Last modified on Thursday, September 24, 1998, by Malcolm R. Forster

1. Subjective or objective? Kuhn’s demarcation criterion appears to be subjective--it depends on what scientists do and what they believe (their psychology). In contrast, Lakatos insists that "a statement may be pseudoscientific even if it is eminently ‘plausible’ and everyone believes in it." Belief that earth is flat may count as an example of that. And "it may be scientifically valuable even if it is unbelievable and nobody believes in it." Copernicus's theory that the sun moves like that, and very few believed in evolution when Darwin introduced his theory.
2. Sociology or logic? Another point of disagreement between Kuhn and Lakatos is whether a demarcation criterion should be talking about which statements are scientific or pseudoscientific, or whether it should be saying which community is scientific or unscientific. Lakatos, as a neo-Popperian, was raised in the tradition in which logic was the main tool in philosophy of science, whereas Kuhn is more interested in the sociology of science.
3. Religion or Science? Kuhn compares science to religion, but Lakatos rejects this comparison.

Any good science can be practiced in a pseudoscientific way. The demarcation between science and pseudoscience refers to its method and not just what the theory says (its content).

• For example, some evolutionists may be tempted to fill in auxiliary assumptions in an ad hoc way by working backwards from what is to be explained. For example, if see from the fossil record that horses teeth become elongated, we may be tempted into using evolutionary theory to infer that there was some change in the environment that made shorter teeth less fit, and then explain the change by appealing to the law of natural selection that "only the fittest survive."
• It would be equally easy for Newtonian mechanics to be practiced in a pseudoscientific way. After all, Newton’s law of inertia says that a body continues in a straight line with uniform velocity until acted on by a force, and then defines a force as anything that diverts a body from uniform motion in a straight line.

1. Lakatos argues that ‘falsifiable’ already refers to how science is practiced. He interprets Popper as demanding that scientists "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.’ If so, Popper does not demarcate scientific statements for pseudoscientific ones, but rather scientific method from non-scientific method."
2. While Popper’s criterion does focus on practice, it is still wrong because it "ignores the remarkable tenacity of theories." Scientists will either invent some rescue hypothesis (accommodate the theory) or ignore the problem and direct their attention to other problems. For example, some problems may be too hard (nobody rejected Newtonian mechanics because it couldn’t predict all the properties of turbulent fluid flow, or the chaotic motion of a physical pendulum).

Earlier, we saw that Popper's two examples, Adler's theory at one extreme, and Einstein's theory at the other, illustrated a difference between accommodation and prediction. Adler's theory merely accommodated the facts because it worked backwards from the evidence E to the auxiliary assumption A needed so that the theory T entailed E (T & A Þ E). At the other extreme, if intellectual honesty requires that a scientist specify a ‘potential’ falsifier’ in advance, then they must specify A in advance. That is a sufficient condition for the theory to make a prediction. But is it necessary?

The typical unit of science is not an isolated hypothesis, but rather a research programme, consisting in a hard core (theory), protective belt (auxiliary assumptions) and a heuristic.

Lakatos quote: A heuristic is a "powerful problem solving machinery, which with the help of sophisticated mathematical techniques, digests anomalies and even turns them into positive evidence. For instance, if a planet does not move exactly as it should, the Newtonian scientist checks his conjectures concerning atmospheric refraction, concerning propagation of light in magnetic storms, and hundreds of other conjectures that 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." (Lakatos, 1977, p. 5)

• In Kuhn's terminology: Heuristics are hints about how to solve normal science puzzles.

• In my terms: A heuristic is a hint about how to change the auxiliary assumptions so that the theory better fits the facts.

The negative heuristic forbids scientists to question or criticize the hard core of a research programme. "The positive heuristic consists of a partially articulated set of suggestions or hints on how to change, develop the 'refutable variants' of the research programme, how to modify, sophisticate, the 'refutable' protective belt." (Lakatos, 1970, p.135).

Example: Le Verrier and Adams were faced with the following problem in Newton's theory of planetary motion. There were discrepancies (unpredicted wobbles) in the motion of the outermost planet known at the time (Uranus). They postulated that these might be caused by a hitherto unknown planet. Based on that conjecture they recalculated the solutions to Newton's equations, and fit the solutions to the known data for Uranus. That fit even predicted the position of the postulated planet, whereupon Neptune was seen for the first time once telescopes were pointed in that direction (actually, it was later discovered that it had been seen before, but mistaken for a comet).

• In this example, the positive heuristic used was something like this: "If there is an anomaly in Newton's theory on the assumption that there are n planets, then try assuming that there are n+1 planets."

We have identified auxiliary assumptions with Lakatos's protective belt. That is, we are assuming that auxiliary assumptions are always provisional in some sense. However, we must now decide whether to count statements of background evidence, prior observations, and data, as auxiliary assumptions. They are auxiliary in the sense that they are needed in order to make predictions. In the Le Verrier-Adams example it would be impossible to predict the position of the postulated planet without making use of the observed positions of Uranus, and the other planets. Let use refer to this background data by the letter D ('D' for data). We now replace the previous pattern of inference (T & A Þ E) by the pattern:

T & A & D Þ E.

