PhilSci-L01b: Popper and Lakatos

Overview

A man pushes a child into a river to drown it. Another man dies trying to pull a child out. Freud explains the first as repression and the second as sublimation. Adler explains both as inferiority feelings. Neither theory can be embarrassed by anything a human being might do.

Meanwhile Einstein said that starlight grazing the sun would be deflected by a specific angle, and that if the deflection were absent his theory was finished. Popper’s whole philosophy comes out of noticing that the second attitude is the scientific one and the first is not, and that this has nothing to do with which theory has more evidence behind it.

Lakatos then agrees that Popper found the right question and gave the wrong answer, because real scientists never abandon a theory just because the facts contradict it. His replacement, the methodology of scientific research programmes, is worth 10 marks on its own (question 2), and the Popper half is worth another 10 (question 3). This note covers Curd & Cover chapter 1, Popper pp. 3-10 and Lakatos pp. 20-26.

1. The problem the chapter is about

Parapsychology, the study of extrasensory perception and paranormal powers, was admitted to the American Association for the Advancement of Science as an affiliate member in 1969. In 1979 the physicist John A. Wheeler wrote to the president of the AAAS demanding the parapsychologists be expelled: “We have enough charlatanism in this country today without needing a scientific organization to prostitute itself to it.”

Wheeler’s letter is an accusation of pseudoscience, and the interesting philosophical question is not whether the accusation is popular but what would make it correct.

If the only concern were to label people, you could just check where their work is published and how the scientific community received it. Astrology, the paranormal, psychoanalysis and creation-science all produce research, books and articles, but in popular magazines rather than refereed journals, and their practitioners are not funded by the National Science Foundation or elected to the National Academy of Sciences. That is sociology. Philosophers want the reasons.

Demarcation criterion

A necessary condition that any discipline or field of study must satisfy in order to count as genuine science. If a discipline fails one of these conditions it is judged non-scientific. The problem of finding such a condition is the problem of demarcation.

Curd & Cover’s chapter 1 sets four incompatible answers against each other: Popper, Kuhn, Lakatos and Thagard, each defending a different set of necessary conditions. Popper’s answer, that a scientific theory must be open to refutation by making testable predictions, has been the most influential, especially among working scientists. Kuhn, Lakatos and Thagard all reject falsifiability as the hallmark of science and disagree about the replacement, but all three make a theory’s scientific legitimacy depend on historical considerations, on how theories have developed over time.

The chapter closes with Michael Ruse against Larry Laudan on creation-science. Ruse was an expert witness in the trial over the Arkansas law requiring public school biology teachers to present creationism as an alternative to evolution, and under his guidance the judge drew up five criteria for genuine science, including Popper’s falsifiability, and found that creation-science failed all five. Laudan attacks the list and doubts that there are any demarcation criteria all sciences satisfy.

2. Popper: Science, Conjectures and Refutations (1963)

The text is a lecture Popper gave at Peterhouse, Cambridge in 1953, published as “Philosophy of Science: A Personal Report” and later reprinted in Conjectures and Refutations.

2.1 The question is demarcation, not truth

Popper is explicit about what he was not asking in 1919.

Question	Popper’s attitude
When is a theory true?	Not my problem, at that stage at least
When is a theory acceptable?	Not my problem
When should a theory be ranked as scientific?	This is the problem

His phrasing: “I wished to distinguish between science and pseudo-science; knowing very well that science often errs, and that pseudo-science may happen to stumble on the truth.”

Note both halves. Science is not defined as the set of true claims, because scientific theories are frequently wrong. Pseudoscience is not defined as the set of false claims, because a fortune-teller can get lucky. Truth and scientific status come apart, and the criterion has to be about something else.

The standard answer of the day was that science is distinguished from pseudo-science, or from metaphysics, by its empirical method, which is essentially inductive, proceeding from observation or experiment. Popper found this useless, and reformulated the problem as distinguishing a genuinely empirical method from a pseudo-empirical one: a method which appeals to observation and experiment but does not come up to scientific standards. Astrology is his example, with its “stupendous mass of empirical evidence based on observation, on horoscopes and on biographies.”

That is the crucial move. Astrology is not short of data. Piling up observations is exactly what it does. So whatever makes science different, it cannot be the mere presence of supporting evidence.

2.2 The four theories in Vienna, 1919

After the collapse of the Austrian Empire the air was full of new and often wild theories. Four of them mattered to Popper.

Theory	Popper’s later verdict
Einstein’s theory of relativity	Science
Marx’s theory of history	Testable once, then rescued into pseudoscience
Freud’s psycho-analysis	Simply non-testable
Adler’s individual psychology	Simply non-testable

Popper knew Adler personally and worked with him in the social guidance clinics Adler ran in the working-class districts of Vienna. He was also, with his circle of student friends, “thrilled with the result of Eddington’s eclipse observations which in 1919 brought the first important confirmation of Einstein’s theory of gravitation.”

What bothered him was not that he doubted the truth of the other three, nor that physics was more exact or more measurable than sociology or psychology. It was that those three, “though posing as sciences, had in fact more in common with primitive myths than with science; that they resembled astrology rather than astronomy.”

2.3 Explanatory power as a symptom of weakness

Popper’s friends who admired Marx, Freud and Adler were impressed above all by the theories’ apparent explanatory power. The theories seemed able to explain practically everything that happened in their fields. Studying one had the effect of “an intellectual conversion or revelation, opening your eyes to a new truth hidden from those not yet initiated.” Once your eyes were opened you saw confirming instances everywhere. Unbelievers were people who did not want to see the manifest truth, either because of their class interest or because of their repressions, which were still un-analysed and crying aloud for treatment.

Three vignettes carry the argument.

• Marxism. A Marxist could not open a newspaper without finding confirming evidence for his interpretation of history on every page: in the news, in the presentation of the news, which revealed the class bias of the paper, and especially in what the paper did not say.
• Freud. Analysts stressed that their theories were constantly verified by their “clinical observations”.
• Adler. In 1919 Popper reported to Adler a case which did not seem particularly Adlerian. Adler analysed it in terms of inferiority feelings without difficulty, having never seen the child. Asked how he could be so sure, Adler said “Because of my thousandfold experience.” Popper: “And with this new case, I suppose, your experience has become thousand-and-one-fold.”

