Imre Lakatos (1922–1974) was a Hungarian-born philosopher ofmathematics and science who rose to prominence in Britain, having fledhis native land in 1956 when the Hungarian Uprising was suppressed bySoviet tanks. He was notable for his anti-formalist philosophy ofmathematics (where “formalism” is not just the philosophyof Hilbert and his followers but also comprises logicism andintuitionism) and for his “Methodology of Scientific ResearchProgrammes” or MSRP, a radical revision of Popper’sDemarcation Criterion between science and non-science which gave riseto a novel theory of scientific rationality.

Although he lived and worked in London, rising to the post ofProfessor of Logic at the London School of Economics (LSE), Lakatosnever became a British citizen, but died a stateless person. Despitethe star-studded array of academic lords and knights who were willingto testify on his behalf, neither MI5 nor the Special Branch seem tohave trusted him, and no less a person than Roy Jenkins, the then HomeSecretary, signed off on the refusal to naturalize him. (See Bandy2009: ch. 16, which includes the transcripts of successiveinterrogations.)

Nonetheless, Lakatos’s influence, particularly in the philosophyof science, has been immense. According to Google Scholar, by the25^th of January 2015, that is, just twenty-five days intothe new year,thirty-three papers had been published citingLakatosin that year alone, a citation rate of over one paperper day. Introductory texts on the Philosophy of Science typicallyinclude substantial sections on Lakatos, some admiring, some critical,and many an admixture of the two (see for example Chalmers 2013 andGodfrey-Smith 2003). The premier prize for the best book in thePhilosophy of Science (funded by the foundation of a wealthy andacademically distinguished disciple, Spiro Latsis) is named in hishonour. Moreover, Lakatos is one of those philosophers whose influenceextends well beyond the confines of academic philosophy. Of thethirty-three papers citing Lakatos published in the first twenty-fivedays of 2015, at mostten qualify as straight philosophy. Therest are devoted to such topics as educational theory, internationalrelations, public policy research (with special reference to thedevelopment of technology), informatics, design science, religiousstudies, clinical psychology, social economics, political economy,mathematics, the history of physics and the sociology of the family.Thus Imre Lakatos was very much more than a philosophers’philosopher.

First, we discuss Lakatos’s life in relation to his works.Lakatos’s Hungarian career has now become a big issue in thecritical literature. This is partly because of disturbing facts aboutLakatos’s early life that have only come to light in the Westsince his death, and partly because of a dispute between the“Hungarian” and the “English” interpreters ofLakatos’s thought, between those writers (not all of themMagyars) who take the later Lakatos to be much more of a Hegelian (andperhaps much more of a disciple of György Lukács) than heliked to let on, and those who take his Hegelianism to be anincreasingly residual affair, not much more, in the end, than a habitof “coquetting” with Hegelian expressions (Marx,Capital: 103). Just as there are analytic Marxists who thinkthat Marx’s thought can be rationally reconstructed without theHegelian coquetry and dialectical Marxists who think that it cannot,so also there are analytic Lakatosians who think that Lakatos’sthought can be largely reconstructed without the Hegelian coquetry anddialectical Lakatosians who think that it cannot (see for instanceKadvany 2001 and Larvor 1998). Obviously, we cannot settle the matterin an Encyclopedia entry but we hope to say enough to illuminate theissue. (Spoiler alert: so far as the Philosophy of Science isconcerned, we tend to favor the English interpretation. We are moreambivalent with respect to the Philosophy of Mathematics.)

Secondly we discuss Lakatos’s big ideas, the two contributionsthat constitute his chief claims to fame as a philosopher, beforemoving on (thirdly) to a more detailed discussion of some of hisprincipal papers. We conclude with a section on the Feyerabend/LakatosDebate. Lakatos was a provocative and combative thinker, and itfalsifies his thought to present it as less controversial (and perhapsless outrageous) than it actually was.

Note: In referring to Lakatos’s chief works (and to a couple ofPopper’s) we have employed a set of acronyms rather than thename/date system, hoping that this will be more perspicuous toreaders. The acronyms are explained in the Bibliography.

• 1. Life
  • 1.1 A Tale of Two Lakatoses
  • 1.2 Life and Works: The Third World and the Second
  • 1.3 From Stalinist Revolutionary to Methodologist of Science
• 2. Lakatos’s Big Ideas
  • 2.1 Against Formalism in Mathematics
  • 2.2 Improving on Popper in the Philosophy of Science
• 3. Works
  • 3.1Proofs and Refutations (1963–4, 1976)
  • 3.2 “Regress” and “Renaissance”
  • 3.3 “Changes in the Problem of Inductive Logic” (1968)
  • 3.4 “Falsification and the Methodology of Scientific Research Programmes” (1970)
  • 3.5 “The History of Science and Its Rational Reconstructions” (1971)
  • 3.6 “Popper on Demarcation and Induction” (1974)
  • 3.7 “Why Did Copernicus’s Research Programme Supersede Ptolemy’s?” (1976)
• 4. Mincemeat Unmade: Lakatos versus Feyerabend
• Bibliography
  • Works by Lakatos
  • Secondary Literature
• Academic Tools
• Other Internet Resources
• Related Entries

1. Life

1.1 A Tale of Two Lakatoses

Imre Lakatos was a warm and witty friend and a charismatic andinspiring teacher ( Feyerabend 1975a). He was also a fallibilist, anda professed foe of elitism and authoritarianism, taking a dim view ofwhat he described as the Wittgensteinian “thought police”(owing to the Orwellian tendency on the part of some Wittgensteiniansto suppress dissent by constricting the language, dismissing the stuffthat they did not like as inherently meaningless) (UT: 225 and228–36). In the later (and British) phase of his career he was adedicated opponent of Marxism who played a prominent part in opposingthe socialist student radicals at the LSE in 1968, arguingpassionately against the politicization of scholarship (LTD; Congden2002).

But in the earlier and Hungarian phase of his life, Lakatos was aStalinist revolutionary, the leader of a communist cell who persuadeda young comrade that it was her duty to the revolution to commitsuicide, since otherwise she was likely to be arrested by the Nazisand coerced into betraying the valuable young cadres who constitutedthe group (Bandy 2009: ch. 5; Long 1998 and 2002; Congden 1997). Sofar from being a fallibilist, the young Lakatos displayed a cocksureself-confidence in his grasp of the historical situation, enough toexclude any alternative solution to the admittedly appalling problemsthat this group of young and mostly Jewish communists were facing inNazi-occupied Hungary. (“Is there no other way?” the youngcomrade asked. The answer, apparently, was “No”: Long2002: 267.) After the Soviet victory, during the late 1940s, he was aneager co-conspirator in the creation of a Stalinist state, in whichthe denunciation of deviationists was the order of the day (Bandy2009: ch. 9). Lakatos was something close to a thought policemanhimself, with a powerful job in the Ministry of Education, vettinguniversity teachers for their political reliability (Bandy 2009: ch.8; Long 2002: 272–3; Congden 1997). Later on, after fallingafoul of the regime that he had helped to establish and doing time ina gulag at Recsk, he served the ÁVH, the Hungarian secretpolice, as an informant by keeping tabs on his friends and comrades(Bandy 2009: ch. 14; Long 2002). And he took a prominent part, as aStalinist student radical, in trying to purge the University ofDebrecen of “reactionary” professors and students and inundermining the prestigious but unduly independent EötvösCollege, arguing passionately against the depoliticized (but covertlybourgeois) scholarship that Eötvös allegedly stood for(Bandy 2009: chs. 4 and 9; Long 1998 and 2002).

1.2 Life and Works: The Second World and the Third

To the many that knew and loved the later Lakatos, some of these factsare difficult to digest. But how relevant are they to assessing hisphilosophy, which was largely the product of his British years? Thisis an important question as Lakatos was wont to draw a Popperiandistinction between World 3—the world of theories, propositionsand arguments—and World 2—the psychological world ofbeliefs, decisions and desires. And he was sometimes inclined tosuggest that in assessing a philosopher’s work we should confineourselves to World 3 considerations, leaving the subjectivities ofWorld 2 to one side (F&AM: 140).

So does a philosopher’s life have any bearing on his works? Wetake our cue from the writings of Lakatos himself. Of course, therewere facts about his early career that Lakatos would not have wantedto be widely known, and which he managed to keep concealed from hisWestern friends and colleagues during his lifetime. But what does hisofficial philosophy have to say about the relevance of biographicaldata to intellectual history?

In “The History of Science and its RationalReconstructions” (HS&IRR) Lakatos develops a theory of howto do the history of science, which, with some adjustments, can beblown up into an account of how to do intellectual history in general.For Lakatos, the default assumption in the history of science is thatthe scientists in question are engaged in a more-or-less rationaleffort to solve a set of (relatively) “pure” problems(such as “How to explain the apparent motions of the heavenlybodies consistently with a plausible mechanics?”). A“rational reconstruction” in the history of science,employs a theory of (scientific) rationality in conjunction with anaccount of the problems as they appeared to the scientists in questionto display some intellectual episode as a series of rational responsesto the problem-situation. On the whole, it is a plus for a theory of[scientific] rationality if it can display the history of science as arelatively rational affair and a strike against it if it cannot. Thusin Lakatos’s opinion, naïve versions of Popper’sfalsificationism are in a sense falsified by the history of science,since they represent too much of it as an irrational affair with toomany scientists hanging on to hypotheses that they ought to haverecognized as refuted. If the rational reconstructionsucceeds—that is if we can display some intellectual developmentas a rational response to the problem situation—then we have an“internal” history of the developments in question. Ifnot, then the “rational reconstruction of history needs to besupplemented by an empirical (socio-psychological) ‘externalhistory’” (HS&IRR: 102). Non-rational or“external” factors sometimes interfere with the rationaldevelopment of science. “No rationality theory will ever solveproblems like why Mendelian genetics disappeared in Soviet Russia inthe 1950s” [the reason being that Lysenko, a Stalin favourite,acquired hegemonic status within the world of Soviet biology andpersecuted the Mendelians] (HS&IRR: 114).

(Perhaps this marks an important departure from Hegel. For a trueHegelian,everything can, in the last analysis, be seen asrationally required for the self-realization of the Absolute. Henceall history is “internal” in something likeLakatos’s sense, since the “cunning of reason”ensures that apparently irrational impulses are subordinated to theultimate goal of history.)

Is there, so to speak, an “internal” history ofLakatos’s intellectual development that can be displayed asrational? Or must it be partly explained in terms of“external” influences? The answer depends on the accountof rationality that we adopt and the problem situation that we takehim to have been addressing.

Whether or not a particular theoretical (or practical) choice issusceptible to an internal explanation depends, in part, on theactor’s problem. Consider, for example, Descartes’ theoryof the vortices, namely that the planets are whirled round the sun bya fluid medium which itself contains little whirlpools in which theindividual planets are swimming. Descartes’ theory of thevortices, isfairly rational if we take it as an attempt (inthe light of what was then known) to explain the motion of theheavenly bodies in a way that is consistent with Copernican astronomy.But it is a lotmore rational if we take to be an attempt toexplain the motion of the heavenly bodies in a way that is consistentwith Copernican astronomywithout formally contradicting theChurch’s teaching thatthe earth does not move. (Theearth goes round the sun but it does not move with respect to thefluid medium that whirls it round the sun, and, for Descartes, motionis defined as motion with respect to the contiguous matter.) So do weread Descartes’ theory as afairly rational attempt tosolveone problem which is distorted by an external factor oras avery rational attempt solve a related but more complexproblem? Well the answer may not be clear, but if we want tounderstand Descartes intellectual development we need to know that itwas an important constraint on his theorizing that his views should beformally consistent with the doctrines of the Church.

Similarly, it is important in understanding Lakatos’s theorizingto realize (for example) that in later life he wanted to develop ademarcation criterion between science and non-science that left SovietMarxism (though not perhaps all forms of Marxism) on thenon-scientific side of the divide. And this holds whether we regardthis constraint as a non-rationalexternal factor or as aconstituent of his problem situation and hence internal to a rationalreconstruction of his intellectual development. Biographical facts canbe relevant to understanding a thinker’s ideas since they canhelp to illuminate the problem situation to which they wereaddressed.

Furthermore, the big issue with respect to Lakatos’s developmentis how much of the old Hegelian-Marxist remained in the laterpost-Popperian philosopher, and how much of his philosophy was areaction against his earlier self. To answer this question we need toknow something about that earlier self—either the self thatsecretly persisted or the self that the later Lakatos was reactingagainst.