We still refer to A as the auxiliary assumption, but with the explicit understanding that it excludes the background observational evidence or data D.

It may be useful at this point to introduce the concept of a model. A model is theoretical statement, (often in the form of an equation) usually deduced from a theory with the aid a auxiliary assumptions. That is, a model M is equal to a theory T combined with an auxiliary assumption A (which will be long list of assumptions in most cases). That is, M = T & A.

Example: In the LeVerrier-Adams example, there was first a Newtonian model of planetary motion that assumed that there are only 7 planets. There were discrepancies between the predictions of this model and the observed motions of Uranus. Therefore, the model was replaced by one that assumed the existence of 8 planets. Not only did that accommodate the anomalous motion of Uranus, but it predicted position of the eighth planet, whereupon Neptune was discovered.

Remarks:

1. A model M is falsified when M & D Þ E because D is not blamed for the failed prediction. Therefore, models are falsifiable, or refutable, even though theories are not.
2. The notion of a 'model' corresponds to Lakatos's notion of a 'refutable variant of a theory'. If a Lakatosian heuristic defines an ordered list of auxiliary assumptions, A₀, A₁, A₂, A₃, ... then it also defines an ordered list of models M₀, M₁, M₂, M₃, ...
3. This use of the term 'model' differs from two other uses that are common in the philosophy of science. (a) A 'model' as in a model airplane. Such models do appear in science, such as in the 'model of the DNA molecule' Watson and Crick used, which was made of wooden balls joined with sticks. (b) 'Model' in the sense used by mathematicians in model theory. There it has a rather technical meaning, which corresponds roughly to what logicians call an interpretation of a language (an assignment of objects to names, set of objects to properties, a set of object pairs to relations, and so on).
4. Scientists use the term 'model' all the time, and it very rarely fits sense (a) and absolutely never fits sense (b). Our use of the term best fits the standard scientific usage.

If a heuristics exists, then a scientist has an ordered list of suggested models M₀, M₁, M₂, M₃, ... Now the theory T is no longer falsifiable in Popper's methodological sense, for if a scientist tries makes the prediction E₀ from model M₀ and E₀ proves to be false, then the scientist does not blame T, but instead moves to M₁, because it is next on the ordered list, and so on. Scientists now predict E₁ because M₁ & B Þ E₁. And so on. There is no falsifiability of the theory, but it can still make predictions. Thus, the idea of a heuristic may save the distinction between accommodation and prediction, and thereby providing a weaker sufficient condition for prediction.

• Note that the research program makes a different set of predictions at different times. This allows Lakatos to introduce the idea of novel predictions--new predictions not make before.

Lakatos does not believe that falsification is important in science, but like Kuhn, he does recognize that theories, or paradigms, are superceded in science. He objects to Kuhn's description of this process, of scientific revolutions, as being a like a religious conversion, or a social revolution. Lakatos things that the process is more objective. Here is his view.

Thesis: A model M¢ supercedes a model M if and only if (1) M¢ has excess empirical content over T : that is, it predicts novel facts, that is, facts improbable in light of, or even forbidden by M; (2) M¢ explains the previous success of M, that is, all the unrefuted content of M is contained (within the limits of observational error) in the content of M¢ ; and (3) some excess content of M¢ is corroborated. (see Lakatos, 1970, p. 116; the phrase "should supercede" is my paraphrase, and I have replaced 'theory' by 'model'.)

• This is Lakatos's account of normal science.

Lakatos introduces some new terminology to help formulate his theory of science.

1. A problemshift is a series of models ...M₁, M₂, ... such that (i) each can explain the empirical success of its predecessor, and (ii) each can explain at least some of the emprical failure of it predecessor as well. In other words, a Lakatosian problemshift occurs whenever a Kuhnian solution to a normal science puzzle is found, since to be a solution is must remove the anomaly with creating new one. Note that a problemshift does not have to make novel predictions.
2. A theoretically progressive problemshift is a problemshift that predicts some novel facts.
3. A problemshift is empirically progressive if it is theoretically progressive and some of the novel predictions have been corroborated.

Note: In Lakatos's original writings, Lakatos uses the word 'theory' instead of 'model', but only because he fails to make the distinction. I think that he models in mind.

Definition: A problemshift is progressive if it is theoretically and empirically progressive. Otherwise the problemshift is degenerating. The idea of a degenerating problemshift corresponds to Kuhn's notion of crisis.

Example 1: The LeVerrier-Adams discovery of Neptune is a great example of a problemshift that was progressive, because (1) it led to novel predictions (the position of Neptune), which (2) were then corroborated.