The Adler exchange contains the whole argument in miniature. Each of Adler’s earlier observations had itself been interpreted in the light of previous experience and then counted as an additional confirmation. What did the thousand cases confirm? Only that a case can be interpreted in the light of the theory, which is worth nothing when every conceivable case can be.

The two men and the child

Case A. A man pushes a child into the water intending to drown it. Case B. A man sacrifices his life trying to save a child from the water.

	Freud	Adler
Case A	Repression, say of some component of his Oedipus complex	Inferiority feelings, producing the need to prove to himself that he dared to commit a crime
Case B	Sublimation	Inferiority feelings, producing the need to prove to himself that he dared to rescue the child

Two opposite behaviours, four confident explanations, zero risk. Popper: “I could not think of any human behaviour which could not be interpreted in terms of either theory. It was precisely this fact, that they always fitted, that they were always confirmed, which in the eyes of their admirers constituted the strongest argument in favour of these theories. It began to dawn on me that this apparent strength was in fact their weakness.”

2.4 The contrast case: Eddington’s eclipse expedition, 1919

Einstein’s gravitational theory implies that light must be attracted by heavy bodies such as the sun, precisely as material bodies are. It follows that light from a distant fixed star whose apparent position is close to the sun reaches the earth from a direction such that the star appears slightly shifted away from the sun, and away from its neighbours. Such stars cannot normally be seen, because daylight drowns them, but during a total eclipse you can photograph them. Photograph the same constellation at night, measure the distances between the stars on the two plates, and compare.

   star * ─────────────╮
                        ╰─────────╮                the ray is pulled
                                   ╰─────╮         towards the sun
                      (  S U N  )         ╰─────╮
                                                  ╰────►  [ EARTH ]

   The observer traces the arriving ray straight back, and therefore sees:

        *  apparent position   <- displaced AWAY from the sun
        ⋮                        by a precisely predicted angle
        *  true position

   TEST: photograph the constellation during the total eclipse (day),
         photograph it again months later (night), measure the star
         separations on both plates, compare with Einstein's number.

   OUTCOME SPACE:  shift matches prediction  → corroborated
                   no shift, or wrong shift  → theory is simply refuted

Two Royal Astronomical Society expeditions organised by Sir Arthur Eddington observed the solar eclipse of 1919 and found that starlight was deflected by the sun by the amount Einstein had predicted. The Times of London called it the most remarkable scientific event since the discovery of Neptune.

Popper's own footnote

“This is a slight oversimplification, for about half of the Einstein effect may be derived from the classical theory, provided we assume a ballistic theory of light.” The full deflection is twice the Newtonian value, so the test discriminates between the theories by a factor of two rather than between a prediction and nothing.

What impressed Popper was the risk. If observation had shown the predicted effect to be definitely absent, the theory would simply be refuted. The theory is incompatible with certain possible results of observation, in fact with results everybody before Einstein would have expected. Compare that with theories compatible with the most divergent human behaviour, where it is practically impossible to describe any behaviour that could not be claimed as a verification.

2.5 The seven conclusions

This is the centre of the text. Learn the numbered list, it is the thing most often quoted back.

Popper, Conjectures and Refutations, p. 7

1. It is easy to obtain confirmations, or verifications, for nearly every theory, if we look for confirmations.
2. Confirmations should count only if they are the result of risky predictions; that is to say, if, unenlightened by the theory in question, we should have expected an event which was incompatible with the theory, an event which would have refuted the theory.
3. Every “good” scientific theory is a prohibition: it forbids certain things to happen. The more a theory forbids, the better it is.
4. A theory which is not refutable by any conceivable event is non-scientific. Irrefutability is not a virtue of a theory (as people often think) but a vice.
5. Every genuine test of a theory is an attempt to falsify it, or to refute it. Testability is falsifiability; but there are degrees of testability: some theories are more testable, more exposed to refutation, than others; they take, as it were, greater risks.
6. Confirming evidence should not count except when it is the result of a genuine test of the theory; and this means that it can be presented as a serious but unsuccessful attempt to falsify the theory. (I now speak in such cases of corroborating evidence.)
7. Some genuinely testable theories, when found to be false, are still upheld by their admirers, for example by introducing ad hoc some auxiliary assumption, or by re-interpreting the theory ad hoc in such a way that it escapes refutation. Such a procedure is always possible, but it rescues the theory from refutation only at the price of destroying, or at least lowering, its scientific status. (I later described such a rescuing operation as a conventionalist twist or a conventionalist stratagem.)

Popper's criterion of demarcation

The criterion of the scientific status of a theory is its falsifiability, or refutability, or testability.

A statement or system of statements, in order to be ranked as scientific, must be capable of conflicting with possible, or conceivable, observations.

Point 3 deserves a picture, because “the more a theory forbids, the better it is” is the least intuitive part.

   Space of all conceivable observation reports:

   Theory A (bold, high content)
   ┌────────────────────────────────────────────────────┐
   │ ████████████████████████████████ FORBIDDEN         │
   │                                  ░░░░ permitted    │
   └────────────────────────────────────────────────────┘
        many ways to be wrong  →  risky  →  highly testable  →  GOOD

   Theory B (vague, low content)
   ┌────────────────────────────────────────────────────┐
   │ ███ FORBIDDEN                                      │
   │     ░░░░░░░░░░░░░░░░░░░░░░░░░░░░ permitted         │
   └────────────────────────────────────────────────────┘
        almost nothing excluded  →  safe  →  barely testable  →  BAD

   Limiting case: a theory that forbids nothing is compatible with every
   possible observation, is irrefutable, and is therefore non-scientific.

The astrologer’s trick is to move a theory from the top box to the bottom box. Make the prophecies vague enough and they can hardly fail.

2.6 The asymmetry between verification and falsification

Popper does not spell out the logic in this text, but it is what the whole criterion stands on, and Lakatos states half of it explicitly (“there can be no valid derivation of a law of nature from any finite number of facts”).