1.3 From Stalinist Revolutionary to Methodologist of Science

Imre Lakatos was born Imre Lipsitz in Debrecen, eastern Hungary, onNovember 9, 1922, the only child of Jewish parents, Jacob MartonLipsitz and Margit Herczfeld. Lakatos’s parents parted when hewas very young and he was largely brought up by his grandmother andhis mother who worked as a beautician. The Hungary into which Lakatoswas born was a kingdom without a king ruled by an admiral without anavy, the “Regent” Admiral Horthy, who had gained hisnaval rank in the service of the then-defunct Austro-Hungarian Empire.The regime was authoritarian, a sort of fascism-lite. After abrilliant school career, during which he won mathematics competitionsand a multitude of prizes, Lakatos entered Debrecen University in1940. Lakatos graduated in Physics, Mathematics, and Philosophy in1944. During his time at Debrecen he became a committed communist,attending illegal underground communist meetings and, in 1943,starting his own illegal study group.

No-one who attended Imre’s groups has forgotten the intensityand brilliance of the atmosphere. “He opened the world tome!” a participant said. Even those who were later disillusionedwith communism or ashamed of acts they committed, remember the senseof inspiration, clear thinking and hope for a new society they felt inImre’s secret seminars. (Long 2002: 265)

However, in Lakatos’s group the emphasis was on preparing theyoung cadres for the coming communist revolution, rather than engagingin public propaganda or antifascist resistance activities (Bandy 2009:ch. 3).

In March 1944 the Germans invaded Hungary to forestall its attempts tonegotiate a separate peace. (The Hungarian government had allied withthe Axis powers, in the hopes of recovering some of the territorieslost at the Treaty of Trianon in 1920. By 1944 they had begun torealize that this was a mistake.) Admiral Horthy, whose anti-Semitismwas a more gentlemanly affair than that of the Nazis (he was fine withsystematic discrimination but apparently drew the line atmass-murder), was forced to accept a collaborationist government ledby Döme Sztójay as prime minister. The new regime had noneof Horthy’s humanitarian scruples and began a policy ofenthusiastic and systematic cooperation with the Nazi genocideprogram. In May, Lakatos’s mother, grandmother and otherrelatives were forced into the Debrecen ghetto, thence to die inAuschwitz—the fate of about 600,000 Hungarian Jews.Lakatos’s father, a wine merchant, managed to get away andsurvived the war, eventually ending up in Australia. A little earlier,in March, Lakatos himself had managed to escape from Debrecen toNagyvárad (now Oradea in Romania) with false papers under thename of Molnár. Later, a Hungarian friend, Vilma Balázs,recalled that

Imre [had been] very close to his mother and they were quite poor. Heoften blamed himself for her death and wondered if he could have savedher (Bandy 2009: 32).

In Nagyvárad Lakatos restarted his Marxist group. The co-leaderwas his then-girlfriend and subsequent wife, ÉvaRévész. In May, the group was joined by ÉvaIzsák, a 19-year-old Jewish antifascist activist who neededlodgings with a non-Jewish family. Lakatos decided that there was arisk that she would be captured and forced to betray them, hence herduty, both to the group and to the cause, was to commit suicide. Amember of the group took her across country to Debrecen and gave hercyanide (Congden 1997, Long 2002, Bandy 2009, ch. 5). To lovers ofRussian literature, the episode recalls Dostoevsky’sThePossessed/Demons (based in part on the real-life Nechaev affair).In Dostoevsky’s novel the anti-Tsarist revolutionary, PyotrVerkhovensky, posing as the representative of a large revolutionaryorganization, tries to solidify the provincial cell of which he is thechief by getting the rest of group to share in the murder of adissident member who supposedly poses a threat to the group. (It doesnot work for the fictional Pytor Verkhovensky and it did work for thereal-life Sergei Nechaev.) Hence the title of Congden’s 1997exposé: “Possessed: Imre Lakatos’s Road to1956”. But to communists or former communists of Lakatos’sgeneration, it recalled a different book:Chocolate, by theBolshevik writer Aleksandr Tarasov-Rodianov. This is a stirring taleof revolutionary self-sacrifice in which the hero is the chief of thelocal Cheka (the forerunner of the KGB). Popular in Hungary, itencouraged a romantic cult of revolutionary ruthlessness and sacrificein its (mostly) youthful readers. As one of Lakatos’scontemporaries, György Magosh put it,

How that book inspired us. How we longed to be professionalrevolutionaries who could be hanged several times a day in theinterest of the working class and of the great Soviet Union (Bandy2009: 31).

It was in that spirit, that the ardent young Marxist, ÉvaIzsák, could be persuaded that it was her duty to kill herselffor the sake of the cause. As for Lakatos himself, a chance remark inhis most famous paper suggests something about his attitude.

One has to appreciate the dare-devil attitude of our methodologicalfalsificationist [or perhaps as he would have said in an earlier phaseof his career, the conscientious Leninist]. He feels himself to be ahero who, faced with two catastrophic alternatives, dares to reflectcoolly on their relative merits and [to] choose the lesser evil.(FMSRP: 28)

If you admire the hero who has the courage to make the tough choicebetween two catastrophic alternatives, isn’t there a temptationto manufacture catastrophic alternatives so that you can heroicallychoose between them?

Late in 1944, following a Soviet victory, Lakatos returned toDebrecen, and changed his name from the Germanic JewishLipsitz to the Hungarian proletarianLakatos(meaning “locksmith”). He became active in the now legalCommunist Party and in two leftist youth and student organizations,the Hungarian Democratic Youth Federation (MADISZ) and the DebrecenUniversity Circle (DEK). As one of the leaders of the DEK, Lakatosagitated for the dismissal of reactionary professors from Debrecen andthe exclusion of reactionary students.

We are aware that this move on our part is incompatible with thetraditional and often voiced “autonomy” of the university[Lakatos stated], but respect for autonomy, in our view, cannot meanthat we have to tolerate the strengthening of fascism and reaction(Bandy 2009: 59 and 61).

Lakatos moved to Budapest in 1946. He became a graduate student atBudapest University, but spent much of his time working towards thecommunist takeover of Hungary. This was a slow-motion affair,characterized by the infamous “salami tactics” of theCommunist leader Mátyás Rákosi. Lakatos workedchiefly in the Ministry of Education, evaluating the credentials ofuniversity teachers and making lists of those who should be dismissedas untrustworthy once the communists had taken over (Bandy 2009: ch.8). He was also a student at Eötvös College, but attacked itpublicly as an elitist and bourgeois institution. The College, andothers like it, was closed in 1950 after the communist takeover. In1947 Lakatos gained his doctorate from Debrecen University for athesis entitled “On the Sociology of Concept Formation in theNatural Sciences”. In 1948, after the communist takeover wassubstantially complete, he gained a scholarship to undertake furtherstudy in Moscow.

Lakatos flew to Moscow in January 1949, only to be recalled for“un-Party-like” behaviour in July. What these“un-party-like” activities were is something of a mysterybut even more of a mystery is why, having returned from Moscow under acloud, he seemed so cool, calm and collected. Lakatos’sbiographers, Long and Bandy, speculate that he was being held inreserve to prepare a case against the communist education chief,József Révai, who was scheduled to appear in a new showtrial. But when Rákosi decided not to prosecute Révaiafter all, Lakatos was thrown to the wolves (Bandy 2009: ch. 12; Long2002). He was arrested in April 1950 on charges of revisionism and,after a period in the cellars of the secret police (including, ofcourse, torture), he was condemned to the prison camp at Recsk.

However Lakatos was probably doomed anyway. In later life Lakatos wasbig admirer of Orwell’sNineteen Eighty-Four. Perhapshe recognized himself in Orwell’s description of the Partyintellectual (and expert on Newspeak) Syme:

Unquestionably Syme will be vaporized, Winston thought again. Hethought it with a kind of sadness, although well knowing thatSyme…was fully capable of denouncing him as a thought-criminalif he saw any reason for doing so. There was something subtly wrongwith Syme. There was something that he lacked: discretion, aloofness,a sort of saving stupidity. You could not say that he was unorthodox.He believed in the principles of Ingsoc, he venerated Big Brother, herejoiced over victories, he hated heretics…. Yet a faint air ofdisreputability always clung to him. He said things that would havebeen better unsaid, he had read too many books…. (Orwell 2008[1949]: 58)

An instance of Lakatos’s Syme-like behaviour is his 1947denunciation of the literary critic and philosopher GyörgyLukács, one of the intellectual luminaries of the communistmovement. Lukács represented the academically respectable faceof communism, and favoured a gradual and democratic transition to thedictatorship of the proletariat. Lakatos organized an“anti-Lukács meeting…held under the aegis of theValóság Circle” to critique Lukács’sfoot-dragging and “Weimarism” (Bandy 2009: 110). Once theregime was firmly in control, Lukács was indeed censured forhis undue concessions to bourgeois democracy, and he spent the earlyfifties under a cloud. But in 1947, Lakatos’s criticisms weredeemed premature and he got into trouble because of his un-Party-likeactivities. (Lukács himself referred to the episode as a“cliquishkaffe klatsch”.) In Communist Hungaryit was important not to be “one pamphlet behind” the Partyline (Bandy 2009: 92). Lakatos was the sort of over-zealous communistwho was sometimes a couple of pamphlets ahead.

After his release from Recsk in September 1953 (minus several teeth),Lakatos remained for a while, a loyal Stalinist. He eked out a livingin the Mathematics Institute of the Hungarian Academy of Science,reading, researching and translating (including a translation intoHungarian of George Pólya’sHow to Solve It).During this time he was informing on friends and colleagues to theÁVH, the Hungarian secret police, though he subsequentlyclaimed that he did not pass on anything incriminating (Long, 2002:290 ). It was whilst working at the Mathematics Institute that hefirst gained access to the works of Popper. Gradually he turnedagainst the Stalinist Marxism that had been his creed. He married (ashis second wife) Éva Pap and lived at her parents’ house(his father-in-law being the distinguished agronomist, Endre Pap). In1956 he joined the revisionist Petőfi Circle and delivered astirring speech on “On Rearing Scholars” which at leastburnt his bridges with Stalinism:

The very foundation of scholarly education is to foster in studentsand postgrads a respect for facts, for the necessity of thinkingprecisely, and to demand proof. Stalinism, however, branded this asbourgeois objectivism. Under the banner ofpartinost[Party-like] science and scholarship, we saw a vast experiment tocreate a science without facts, without proofs.

… a basic aspect of the rearing of scholars must be anendeavour to promote independent thought, individual judgment, and todevelop conscience and a sense of justice. Recent years have seen anentire ideological campaign against independent thinking and againstbelieving one’s own senses. This was the struggle againstempiricism [Laughter and applause] (Bandy 2009: 221. Bandy quotes thetranscripts which seem to differ slightly from the prepared text inthe Lakatos archives, reprinted in F&AM)

But Lakatos was not just explicitly repudiating Stalinism. He was alsoimplicitly criticizing another prominent member of the PetőfiCircle who had been a big influence on his first PhD, namelyGyörgy Lukács. (See Ropolyi 2002 for the early influence.)For Lukács’s work is pervaded by just the kind ofhostility towards empiricism and disdain for facts that Lakatos isdenouncing in his speech, as well as an arts-sider’s contemptfor the natural sciences, all of which would have been anathema to thelater Lakatos. Indeed Lukács was notorious for the view thatthat

even if the development of science had proved all Marx’sassertions to be false…we could accept this scientificcriticism without demur and still remain Marxists—as long as weadhered to the Marxist method

and that

the orthodox Marxist who realizes that…the time has come forthe expropriation of the exploiters, will respond to thevulgar-Marxist litany of “facts” which contradict thisprocess with the words of Fichte, one of the greatest of classicalGerman philosophers: “So much the worse for the facts”.(Lukács 2014 [1919]: ch. 3.)

Thus the Stalinist Lakatos of 1947 had explicitly denouncedLukács for not being Stalinist enough, but the revisionistLakatos of 1956 was implicitly denouncing Lukács for beingmethodologically too much of a Stalinist. For the later Lakatos, whatwas wrong with “orthodox Marxism” was chiefly that itsnovel factual predictions had been systematically falsified (see§3.2 below). But that was pretty much the complaint of early revisionistssuch as Bernstein (see Kolakowski 1978: ch. 4) and it was against thatkind of revisionism that Lukács’s Bolshevik writings werea protest. (See Lukács 1971 [1923] and 2014 [1919].) Thoughfactual “refutations” of a research programme are notalways decisive, a Lukács-like indifference to the facts is,for Lakatos, the mark of a fundamentally unscientific attitude. In ouropinion, this puts paid to Ropolyi’s claim that Lukácscontinued to be a major influence on the later Lakatos.

