methodology walkabout

Methodology Walkabout

Every subject has its own methodology. Obviously, some are more interesting than others. Methodologies change over time. As Darwinian creatures under the rubric of evolutionary epistemology we have to track the changes and adapt.


After I have given a sketch of the Lakatos model below I shall show how it may be applied to Andrew Wiles' proof of Fermat's Last Theorem.


The unit of change for Lakatos is not a paradigm (Kuhn), not a theory or hypothesis or basic statement (Popper), not theories and observation sentences (Quine & the justificationist fallibilists) but a Scientific Research Programme (SRP).

A Scientific Research Programme is a sequence of scientific theories such that each theory in the sequence is a modification of its predecessor.

A Scientific Research Programme has one central sub-component, two accompanying structures and a protective auxiliary belt.

The central sub-component is the hard core, which is a set of theoretical assertions or statements. Any theory which belongs to a Scientific Research Programme must subscribe to the truth of the statements in the hard core. The hard core is "conventionally accepted" and is provisionally not refutable.
The first companion structure is the negative heuristic which is a methodological principle which implies that the theoretical assertions in the hard core are not to be abandoned in the face of anomalies and counter-examples. You may abandon auxiliary observational hypotheses, or basic statements, or statements of initial conditions.

The second companion structure is the positive heuristic which is a partially articulated set of suggestions or hints on how to develop, expand or change the potentially refutable variants of the research programme, and a set of suggestions on how to make the refutable protective belt more sophisticated.

The current theory in a SRP always has a protective belt of auxiliary observational hypotheses, and is able to specify initial conditions. Testable predictions are derived from initial conditions and auxiliary observational hypotheses. The theory's auxiliary belt (TAB) is the set of all observational hypotheses which are testable.

A SRP is said to be progressive if its theoretical growth anticipates its empirical growth. Progressive SRP's have increasing empirical content and predict new facts. A SRP is said to be degenerating if its theoretical growth has slowed down and lags behind its empirical growth, and when it gives post hoc explanations of facts predicted by or discovered by a competitor SRP.


Lakatos says we should regard theory T as falsified if and only if (iff):

1) another theory R has excess empirical content of T; that is it predicts novel facts; i.e. facts improbable in the light of, or even forbidden by T.

2) R explains the previous success of T, i.e., all the unrefuted content of T is included (within the limits of observational error) in the content of R; AND

3) some of the excess content of R is corroborated.

Lakatos believes we should not model the growth of scientific knowledge as a two cornered fight between theory and experiment. We should view it as a three cornered fight between 2 rival theories and an experiment. In the fight the world acts as referee. Lakatos wants to defend a realist view of science.

An example of FALSIFICATION in MATHEMATICS if we use the falsificationist methodology of Imre Lakatos

The monograph PROOFS AND REFUTATIONS by Imre Lakatos, C.U.P. 1976, was based on the first 3 chapters of his 1961 Ph.D. thesis for the London School of Economics.
Reuben Hersh says that Proofs and Refutations is "... an overwhelming work. The effect of its polemical brilliance, its complexity of argument and self-conscious sophistication, its sheer weight of historical learning, is to dazzle the reader."

In PROOFS Lakatos tries to show that the best understanding of what mathematicians do when they produce proofs for theorems is a variation of Popperian falsificationism. That is, mathematicians advance their subject much like natural scientists do by conjecturing the truth of a hypothesis, lemma or theorem and then showing that the theorem is not false or cannot be falsified, by providing a logic chain, from axioms or pre-established accepted mathematical truths to the desired conclusion, the truth of the theorem in question.
In the case of natural science according to Lakatos, you conjecture a whole set of alleged scientific truths, which are embedded in a research programme, and it is in a Darwinian knowledge world that the research programme competes against other research programmes for survival.

One of the most important mathematical proofs of the 20th Century was that of Fermat's Last Theorem by Andrew Wiles. I think that if you break up the proof, which is more than 200 pages long, you get logical chunks which are best understood in the way Lakatos is suggesting we understand them. I shall try to sketch how this works below.