A scientific law is a universal statement. Take “all swans are white”:

$\forall x(Sx\to Wx)$

where:

• $Sx$ means ”$x$ is a swan”
• $Wx$ means ”$x$ is white”
• the quantifier ranges over all swans, past, present, future and unobserved

Verification fails. From any finite conjunction of observed instances

$(S{a}_1\wedge W{a}_1)\wedge (S{a}_2\wedge W{a}_2)\wedge \cdots \wedge (S{a}_n\wedge W{a}_n)$

nothing deductively follows about the unobserved swans. No finite $n$ gets you to the universal statement. This is Hume’s problem of induction, and it is why Popper says confirmations are cheap.

Falsification succeeds. From a single counter-instance

$Sa\wedge \neg Wa$

it follows deductively that

$\neg \forall x(Sx\to Wx)$

The general form is modus tollens, applied to a theory $T$ that entails an observational consequence $O$:

$\frac{T\to O,\neg O}{\therefore \neg T}$

Why the asymmetry does all the work

Universal statements are infinitely generous in what they claim and therefore cheap to kill and impossible to prove. Existential statements (“there exists a white raven”) are the mirror image: provable by one sighting, unfalsifiable by any number of failures to sight one.

Popper’s whole system is built on standing on the side of the asymmetry that logic actually supports. Science never proves anything. It makes bold conjectures and then tries to destroy them, and what survives serious attempts at destruction is corroborated, not confirmed and certainly not proved.

Corroboration is not probability

“Corroborated” means “has survived our best attempts to refute it so far.” It is a report on a past track record, not a measure of how likely the theory is to be true. Popper argued in 1934 that the mathematical probability of any theory, scientific or pseudoscientific, given any amount of evidence, is zero. Writing “well corroborated, therefore probably true” in an exam answer is exactly the inductive step Popper denies. Lakatos uses this result in section 3.5 below.

2.7 Applying the criterion: the scorecard

Theory	Verdict	Why
Einstein’s gravitation	Scientific	Clearly satisfied falsifiability. Even where instruments of the day did not allow a fully assured verdict, there was clearly a possibility of refuting the theory
Astrology	Failed	Astrologers were impressed and misled by what they took to be confirming evidence, so much so that they were unimpressed by any unfavourable evidence. By making interpretations and prophecies sufficiently vague they could explain away anything. “In order to escape falsification they destroyed the testability of their theory”
Marxist theory of history	Failed, but not originally	Earlier formulations, such as Marx’s analysis of the coming social revolution, were testable, and in fact falsified. Instead of accepting the refutations, followers re-interpreted both the theory and the evidence to make them agree. They rescued the theory at the price of a device that made it irrefutable: a conventionalist twist, which destroyed its claim to scientific status
Psycho-analysis and individual psychology	Failed, in a different class	Simply non-testable, irrefutable. There is no conceivable human behaviour that could contradict them. Freud’s epic of the Ego, Super-ego and Id has no stronger claim to scientific status than Homer’s collected stories from Olympus

Two subtleties worth marks.

Marxism and psychoanalysis fail in different ways, and Popper is careful about this. Marxism was once genuine science and was destroyed by its defenders. Psychoanalysis never made a risky claim to begin with. If a question asks about the Marxist case specifically, the answer is that it was falsified and then rescued.

Popper does not say Freud and Adler are seeing nothing correctly. He personally does not doubt that much of what they say is of considerable importance and “may well play its part one day in a psychological science which is testable.” The verdict is about the form of the claims, not their content.

2.8 Ad hoc rescue and the conventionalist stratagem

This is conclusion 7 and it is the mechanism behind exam question 3, so it needs to be exact.

Ad hoc rescue

When a genuinely testable theory is contradicted by evidence, its defenders can save it by introducing ad hoc an auxiliary assumption, or by re-interpreting the theory ad hoc so that it escapes refutation. The manoeuvre is always available. Popper’s objection is not that it is impossible but that it costs you something: it rescues the theory from refutation “only at the price of destroying, or at least lowering, its scientific status.” Popper’s names for the move: the conventionalist twist, the conventionalist stratagem.

The word doing the work is ad hoc, which means “for this purpose only”. A modification is ad hoc when its only motivation is to absorb the refuting evidence, so that it adds no new testable consequences of its own.

Popper's escape clause, and the exam depends on it

Popper is not committed to the naive view that any negative result must kill the theory. A prediction is never derived from the theory alone, so the scientist may in principle blame an auxiliary assumption or the measurement instead. See PhilSci-L03 - Under-determination for the full Duhem-Quine machinery.

Popper’s condition on that move: it is legitimate only if there are independent reasons for rejecting the measurement, reasons that do not consist merely in the fact that the theory would otherwise be refuted. Independent reasons make it a normal scientific correction. No independent reasons make it an ad hoc hypothesis, and the theory’s scientific status drops.

This one sentence is the difference between a pass and a good mark on question 3.

2.9 Non-scientific does not mean meaningless

Popper is often lumped in with the logical positivists of PhilSci-L01 - Introduction and Logical Empiricism. He is not one of them, and this section is where the difference shows.

He notes that myths may be developed and become testable, that historically all or very nearly all scientific theories originate from myths, and that a myth may contain important anticipations of scientific theories. Empedocles’ theory of evolution by trial and error is one example. Parmenides’ myth of the unchanging block universe in which nothing ever happens is another: add a dimension and it becomes Einstein’s block universe, in which nothing ever happens either, since everything is four-dimensionally determined and laid down from the beginning.

So a theory found to be non-scientific or metaphysical “is not thereby found to be unimportant, or insignificant, or meaningless, or nonsensical.” It just cannot claim to be backed by empirical evidence in the scientific sense.