Lakatos left Hungary in November 1956 after the Soviet Union crushedthe short-lived Hungarian revolution. He walked across the border intoAustria with his wife and her parents. Within two months he was atKing’s College Cambridge, with a Rockefeller Fellowship to writea PhD under the supervision of R.B. Braithwaite, which he completed in1959 under the title “Essays in the Logic of MathematicalDiscovery”. If we set aside his romantic adventures, the storyof Lakatos’s life thereafter is largely the story of his work,though we should not forget his activities as an academic politician.Even his friendship with Feyerabend and his friendship and subsequentbust-up with Popper were very much work-related. In Britain hisacademic career was meteoric. In 1960 he was appointed AssistantLecturer in Karl Popper’s department at the London School ofEconomics. By 1969 he was Professor of Logic, with a worldwidereputation as a philosopher of science. During the student revolts ofthe 1960s, which in Britain were centred on the LSE, Lakatos became anestablishment figure. He wrote a “Letter to the Director of theLondon School of Economics” defending academic freedom andacademic autonomy, which was widely circulated. It denounces thestudent radicals for allegedly trying to do what he himself had doneat Debrecen and Eötvös (though he was careful to conceal theparallel, citing Nazi and Muscovite precedents instead) (LTD:247).

Lakatos died suddenly in 1974 of a heart attack at the height of hispowers. He was 51.

2. Lakatos’s Big Ideas

Imre Lakatos has two chief claims to fame.

2.1 Against Formalism in Mathematics

The first is his Philosophy of Mathematics, especially as set forth in“Proofs and Refutations” (1963–64) a series of fourarticles, based on his PhD thesis, and written in the form of amany-sided dialogue. These were subsequently combined in a posthumousbook and published, with additions, in 1976. The title is an allusionto a famous paper of Popper’s, “Conjectures andRefutations” (the signature essay of his best-known collection),in which Popper outlines his philosophy of science. Lakatos’spoint is that the development of mathematics is much more like thedevelopment of science as portrayed by Popper than is commonlysupposed, and indeed much more like the development of science asportrayed by Popper thanPopper himself supposed.

What Lakatos does not make so much of (though he does not conceal iteither) is that in his view the development of mathematics is alsomuch more like the development of thoughtin general asanalysed by Hegel thanHegel himself supposed. There isthesis, antithesis and synthesis, “Hegelian language, which[Lakatos thinks would] generally be capable of describing the variousdevelopments in mathematics” (P&R: 146). Thus there is acertain sense in which Lakatos out-Hegels Hegel, giving a dialecticalanalysis of a discipline (mathematics) that Hegel himself despised asinsufficiently dialectical (see Larvor 1998, 1999, 2001). HenceFeyerabend’s gibe (which Lakatos took in good part) that Lakatoswas a Pop-Hegelian, the bastard child of Popperian father and aHegelian mother (F&AM: 184–185).

Proofs and Refutations is a critique of“formalist” philosophies of mathematics (includingformalism proper, logicism and intuitionism), which, inLakatos’s view, radically misrepresent the nature of mathematicsas an intellectual enterprise. For Lakatos, the development ofmathematics should not be construed as series of Euclidean deductionswhere the contents of the relevant concepts has been carefullyspecified in advance so as to preclude equivocation. Rather, thesewater-tight deductions from well-defined premises are the (perhapstemporary)end-points of an evolutionary, and indeed adialectical, process in which the constituent concepts areinitially ill-defined, open-ended or ambiguous but become sharper andmore precise in the context of a protracted debate. The proofs arerefined in conjunction with the concepts (hence “proof-generatedconcepts”) whilst “refutations” in the form ofcounterexamples play a prominent part in the process. [One mightalmost say, paraphrasing Hegel, that in Lakatos’s view“when Euclidean demonstrations paint their grey in grey, thenhas a shape of mathematical life grown old…The owl of theformalist Minerva begins its flight only with the falling ofdusk” (Hegel 2008 [1820/21]: 16).]

Lakatos is also keen to display the development of mathematics as arational affair even though the proofs (to begin with) areoften lacking in logical rigour and the key concepts are oftenopen-ended and unclear

The idea—expressed so clearly by Seidel [and clearly endorsed byLakatos himself]—that a proof can be respectable without beingflawless, was a revolutionary one in 1847, and, unfortunately, stillsounds revolutionary today. (P&R: 139)

A corollary of this is that in mathematics many of the“proofs” are not really proofs in the full sense of theword (that is, demonstrations that proceed deductively from apodicticpremises via unquestionable rules of inference to certain conclusions)and that many of the “refutations” are not reallyrefutations either, since something rather like the“refuted” thesis often survives the refutation and arisesrefreshed and invigorated from the dialectical process.

This becomes apparent early on in the dialogue, when the PopperianGamma protests at the Teacher’s insouciance with respect torefutation, a counterexample to Euler’s thesis (and therefore toCauchy’s proof) that, for all regular polyhedra, the number ofvertices, minus the number of edges, plus the number of faces equalstwo. The counterexample is a solid bounded by a pair of nested cubes,one of which is inside, but does not touch the other:

For this hollow cube, \(V - E + F\) (including both the inner and theouter ones) \(= 4\). According to Gamma, this simply refutesEuler’s conjecture and disproves Cauchy’s proof:

GAMMA: Sir, your composure baffles me. A single counterexample refutesa conjecture as effectively as ten. The conjecture and its proof havecompletely misfired. Hands up! You have to surrender. Scrap the falseconjecture, forget about it and try a radically new approach.

TEACHER: I agree with you that theconjecture has received asevere criticism by Alpha’s counterexample. But it is untruethat the proof has “completely misfired”. If, for the timebeing, you agree to my earlier proposal to use the word“proof” for a “thought-experiment which leads todecomposition of the original conjecture into subconjectures”,instead of using it in the sense of a “ guarantee of certaintruth”, you need not draw this conclusion. My proof certainlyproved Euler’s conjecture in the first sense, but notnecessarily in the second. You are interested only in proofs which“prove” what they have set out to prove. I am interestedin proofs even if they do not accomplish their intended task. Columbusdid not reach India but he discovered something quite interesting.

Thus even in his earlier work, when he is still a professed discipleof Popper, Lakatos is already a rather dissident Popperian. Firstly,there are the hat-tips to Hegelas well as to Popper thatcrop up from time to time inProofs and Refutations includingthe passage where he praises (and condemns) them both in the samebreath. (“Hegel and Popper represent the only fallibilisttraditions in modem philosophy, but even they both made the mistake ofreserving a privileged infallible status for mathematics”.P&R: 139n.1.) Given that Hegel was anathema to Popper (witness hisfamous or notorious anti-Hegel “scherzo” inThe OpenSociety and Its Enemies, (1945 [1966])) this strongly suggeststhat Lakatos took his Popper with a large pinch of salt. Secondly, forPopper himself a proof is a proof and a refutation is supposed to killa scientific conjecture stone-dead. Thus non-demonstrative proofs andnon-refuting refutations mark a major departure from Popperianorthodoxy.

2.2 Improving on Popper in the Philosophy of Science

The dissidence continues with Lakatos’s second majorcontribution to philosophy, his “Methodology of ScientificResearch Programmes” or MSRP (developed in detail in in hisFMSRP), a radical revision of Popper’s Demarcation Criterionbetween science and non-science, leading to a novel theory ofscientific rationality. This is arguably a lot more realistic than thePopperian theory it was designed to supplant (or, in earlierformulations, the Popperian theory that it was designed to amend). ForPopper, a theory is onlyscientific if is empiricallyfalsifiable, that is if it is possible to specify observationstatements which would prove it wrong. A theory isgoodscience, the sort of theory you should stick with (though not the sortof thing you should believe since Popper did not believe in belief),if it is refutable, risky, and problem-solving and has stood up tosuccessive attempts at refutation. It must be highly falsifiable,well-tested but (thus far) unfalsified.

Lakatos objects that although there is something to be said forPopper’s criterion, it is far too restrictive, since it wouldrule out too much of everyday scientific practice (not to mention thevalue-judgments of the scientific elite) as unscientific andirrational. For scientists often persist—and, it seems,rationally persist—with theories, such as Newtoniancelestial mechanics that by Popper’s standards they ought tohave rejected as “refuted”, that is theories that (inconjunction with other assumptions) have led to falsified predictions.A key example for Lakatos is the “Precession of Mercury”that is, the anomalous behaviour of the perihelion of Mercury, whichshifts around the Sun in a way that it ought not to do ifNewton’s mechanics were correct and there were no other sizablebody influencing its orbit. The problem is that there seems to be nosuch body. The difficulty was well known for decades but it did notcause astronomers to collectively give up on Newton untilEinstein’s theory came along. Lakatos thought that theastronomers were right not to abandon Newton even though Newtoneventually turned out to be wrong and Einstein turned out to beright.

Again, Copernican heliocentric astronomy was born“refuted” because of the apparent non-existence of stellarparallax. If the earth goes round the sun then the apparent positionof at leastsome of the fixed stars (namely the closest ones)ought to vary with respect to the more distant ones as the earth ismoving with respect to them. Some parts of the night sky should look alittle different at perihelion (when the earth is furthest from thesun) from the way that they look at aphelion (when the earth is at itsnearest to the sun, and hence at the other end of its orbit). But fornearly three centuries after the publication of Copernicus’De Revolutionibus 1543, no such differences were observed. Infact, there is a very slight difference in the apparent positions ofthe nearest stars depending on the earth’s position in itsorbit, but the difference is sovery slight as to be almostundetectable. Indeed it wascompletely undetectable until1838 when sufficiently powerful telescopes and measuring techniqueswere able to detect it, by which time the heliocentric view had longbeen regarded as an established fact. Thus astronomers had not givenup on either Copernicus or his successors despite this apparentfalsification.

But if scientists often persist with “refuted” theories,either the scientists are being unscientific or Popper is wrong aboutwhat constitutes good science, and hence about what scientists oughtto do. Lakatos’s idea is to construct a methodology of science,and with it a demarcation criterion, whose precepts are more inaccordance with scientific practice.

How does it work? Well, falsifiability continues to play a part inLakatos’s conception of science but its importance is somewhatdiminished. Instead of anindividual falsifiable theory whichought to be rejected as soon as it is refuted, we have asequence of falsifiable theories characterized by shared ahard core of central theses that are deemedirrefutable—or, at least, refutation-resistant—bymethodological fiat. This sequence of theories constitutes aresearch programme.

The shared hard core of this sequence of theories is oftenunfalsifiable intwo senses of the term.

Firstly scientists working within the programme are typically (andrightly) reluctant to give up on the claims that constitute the hardcore.

Secondly the hard core thesesby themselves are often devoidof empirical consequences. For example, Newtonian mechanicsbyitself—the three laws of mechanics and the law ofgravitation—won’t tell you what you will see in the nightsky. To derive empirical predictions from Newtonian mechanics you needa whole host ofauxiliary hypotheses about the positions,masses and relative velocities of the heavenly bodies, including theearth. (This is related to Duhem’s thesis that, generallyspeaking, theoretical propositions—and indeedsets oftheoretical propositions—cannot be conclusively falsified byexperimental observations, since they only entailobservation-statements in conjunction with auxiliary hypotheses. Sowhen something goes wrong, and the observation statements that theyentail turn out to be false, we havetwo intellectualoptions: modify the theoretical propositions or modify the auxiliaryhypotheses. See Ariew 2014.) For Lakatos an individual theory within aresearch programme typically consists of two components: the (more orless) irrefutable hard core plus a set of auxiliary hypotheses.Together with the hard core these auxiliary hypotheses entailempirical predictions, thus making the theory as a whole—hardcore plus auxiliary hypotheses—a falsifiable affair.

What happens when refutation strikes, that is when the hard core inconjunction with the auxiliary hypotheses entails empiricalpredictions which turn out to be false? What we have essentially is amodus tollens argument in which science supplies one of thepremises and nature (plus experiment and observation) supplies theother:

But logic leaves us with a choice. Theconjunction of thehard core plus the auxiliary hypotheses has to go, but we can retaineither the hard core or the auxiliary hypotheses. What Lakatos callsthe negative heuristic of the research programme, bids usretain the hard core but modify the auxiliary hypotheses:

The negative heuristic of the programme forbids us to direct themodus tollens at this “hard core”. Instead, wemust use our ingenuity to articulate or even invent “auxiliaryhypotheses”, which form a protective belt around this core, andwe must redirect themodus tollens to these. It is thisprotective belt of auxiliary hypotheses which has to bear thebrunt of tests and gets adjusted and re-adjusted, or even completelyreplaced, to defend the thus-hardened core. (FMSRP: 48)

Thus when refutation strikes, the scientist constructs anewtheory, the next in the sequence, with the same hard core but amodified set of auxiliary hypotheses. How is she supposed to do this?Well, associated with the hard core, there is what Lakatos calls thepositive heuristic of the programme.