Andrew Wiles and Fermat's Last Theorem

1. Frey at the Oberwolffach conference showed that; If a certain equation in number theory, which he identified, is possible, then the Taniyama-Shimura (T-S) conjecture is false, and Fermat's Last Theorem (F.L.T.) is false.
So Wiles was able to Conjecture that if Frey is correct, then if the Taniyama-Shimura conjecture is true, then Fermat's Last Theorem must also be true. And this is only possible if Frey's equation is false. But the exact way in which the truth of (T-S) would imply (F.L.T.) was not evident to Wiles in the early stages of constructing the proof of (F.L.T.).
2. Ken Ribet was able to show, and communicate to Wiles, a rough sketch or more or less how, given that Frey is correct, (T-S) conjecture implies the truth of (F.L.T.)
3. Wiles therefore settled down to prove the truth of the (T-S) conjecture. There are other more human conjectures at play here. Wiles had to conjecture that he could prove FLT, provided he isolated himself from the Princeton maths dept., provided he immersed himself in certain methods and techniques he was not at home with, etc.
4. Wiles then conjectured that he could use the methods and work of Iwasawa to establish the link between elliptical curves and modular forms. This way ahead did not work, and Wiles had to admit that his conjecture was false.
5. Wiles then conjectured that he could use the methods and work of Kolyvagin-Flach, instead of Iwasawa, with the use of Hecke algebras, to link the infinite number of elliptical curves to the infinite number of modular forms. This conjecture was falsified by Wiles and his assistant Taylor.
6. Wiles then conjectured that both the above methods taken together, Iwasawa and Kolyvagin-Flach, with the use of Hecke algebras, could jointly be used to link elliptical curves to modular forms. Wiles and Taylor were then able create the maths to to prove this, i.e. the conjecture wass not falsified.
7. The proof was then submitted, refereed and published. This was the second time that Wiles had submitted the proof of (F.L.T.) for publication. The first time round a gap was discovered in the logic chain, thus showing a 'local' counter-example to the proof. According to Lakatos a 'local counter example' is one which falsifies a part of the logic chain, but does not threaten the proof as a whole. A error or mistake that threatens the proof as a whole he calls a 'global counter-example'. The function of the referees in both rounds was to try to falsify the logic by finding local or global counter-examples.
8. So in overview, the global conjectures which formed the backbone of the proof of (F.L.T.) are those identified in pargraphs 1, 2 and 6 above. In each case Wiles or Wiles and his assistant Taylor, had to provide a logic chain to establish the truth of the conjecture, in order to show that the conjecture was not false and given the nature of the logic chain probably not falsifiable.

LAKATOS' MODEL applied to:


I take the following example from "The Invisible Ape", by Jerold Lowenstein and Adrienne Zihlman in New Scientist, 1988, and in some places I have, in order to specify their example accurately, borrowed some of the terminology used by Lowenstein and Zihlman.

The example fits the Lakatos analysis, and shows how accepted evidence, which is apparently "absolutely obvious", for a theory, can be overturned by non-obvious, counter-intuitive evidence, which rests on a new technique. It particularly highlights the idea of a degenerating problemshift, as opposed to a progressive problemshift.

The original conjecture was that:
Chimpanzees and gorillas are more closely related to each other than to humans. This was held to be an obvious fact by the physical anthropologists because of the evidence:

They look more like each other. They are hairy; Men are smooth. Chimpanzees and gorillas walk on all fours;we walk on our hind limbs. Chimpanzees and gorillas have short legs and long arms but with not very flexible hands; we have long legs and short arms with very flexible hands. They walk on their knuckles; we do not, and cannot easily walk on our knuckles, since our hands cannot bear much weight. Their brains are small; ours are large. Their canine teeth are large; ours small. Their molars have thin enamel; ours have thick enamel.

For more than 100 years these differences convinced comparative anatomists and physical anthropologists of the truth of the conjecture. If it were true then our common ancestor the invisible conjectured ape would remain a mystery.
Was it a knuckle walker like Chimps? Or a biped like us? Or something very different looking?

According to Lowenstein and Zihlman the attitudes adopted by the physical anthropologists during the debate correspond to the four stages of human reaction to a bereavement:"first denial, then rage, next grief, and finally sadness and reluctant acceptance".

Denial Stage: In the decade of the 1960's, Morris Goodman and Vincent Sarich (U.C Berkeley) showed by immunological tests of blood proteins that humans, chimps and gorillas are closely related. This implied that the three lineages separated only 5 million years ago.
The physical anthropologists denied this. They already had a 14 million year old human ancestor "Ramapithecus". This implied a divergence of apes and humans between 15-20 million years ago.
The molecular data contradicted the morphological evidence and fossil record.

Rage: The issue during the decade of the 1970's was: What kind of evidence best establishes genetic relationships through time; morphology and the fossil record or molecules?