Verifiability versus falsifiability: the distinction question 1 depends on

	Carnap and the Vienna Circle	Popper
The criterion	Verifiability: a statement is meaningful if its truth can in principle be determined by observation or experiment. “The meaning of a statement is its method of verification”	Falsifiability: a statement is scientific if it is capable of conflicting with possible observations
What it demarcates	Meaningful from meaningless. Unverifiable statements are pseudo-statements: they look as if they say something, but they are literally meaningless	Science from non-science. Non-scientific statements are perfectly meaningful, sometimes important, and sometimes the ancestors of later science
Verdict on metaphysics	Nonsense, to be eliminated	Not empirically supported, but possibly valuable and possibly the seed of a future testable theory
Direction of the logic	Wants observations to establish the statement, which universal laws make impossible	Wants observations to be able to destroy the statement, which the logic actually permits

Popper’s own summary: “the problem which I tried to solve by proposing the criterion of falsifiability was neither a problem of meaningfulness or significance, nor a problem of truth or acceptability. It was the problem of drawing a line between the statements, or systems of statements, of the empirical sciences, and all other statements.”

Popper called this “the problem of demarcation” in 1928 or 1929, years after the 1919 experience that produced it.

3. Lakatos: Science and Pseudoscience (1973)

A radio lecture broadcast by the Open University on 30 June 1973, reprinted as the opening of Lakatos’s Philosophical Papers, vol. 1.

3.1 Why demarcation is not armchair philosophy

Lakatos opens and closes on the political stakes, and it is a fair bet for a short question.

• The Catholic Church excommunicated Copernicans. Copernicus’s theory was banned in 1616 as pseudoscientific and taken off the Index in 1820, because by then the Church deemed that the facts had proved it and it had therefore become scientific.
• The Central Committee of the Soviet Communist Party declared Mendelian genetics pseudoscientific in 1949 and had its advocates, such as Academician Vavilov, killed in concentration camps. After Vavilov’s murder Mendelian genetics was rehabilitated, but the Party’s right to decide what is science and publishable and what is pseudoscience and punishable was upheld.
• The liberal Establishment of the West exercises the same right to deny freedom of speech to what it regards as pseudoscience, as in the debate concerning race and intelligence.

All of these judgments were based on some sort of demarcation criterion. “This is why the problem of demarcation between science and pseudoscience is not a pseudo-problem of armchair philosophers: it has grave ethical and political implications.”

3.2 Knowledge is not strong belief

The obvious answer, that a statement counts as knowledge when sufficiently many people believe it sufficiently strongly, dies immediately. Many people have been totally committed to absurd beliefs. If strength of belief were the hallmark of knowledge, tales about demons, angels, devils, heaven and hell would qualify.

The inversion is neat: scientists are the ones who do not believe their theories very hard. Newton’s is the most powerful theory science has yet produced, and Newton himself never believed that bodies attract each other at a distance.

Lakatos, p. 20

Indeed, the hallmark of scientific behaviour is a certain scepticism even towards one’s most cherished theories. Blind commitment to a theory is not an intellectual virtue: it is an intellectual crime.

Thus a statement may be pseudoscientific even if it is eminently “plausible” and everybody believes in it, and it may be scientifically valuable even if it is unbelievable and nobody believes in it. A theory may even be of supreme scientific value even if no one understands it, let alone believes it.

The underlying principle: belief, commitment and understanding are states of the human mind, and the objective scientific value of a theory is independent of the mind that creates or understands it. Its value depends only on what objective support the conjectures have in facts.

3.3 Hume’s fork and the witchcraft problem

Hume, An Enquiry Concerning Human Understanding (1748), final paragraph

If we take in our hand any volume; of divinity, or school metaphysics, for instance; let us ask, does it contain any abstract reasoning concerning quantity or number? No. Does it contain any experimental reasoning concerning matter of fact and existence? No. Commit it then to the flames. For it can contain nothing but sophistry and illusion.

Lakatos accepts the spirit and rejects the confidence. What is “experimental” reasoning? The vast seventeenth-century literature on witchcraft is full of careful observations, sworn evidence and even experiments. Glanvill, the house philosopher of the early Royal Society, regarded witchcraft as the paradigm of experimental reasoning.

“We have to define experimental reasoning before we start Humean book burning.”

This is the same point Popper made with astrology. Evidence-gathering is not the differentiator, because the pseudosciences gather evidence too.

3.4 Facts cannot prove theories, and Newton is the proof

Newton thought he had proved his laws from facts. He was proud of not uttering mere hypotheses, and claimed to have deduced his laws from the “phenomena” provided by Kepler.

Why Newton's boast was nonsense

• Kepler: planets move in ellipses.
• Newton: planets would move in ellipses only if they did not disturb each other in their motion.
• But they do. Which is why Newton had to devise a perturbation theory, from which it follows that no planet moves in an ellipse.

So the premises Newton claimed to deduce his theory from are inconsistent with the theory he deduced. He did not derive his laws from Kepler’s laws; he replaced them.

Generalised: “One can today easily demonstrate that there can be no valid derivation of a law of nature from any finite number of facts.” That is section 2.6’s asymmetry again, stated from the other side.

Why does everyone keep resisting this bit of elementary logic? Lakatos gives a historical explanation.

Science was born in the seventeenth century, when the most relevant knowledge concerned God, the Devil, Heaven and Hell, and getting your conjectures about divinity wrong meant eternal damnation. Theological knowledge could not be fallible, it had to be beyond doubt. The Enlightenment then decided that we are fallible and ignorant about theological matters, so there is no theological knowledge, and knowledge can only be about Nature. But the new knowledge was judged by standards taken over straight from theology: it had to be proven beyond doubt. Science had to achieve the very certainty that had escaped theology. A scientist worthy of the name was not allowed to guess, he had to prove each sentence he uttered from facts. Theories unproven from facts were sinful pseudoscience, heresy in the scientific community.

Ampère, in the early nineteenth century, felt obliged to call his book Mathematical Theory of Electrodynamic Phenomena Unequivocally Deduced from Experiment, then casually confessed at the end of the volume that some of the experiments were never performed and that the necessary instruments had not even been constructed.

It took the downfall of Newtonian theory in the twentieth century to make scientists realise that their standards of honesty had been utopian.

3.5 Probabilism, and why it collapses

If all scientific theories are equally unprovable, what separates science from pseudoscience?