The positive heuristic consists of a partially articulated set ofsuggestions or hints on how to change, develop the “refutablevariants” of the research programme, how to modify,sophisticate, the “refutable” protective belt. (FMSRP:50)

For example, if a planet is not moving in quite the smooth ellipsethat it ought to follow a) if Newtonian mechanics were correct and b)if there were nothing but the sun and the planet itself to worryabout, then the positive heuristic of the Newtonian programme bids uslook foranother heavenly body whose gravitational forcemight be distorting the first planet’s orbit. Alternatively, ifstellar parallax is not observed, we can try to refute this apparentrefutation by refining our instruments and making more carefulmeasurements and observations.

Lakatos evidently thinks that when one theory in the sequence has beenrefuted, scientists can legitimately persist with the hard corewithout being in too much of a hurry to construct the next refutabletheory in the sequence. The fact that some planetary orbits are notquite what they ought to be should not lead us to abandon Newtoniancelestial mechanics, even if we don’t yet have a testable theoryabout what exactly is distorting them. It is worth remarking too thatthe auxiliary hypotheses play a rather paradoxical part inLakatos’s methodology. On the one hand, theyconnectthe central theses of the hard core with experience, allowing to themto figure in testable, and hence, refutable theories. On the otherhand, theyinsulate the theses of the hard core fromrefutation, since when the arrow ofmodus tollens strikes, wedirect it at the auxiliary hypotheses rather than the hard core.

So far we have had an account of what scientists typicallydodo and what Lakatos thinks that theyought to do. But whatabout the Demarcation Criterion between science and non-science orbetween good science and bad? Even if it issometimesrational to persist with the hard core of a theory when the hard coreplus some set of auxiliary hypotheses has been refuted, there mustsurely besome circumstances in which is it rational to giveit up! The Methodology of Scientific Research Programme has got to besomething more than a defence of scientific pig-headedness! As Lakatoshimself puts the point:

Now, Newton’s theory of gravitation, Einstein’s relativitytheory, quantum mechanics, Marxism, Freudianism [the last two stockexamples of bad science or pseudo-science for Popperians], are allresearch programmes, each with a characteristic hard core stubbornlydefended, each with its more flexible protective belt and each withits elaborate problem-solving machinery. Each of them, at any stage ofits development, has unsolved problems and undigested anomalies. Alltheories, in this sense, are born refuted and die refuted. But arethey [all] equally good? (S&P: 4–5.)

Lakatos, of course, thinks not. Some science is objectively betterthan other science and some science is so unscientific as to hardlyqualify as science at all. So how does he distinguish between “ascientific or progressive programme” and a“pseudoscientific or degenerating one”? (S&P:4–5.)

To begin with, the unit of scientific evaluation is no longer theindividual theory (as with Popper), but thesequence oftheories, theresearch programme. We don’t askourselves whether this or that theory is scientific or not, or whetherit constitutes good or bad science. Rather we ask ourselves whetherthesequence of theories, the research programme, isscientific or non-scientific or constitutes good or bad science.Lakatos’s basic idea is that a research programme constitutesgood science—the sort of science it is rational tostick with and rational to work on—if it isprogressive, andbad science—the kind ofscience that is, at least, intellectuallysuspect—if itisdegenerating. What is it for a research programme to beprogressive? It must meet two conditions. Firstly it must betheoretically progressive. That is, each new theory in thesequence must have excess empirical content over its predecessor; itmust predict novel and hitherto unexpected facts (FMSRP: 33). Secondlyit must beempirically progressive. Some of that novelcontent has to be corroborated, that is,some of the new“facts” that the theory predicts must turn out to be true.As Lakatos himself put the point, a research programme “isprogressive if it is both theoretically and empiricallyprogressive, anddegenerating if it is not” (FMSRP:34). Thus a research programme is degenerating if the successivetheories do not deliver novel predictions or if the novel predictionsthat they deliver turn out to be false.

Novelty is, in part, a comparative notion. The novelty of a researchprogramme’s predictions is defined with respect to its rivals. Aprediction isnovel if the theory not only predicts somethingnot predicted by the previous theories in the sequence, butif the predicted observation is predictedneither by anyrival programme that might be in the offingnor by theconventional wisdom. A programme gets no brownie points by predictingwhat everyone knows to be the case but only by predicting observationswhich come as some sort of a surprise. (There is some ambiguity hereand some softening later on—see below§3.6—but to begin with, at least, this was Lakatos’s dominant idea.)

One of Lakatos’s key examples is the predicted return ofHalley’s comet which was derived by observing part of itstrajectory and using Newtonian mechanics to calculate the elongatedellipse in which it was moving. The comet duly turned up seventy-twoyears later, exactly where and when Halley had predicted, a novel factthat could not have been arrived at without the aid of Newton’stheory (S&P: 5). Before Newton, astronomers might have noticed acomet arriving every seventy-two years (though they would have beenhard put to it to distinguish that particular comet from any others),but they could not have been as exact about the time and place of itsreappearance as Halley managed to be. Newton’s theory deliveredfar more precise predictions than the rival heliocentric theorydeveloped by Descartes, let alone the earth-centered Ptolemaiccosmology that had ruled the intellectual roost for centuries.That’s the kind of spectacular corroboration that propels aresearch programme into the lead. And it was a similarly novelprediction, spectacularly confirmed, that dethroned Newton’sphysics in favour of Einstein’s. Here’s Lakatos again:

This programme made the stunning prediction that if one measures thedistance between two stars in the night and if one measures thedistance between them during the day (when they are visible during aneclipse of the sun), the two measurements will be different. Nobodyhad thought to make such an observation before Einstein’sprogramme. Thus, in progressive research programme, theory leads tothe discovery of hitherto unknown novel facts. (S&P: 5.)

A degenerating research programme, on the other hand (unlike thetheories of Newton and Einstein) either fails to predict novel factsat all, or makes novel predictions that are systematically falsified.Marxism, for example, started out as theoretically progressive butempirically degenerate (novel predictions systematically falsified)and ended up as theoretically degenerate as well (no more novelpredictions but a desperate attempt to explain away unpredicted“observations” after the event).

Has…Marxism ever predicted a stunning novel fact successfully?Never! It has some famous unsuccessful predictions. It predicted theabsolute impoverishment of the working class. It predicted that thefirst socialist revolution would take place in the industrially mostdeveloped society. It predicted that socialist societies would be freeof revolutions. It predicted that there will be no conflict ofinterests between socialist countries. Thus the early predictions ofMarxism were bold and stunning but they failed. Marxists explained alltheir failures: they explained the rising living standards of theworking class by devising a theory of imperialism; they even explainedwhy the first socialist revolution occurred in industrially backwardRussia. They “explained” Berlin 1953, Budapest 1956,Prague 1968. They “explained” the Russian-Chineseconflict. But their auxiliary hypotheses were all cooked up after theevent to protect Marxian theory from the facts. The Newtonianprogramme led to novel facts; the Marxian lagged behind the facts andhas been running fast to catch up with them. (S&P: 4–5.)

Thus good science is progressive and bad science is degenerating and aresearch programme may either begin or end up as such a degenerateaffair that it ceases to count as science at all. If a researchprogramme either predicts nothing new or entails novel predictionsthat never come to pass, then it may have reached such a pitch ofdegeneration that it has transformed into a pseudoscience.

It is sometimes suggested that in Lakatos’s opinion no theoryeither is or ought to be abandoned, unless there is a better one inexistence (Hacking 1983: 113). Does this mean that no researchprogramme should be given up in the absence of a progressivealternative,no matter how degenerate it may be? If so, thisamounts to the radically anti-sceptical thesis that it is better tosubscribe to a theory that bears all the hallmarks of falsehood, suchas the current representative of a truly degenerate programme, than tosit down in undeluded ignorance. (The ancient sceptics, by contrastthought that it is better not to believeanything at allrather than believe something thatmight be false.) We arenot sure that this was Lakatos’ opinion, though he clearlythinks it a mistake to give up on aprogressive researchprogramme, unless there is a better one to shift to. But consideragain the case of Marxism. What Lakatos seems to be suggesting in thepassage quoted above, is that it is rationallypermissible—perhaps even obligatory—to give up on Marxismeven if it hasno progressive rival, that is, if there iscurrentlyno alternative research programme with a set ofhard core theses about the fundamental character of capitalism and itsultimate fate. (After all, the later Lakatos probably subscribed tothe Popperian thesis that history in the large is systematicallyunpredictable. In which case therecould not be a genuinelyprogressive programme which foretold the fate of capitalism. At bestyou could have a conditional theory, such as Piketty’s, whichsays that under capitalism, inequality is likely togrow—unless something unexpected happens orunless we decide to do something about it. See Piketty 2014:35.) So although Lakatos thinks that the scientific community seldomgives up on a programme until something better comes along, it is notclear that he thinks that this is what they alwaysought todo.

There are numerous departures from Popperian orthodoxy in all this. Tobegin with, Lakatos effectively abandons falsifiability as theDemarcation Criterion between science and non-science. A researchprogramme can be falsifiable (in some senses) but unscientific andscientific but unfalsifiable. First, the falsifiable non-science.Every successive theory in a degenerating research programme can befalsifiable but the programme as whole may not be scientific. Thismight happen if it only predicted familiar facts or if its novelpredictions were never verified. A tired purveyor of old and boringtruths and/or a persistent predictor of novel falsehoods might fail tomake the scientific grade. Secondly, the non-falsifiable science. InLakatos’s opinion, it need not be a crime to insulate thehard-core of your research programme from empirical refutation. ForPopper, it is a sin against science to defend a refuted theory by“introducingad hoc some auxiliary assumption, or byre-interpreting the theoryad hoc in such a way that itescapes refutation” (C&R, 48). Not so for Lakatos, thoughthis is not to say that when it comes to ad hocery “anythinggoes”.

Thirdly, Lakatos’s Demarcation Criterion is a lot more forgivingthan Popper’s. For a start, aninconsistent researchprogramme need not be condemned to the outer darkness as hopelesslyunscientific. This is not because any of its constituent theoriesmight betrue. Lakatos rejects the Hegelian thesis that thereare contradictions in reality. “If science aims at truth, itmust aim at consistency; if it resigns consistency, it resignstruth.” But though science aims at truth andthereforeat consistency, this does not mean that it can’t put up with alittle inconsistency along the way.

The discovery of an inconsistency—or of an anomaly—[neednot] immediately stop the development of a programme: it may berational to put the inconsistency into some temporary,ad hocquarantine, and carry on with the positive heuristic of the programme(FMSRP: 58).

Thus it was both rationaland scientific for Bohr to persistwith his research programme, even though its hard core theses on thestructure of the atom were fundamentally inconsistent (FMSRP:55–58). So although Lakatos rejects Hegel’s claim thatthere are contradictions in reality (though not, perhaps in Reality),healso rejects Popper’s thesis that becausecontradictions imply everything, inconsistent theories exclude nothingand must therefore be rejected as unfalsifiable and unscientific. ForLakatos, Bohr’s theory of the atom is fundamentallyinconsistent, but this does not mean that it implies that the moon ismade of green cheese. Thus what Lakatos seems to be suggesting is here(though he is not as explicit as he might be) is that, when it comesto assessing scientific research programmes, we should sometimesemploy a contradiction-tolerant logic; that is a logic that rejectsthe principle, explicitly endorsed by Popper, that anything whateverfollows from a contradiction (FMSRP: 58 n. 2). In today’sterminology, Lakatos is a paraconsistentist (since he implicitlydenies that from a contradiction anything follows) butnot adialetheist (since he explicitly denies that there are truecontradictions). Thus he is neither a follower of Popper with respectto theories nor a follower of Hegel with respect to reality. (SeePriest 2006 and 2002, especially ch. 7, and Brown and Priest2015.)