Mary Clair-King and Allen Wilson (U.C. Berkeley) asked: How could humans look so different from chimps and gorillas when all showed the same degree of difference at the molecular level? (from 1%to 5%)
Answer: Only 1% to 5% of the DNA Genome is expressed as proteins. Between 95 and 99% consists of Introns or pseudogenes, so called "junk" genes. This is DNA that goes along for the ride, without doing any work. The "junk" genes replicate from generation to generation without affecting morphology. All this extra DNA is not much use to the organism but it is useful to researchers.

This DNA is not impeded by natural selection. It accumulates mutations at an even faster rate than the coding sequences of DNA. So it provides a fast biological clock for timing evolutionary differences, and a possible way of resolving the problem.
Three techniques called DNA sequencing, Mitochondrial DNA sequencing, and DNA hybridisation, suggest three different lines of evidence which support the chimp/human similarity, and chimp/human versus gorilla difference.
DNA Hybridisation bears same relationship to DNA sequencing as protein immunology does to protein sequencing.
It compares two large molecules by measuring their overall similarities and differences.
The double strands in the human DNA helix can be "melted" by heat into single strands. Then these can be "melted" with strands from chimpanzee molecules into a single strand. The hybrid is a chimp-human strand. The hybrids separate at a lower temperature (like sections of a defective zipper) than the human or chimp originals because of mismatches, in the base pairs. A 1º difference of temp. represents a 1% difference in the sequence.

Grief: Charles Sibley and Jon Ahlquist (Yale) found that chimp-human hybrids are 20% more stable than chimp-gorilla or human-gorilla hybrids. This implies that gorillas split off from chimps/humans approximately 1 million years before the chimps/humans split from each other.

Sadness and reluctant acceptance: In the mid 1980's after 20 years of defence the physical anthropologists and palaeontologists abandoned their original hypothesis that Ramapithecus was a human ancestor, and that chimps and gorillas are more closely related to each other than to humans. On the basis of the bone and teeth fragments that they thought supported their original theory, and which, with benefit of hindsight, led them astray, the palaeontologists now proclaim that Ramapithecus is an ancestor to orang-utans.

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Its easy to explain the conflict above using Lakatos' model....
The example is a perfect fit for the Lakatos model, becuse it shows how accepted evidence, which is apparently "absolutely obvious", for a theory, can be overturned by non-obvious, counter-intuitive evidence, which rests on a new technique. It particularly highlights the Lakatosian idea of a degenerating problemshift, as opposed to a progressive problemshift.


You start with the data to be explained. This maybe some feature like sex, or aggression or altruism or parental investment or whatever. (or it might be an aspect of leadership; or some aspect of how leaders lead, or of why others follow their leadership etc. How leaders are chosen, or what features they have)

You bring the assumptions and techniques and tools of SOCIO-BIOLOGY (a.k.a. POPULATION BIOLOGY) to bear on the data.
What you are looking for is an applied explanation for some aspect of the chosen feature which relies also on some of the supplementary theories listed below.

So for the chosen aspect of sex, or aggression, or altruism, or parental investment or leadership or whatever) one needs:

1. an explanation of the the chosen feature in primate & hunter gatherer societies & now in modern humans;
followed by,
(2) how it is physically operated in real time in a phenotype through memory lookup and the application of rules or precedents;
followed by (3) what happens at the neuroscience level in the left cerebral hemisphere that co-ordinates the chosen feature;
followed by (4) how this aspect is developed in pre-teenagers & teenagers;
followed by an (5) explication of the modifications of brain circuitry in our ancestors which allowed them to benefit (their inclusive fitness etc. from the chosen feature.

The set of hierarchical explanations used would invoke the supplementary theories listed below.

Supplementary intermediate theories - which are supplementary to - sociobiology are used in (hierarchical reductive) explanations for this data;

* evolutionary psychology (linking biology to culture)
*cognitive science ( linking biology to culture)
*cognitive neuroscience (linking the social or tribal mind through the individual mind to matter)
*behavioural genetics (linking group behaviour to individuals to genes)
*genetics (linking the individual to genes)

If you set the socio-biological explanations, supported by specialised sub-explanations from, cognitive science, cognitive neuroscience, behavioural genetics and genetics for your chosen feature side by side with an explanation from sociology under standard social science model (SSSM) or some standard theory of psychology under (SSSM) there could be very little contest from the old paradigm. And there would be very little common ground. The explanations under the evolutionary rubric, (with specialised sub-explanations from, cognitive science, cognitive neuroscience, behavioural genetics and genetics) would be incomparably richer than those from the old SSSM paradigm. And they would also be scientific, something which the old SSSM is not.