The twentieth-century inductive logicians answered with probability. Inductive logic sets out to define the probabilities of different theories relative to the total available evidence. High mathematical probability means scientific, low or zero means not. The hallmark of scientific honesty becomes never saying anything that is not at least highly probable.

Probabilism has a genuine attraction: instead of a black-and-white distinction it gives a continuous scale from poor theories with low probability to good theories with high probability.

It dies in 1934. Popper argued that the mathematical probability of all theories, scientific or pseudoscientific, given any amount of evidence, is zero. If he is right, theories are not only equally unprovable but equally improbable, and the scale collapses to a point. A new demarcation criterion was needed.

3.6 Popper’s criterion as Lakatos states it, and why it fails

Popper's criterion, in Lakatos's formulation

A theory is scientific if one is prepared to specify in advance a crucial experiment (or observation) which can falsify it, and it is pseudoscientific if one refuses to specify such a potential falsifier.

Lakatos calls this “rather stunning” and draws out the consequence that a theory may be scientific with not a shred of evidence in its favour, and pseudoscientific even if all the available evidence supports it. The scientific character of a theory can be determined independently of the facts.

He then makes a sharp observation that is easy to miss: if this is the criterion, “we do not demarcate scientific theories from pseudoscientific ones, but rather scientific method from non-scientific method.” Marxism is scientific, for a Popperian, if Marxists are prepared to specify facts which, if observed, would make them give up Marxism. If they refuse, it becomes a pseudoscience. The same proposition can petrify into pseudoscientific dogma or become genuine knowledge depending on the attitude of the people holding it.

Lakatos’s test question: “It is always interesting to ask a Marxist, what conceivable event would make him abandon his Marxism.”

The objection, and it is the whole hinge of the lecture

“Popper’s criterion ignores the remarkable tenacity of scientific theories. Scientists have thick skins. They do not abandon a theory merely because facts contradict it.”

What scientists actually do when the facts contradict them:

1. Invent a rescue hypothesis to explain what they then call a mere anomaly, or
2. If they cannot explain the anomaly, ignore it and direct their attention to other problems.

Note the vocabulary. Scientists talk about anomalies and recalcitrant instances, not refutations. The history of science is full of accounts of crucial experiments allegedly killing theories, but “such accounts are fabricated long after the theory had been abandoned.”

The killer line: “Had Popper ever asked a Newtonian scientist under what experimental conditions he would abandon Newtonian theory, some Newtonian scientists would have been exactly as nonplussed as are some Marxists.”

So Popper’s test, applied honestly to real physics, fails to separate Newton from Marx. That is a demarcation criterion that does not demarcate.

The obvious next step is Kuhn’s: if refutation does not drive theory change, maybe theory change is a conversion experience and revolutions are irrational. Lakatos names Kuhn as “a distinguished American philosopher of science” who “arrived at this conclusion after discovering the naivety of Popper’s falsificationism”, and refuses to follow him: if Kuhn is right there is no explicit demarcation, no distinction between scientific progress and intellectual decay, and no objective standard of honesty. See PhilSci-L02 - Kuhn on Scientific Practice for Kuhn’s side of this, and for Lakatos’s charge elsewhere that Kuhn reduces science to mob psychology.

Lakatos wants a third option that keeps the rationality without pretending scientists behave like Popperians.

3.7 The methodology of scientific research programmes

The unit of appraisal

“The typical descriptive unit of great scientific achievements is not an isolated hypothesis but rather a research programme.”

Science is not simply trial and error, a series of conjectures and refutations. “All swans are white” may be falsified by the discovery of one black swan, but such trivial trial and error does not rank as science.

This is the move. Popper appraises single theories against single observations. Lakatos appraises a series of theories over time, sharing a common structure and generated by a common plan. Nothing shorter than a programme can be called progressive or degenerating, because those words describe a direction of travel, and a single snapshot has no direction.

Newtonian science is not simply a set of four conjectures. The three laws of mechanics and the law of gravitation “constitute only the hard core of the Newtonian programme.”

The four components of a research programme

1. Hard core. The fundamental theoretical assumptions that define the programme and give it its identity. For the Newtonian programme: the three laws of mechanics plus the law of universal gravitation. The core is held irrefutable by methodological decision: practitioners agree not to give it up, and abandoning it means leaving the programme rather than modifying it.
2. Protective belt of auxiliary hypotheses. The core is “tenaciously protected from refutation by a vast protective belt of auxiliary hypotheses.” These are the adjustable parts: initial conditions, assumptions about the apparatus, theories of the observing instruments, models of the particular system under study. The belt is what actually meets the evidence, and the belt is what gets modified, replaced and rebuilt when an anomaly turns up.
3. Negative heuristic. The rule telling you where not to go: never direct modus tollens at the hard core. Any refuting instance must be absorbed by changing something in the belt. This is what makes the core irrefutable, and it is a decision, not a discovery.
4. Positive heuristic. The programme’s “heuristic, that is, a powerful problem-solving machinery, which, with the help of sophisticated mathematical techniques, digests anomalies and even turns them into positive evidence.” It is a partially articulated plan for what to build next: which increasingly realistic models to construct, which anomalies to attack and in which order, which mathematical techniques to develop. It lets scientists get on with work for years without being derailed by every recalcitrant fact.

                 POSITIVE HEURISTIC
        the plan: which model to build next, which
        anomaly to digest, which technique to develop
                          │
                          ▼
   ┌───────────────────────────────────────────────────────┐
   │  PROTECTIVE BELT                                      │
   │  auxiliary hypotheses, initial conditions, theories   │
   │  of the instruments, models of the system.            │
   │  Adjustable. This is where modus tollens is aimed.    │
   │                                                       │
   │          ┌─────────────────────────────────┐          │
   │          │           HARD CORE             │          │
   │          │  Newton: the 3 laws of motion   │          │
   │          │  + the law of gravitation       │          │
   │          │  Irrefutable BY DECISION        │          │
   │          └─────────────────────────────────┘          │
   │                      ▲                                │
   │                      │  NEGATIVE HEURISTIC:           │
   │                      │  do NOT aim modus tollens here │
   │                      X                                │
   └───────────────────────────────────────────────────────┘
              ▲            ▲             ▲
              │            │             │
          anomaly      anomaly       anomaly      <- absorbed by the belt,
      (recalcitrant experience arriving from outside)   never by the core

Where the four names come from

The radio lecture reproduced in Curd & Cover names the hard core and the protective belt explicitly, and speaks of “a heuristic” in the singular. The split into positive and negative heuristic is Lakatos’s own terminology from his fuller statement of the methodology, and it is what the mock exam answer key lists as components (3) and (4). Learn all four names: the marker is working from that key.

