Isaac Newton’s theory that the masses of gravitating bodies are located at their centres. Others are necessary to simplify calculations, such as the assumption that in experimental studies of the electromagnetic force, the effects of other forces (such as gravity) can be safely ignored. This means that the resulting predictions are never derived directly from the theory itself, but rather from the theory as adapted by one or more ‘auxiliary’ hypotheses. If these predictions are then falsified, it’s never clear what’s gone wrong. It might be that the theory is indeed false, but it could be that one or more of the auxiliary hypotheses is invalid: the evidence can’t tell us which.

Lakatos wrote:

Is this [disagreement] regarded as a refutation of Newtonian science? No. Either yet another ingenious auxiliary hypothesis is proposed or … the whole story is buried in the dusty volumes of periodicals and the story never mentioned again.

Suitably imaginative adjustment of the hypotheses can in principle render any scientific theory virtually irrefutable.

Lakatos argued that Popper’s criterion is just too restrictive. But he was also uncomfortable with Kuhn’s description of the process of scientific revolution. If, as Kuhn argued, the standards we use to judge the success of scientific theories change from one paradigm to the next, then the question of which is ‘better’ becomes rather moot. For Kuhn, a revolution is driven by a crisis of confidence, and the contagious panic that results. Lakatos wrote: ‘Thus in Kuhn’s view scientific revolution is irrational, a matter for mob psychology …’ This leads to a rather ambiguous notion of scientific progress based on human psychology and sociology, and thence to accusations of relativism. Kuhn resisted this charge, but it is hard to discount.

Despite these contradictions, Lakatos saw merits in both Popper’s and Kuhn’s approaches. His ‘research programme’ has parallels with Kuhn’s paradigm. A research programme consists of a ‘hard core’ theory or collection of theories surrounded by a ‘protective belt’ of auxiliary hypotheses. The auxiliary hypotheses serve two purposes. They help to connect the hard core to the empirical world through predictions, and they also serve to insulate the core and render it essentially irrefutable. It is the combination of hard core and auxiliary hypotheses that is subjected to empirical test and is in principle falsifiable.

In what Lakatos referred to as the ‘negative heuristic’, failed predictions encourage scientists to retain the irrefutable hard core and tinker with the hypotheses. The ‘positive heuristic’ is the ‘partially articulated set of suggestions or hints on how to change, develop the “refutable variants” of the research programme, how to modify, sophisticate, the “refutable” protective belt’. Or, if you prefer, ‘conjectures’. Albert Einstein’s work on general relativity developed not from puzzling over awkward unexplained anomalies such as the precession of the perihelion of Mercury (the negative heuristic), but rather from a creative shift – the conjecture that gravity is related to the curvature of space-time – in the positive heuristic of his programme.

This methodology allows for a rather fascinating take on demarcation. Lakatos judged a programme to be ‘progressive’ if it is both theoretically progressive – the hard core plus auxiliary hypotheses predict novel empirical facts – and experimentally progressive: at least some of these novel facts can be tested. In contrast, a programme is ‘degenerating’ if it is theoretically degenerating – it doesn’t predict any novel facts – or it is theoretically progressive but experimentally degenerating: none of the novel facts can be tested.

As an example of a novel fact, Lakatos volunteered the bending of starlight during a total solar eclipse, correctly predicted by Einstein’s general theory of relativity but not by Newton’s universal gravitation. As Lakatos explained: ‘Nobody had thought to make such an observation before Einstein’s programme …’ Over time, this demand for novelty was softened and extended to include novel predictions for already existing facts. That the general theory of relativity correctly predicts the precession of the perihelion of Mercury, an already established empirical fact that the general theory wasn’t explicitly designed to solve, was nevertheless rightly counted in Einstein’s favour.

At a stroke, Lakatos merged the distinction between science and non-science, and between good and bad science. If a programme predicts nothing new or its predictions can’t be tested, then it is bad science, and might be degenerating to the point of pseudoscience. Empirical tests serve to refine the auxiliary hypotheses and a programme continues to be progressive for as long as new facts are predicted and new tests are possible. A scientific revolution occurs when a dominant programme has completely degenerated and is unable to respond to accumulating anomalies – creating precisely the crisis of confidence that Kuhn anticipated – until it can be replaced by an alternative, progressive programme. But, according to Lakatos, when the time comes, a revolution is driven by logic and method, not irrational mob psychology: ‘the Kuhnian “Gestalt-switch” can be performed without removing one’s Popperian spectacles’.

But, make no mistake, there are problems here, too. Lakatos bid philosophers and historians to look for examples of his methodology at work in the history of science. The results were mixed. Lakatos’s methodology allows the possibility that a research programme might exhibit changing fortunes over time, maybe starting off as progressive but then degenerating. This was very much his perspective on the Marxist theory that had captured the imagination of his younger self. However, by the same token, there’s nothing to rule out the possibility that a degenerating programme could somehow stage a spectacular recovery, no matter how unlikely this might seem.