There is another respect in which Lakatos’s DemarcationCriterion is more forgiving than Popper’s. For Popper, if atheory is not falsifiable, then it’s not scientific andthat’s that. It’s an either/or affair. For Lakatos beingscientific is a matter of more or less, and the more the less can varyover time. Aresearch programme can be scientific at onestage, less scientific (or non-scientific) at another (if it ceases togenerate novel predictions and cannot digest its anomalies) but cansubsequently stage a comeback, recovering its scientific status. Thusthe deliverances of the Criterion are matters of degree, and they arematters of degree that can vary from one time to another. We canseldom say absolutely that a research programme is not scientific. Wecan only say that it is not looking very scientifically healthyright now, and that the prospects for a recovery do not lookgood. Thus Lakatos is much more of a fallibilist than Popper. ForPopper, we can tell whether a theory is scientific or not byinvestigating its logical implications. For Lakatos our best guessesmight turn out to be mistaken, since the scientific status of aresearch programme is determined, in part, by its history, not just byits logical character, and history, as Popper himself proclaimed, isessentially unpredictable.

There is another divergence from Popper which helps to explain theabove. Lakatos collapses two of Popper’s distinctions into one;the distinction between science and non-science and the distinctionbetween good science and bad. As Lakatos himself put the point in hislectures at the LSE:

The demarcation problem may be formulated in the following terms: whatdistinguishes science from pseudoscience? This is an extreme way ofputting it, since the more general problem, called the GeneralizedDemarcation Problem, is really the problem of the appraisal ofscientific theories, and attempts to answer the question: when is onetheory better than another? We are, naturally, assuming a continuousscale whereby the value zero corresponds to a pseudo-scientific theoryand positive values to theories considered scientific in a higher orlesser degree. (F&AM: 20)

Apart from the fact that, for Lakatos, a) it can be rational topersist with a “falsified” theory, and indeed with theorythat is actually inconsistent—both anathema to Popper—andthat b) that for Lakatos “all theories are born refuted and dierefuted” (S&P: 5) so that there areno unrefutedconjectures for the virtuous scientist to stick with (thus making whatPopper would regard as good science practically impossible),Lakatos’s methodology of scientific research programmes replacestwo of Popper’s criteria with one. For Popper hasone criterion to distinguish science from non-science (orscience from pseudoscience if it is a theory with scientificpretensions) andanother to distinguish good science from badscience. In Popper’s view, a theory is scientific if it isempirically falsifiable and non-scientific if it is not. Beingscientific or not is an absolute affair, a matter of either/or, sincea theory is scientific so long as there aresome observationsthat would falsify it. Beinggood science is a matter ofdegree, since a theory may give more or less hostages to empiricalfortune, depending on the boldness of its empirical predictions. ForLakatos on the other hand, non-science or pseudo-science is at one endof a continuum with the best science at the other end of the scale.Thus a theory—or better, a research programme—can startout as genuinely scientific, gradually becoming less so over thecourse of time (which was Lakatos’s view of Marxism) withoutaltogether giving up the scientific ghost. Was the Marxism ofLakatos’s day bad science or pseudo-science? From Lakatos’point of view, the question does not have a determinate answer, thepoint being that it isn’tgood science since itrepresents a degenerating research programme. But although Lakatosevidently considered Marxism to be in bad way, he could not consign itto the dustbin of history as definitively finished, since (as he ofteninsisted) degenerating research programmes can sometimes stage acomeback.

3. Works

3.1Proofs and Refutations (1963–4, 1976)

As we have seen, Lakatos’s first major publication in Britainwas the dialogue “Proofs and Refutations” which originallyappeared as a series of four journal articles. The dialogue isdedicated to George Pólya for his “revival ofmathematical heuristic” and to Karl Popper for his criticalphilosophy.

Proofs and Refutations is a highly original production. Theissues it discusses are far removed from what was then standard farein the philosophy of mathematics, dominated by logicism, formalism andintuitionism, all attempting to find secure foundations formathematics. Its theses are radical. And its dialogue form makes it aliterary as well as a philosophicaltour de force.

Its official target is “formalism” or“metamathematics”. But (as we have noted)“formalism” doesn’t just mean“formalism” proper, as this term is usually understood inthe Philosophy of Mathematics. For Lakatos “formalism”includes not just Hilbert’s programme but also logicism and evenintuitionism. Formalism sees mathematics as the derivation of theoremsfrom axioms in formalised mathematical theories. The philosophicalproject is to show that the axioms are true and the proofs valid, sothat mathematics can be seen as the accumulation of eternal truths. Anadditional philosophical question is what these truths areabout, the question of mathematical ontology.

Lakatos, by contrast, was interested in thegrowth ofmathematical knowledge. How were the axioms and the proofs discovered?How does mathematics grow from informal conjectures and proofs intomore formal proofs from axioms? Logical empiricist (and Popperian)orthodoxy distinguished the “context of discovery” fromthe “context of justification”, consigned the former tothe realm of empirical psychology, and thought it a matter of“unregimented insight and good fortune”, hardly a fitsubject for philosophical analysis. Philosophy of mathematics consistsof the logical analysis of completed theories. Formalism manifeststhis orthodoxy and “disconnects the history of mathematics fromthe philosophy of mathematics” (P&R: 1). Against theorthodoxy, Lakatos paraphrased Kant (the paraphrase has become almostas famous as the original):

the history of mathematics…has becomeblind, while thephilosophy of mathematics… has becomeempty. (P&R:2)

[Lakatos had stated this Kantian aphorism more generally at aconference in Oxford in 1961: “History of science withoutphilosophy of science is blind. Philosophy of science without historyof science is empty”. See Hanson 1963: 458.]

Suppose we agree with Lakatos that there is room for heuristics or alogic or discovery. Still, orthodoxy could insist that discovery isone thing, justification another, and that the genesis of ideas hasnothing to do with their justification. Lakatos, more radically,disputed this. First, he rejected the foundationalist orjustificationist project altogether: mathematics has no foundation inlogic, or set theory, or anything else. Second, he insisted that theway in which a theory grows plays an essential role in itsmethodological appraisal. This is as much a central theme of hisphilosophy of empirical science as it is of his philosophy ofmathematics.

As noted above,Proofs and Refutations takes the form of animaginary dialogue between a teacher and a group of students. Itreconstructs the history of attempts to prove the Descartes-Eulerconjecture about polyhedra, namely, that for all polyhedra, the numberof verticesminus the number of edgesplus thenumber of faces is two (V –E + F =2). Theteacher presents an informal proof of this conjecture, due to Cauchy.This is a “thought experiment which suggest a decompositionof the original conjecture into subconjectures or lemmas”from which the original conjecture is supposed to follow. We now have,as well as the original conjecture or conclusion, the subconjecturesor premises, and the meta-conjecture that the latter entail theformer. Clearly, this kind of “informal proof” is quitedifferent from the “formalist” idea that an informal proofis a formal proof with gaps (PP2: 63). Equally clearly, any of theseconjectures might be refuted by counterexamples.

In the dialogue, the students, who are rather advanced, demonstratethe point—they demolish the Teacher’s “proof”by producing counterexamples. The counterexamples are of threekinds:

(1) Counterexamples to the conclusion that are not alsocounterexamples to any of the premises (“global but not localcounterexamples”): These establish that the conclusion does notreally follow from the stated premises. They require us to improve theproof, to unearth the “hidden lemma” which thecounterexample also refutes, so that it becomes a “local as wellas global” counterexample—see (3), below.

(2) Counterexamples to one of the premises that are not alsocounterexamples to the conclusion (“local but not globalcounterexamples”): These require us to improve the proof byreplacing the refuted premise with a new premise which is not subjectto the counterexample and which (we hope) will do as much to establishthe conclusion as the original refuted premise did.

(3) Counterexamples both to the conclusion and to (at least one of)the premises (“global and local counterexamples”): Thesecan be dealt with by incorporating the refuted premise or lemma intothe original conclusion, as a condition of its correctness. Forexample, a picture-frame is a polyhedron with a hole or tunnel init:

So if we define a polyhedron as “normal” if it has noholes or tunnels in it, we can restrict the original conjecture to“normal” polyhedra and avoid this refutation. The troublewith this method is that it reduces the content of the originalconjecture, and an empty tautology threatens—“For allEulerian polyhedra (polyhedra for which \(V - E + F = 2\)V–E + F =2),V –E + F =2\(V - E +F = 2\)”. More particularly, a blanket exclusion of polyhedrawith holes or tunnels rules out some polyhedra for which \(V - E + F =2\),despite the presence of a hole—a cube with asquare hole drilled through it and two ring-shaped faces being anexample – the formulaV –E + F =2 holdsgood. This suggests a deeper problem than finding the domain ofvalidity of the original conjecture—finding a generalrelationship betweenV,E andF for all polyhedrawhatsoever.

We see from this analysis what Lakatos calls the “dialecticalunity of proofs and refutations”. Counterexamples help us toimprove our proof by finding hidden lemmas. And proofs help us improveour conjecture by finding conditions on its validity. Either way, orboth ways, mathematical knowledge grows. And as it grows, its conceptsare refined. We begin with a vague, unarticulated notion of what apolyhedron is. We have a conjecture about polyhedra and an informalproof of it. Counterexamples or refutations “stretch” ouroriginal concept: is a picture frame a genuine polyhedron, or acylinder, or two polyhedra joined along a single edge?

Attempts to rescue our conjecture from refutation yield“proof-generated definitions” like that of a “normalpolyhedron”.

Is there any limit to this process of“concept-stretching”, or any distinction to be drawnbetween interesting and frivolous concept-stretching? Can this processyield, not fallible conjectures and proofs, but certainty?Lakatos’s editors distinguish the certainty of proofs from thecertainty of the axioms from which all proofs must proceed. They claimthat rigorous proof-procedures have been attained, and that“There is no serious sense in which such proofs arefallible” (P&R: 57). Quite so. But only because we havedecided not to “stretch” the logical concepts that liebehind those rigorous and formalizable proof-procedures. A rigorousproof in classical logic may not be valid in intuitionistic orparaconsistent logics. And the key point is that a proof, howeverrigorous, only establishes thatif the axioms are true,then so is the theorem. If the axioms themselves remainfallible, then so do the theorems rigorously derived from them.Providing foundations for mathematics requires the axioms to be madecertain, by deriving them from logic or set theory or something else.Lakatos claimed that this foundational project had collapsed (seebelow,§3.2).

To what extent is this imaginary dialogue a contribution to thehistory of mathematics? Lakatos explained that

The dialogue form should reflect the dialectic of the story: it ismeant to contain a sort ofrationally reconstructed or“distilled” history. The real history will chime in in thefootnotes, most of which are to be taken, therefore, as an organicpart of the essay (P&R: 5).

This device, first necessitated by the dialogue form, became apervasive theme of Lakatos’s writings. It was to attract muchcriticism, most of it centred around the question whether rationallyreconstructed history was real history at all. The trouble is that therational and the real can come apart quite radically. At one point inProofs and Refutations a character in the dialogue makes ahistorical claim which, according to the relevant footnote, is false.Lakatos says that the statement

although heuristically correct (i.e. true in a rationalhistory of mathematics) is historically false. This should not worryus: actual history is frequently a caricature of its rationalreconstructions. (P&R: 21)

On occasions, Lakatos’s sense of humour ran away with him, aswhen the text contains a made-up quotation from Galileo, and thefootnote says that he “was unable to trace this quotation”(P&R: 62). (Though this does rather smack of his youthful habit ofwinning arguments with “bourgeois” students by fabricatingon-the-spot quotations from the authorities they respected. See Bandy2009: 122.) Horrified critics protested that rationally reconstructedhistory is a caricature of real history, not in fact real history atall but rather “philosophy fabricating examples”. Onecritic said that philosophers of science should not be allowed towrite history of science. This academic trade unionism is misguided.You do not falsify history by pointing out that what ought to havehappened did not, in fact, happen.

There is an important pedagogic point to all this, too. The dialecticof proofs and refutations can generate, in the ways explained above,quite complicated definitions of mathematical concepts, definitionsthat can only really be understood by considering the process thatgave rise to them. But mathematics teaching is not historical, or evenquasi-historical. (One sense in which Lakatos’s theory isdialectical: it represents a process as rational even though the termsof the debate are not clearly defined.) But students nowadays arepresented with the latest definitions at the outset, and required tolearn them and apply them, without ever really understanding them.

One question aboutProofs and Refutations is whether theheuristic patterns depicted in it apply to the whole of mathematics.While some aspects clearly are peculiar to the particular case-studyof polyhedra, the general patterns are not. Lakatos himself appliedthem in a second case-study, taken from the history of analysis in thenineteenth century (“Cauchy and the Continuum”,1978c).