Lakatos’s worked illustration of the positive heuristic at work:

The Newtonian astronomer digesting an anomaly

A planet does not move exactly as it should. The Newtonian scientist does not conclude that the law of gravitation is false. He checks:

• his conjectures concerning atmospheric refraction,
• his conjectures concerning the propagation of light in magnetic storms,
• hundreds of other conjectures which are all part of the programme.

“He may even invent a hitherto unknown planet and calculate its position, mass and velocity in order to explain the anomaly.”

Every one of those moves is a change in the protective belt. The three laws and the inverse square law are never on trial.

Background: the invented planet is not hypothetical

Lakatos does not name the case in this text, but he is pointing at Uranus. Its orbit deviated from Newtonian predictions, and Le Verrier and Adams independently postulated an unknown outer planet and calculated where it must be. Neptune was found there in 1846, which was a spectacular success. The same move made for Mercury’s perihelion produced the planet Vulcan, which was never found, and the anomaly was eventually resolved by general relativity instead.

This pair is the perfect illustration of Lakatos’s central claim: the manoeuvre was identical in both cases, so you cannot judge it by its form. You judge it by whether it produced a novel fact.

3.8 All theories are born refuted and die refuted

Newton’s theory of gravitation, Einstein’s relativity theory, quantum mechanics, Marxism and Freudianism are all research programmes, each with a characteristic hard core stubbornly defended, each with a more flexible protective belt, each with an elaborate problem-solving machinery. Each of them, at any stage of its development, has unsolved problems and undigested anomalies.

So the Popperian distinction cannot be that some are still unrefuted while others are already refuted.

• When Newton published the Principia it was common knowledge that it could not properly explain even the motion of the moon. Lunar motion refuted Newton.
• Kaufmann, a distinguished physicist, refuted Einstein’s relativity theory in the very year it was published.

The editors' footnote, and you should know it

Curd & Cover note that Lakatos uses “refuted” loosely. For Lakatos a refutation is any apparently well-founded result that seems to be inconsistent with a theory. In both cases he cites, the “refutations” were later shown to be spurious: the moon’s motion is not actually inconsistent with Newton’s theory, and Kaufmann’s results on beta rays were due to experimental error.

This matters because it shows how bad an idea instant falsification is. If Einstein had behaved as Popper prescribes, he would have abandoned relativity in 1906 on the strength of a measurement that was simply wrong. Tenacity is not a character flaw, it is sometimes the only thing that saves a correct theory.

3.9 Progressive versus degenerating programmes

Lakatos's demarcation criterion

“All the research programmes I admire have one characteristic in common. They all predict novel facts, facts which had been either undreamt of, or have indeed been contradicted by previous or rival programmes.”

• Progressive (scientific): theory leads to the discovery of hitherto unknown novel facts. The programme runs ahead of the evidence.
• Degenerating (pseudoscientific): “theories are fabricated only in order to accommodate known facts.” Theory lags behind the facts and is running fast to catch up.

Note what has been demarcated. Not theories, and not attitudes, but directions of travel over time. Whether a programme is scientific is a question about its track record, which means it is a historical question, and it can change: a degenerating programme can be turned around, and a progressive one can run out.

   PROGRESSIVE                          DEGENERATING

   theory ──────►  prediction           fact ──────► theory patched
                        │                                  │
                        ▼                                  ▼
                   go and look                       "we always said that"
                        │                                  │
                        ▼                                  ▼
                   novel fact found            no new fact, only the old one
                                                     re-described

   theory runs AHEAD of the facts      theory runs BEHIND the facts

The four worked examples, all of which are quotable in the exam.

Halley's comet, the flagship case

In 1686, when Newton published his theory of gravitation, there were two current theories about comets:

• the popular one, that a comet is a signal from an angry God warning that He will strike and bring disaster;
• a little-known theory of Kepler’s, that comets are celestial bodies moving along straight lines.

Newtonian theory says some comets move in hyperbolas or parabolas and never return, while others move in ordinary ellipses. Halley, working inside the Newtonian programme, observed a brief stretch of one comet’s path and calculated that it would return in seventy-two years, to the minute, at a well-defined point of the sky.

“This was incredible. But seventy-two years later, when both Newton and Halley were long dead, Halley’s comet returned exactly as Halley predicted.”

The other three

• Unobserved planets. Newtonian scientists predicted the existence and exact motion of small planets which had never been observed before.
• Einstein’s eclipse. The Einsteinian programme “made the stunning prediction that if one measures the distance between two stars in the night and if one measures the distance between them during the day (when they are visible during an eclipse of the sun), the two measurements will be different.” Nobody had thought to make such an observation before Einstein’s programme. Same episode as Popper’s section 2.4, redescribed as a programme predicting a novel fact rather than a theory surviving a refutation attempt.
• Marxism. “Has, for instance, Marxism ever predicted a stunning novel fact successfully? Never!”

The Marxist record, in Lakatos's own list

Bold early predictions, all failed:

1. The absolute impoverishment of the working class.
2. That the first socialist revolution would take place in the industrially most developed society.
3. That socialist societies would be free of revolutions.
4. That there would be no conflict of interests between socialist countries.

The accommodations, all after the event:

• Rising living standards of the working class were explained by devising a theory of imperialism.
• The revolution occurring in industrially backward Russia was explained.
• Berlin 1953, Budapest 1956, Prague 1968 were “explained”.
• The Russian-Chinese conflict was “explained”.

“But their auxiliary hypotheses were all cooked up after the event to protect Marxian theory from the facts. The Newtonian programme led to novel facts; the Marxian lagged behind the facts and has been running fast to catch up with them.”