For anyone seeking an unambiguously definitive demarcation criterion, this is a death-knell. On the one hand, scientists doggedly pursuing a degenerating research programme are guilty of an irrational commitment to bad science. But, on the other hand, these same scientists can legitimately argue that they’re behaving quite rationally, as their research programme ‘might still be true’, and salvation might lie just around the next corner (which, in the string theory programme, is typically represented by the particle collider that has yet to be built). Lakatos’s methodology doesn’t explicitly negate this argument, and there is likely no rationale that can.

Lakatos argued that it is up to individual scientists (or their institutions) to exercise some intellectual honesty, to own up to their own degenerating programmes’ shortcomings (or, at least, not ‘deny its poor public record’) and accept that they can’t rationally continue to flog a horse that appears, to all intents and purposes, to be quite dead. He accepted that: ‘It is perfectly rational to play a risky game: what is irrational is to deceive oneself about the risk.’ He was also pretty clear on the consequences for those indulging in such self-deception: ‘Editors of scientific journals should refuse to publish their papers … Research foundations, too, should refuse money.’

But the Austrian-born American philosopher Paul Feyerabend (1924-94) wasn’t satisfied. If a demarcation criterion cannot dictate what scientists should or shouldn’t do, then he argued that it is of little value. We might just as well abandon the scientific method altogether and accept that ‘anything goes’. Feyerabend expanded on this anarchistic approach to science in his book Against Method (1975). In 1983, the American philosopher Larry Laudan dismissed demarcation as a ‘non-problem’, effectively signalling its end as a valid research topic for philosophers of science.

Bad science of one form or another might be all that is available given our current predicament

This is extremely unfortunate. Just at a time when developments in foundational theoretical physics were beginning to demand a lively and constructive engagement between scientists and philosophers on the very definition of science, the philosophy community was backing away from the debate entirely, leaving the scientists to squabble among themselves.

Let’s at least acknowledge that the current crisis is not science’s fault. We’re faced with a choice. We could choose to accept that we’re now in uncharted territory, and so we need to adapt the definition of what it means to ‘do science’. This is essentially what the Austrian-born philosopher Richard Dawid encourages us to do in his book String Theory and the Scientific Method (2013). Dawid advocates adapting the meaning of science to embrace what he calls ‘non-empirical theory assessment’, arguably a short step from the oxymoron that is ‘post-empirical science’. In essence, this means breaking up Lakatos’s methodology, setting aside empirical judgments – because these are impossible – in preference to purely theoretical judgments. Only on this basis can string theory be regarded as a progressive programme, and only then because it has managed to establish some novel mathematical relationships, rather than novel empirical facts.

Or we could choose to push back, and insist that the desires of a few theoretical physicists to indulge their fantasies are insufficient reason to start messing around with the meaning of science. A research programme that is theoretically progressive but experimentally degenerating is a degenerating programme, as Lakatos declared. It is bad science, and this should have consequences. That bad science of one form or another might be all that is available given our current predicament is a different (but no less fascinating) discussion.

In later life, Lakatos was justifiably optimistic about his prospects as part of the British academic establishment. He applied to become a British citizen, and was interviewed extensively by both MI5 and Special Branch. Declassified interview transcripts reveal him as he wished to appear to the authorities. According to him, poor Éva Izsák had chosen suicide (Lakatos variously claimed that he suspected she had a heart condition, or that a failed relationship with another member of the group had broken her heart). He claimed that he had reluctantly agreed, and one interviewer observed that ‘the memory of this incident had remained with him to the present day in his nightmares and in his waking hours’. But it seems that Lakatos never privately expressed any regret over this incident, or his role in it. Indeed, according to several of his close acquaintances: ‘He seemed proud of it. He saw it as a revolutionary deed.’

Despite personal endorsements from several academic luminaries – including Popper – it seems that the British authorities never overcame reservations born of their suspicion of his past connections to the ÁVH. He was denied citizenship in July 1963 and again in January 1967. There were signs that a third application might have been successful, but he never got the chance to make it. He died stateless in February 1974, aged 51.

Although his influence on the philosophy of science has been enormous, Lakatos’s name is not as well-known among scientists as those of Popper and Kuhn. This needs to change. His methodology has its merits and its faults but, in the absence of viable alternatives, I’d suggest that it provides a useful framework for what will surely be a protracted debate.

Jim Baggott

is an awardwinning British popular-science author, with more than 25 years’ experience writing on topics in science, philosophy and history. He is the author of Quantum Space: Loop Quantum Gravity and the Search for the Structure of Space, Time, and the Universe (2018) and Quantum Reality: The Quest for the Real Meaning of Quantum Mechanics – A Game of Theories (forthcoming, 2020) He lives in Reading, UK.
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