& & &

The major theories: Regular Biology & Sociobiology ( a.k.a. Population Biology)

Data Box A
Data to be explained by the major theory
1. behaviour of human populations & human culture & “social or tribal mind”
Supplementary intermediate theories used in hierarchical reductive explanations
* evolutionary psychology
*cognitive science
*cognitive neuroscience
*behavioural genetics

& & &

On the old (not yet discarded) paradigms the explanatory job above was supposed to be done by the SSSM using a standard theory of sociology (Durkheim / structural functionalism/ etc) or some version of Marxism with a little help from, so called, .

Data Box B
Data to be explained by the major theory
1. behaviour of human individuals & individual human culture & individual mind
Intermediate theories used in hierarchical reductive explanations
* evolutionary psychology
*cognitive science
*cognitive neuroscience
*behavioural genetics
* genetics

& & &

On the old (not yet discarded) paradigms the explanatory job above was supposed to be done by behaviourism or Freudianism or some other chosen theory of psychology using the same misguided assumptions from the SSSM.

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Contemporary Issues in the Philosophy of Science - 1981-1986

Published in the Human Sciences Research Council; Research Bulletin; pp. 51-57, vol. 16 No.5 1986

Zak Van Straaten, Anne Bezuidenhout and Helen Brown
Institute for Advanced Studies in Philosophy, University of Cape Town

Published in the Human Sciences Research Council; Research Bulletin; pp. 51-57, vol. 16 No.5 1986

Contemporary Issues in the Philosophy of Science 1981-1986

The purpose of this paper is to give an indication of the nature of the questions to which contemporary philosophers of science address themselves and to indicate the nature of the answers they offer to such questions. We begin by listing some of the topics that philosophers of science are interested in: “What is the structure of scientific theories?”, “What constitutes an adequate scientific theory?”, “Can a distinction be made between observation and theory?”, “What is the relation between a scientific theory and the evidence we have for it?” “How can the simplicity of theories be measured?”, “What is the relation between the philosophy and the history of science?”, “Can the distinction between the context of discovery of a theory and the context of its justification be made?”. However, owing to space limits we shall discuss only two current debates in which some of these topics are central.


Much of the philosophy of science done in the last thirty years can be seen as a debate between those who hold a rationalist, and those who hold an anti-rationalist view of science. In general, the rationalist believes that there has been, and can be, progress in science, that there is such a thing as scientific method and that there are rationally justifiable criteria for choosing between competing scientific theories. The anti-rationalist on the other hand typically believes that the historical succession of scientific theories about a subject is merely a series of changes of view about that subject. There can be no progress in science. There are no rationally-justifiable criteria for choosing between theories, and all changes of theory have to be explained by appeal to sociological factors. Moreover, there is no such thing as scientific method. Scientists do not have a fixed set of methodological rules that they use foe generating and testing theories. In this section we will briefly outline the view of four philosophers of science.(*) Two of these philosophers, namely Karl Popper and Imre Latatos are, or purport to be, rationalists and the other two, namely Thomas Kuhn and Paul Feyerabend, are, or claim to be, anti-rationalists.(1) Our intention is to illuminate some problems in the philosophy of science by sketching the positions that four contemporary philosophers of science have taken with regard to these problems.


Popper believes that it is possible to give a rationalist account of science. Following John Herschel and Hans Reichenbach, he draws a distinction between the context of discovery and the context of justification of scientific theories. How a scientist comes to propose a theory is strictly irrelevant to the question of whether the theory is acceptable or not. How theories are discovered is no doubt an interesting question, but is one which should be left to phychologists and sociologists to answer. It has nothing to do with the philosophical problem of justifying theories. The point is that even a theory which is the product of the ravings or a lunatic can be submitted to rational criticism and to rational testing procedures, with a view to establishing its acceptability. According to Popper, then, the questions that philosophers should concern themselves with are questions such as “Can this statement be justified?”, “Is it testable?”, “How does it relate to statements about observations?”. The philosopher is interested in investigating the methods scientists use for critically examing and testing their theories; he or she is concerned with the logic, as opposed to the psychology, of scientific knowledge.