Lakatos’s summary of the whole disagreement with Popper:

Lakatos, p. 25

To sum up. The hallmark of empirical progress is not trivial verifications: Popper is right that there are millions of them. It is no success for Newtonian theory that stones, when dropped, fall towards the earth, no matter how often this is repeated. But so-called “refutations” are not the hallmark of empirical failure, as Popper has preached, since all programmes grow in a permanent ocean of anomalies. What really count are dramatic, unexpected, stunning predictions: a few of them are enough to tilt the balance; where theory lags behind the facts, we are dealing with miserable degenerating research programmes.

The distinction that loses people marks

A modification to the protective belt is not automatically an ad hoc rescue.

Popper condemns the modification by its motive and its form: if it was introduced only to absorb the refutation, it lowers the theory’s scientific status. Lakatos says belt modification is normal, constant and necessary, since that is what the positive heuristic is for, and the modification is judged only by its consequences: did the modified programme go on to predict a novel fact that was then found?

Le Verrier’s invented planet and a Marxist’s theory of imperialism are the same manoeuvre in Popper’s terms. In Lakatos’s terms one gave us Neptune and the other gave us nothing, and that is the entire difference.

3.10 Revolutions without irrationality

Lakatos, pp. 25-26

Now, how do scientific revolutions come about? If we have two rival research programmes, and one is progressing while the other is degenerating, scientists tend to join the progressive programme. This is the rationale of scientific revolutions.

Four qualifications, each of which is a point Lakatos is making against somebody.

• Against a naive reading of his own view: “while it is a matter of intellectual honesty to keep the record public, it is not dishonest to stick to a degenerating programme and try to turn it into a progressive one.” Loyalty to a losing programme is allowed. Hiding the score is not.
• Against Popper: “the methodology of scientific research programmes does not offer instant rationality.” Budding programmes must be treated leniently, since a programme may take decades before it gets off the ground and becomes empirically progressive. There is no moment at which a rule tells you to give up.
• Against Popper again: “Criticism is not a Popperian quick kill, by refutation. Important criticism is always constructive: there is no refutation without a better theory.” You do not remove a programme by falsifying it, you remove it by having somewhere better to go.
• Against Kuhn: “Kuhn is wrong in thinking that scientific revolutions are sudden, irrational changes in vision.”

Lakatos, p. 26

The history of science refutes both Popper and Kuhn: on close inspection both Popperian crucial experiments and Kuhnian revolutions turn out to be myths: what normally happens is that progressive research programmes replace degenerating ones.

4. The three positions side by side

	Popper	Kuhn	Lakatos
Unit of appraisal	The individual theory or hypothesis	The paradigm and the community practising under it	The research programme, a series of theories over time
Demarcation criterion	Falsifiability: is a potential falsifier specified in advance?	No explicit criterion; puzzle-solving tradition and a stable community	Progressive versus degenerating: does it predict novel facts?
What a contradiction from experience does	Refutes the theory, which must then be rejected	Becomes an anomaly, tolerated until anomalies accumulate into crisis	Hits the protective belt, is digested by the positive heuristic, never touches the core
Attitude to tenacity	A vice, a conventionalist stratagem, lowers scientific status	A fact about normal science, and functional: it lets puzzle-solving happen	Rational and often correct, since all theories are born refuted
How theory change happens	A crucial experiment kills the theory	A revolution, a Gestalt switch, a conversion experience	Scientists desert a degenerating programme for a progressive rival
Is theory change rational?	Yes, by logic	Not by any algorithm, which is the accusation of irrationalism	Yes, but with no instant rationality and no deadline for surrender
Verdict on crucial experiments	The heart of scientific method	Rare and reconstructed after the fact	A myth, fabricated long after the theory was abandoned

5. Where the lecture lands

• Popper is right that confirmations are cheap and that the interesting question is what a theory forbids.
• Popper is right that the logic of universal statements is asymmetric: no finite evidence proves a law, one counter-instance refutes it.
• Popper is wrong, according to Lakatos, that scientists reject falsified theories, and the history of science does not contain the crucial experiments his methodology requires.
• Lakatos keeps Popper’s demand for objective standards and Kuhn’s respect for actual scientific practice, by shifting the unit of appraisal from the theory to the programme and the test from refutation to novel prediction.
• The cost of Lakatos’s position is that verdicts are only available retrospectively. You can say a programme has been degenerating for thirty years; you cannot tell a scientist today that he must abandon it.

Key Takeaways

Exam Focus

This material is worth 20 points on the mock exam, in two separate questions.

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Question 2 (10 points), verbatim:

Imre Lakatos analyses the development of science in terms of “scientific research programmes”. Describe the components of research programmes, and explain what, according to Lakatos, scientific progress consists in.

The official answer key is only a skeleton: “(1) Hard core; (2) protective belt with auxiliary hypotheses; (3) positive heuristic; (4) negative heuristic. Progressive programme: leads to new discoveries. Degenerating programme: only accommodates known facts.”

A model answer at the half page the rubric allows:

For Lakatos the unit of appraisal is not the isolated hypothesis but the research programme, a series of theories developed over time and sharing a common structure with four components. The hard core is the set of fundamental assumptions that define the programme and give it its identity: for the Newtonian programme, the three laws of mechanics and the law of gravitation. It is held irrefutable by a methodological decision of its practitioners. The protective belt consists of the auxiliary hypotheses, initial conditions and theories of the instruments that surround the core. The belt is what actually confronts the evidence and it is what gets modified when an anomaly appears. The negative heuristic is the rule that modus tollens is never to be directed at the hard core, so the blame for any anomaly must be placed somewhere in the belt. The positive heuristic is the programme’s problem-solving machinery, a partially articulated plan for how to develop the belt, which models to build next and which anomalies to digest. A Newtonian facing a misbehaving planet checks atmospheric refraction, the propagation of light in magnetic storms, and hundreds of other conjectures, and may even invent an unknown planet and calculate its position, mass and velocity.