3.2 “Regress” and “Renaissance”

The onslaught on formalism continues in a pair of papers“Infinite Regress and the Foundations of Mathematics”(1962) and “A Renaissance of Empiricism in the Recent Philosophyof Mathematics?” (1967a). Here Popper predominates and Hegelrecedes.Regress is a critique of both logicism andformalism proper (that is, Hilbert’s programme), concentratingprimarily on Russell. Russell sought to rescue mathematics from doubtand uncertainty by deriving the totality of mathematics fromself-evident logical axioms via stipulative definitions andwater-tight rules of inference. But the discovery of Russell’sParadox and the felt need to deal with the Liar and related paradoxesblew this ambition sky-high. For some of the axioms that Russell wasforced to posit—the Theory of Types which Lakatos sees, ineffect, as a monster-barring definition (elevated into an axiom) thatavoids the paradoxes by excluding self-referential propositions asmeaningless; the Axiom of Reducibility which is needed to relax theunduly restrictive Theory of Types; the Axiom of Infinity which positsan infinity of objects in order to ensure that every natural numberhas a successor; and the Axiom of Choice (which Russell refers to asthe multiplicative axiom)—were eithernot self-evident,not logical or both. Russell’s fall-back position wasto argue that mathematics was not justified by being derivable fromhis axioms but that his axioms were justified because the truths ofmathematics could be derived from them whilst avoidingcontradictions:

When pure mathematics is organized as a deductive system…itbecomes obvious that, if we are to believe in the truth of puremathematics, it cannot be solely because we believe in the truth ofthe set of premises. Some of the premises are much less obvious thansome of their consequences, and are believed chiefly because of theirconsequences. (Russell 2010 [1918]: 129)

As Lakatos amply documents inRenaissance, asurprising number of labourers in the foundationalistvinyard—Carnap and Quine, Fraenkel and Gödel, Mostowski andvon Neumann—were prepared to make similar noises. Lakatos dubsthis development “empiricism” (or“quasi-empiricism”) and hails it on the one hand whilstcondemning it on the other.

Why “empiricism”? Not because it revives Mill’s ideathat the truths of arithmetic are empirical generalizations, butbecause it ascribes to mathematics the same kind ofhypothetico-deductive structure that the empirical sciences supposedlydisplay, with axioms playing the part of theories and theirmathematical consequences playing the part of observation-statements(or in Lakatos’s terminology, “potentialfalsifiers”).

Why does Lakatos hail the “empiricism” that he alsocondemns? Because it means that mathematics has the same kindepistemic structure that science has according to Popper. It’s amatter of axiomatic conjectures that can be mathematically refuted.(The difference between science and mathematics consists in thedifferences between the potential falsifiers.)

Why does Lakatos condemn the “empiricism” that he alsocommends? Because Russell, like most of his supporters, succumbs tothe “inductivist” illusion that the axioms can beconfirmed by the truth of their consequences. In Lakatos’sopinion this is simply a mistake. Truth can trickle down from theaxioms to their consequences and falsity can flow upwards from theconsequences to the axioms (or at least to the axiom set). But neithertruth nor probability nor justified belief can flow up from theconsequences to the axioms from which they follow. Here Lakatosout-Poppers Popper, portraying not just science but even mathematicsas a collection of unsupported conjectures that can be refuted but notconfirmed, anything else being condemned as to“inductivism”. However the inductivism that Lakatosscornfully rejects inRenaissance is just the kind ofinductivism that he would be recommending to Popper just a few yearslater.

3.3 “Changes in the Problem of Inductive Logic” (1968)

In 1964 Lakatos turned from the history and philosophy of mathematicsto the history and philosophy of the empirical sciences. He organiseda famous International Colloquium in the Philosophy of Science, heldin London in 1965. Participants included Tarski, Quine, Carnap, Kuhn,and Popper. The Proceedings ran to four volumes (Lakatos (ed.) 1967& 1968, and Lakatos and Musgrave (eds.) 1968 & 1970). Lakatoshimself contributed three major papers to these proceedings. The firstof these (Renaissance) has been dealt with already.The second, “Changes in the Problem of Inductive Logic”(Changes), analyses the debate between Carnap andPopper regarding the relations between theory and evidence in science.It is remarkable both for its conclusions and for its methodology. Theconclusion, to put it bluntly, is that a certain brand of inductivismis bunk. The prospects for an inductive logic that allows you toderive scientific theories from sets of observation statements, thusproviding them with a weak or probabilistic justification, are dimindeed. There is no inductive logic according to which real-lifescientific theories can be inferred, “partially proved” or“confirmed (by facts) to a certain degree”’(Changes: 133). But Lakatos sought to prove his pointby analysing the Popper/Carnap debate and reversing the common verdictthat Carnap had won and that Popper had lost. And here he faced aproblem. As Fox (1981) explains:

The facts on which the verdict was based were that Popper’sclaimed refutations of Carnap all failed, through either fallacy ormisrepresentation, and that Carnap was a careful, precise, irenicthinker, in the habit of stating as his conclusions exactly what hispremises warranted. The standards on which the verdict was based werethe respectable professional ones by which we mark third-year essays.The verdict was: Carnap gets an A+, and Popper’s refusal towither away is a moral and intellectual embarrassment. (Fox 1981:94.)

Lakatos’s strategy was to accept the facts but reverse thevalue-judgment by developing the twin concepts of adegeneratingresearch programme and adegenerating problem-shift andapplying them to Carnap’s successive endeavours. ButCarnap’s programme was philosophico-mathematical rather thanscientific. So what was wrong with it could not be that it failed topredict novel facts or that its predictions were mostly falsified. Forit was not in the business of predicting empirical observationswhether novel or otherwise. (Indeed Lakatos’s concept of adegeneratingphilosophical programme seems to have precededhis concept of a degeneratingscientific programme.) So whatwas wrong with Carnap’s enterprise? In an effort to solve hisoriginal problem, Carnap had to solve a series of sub-problems. Somewere solved, others were not, generating sub-sub-problems of theirown. Some of these were solved, others were not, generatingsub-sub-sub-problems and sub-sub-sub-sub-problems etc. Since some ofthese sub-problems (or sub-sub-problems) were solved, the programmeappeared to its proponents be busy and progressive. But it wasdrifting further and further away from achieving its originalobjectives.

Now for Lakatos, such problem-shifts are not necessarily degenerating.If a programme ends up solving a problem that it did not set out tosolve, that is all fine and dandy so long as the problem that itsucceeds in solving is more interesting and important than the problemthat itdid set out to solve.

But one may solve problems less interesting than the original one;indeed, in extreme cases, one may end up solving (or trying to solve)no other problems but those which one has oneself created while tryingto solve the original problem. In such cases we may talk about adegenerating problem-shift. (Changes:128–9.)

Thus Carnap starts off with the exciting problem of showing howscientific theories can be partially confirmed by empirical facts andends up with technical papers about drawing different coloured ballsout of an urn. In Lakatos’s opinion this does not constituteintellectual progress. Carnap had lost the plot.

3.4 “Falsification and the Methodology of Scientific Research Programmes” (1970)

The best-known of Lakatos’s “Conference Proceedings”isCriticism and the Growth of Knowledge, which became aninternational best-seller. It contains Lakatos’s important paper“Falsification and the Methodology of Scientific ResearchProgrammes” (FMSRP) which we have discussed already. A brieferaccount of this methodology had already appeared (Lakatos 1968a), inwhich Lakatos distinguished dogmatic, naïve and sophisticatedfalsificationist positions, attributing them to“Popper₀, Popper₁ andPopper₂”—or as he otherwise put it,“proto-Popper, pseudo-Popper and proper-Popper”. (Popperdid not appreciate being disassembled into temporal or ideologicalparts and protested “I am not a Trinity”.)

Lakatos’s methodology has been seen, rightly, as an attempt toreconcile Popper’s falsificationism with the views of ThomasKuhn. Popper saw science as consisting of bold explanatoryconjectures, and dramatic refutations that led to new conjectures.Kuhn (and Polanyi before him) objected that

No process yet disclosed by the historical study of scientificdevelopment at all resembles the methodological stereotype offalsification by direct comparison with nature (Kuhn 1962: 77).

Instead, science consists of long periods of “normalscience”, paradigm-based research, where the task is to forcenature to fit the paradigm. When nature refuses to comply, this is notseen as a refutation, but rather as an anomaly. It casts doubt, not onthe ruling paradigm, but on the ingenuity of thescientists—“only the practitioner is blamed, not histools”. It is only in extraordinary periods of“revolutionary science” that anything like Popperianrefutations occur.

Lakatos proposed a middle-way, in which Kuhn’ssocio-psychological tools were replaced by logico-methodological ones.The basic unit of appraisal is not the isolated testable theory, butrather the “research programme” within which a series oftestable theories is generated. Each theory produced within a researchprogramme contains the same common or “hard core”assumptions, surrounded by a “protective belt” ofauxiliary hypotheses. When a particular theory is refuted, adherentsof a programme do not pin the blame on their hard-core assumptions,which they render “irrefutable by fiat”. Instead,criticism is directed at the hypotheses in the “protectivebelt” and they are modified to deal with the problem.Importantly, these modifications are not random—they are in thebest cases guided by the heuristic principles implicit in the“hard core” of the programme. A programme progressestheoretically if the new theory solves the anomaly faced by the oldand is independently testable, making new predictions. A programmeprogresses empirically if at least one of these new predictions isconfirmed.

Notice that a programme can make progress, both theoretically andempirically, even though every theory produced within it is refuted. Aprogramme degenerates if its successive theories are nottheoretically progressive (because it predicts no novelfacts), or notempirically progressive (because novelpredictions get refuted). Furthermore, and contrary to Kuhn’sidea that normally science is dominated by a single paradigm, Lakatosclaimed that the history of science typically consists ofcompeting research programmes. A scientific revolution occurswhen a degenerating programme is superseded by a progressive one. Itacquires hegemonic status though its rivals may persist as minorityreports.

Kuhn saw all this as vindicating his own view, albeit with differentterminology (Kuhn 1970: 256, 1977: 1). But this missed thesignificance of replacing Kuhn’s socio-psychologicaldescriptions with logico-methodological ones. It also missedLakatos’s claim that there are always competing programmes orparadigms. Hegemony is seldom as total as Kuhn seems to suggest.

3.5 “The History of Science and Its Rational Reconstructions” (1971)

As we have seen, inProofs and Refutations Lakatos hadalready joked that “actual history is frequently a caricature ofits rational reconstructions”. The use of theplural—“reconstructions”—isimportant. There is more than one way of rationally reconstructinghistory, and how you do it depends upon what you count as rational andwhat not—it depends, in short, in your theory of rationality.There is not one “rational history”—as Hegel mayhave thought—but several competing ones. And, in a remarkabledialectical turn, Lakatos proposed that one can evaluate competingtheories of rationality by asking how well they enable one toreconstruct the history of science (whether it be mathematics orempirical science). The thought is that if your philosophy of science,or theory of scientific rationality, deems most of “greatscience” irrational, then something is wrong with it.Contrariwise, the more of the history of “great science”your theory of rationality deems rational, the better that theoryis.

The obvious worry is that this meta-criterion for theories ofscientific rationality threatens to deprive the philosophy of scienceof any critical bite. Will not the best philosophy of science simplysay that whatever scientists do is rational, that scientific might isright, that the best methodology is Feyerabend’s “Anythinggoes”? Lakatos’s Kantian epigram “Philosophy ofscience without history of science is empty; history of sciencewithout philosophy of science is blind” threatens to eliminatethe philosophy of science altogether, in favour ofhistorical-sociological studies of the decisions of scientificcommunities. (One of us discusses this problem, and attempts to disarmthe worry, in Musgrave 1983.)

Another worry, which is perhaps less obvious, is that Lakatos seems tobe implicitly appealing to the kind of inductive principle that hescorns elsewhere. Isn’t he saying that a sequence of successesin the history of science displaying key episodes as rational tends toconfirm a theory of scientific rationality?

Lakatos himself was a master of philosophically inspired case-studiesof episodes in the history of science—Feyerabend said he hadturned this into an art form. His “Hegelian” idea that the“rationally reconstructed” history of thought has primacyis emphasised in two books, Larvor 1998 and Kadvany 2001. After hisdeath, a Colloquium was held in Nafplion, Greece, where case-studiesapplying Lakatos’s ideas to episodes from the history of boththe natural and social sciences were presented by his students andcolleagues. The Proceedings of this “Nafplion Colloquium”were subsequently published in two volumes—Howson (ed.) 1976 andLatsis (ed.) 1976. Further case-studies include Zahar 1973 and Urbach1974.