Example 2: Ptolemaic astronomy was degenerating not because it failed to be theoretically progressive (Ptolemaic astronomers had the option of adding more epicycles) but because it was not empirically progressive. That is, adding an epicycle would lead to novel predictions, but they were not corroborated (confirmed).

What is Lakatos's theory about when one theory should supercede another? In fact, Lakatos does not provide such a criterion. Not even when one research program is degenerating and another is progressive does Lakatos say that scientists do or should only work on the progressive one, because like the stock-market, they may change their status over time.

• The methodology of scientific research programmes does not offer instant rationality.

It is not irrational for a scientist to work on a young research programme if she thinks it shows potential. Nor is it irrational for a scientist to stick with an old programme in the hope of making it progressive. Thus, Lakatos appears to agree with Kuhn that theory change is a rather fuzzy phenomenon. But he does insist that it depends on the assessment of objective facts--the future progressiveness or degeneration of research programs. The decision of scientists, however, must rely of their subjective predictions of the future course of science. Unlike Kuhn, Lakatos does not think that the uncertainty makes these decisions irrational.

Example 3: Prout's program. Prout, in 1815, claimed that the atomic weights of all pure elements were whole numbers. He knew that the experimental results known at the time did not confirm his theory, but he thought that this arose because chemical substances as they naturally occurred were impure. Thus, there ensued a program of research whereby chemical substances were purified by chemical means. This program led from one failure to the next. The program at this stage was degenerating. However, Rutherford's school explained this failure by the fact that different elements can be chemically identical (as explained by the periodic table). They proposed that the substances should be purified by physical means (powerful centrifuges), whereupon the program made a progressive shift. Lakatos (1970, pp.138-140) uses this as an example of why it would be wrong to advise scientists to instantly abandon a degenerating research program.

Question: We have talked about Lakatos's view of normal science and revolutionary science. However, this is separate from the demarcation issue. Popper thinks that the essence of science lies in the nature of revolutions, but Kuhn thinks that the essence of science lies in the nature of non-revolutionary science. Where does Lakatos stand on this issue?

Lakatos is not explicit about his demarcation criterion in the passage we read, but he is explicit about in his 1970 article: "We 'accept' problemshifts as 'scientific' only if they are at least theoretically progressive; if they are not, we 'reject' them as 'pseudoscientific.'" (1970, p. 118)

Presumably, therefore, a research program is scientific if and only if it is at least theoretically progressive. Note that it is possible for a research program to be scientific at one time, but not at another. It is even that a program practiced by one group is scientific, while the practice of another group is pseudoscientific. This is how Lakatos is agreeing with Kuhn's point that even a good theory can always be practiced in a pseudoscientific was. Thus, Adler's theory (about inferiority complexes) might potentially be a good theory, but the fact is that it was being practiced in a pseudoscientific way (if Popper's account is correct).

• Lakatos is agreeing with Kuhn, against Popper, that the essence of science lies in the nature of normal science.

Example 4: Astrology. Astrology has no theoretically progressive problemshifts, and therefore no empirically progressive problemshifts. That is, it made no novel predictions, despite that fact that it made predictions. Therefore, astrology was not a science.

Example 5: Prout's program. While Prout's program was degenerating, it was still theoretically progressive, and hence scientific.

Example 6: Jeane Dixon was a self-proclaimed psychic who predicted that JFK's assassination. She made over 200 predictions each year (most of them wrong of course). Did her method count as scientific? It would be by Popper's criterion, but not by Kuhn's or Lakatos's demarcation criteria. Like astrology, there was no Kuhnian puzzle solving, and no theoretically progressive problemshifts.

In an article called "Method or Madness" (in Cohen, R. S., Feyerabend, P. K.. and Wartofsky, M. W. (eds) Essays in Memory of Irme Lakatos, Dordrecht, Holland, D. Reidel), Alan Musgrave (1976) raises some interesting objections to Lakatos's theory of science, which I have expanded upon in places.

1. Is the negative heuristic needed? Before 1850, Newtonian seldom treated Newton's law of gravitation as part of the hard core. Therefore, scientists did not follow Lakatos's methodology and render Newton's laws unfalsifiable by fiat. And why should scientists have to specify in advance not to modify or renounce them in the face of difficulties. Surely, it is enough that it is harder to produce theoretically problemshifts by changing central assumptions because it is then harder to explain all the successes of the superceded model. But there is no reason to rule it out in advance.
2. Are positive heuristics always specified in advance? Where was the positive heuristic in the example of Prout's program? No-one tried physical separation of chemical substances as soon as the chemical methods failed. They kept trying to improve the chemical methods. It was only after the discovery of chemical similarities that the hint or suggestion appeared.
3. Why not compare one research program against another? Musgrave thinks that Lakatos is overcautious in not recommending any rule for choice between competing research programs. Why not say, that on the whole, the scientific community should devote more resources to progressive as opposed to degenerating research programs?