Progress cannot consist in remaining unrefuted, because all programmes grow in a permanent ocean of anomalies and all theories are born refuted and die refuted. A programme is progressive when it predicts novel facts, facts that were undreamt of or were contradicted by rival programmes: Halley calculated from a short stretch of a comet’s path that it would return in seventy-two years, and it did; Einstein’s programme predicted that the separation of two stars measured during an eclipse would differ from their separation measured at night, an observation nobody had thought to make. A programme is degenerating when its theories are fabricated only to accommodate facts already known, so that theory lags behind the facts and runs to catch up. Marxism never predicted a stunning novel fact, and its auxiliary hypotheses, the theory of imperialism among them, were cooked up after the event. Scientific revolutions consist in scientists deserting a degenerating programme for a progressive rival.

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Question 3 (10 points), verbatim:

Popper praised Albert Einstein’s theory of general relativity as a truly scientific theory, citing the example of Eddington’s expedition. This expedition set out to measure the shift of a distant star during a solar eclipse. Einstein’s theory states that large masses, like the sun, curve space-time. Thus, incoming light rays will follow a curved path around the sun and will appear in a different spot as seen from the earth. The theory makes a very precise prediction about this shift. In 1953, however, Einstein was asked how he would have responded to a measurement outcome that did not show this shift: “Then I am very sorry for the dear Lord [Eddington], for the theory is correct.” Would, and-or could, this be acceptable for Popper? Explain your answer.

The key: “No, assuming that the measurement was correct: the theory is falsified and has to be rejected. Einstein shows a dogmatic attitude. However: perhaps the measurement was not correct. Given the Duhem-Quine thesis, scientists can always put blame elsewhere and retain the theory/hypothesis. However, according to Popper, this is only acceptable if there are independent reasons for rejecting the measurement result (no ad hoc hypothesis).”

A model answer:

No, not if the measurement was sound. For Popper the criterion of the scientific status of a theory is its falsifiability, and Eddington’s expedition is precisely the kind of risky prediction that earns general relativity that status: the theory forbids the null result that everybody before Einstein would have expected, so a null result would simply refute it and the theory would have to be given up. Einstein’s reply is dogmatic in exactly Popper’s sense. It is the same move as the Marxists who re-interpreted theory and evidence to make them agree, and it rescues the theory only at the price of destroying, or at least lowering, its scientific status.

Could he make the move at all? Yes, and this is the second half of the answer. The prediction is not derived from general relativity alone but from the theory conjoined with auxiliary assumptions: the optics of the telescopes, the behaviour of the photographic plates, the reduction of the data, the identification of the stars. By the Duhem-Quine thesis a negative result falsifies only the conjunction of all of these, not general relativity in particular, so the scientist can always place the blame elsewhere and doubt the measurement.

Popper allows this under one condition. Rejecting the measurement is legitimate only if there are independent reasons for rejecting it, reasons that do not consist merely in the fact that the theory would otherwise be refuted. With independent reasons it is a normal correction. Without them it is an ad hoc auxiliary hypothesis, a conventionalist stratagem, and it is illegitimate. Einstein as quoted offers no independent reason, only his confidence in the theory, so on Popper’s criterion the reply is not acceptable.

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Question 1 is also half this material. It asks for the verifiability criterion of meaning and its significance for demarcation. Have the Carnap-versus-Popper contrast in section 2.9 ready: verifiability demarcates meaningful from meaningless, falsifiability demarcates scientific from non-scientific, and for Popper the non-scientific is still meaningful and sometimes the ancestor of later science.

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Memorise cold:

1. The four components, in the key’s order: hard core, protective belt of auxiliary hypotheses, positive heuristic, negative heuristic.
2. Progressive predicts novel facts. Degenerating only accommodates known facts. Use those exact words.
3. Popper’s criterion in one sentence: the criterion of the scientific status of a theory is its falsifiability, or refutability, or testability.
4. “Irrefutability is not a virtue of a theory but a vice”, and “the more a theory forbids, the better it is.”
5. The ad hoc condition: blaming the measurement is allowed only with independent reasons.
6. One progressive example (Halley’s comet, seventy-two years) and one degenerating example (Marxism’s four failed predictions plus the theory of imperialism cooked up afterwards).
7. Lakatos’s objection to Popper in one line: scientists have thick skins, they call contradictions anomalies rather than refutations, and a Newtonian asked to name a potential falsifier would be as nonplussed as a Marxist.

Three traps

1. Do not write that Lakatos says the hard core is unfalsifiable in principle. It is protected by a methodological decision (the negative heuristic), not by logic or by meaning. That is what makes the protection revocable when the programme degenerates.
2. Do not treat protective-belt modification as automatically ad hoc. For Popper the motive damns it; for Lakatos it is normal science, and only the absence of subsequent novel predictions damns it.
3. Do not say Popper thinks a falsified theory is proved false and gone forever. Falsification is a decision to reject, taken under Duhem-Quine ambiguity about where the blame lies, and Popper’s own escape clause about independent reasons is what question 3 is testing.

Links

• Course: Course overview
• Same week: PhilSci-L01 - Introduction and Logical Empiricism for Carnap, verificationism and the Vienna Circle that Popper is arguing against
• Next: PhilSci-L02 - Kuhn on Scientific Practice for paradigms, normal science and the irrationalism charge Lakatos is trying to avoid
• Related: PhilSci-L03 - Under-determination for the Duhem-Quine machinery behind the ad hoc rescue and behind the protective belt
• Source: Curd & Cover, Philosophy of Science: The Central Issues, chapter 1. Popper, “Science: Conjectures and Refutations”, pp. 3-10 (week 1 reading). Lakatos, “Science and Pseudoscience”, pp. 20-26 (listed under week 2 in the syllabus, taught with the Popper material). Chapter introduction, pp. 1-2.
• Primary texts: Popper, Conjectures and Refutations (Routledge and Kegan Paul, 1963), pp. 33-39, originally a 1953 Peterhouse lecture published as “Philosophy of Science: A Personal Report”. Popper, The Logic of Scientific Discovery (1934, English 1959), Appendix vii for the zero-probability argument. Lakatos, Philosophical Papers, vol. 1 (Cambridge, 1977), pp. 1-7, originally an Open University radio lecture broadcast 30 June 1973.