However, Urbach’s paper, which was written with Lakatos’sactive collaboration and encouragement (F&AM: 348–34),represents something of an “own goal” for the MSRP. Urbachargued that the environmentalist programme in IQ Studies, which triesto explain intergroup differences in tested intelligence as due toenvironmental causes, was a degenerating research programme. At leastit was degenerating when compared to its hereditarian rival which putsthese differences down to differences in hereditary endowments. Thetables were dramatically turned just thirteen years later with thediscovery of the Flynn effect (1987) which showed massive differencesin intergroup IQs which simplycould not be explained byhereditary differences. (The groups in question were geneticallyidentical, the higher scoring groups being the children or thegrandchildren of the lower scoring groups. See Flynn 1987 and 2009.)Thus the supposedly “degenerate” programme was propelledinto the lead. Of course the MSRPallows for such dramaticreversals of fortune, but it is at least a bit embarrassing if aprogramme damned as degenerate by both the Master and one of his chiefdisciples is spectacularly vindicated just thirteen years later.

3.6 “Popper on Demarcation and Induction” (1974)

“Popper on demarcation and induction” (PDI) was written in1970 for the Popper volume in theLibrary of LivingPhilosophers series (Schilpp (ed.) 1974). Sadly, it caused amajor falling out with Popper despite the generous praise in itsopening sections:

Popper’s ideas represent the most important development in thephilosophy of the twentieth century; an achievement in thetradition—and on the level—of Hume, Kant, or Whewell.… More than anyone else, he changed my life. I was nearly fortywhen I got into the magnetic field of his intellect. His philosophyhelped me to make a final break with the Hegelian outlook which I hadheld for nearly twenty years. (PDI: 139.)

Much of the paper is devoted to criticizing Popper’s demarcationcriterion and arguing for his own. Most of these criticisms have beencanvased already. Lakatos argues, for instance, that Popper’sfalsificationism can be falsified

by showing that the best scientific achievements were unscientific [byPopper’s standards] and that the best scientists, in theirgreatest moments, broke the rules of Popper’s game of science(PDI: 146).

But Lakatos also develops a criticism that has nothing much to do withthe differences between his demarcation criterion and Popper’s,indeed a criticism that seems equally telling against Popper’sphilosophy and his own.

Lakatos points out that when Popper first wrote his classicLogikder Forschung (LSD) in the early 1930s, the correspondence theoryof truth was regarded with deep suspicion by the empiricistphilosophers that he was trying to convince. Accordingly Popper wascareful to state that

in the logic of science here outlined it is possible to avoid usingthe concepts “true” and “false” … Weneed not say that the theory is “false” [or“falsified”], but we may say instead that it iscontradicted by a certain set of accepted basic statements. Nor needwe say of basic statements that they are “true” or“false”, for we may interpret their acceptance as theresult of a conventional decision, and the accepted statements asresults of this decision. (LSD: 273–274.)

But shortly thereafter Popper met Tarski who convinced him that thecorrespondence theory of truth was philosophically respectable, andthis liberated him to declare that truth, or truth-likeness was theobject of the scientific enterprise (LSD: 273n). Lakatos apparentlyendorses this development.

Tarski’s rehabilitation of the correspondence theory oftruth…stimulated Popper to complement his logic of discoverywith his own theory of verisimilitude and of approximation to theTruth, an achievement marvellous both in its simplicity and in itsproblem-solving power. (PDI: 154.)

But Lakatos points out a problem. There is now a disconnect betweenthegame of science and theaim of science. Thegame of science consists in putting forward falsifiable,risky and problem-solving conjectures and sticking with the unrefutedand the well-corroborated ones. But theaim of scienceconsists in developing true or truth-like theories about a largelymind-independent world. And Popper has given us no reason to supposethat by playing the game we are likely to achieve the aim. After all,a theory can be falsifiable, unfalsified, problem-solving andwell-corroborated without being true.

To restore the connection between the game and its aim Lakatos makes aplea with Popper for a “whiff of‘inductivism’” (PDI: 159). What is this whiff?

An inductive principle which connects realist metaphysics withmethodological appraisals, verisimilitude with corroboration, whichreinterprets the rules of the “scientific game” asa—conjectural—theory about thesigns of thegrowth of knowledge, that is, about the signs ofgrowingverisimilitude of our scientific theories (PDI: 156).

In other words, it is a metaphysical principle which states thathighly falsifiable but well-corroborated theories are (in some sense)more likely to be true (or truth-like) than their low-riskcounterparts. Corroborations tend to confirm. Thus by playing the gamewe approximate the aim. Lakatos goes on to urge that this whiff ofinductivism is not much of an ask, since Popper sometimes seems topresuppose it without fully realizing that he is doing so.

There are three points to note.

(1) If this criticism holds good against Popper it is equally goodagainst Lakatos himself. He too has a disconnect between thegame of science—which, when it is played well, consistsin developing progressive research programmes—and theaim of science—which, like Popper, he takes to be truth(FMSRP: 58). To solve this problem, we need a metaphysical principlewhich states that highly progressive research programmes are (in somesense) more likely to be true (or truth-like) than their degeneratingrivals. Thus if Popper could do with a whiff of inductivism, the samegoes for Lakatos.

(2) The inductivism that Lakatos recommends to Popper looks remarkablylike the inductivism that he condemned in Russell. (“I do notsee any way out of a dogmatic assertion that weknow theinductive principle, or some equivalent; the only alternative is tothrow over almost everything that is regarded as knowledge by scienceand common sense.” Russell 1944: 683, quoted disdainfully byLakatos atRegress: 18.) But if inductivism ispermissible (or evende rigueur) in the Philosophy ofScience, perhaps it is permissible (or evende rigueur) inthe Philosophy of Mathematics! In which case, the Renaissance ofEmpiricism in the Philosophy of Mathematics may count as a genuinerenaissance after all, since the logical or set-theoretic axioms may(as Russell supposed) be confirmed (and hence rationally believed)because of their mathematical consequences. If epistemic support canflow upwards from evidence to theory (where the evidence consists of asequence of novel and successful predictions), perhaps it can flowupwards from consequences to axioms.

(3) This episode undermines an influential “Hegelian”reading of Lakatos due to Ian Hacking. According to Hacking,

Lakatos, educated in Hungary in an Hegelian and Marxist tradition,took for granted the post-Kantian, Hegelian, demolition ofcorrespondence theories (Hacking 1983: 118).

This is an odd assertion as Lakatos explicitly endorses thecorrespondence theory on a number of occasions and even declares truthto be the aim of science, which is why contradictions are intolerablein the long term (FMSRP: 58). But in Hacking’s view, Lakatoswas

down on truth, not just a particular theory of truth. He [did] notwant a replacement for the correspondence theory, but a replacementfor truth itself (Hacking 1983: 119).

He found his replacement in the concept of progress.

Lakatos then defines objectivity and rationality in terms ofprogressive research programmes, and allows an incident in the historyof science to be objective and rational if its internal history can bewritten as a sequence of progressive problem shifts (Hacking 1983:126).

Progress becomes a surrogate for truth. We don’t ask whether atheory is true or not but only whether it is part of a progressiveprogramme. To paraphrase the young Karl Popper,

in the logic of science [that Lakatos has] outlined it is possible toavoid using the concepts “true” and “false”[which, in Lakatos’s opinion, is a jolly good thing!] (LSD:273).

But if Lakatos had really been such an anti-truth-freak, he would nothave congratulated Popper on his Tarskian turn. Rather he would havecondemned him for taking the vacuous concept of truth to be the aim ofscience. As for the disconnect between theaim of science andthegame of science, he would have recommended that Popperresolve it by dropping the aim and substituting the game (which,according to Hacking, was what Lakatos himself was trying to do). Iftruth were not the object of the exercise, there would be no need fora whiff of inductivism to connect Popper’s method withscience’s ultimate objective. But Lakatosdid thinkthat a whiff of inductivism was needed to connect Popper’smethod with science’s objective. Hence Lakatos believed thattruth was the object of the scientific enterprise. Whatever theremnants of Hegelianism that Lakatos retained in later life, anaversion to truth (or to the correspondence theory of truth ) was notone of them.

3.7 “Why Did Copernicus’s Research Programme Supersede Ptolemy’s?” (1976)

Lakatos’s last publication was an historical a case-study,co-authored with Elie Zahar and published after his death. It arguesthat the methodology of scientific research programmes can explain theCopernican Revolution as a rational process by which an earlier theory(Ptolemy’s geocentric theory of the Cosmos) was dethroned infavour another objectively better one (Copernicus’s heliocentrictheory). It thus demonstrates the rationality of the CopernicanRevolution (one of the most dramatic episodes in the history ofthought) and confirms the MSRP as a theory of scientific rationality(so long as we accept the inductive principle that the more“great science” that a demarcation criterion can representas rational, the more likely it is to be correct).

Apart from the intrinsic interest of the subject, the paper marks amodification of Lakatos’s conception of factual novelty andhence a modification to the MSRP. For the earlier Lakatos, a factcounts as novel with respect to a research programme if it is notpredicted by any of its rivals and if it is not already known. InWDCRPSP Lakatos accepts an amendment due to his co-author Elie Zahar.Zahar’s original problem was our old friend the Precession ofMercury. This was explained by Einstein’sprogramme—specifically the General Theory ofRelativity—but not by Newton’s, and this was generallythought to count in Einstein’s favour. The difficulty is that inLakatos’s lexicon the Precession of Mercury did not count as anovel fact. After all it had been known to astronomers for nearly acentury. Thus, given the original version of the MSRP, the discoverythat that the General Theory could explain the Precession of Mercury(whilst Newton’s theory could not) did not mean thatEinstein’s programme was any more progressive thanNewton’s. (That had to be argued on other grounds.) Butthis is such a counterintuitive result that it suggests a defect inthe MSRP. Zahar’s modification is that a fact counts as a novelprediction with respect to a research programme if a) it is notpredicted by any of the programme’s rivals and b) either it isnot already known or if itis already known, thehard core of the programme was not devised to explain it.

By this modified criterion the Precession of Mercury counts as a novelfact with respect to Einstein’s programme. For the GeneralTheory was designed to solve adifferent set of problems. Theprediction that if the General Theory were correct, the perihelion ofMercury would shift as it does without the influence of any otherheavenly body came as an “unexpected present fromSchwarzschild” (the man who did the sums). It was therefore“an unintended by-product of Einstein”s programme’(WDCRPSP: 185). So despite its antiquity, the Precession of Mercurycounts as a novel fact or a novel prediction with respect toEinstein’s programme, thus making the programme a lot moreprogressive. Some might regard Zahar’s amendment as asuspiciouslyad hoc move, butad hoc or not, itlooks like an improvement on the original MSRP. Lakatos and Zahar goon to use this idea to explain why Copernicus’s programme veryproperly superseded Ptolemy’s.

4. Mincemeat Unmade: Lakatos versus Feyerabend

According to his friend Paul Feyerabend, Lakatos was “was afascinating person, an outstanding thinker and the best philosopher ofscience of our strange and uncomfortable century” (Feyerabend1975a: 1). Writing in 1981, John Fox raised a cynical eyebrow:

As when Lakatos similarly praises Popper, it is easy to suspectindirect self-advertisement: building up one’s opponent so thatthe announced victory is taken as winning a world title (Fox 1981:92).

With Motterlini’s publication of the Feyerabend/Lakatoscorrespondence (F&AM), Fox’s suspicions have been amplyconfirmed. It is quite clear that Lakatos and Feyerabend were engagedin a self-conscious campaign of mutual boosterism, leading up to aplanned epic encounter between a fallibilistic rationalism, asrepresented by Lakatos, and epistemological anarchism, as representedby Feyerabend. As Feyerabend put it “I was to attack therationalist position, Imre was to restate and defend it, makingmincemeat of me in the process” (Feyerabend 1975b: preface).This Battle of the Titans was to consist of Feyerabend’sAgainst Method and Lakatos’s projected reply, which isreferred to, in their correspondence, by the mysterious acronym“MAM”.

Sometimes the mutual boosterism went a bit too far, causing pain anddistress to serious-minded philosophers who regarded Popperiancritical rationalism as a bulwark against a resurgent Nazism:

Hans Albert is on the verge of suicide [writes Lakatos to Feyerabend].Allegedly somebody told him that in Kiel you will describe criticalrationalism as a “mental disease”, and he thinks that willbe the end of Reason in Germany. I told him that though you are ANEXTREMELY GREAT MAN, that you will not bring Nazism backsingle-handedly…. (F&AM: 291).