Another feature of Popper’s philosophy is his skepticism about induction. Following David Hume, he says that it is not possible to prove the truth of any statement using inductive reasoning. Since inductive proofs are impossible, we should reject as unjustifiable all reasoning that relies on induction. Only deductive reasoning can be relied upon to establish truth. (2) Popper’s skepticism about induction leads him to deny that we can ever conclusively verify general statements of the form “All F are G”. No amount of observations of Fs which have turned out to be Gs will allow us to conclude that some trend that occurred in that past will continue into the future. Furthermore, Popper believes that it is not possible to show that statements of the form “All F are G” are probably true. Philosophers who do not reject inductive reasoning would agree with Popper that “All F are G” cannot be verified, but would say that the observation of a large number of positive instances of such a generalization would tend to confirm the generalization; such observations would increase the likelihood of probability of such a generalization’s being true. Popper would deny this. (3) Statements such as “All F are G” can neither be verified nor confirmed.

Popper, then, is interested in the methods scientists do, or should, use for justifying and testing their claims. And he believes that only deductive reasoning is to be relied upon. So Popper has to show that the methods which scientists use do not depend on inductive reasoning in any way. The nature of the scientific enterprise, as Popper sees it, is as follows: science proceeds by means of a series of conjectures and refutations. Scientists conjecture that such-and-such is an explanation for the phenomena that are interested in accounting for. (4) They then set about testing their conjecture or theory by attempting to falsify or refute it. Popper says: “Only the falsity of the theory can be inferred from empirical evidence, and this inference is a purely deductive one”. (5) A theory will entail that certain observable effects should occur in certain circumstances. The theory is tested by checking to see whether or not the effects occur. If they do not occur, the theory is refuted. (6) If they do occur, this does not mean that the theory is verified. Nor does it mean that the theory is confirmed or made more probable or supported in any way. Popper introduces the technical term ‘corroboration’, not to be confused with the inductivist notion of “confirmation”. A theory which makes accurate predictions, that is, a theory which withstands tests, is corroborated. The fact that a theory is highly corroborated this doesn’t mean that the theory will continue to make accurate predictions. It tells one only about the past performance of the theory. It tells one that the theory has been subjected to sever tests and has withstood them; in other words, that theory has not yet been refuted.

According to Popper what distinguishes science from non-science is the critical method scientists use for establishing and justifying their claims. Scientists should be prepared to subject their theories to sever tests. That is, they should not be dogmatic. Even those theories which seem to be supported by the evidence should be held only tentatively. Moreover, since scientists should be trying to falsify their theories, only those theories which are (in principle) falsifiable are acceptable. And the more falsifiable a theory, the better it is. A theory with a high degree of falsifiability is one which has a low probability. Because such a theory says more about the world, it is riskier, and thus is more likely to be falsified. For example, the claim that the next can I see will be red is more falsifiable that the claim that the next car I see will be red or blue or green or yellow. The former claim says more about the world in the sense that it excludes more possibilities. It excludes the possibilities that the next car I see will be blue or green or yellow, whereas the latter claim allows all of the possibilities. Popper also believes that science has a goal. He denies that it is possible to establish the truth of any claim, so it cannot be the goal of science to discover the truth about reality. All out theories about reality are strictly speaking false. Nevertheless, it is possible to say that one theory is better than another in the sense that it has a greater truth-content and a smaller falsity content than the other theory. Popper says that such a theory has greater verisimilitude that its rival. The goal of science, then, it to increase the verisimilitude of our theories. Popper admits that there is no direct means of measuring a theory’s verisimilitude. However, the degree of corroboration of a theory can be used as an indicator of its verisimilitude. The higher the degree of corroboration of a theory, the greater its verisimilitude. I other words, the greater will be the ration of its truth-to its falsity-content.

It can now be seen in what sense it is true to call Popper a rationalist. Popper believes that there can be progress in science, in the sense that it is possible to assess theories and to judge whether they are getting closer to the goal he posits for science, namely to increase the verisimilitude of our theories. A theory is to be preferred to a rival if it is more falsifiable, it more highly corroborated and has greater verisimilitude that its rival. So it is possible to rationally choose between competing theories. And Popper believes that there is such a thing as scientific method. He says: ‘there is no more rational procedure that the method of trial and error – of conjecture and refutation: of boldly proposing theories; of trying our best to show that there are erroneous; and of accepting them tentatively if our critical efforts are unsuccessful”. (7)