But although they had interested motives for talking each other up, itis clear that the mutual admiration between Feyerabend and Lakatos wasquite sincere. Each genuinely regarded the other as the man tobeat.

Feyerabend’s criticism of Lakatos is summed up in his jokingdedication toAgainst Method: To IMRE LAKATOSFriend andFellow-Anarchist. In other words Feyerabend’s charge isthat for all his law-and-order pretensions as a defender of therationality of science and a critic of pseudoscience, Lakatos isreally an epistemic anarchistmalgré lui.Feyerabend’s epistemological anarchism is sometimes summed up bythe slogan “Anything goes” but that is a littlemisleading. His point is rather this:If you want a set ofmethodological rules distinguishing between good science and badscience, the only thing thatwon’t exclude some ofwhatyou (Dear Reader) regard as the best science is theprinciple “Anything goes”. Anything else would rule outwhat is widely regarded as some of the best science as unscientific.Thus a large proportion of Feyerabend’sAgainst Methodis devoted to “praising” Galileo for his allegedlyanti-Popperian practices and his dodgy (but progressive) rhetoricaltricks. Everyone agrees that Galileo was a great scientist. But ifGalileo was great, then the rules that supposedly constitute greatscience are defective since they would exclude some of the greatest ofGalileo’s great deeds.

But what about Lakatos? Feyerabend poses a dilemma. Suppose we applythe Lakatos’s methodology of scientific research programmes in aconservative or rigouristic spirit. Scientists are urged to abandondegenerating research programmes in favour of the progressive, andgrant-giving agencies are urged to defund them. After all, suchprogrammes are condemned by the Demarcation Criterion asbadscience or evennon-science! At the very least, the adherentsof degenerating research programmes must bear the stigma ofirrationality, owning up to their scientific sins. But in that caseLakatos’s MSRP would be condemning some research programmes todeath as bad science or even non-science that might otherwise recovertheir progressive (and hence their scientific) status. Thus Lakatoswould be vulnerable to the same criticism that he himself applies toPopper—he would be excluding some of the best science asunscientific (that is, research programmes that have suffered adegenerating phase only to stage a magnificent comeback). In responseto this, Lakatos distinguished appraisal from advice, and said thatthe task of the philosopher of science is to issue rules of appraisal,not to advise scientists (or grant-giving agencies) about what theyought to do. The Demarcation Criterion can evaluate the current stateof play but it does not tell anyone what to do about it. (Toparaphrase Marx’s Thesis XI, “Methodologists hitherto haveattempted tochange the world of scientific research invarious ways; the point, however is toappraise it”.)The MSRP does enjoin a principle of scientific honesty, namely thatthe adherents of degenerating research programmes should own up totheir methodological shortcomings, such as the lack of novelpredictions or the falsification of the predictions that they havemade. However, so long as they admit to these failures they can(rationally?) persist in their degenerate ways.

But in that case Lakatos is gored by the other horn ofFeyerabend’s dilemma. For Feyerabend argues that a DemarcationCriterion that cannot tell anyone what to do or not to do is scarcelydistinguishable from “Anything goes”. To revert toFeyerabend’s political analogy, what is the difference betweenan anarchist society and a “state” where the“police” canappraise people for their“criminal” or “law-abiding” behaviour but cannever make an arrest or send anyone to jail? That’s a“state” which isn’t a state and a “policeforce” which isn’t a police force! We have not scientificlaw-and-order but anarchy, accompanied by uplifting sermons andbenedictions posthumously bestowed on the mighty scientific dead.

What was Lakatos’s response to this dilemma? It is sometimessuggested, not least by Feyerabend himself, that Lakatos did have, orwould have had, an answer but that he did not live to write it up.Their correspondence suggests otherwise. Although thelocusclassicus of Feyerabend’s argument is chapter 16 ofAgainst Method (1975b) he had already developed his dilemmain “Consolations for the Specialist” (1968) and Lakatoshad access to successive versions of the argument in the successivedrafts that Feyerebend sent him in the last is six years of his life.Yet there is no trace of a counterargument in Lakatos’ssurviving letters to Feyerabend. Instead there are a series offearsome threats.

I am now greatly grateful for your depicting me asGod andyourself as theDevil. I also return the compliment: for meyou are the only philosopher worth demolishing. But there isone trouble: Ican take you to such little piecesthat only an electromicroscope can discover you again. Will you bevery hurt? (F&AM: 268–9.)

However, aside from these threats, a developed answer toFeyerabend’s dilemma is conspicuous by its absence. One isreminded of King Lear:

I will do such things,—
What they are, yet I know not: but they shall be
The terrors of the earth.

The upshot is that if there is a Lakatosian answer toFeyerabend’s dilemma, it is an answer that has to be concoctedon his behalf. One of us has a go in Musgrave 1976, but for theMethodology of Scientific Research Programmes, it is still, very much,an open problem.

Bibliography

Works by Lakatos

• 1946a: “Citoyen és Munkásosztály”(Citoyen and the working class),Valóság, 1:77–88.
• 1946b: “A fizikai Idealizmus Bírálata”(A critique of idealism in physics); a review of SusanStebbing’sPhilosophy and the Physicists,Athenaeum, 1: 28–33.
• 1947a: “Huszadik Század”,Forum, 1:316–20.
• 1947b: “Eötvös Collégium—GyörffyKollégium”,Valóság, 2:107–24.
• 1947c: “Jeges Károly:Megtanulom afizikát”, Társadalmi Szemle, 1: 472.
• 1947d: “Természettudományosvilágnézet és demokratikus nevelés”(Scientific worldview and democratic upbringing),Embernevelés, 2: 63–66.
• 1947e: “Modern fizika—modern társadalom”(Modern physics—modern society), in Kemény Gábor(ed.),Továbbképzés ésdemokrácia. [There is an English translation of this essayin Kampis et al. 2002: 356–368.]
• 1947f: “‘Haladó tudós’ ademokráciában” (A “progressivescholar” in a democracy),Tovább, June 13.
• 1956: Speech at the Pedagogy Debate of the Petőfi Circle onSeptember 28, 1956; transcript published in András B.Hegedűs (ed.),A Petőfi Kör vitái (Thedebates of the Petőfi Circle), Vol. VI, Budapest: Intézetand Múzsák Kiadó, 1992, 34–38. [Englishtranslation “On rearing scholars” in Motterlini 1999:375–381.]
• 1961: “Essays in the Logic of Mathematical Discovery”.Unpublished PhD dissertation, Cambridge University.
• 1962 [Regress]: “Infinite Regress andFoundations of Mathematics”,Aristotelian SocietySupplementary Volume, 36: 155–94. [Republished as chapter 1of Lakatos 1978b (PP2), cited pages from this version.]
• 1963: Discussion of “History of Science as an AcademicDiscipline” by A.C. Crombie and M.A. Hoskin, in A.C. Crombie(ed.),Scientific Change, London: Heinemann, pp. 781–5.[Republished as chapter 13 of Lakatos 1978b (PP2).]
• 1963–4: “Proofs and Refutations”, in theBritish Journal for the Philosophy of Science, 14:1–25, 120–139, 221–243, 296–342. [Reprinted inLakatos 1976c (P&R). cited pages from this version.]
• 1967a [Renaissance]: “A Renaissance ofEmpiricism in the Recent Philosophy of Mathematics”, in Lakatos1967b: 199–202. [Republished in an expanded form as 1978b (PP2),cited pages from this version.]
• 1967b: (ed.),Problems in the Philosophy of Mathematics,Amsterdam: North-Holland.
• 1968a: “Criticism and the Methodology of Scientific ResearchProgrammes”,Proceedings of the Aristotelian Society,69: 149–186.
• 1968b [Changes]: “Changes in the Problem ofInductive Logic”, in Lakatos 1968c, 315–417 [Reprinted aschapter 8 of PP2, cited pages from this version.]
• 1968c: (ed.),The Problem of Inductive Logic, Amsterdam:North-Holland.
• 1968d: (edited with A. Musgrave)Problems in the Philosophy ofScience, Amsterdam: North-Holland.
• 1968e: “A Letter to the Director of the London School ofEconomics”, in C.B. Cox and A.E. Dyson (eds.),Fight forEducation, A Black Paper, London: Critical Quarterly Society,28–31. [Republished as chapter 12 of Lakatos 1978b (PP2),referred to, in this reprint, as LTD.]
• 1970a [FMSRP]: “Falsification and the Methodology ofScientific Research Programmes”, in Lakatos 1970b, 91–196(Republished as chapter 1 of Lakatos 1978a, PP1, cited pages from thisversion.)
• 1970b, editor with A. Musgrave:Criticism and the Growth ofKnowledge, Cambridge: Cambridge University Press.
• 1970c: Discussion of “Knowledge and Physical Reality”by A. Mercier, in A.D. Breck and W. Yourgrau (eds.),Physics,Logic and History, New York: Plenum Press, pp. 53–4.
• 1970d: Discussion of ‘Scepticism and the Study ofHistory’ by Richard H. Popkin, in A.D. Breck and W. Yourgrau(eds.),Physics, Logic and History, New York: Plenum Press,pp. 220–3.
• 1971a [HS&IRR]: “The History of Science and its RationalReconstructions”, in R.C. Buck and R.S. Cohen (eds.),PSA1970: Boston Studies in the Philosophy of Science, 8, Dordrecht:Reidel, pp. 91–135. [Republished as chapter 2 of Lakatos 1978a(PP1), cited pages from this version]
• 1971b: “Replies to Critics”, in R.C. Buck and R.S.Cohen (eds.):PSA 1970: Boston Studies in the Philosophy ofScience, 8, Dordrecht: Reidel, pp. 174–82.
• 1974a: “Discussion Remarks on Papers by Ne‘eman,Yahil, Beckler, Sambursky, Elkana, Agassi, Mendelsohn”, in Y.Elkana (ed.),The Interaction Between Science and Philosophy,Atlantic Highlands, New Jersey: Humanities Press, pp. 41, 155–6,163, 165, 167, 280–3, 285–6, 288–9, 292,294–6, 427–8, 430–1, 435.
• 1974b [PDI]: “Popper on Demarcation and Induction”, inP.A. Schilpp (ed.),The Philosophy of Karl Popper, La Salle:Open Court, 241–73. [Republished as chapter 3 of Lakatos 1978a(PP1), cited pages from this version.]
• 1974c: “The Role of Crucial Experiments in Science”,Studies in the History and Philosophy of Science, 4:309–25.
• 1974d [S&P]: “Science and Pseudoscience”, inVesey, G. (ed.),Philosophy in the Open, Open UniversityPress. [Republished as the introduction to Lakatos1978a (PP1), citedpages from this version.]
• 1976a: [UT] “Understanding Toulmin”,Minerva,14: 126–43. [Republished as chapter 11 of Lakatos 1978b.]
• 1976b [Renaissance]: “A Renaissance ofEmpiricism in the Recent Philosophy of Mathematics?”,British Journal for the Philosophy of Science, 27:201–23. [Republished as chapter 2 of Lakatos 1978b (PP2), citedpages from this version.]
• 1976c [P&R]:Proofs and Refutations: The Logic ofMathematical Discovery, J. Worrall and E. Zahar (eds.),Cambridge: Cambridge University Press
• 1976d [WDCRPSP]: “Why Did Copernicus’s ProgrammeSupersede Ptolemy’s?”, by I. Lakatos and E.G. Zahar, in R.Westman (ed.),The Copernican Achievement, Los Angeles:University of California Press, 354–83. [Republished as chapter5 of PP1, cited pages from this version.]
• 1978a [PP1]:The Methodology of Scientific ResearchProgrammes (Philosophical Papers: Volume 1), J. Worralland G. Currie (eds.), Cambridge: Cambridge University Press.
• 1978b [PP2]:Mathematics, Science and Epistemology(Philosophical Papers: Volume 2), J. Worrall and G. Currie(eds.), Cambridge: Cambridge University Press.
• 1978c: “Cauchy and the Continuum:the Significance ofNon-Standard Analysis for the History and Philosophy ofMathematics”. [Published as chapter 5 of PP1]
• 1999a: “Lectures on Scientific Method” in Motterlini1999: 19–109
• 1999b: “Lakatos-Feyerabend Correspondence” inMotterlini 1999: 119–374.
• 1999c: “On Rearing Scholars” in Motterlini 1999:375–381.
• 1999d: “The Intellectuals’ Betrayal of Reason”in Motterlini 1999: 393–397.

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