There are a number of problems that Popper has to face. For example, to support his claim that there is a criterion of progress and that progress in science can be assessed rationally, he as to give us reasons for believing that we can rationally decide which if two theories is better in the sense of being closer to the goal of science. We have, that is, to be able to rationally decide which of two theories has greater verisimilitude. Popper claims that we can do this by choosing the theory with the highest degree of corroboration. (8) But what reasons do we have for believing that a theory which is more highly corroborated that a rival also has greater verisimilitude that its rival? Why should a theory which has withstood more severe tests in the past have greater verisimilitude than its rival? Perhaps the future will reveal that the highly corroborated theory has a large falsity-content which is hidden from us at the moment. And perhaps its rival, which is “refuted”, will turn out TO have a large truth content which has yet to be detected. So the more highly corroborated theory may turn out to have less verisimilitude. (9) Of course, it a theory has withstood sever tests in the past, one might say that we have good inductive reasons for thinking that it will continue to yield accurate predictions in the future. We can, that is, offer inductive reasons for thinking that a theory which is more highly corroborated than a rival will also have greater verisimilitude that its rival. But this route is not open to Popper, as he rejects all inductive reasoning. Popper’s rejection of induction has the consequence that he cannot show that there are rationally justifiable criteria for choosing between theories or that there is progress in science. So Popper’s attempt to offer a rationalist account of science fails.


The late Imre Lakatos, a student of Popper’s, offered an account of science which was meant to deal with some of the problems facing Popper’s account, but which was nevertheless Popperian in spirit. According to Lakatos, scientists do not abandon a theory simply because it is refuted. A theory is rejected only if there is another, better theory available to replace it. After all, a bad theory is better than no theory at all. However, even when there is an alternative available, scientists will not abandon the current theory until they are certain that there are no modifications that can be made to it that makes it better that its rival. Lakatos believes that the unit we should be concerned with is not an individual theory but a research program. A research program is a sequence of theories, each theory being a modification of the preceding theory in the sequence. All the theories in a research program share a common core of hypotheses. Lakatos call this the hard core of the research program. Each theory within the research program contains a number of auxiliary hypotheses, which Lakatos envisages as forming a kind of protective belt around the hard core. Scientists, says Lakatos, make a methodological decision to treat the hypotheses forming the hard core of a research program as effectively irrefutable. So when a theory fails a test or makes an unverified prediction or cannot account for some observed phenomenon, alterations are made to the auxiliary hypotheses of the theory, yielding a new variant of the research program. Work then continues on this version of the research program until it is faced with anomalies that it cannot deal with, and then suitable adjustments are made to the hypotheses in the protective belt, yielding yet another variant of the program, and so on. Lakatos believes that there are two non-empirical, metaphysical components of a research program. These are the negative and positive heuristics. The negative heuristic is the decision scientists make to stick by the hypotheses in the hard core. The positive heurisic is a set of suggestions or hints on how to modufy the protective belt in the face of anomalies.

Lakatos is a rationalist, in the sense that he believes that research programs can be objectively assessed. He says that a research program is degenerate if the only way scientists can deal with an anomaly is to abandon one or more auxiliary hypotheses, yielding a new variant of the program which has decreased empirical content. A program is progressive if, in the face of anomaly, a new version of the program can be derived that gives rise to new predictions, which are then corroborated. Scientists are justified in continuing to work on a research program as long as it remains progressive. (10) Lakatos believes that it is possible to rationally choose between two competing theories. Theories are compared by comparing the research programs in which they are embedded. A theory is to be preferred if the research program in which it is embedded is more progressive that the research program in which its rival is embedded. A research program is more progressive than another if it generates a number of new, corroborated predictions. Lakatos believes, as does Popper, that the goal of science is to increase the verisimilitude to our theories, and believes that there can be progress in science. If we can objectively assess theories, then, it seems, we would have objective grounds for thinking that one theory is closer to the goal of science than another, and hence we would have a criterion of progress.

Lakatos, like Popper, doesn’t think that one can directly measure a theory’s verisimilitude. He believes that increasing corroboration is a sign of increasing verisimilitude. (11) But if increasing corroboration is to be an objectively justifiable criterion for assessing theories, Lakatos has to give us a reasons for believing that theories with a high degree of corroboration have verisimilitude than theories which are not corroborated. We noted earlier, in our discussion of Popper’s views, that it is possible to give inductive reasons. Instead, he says merely that we can accept as a tentatively metaphysical assumption that corroboration is a sign of verisimilitude. Moreover, he thinks that we can accept this assumption without believing it. (12) But clearly, if Lakatos’ rationalism is to have any foundation, this assumption must be argued for. Lakatos’ account of the scientific enterprises is in many ways more satisfactory than Popper’s. It would be wrong to conclude that because Popper’s and Lakatos’ attempts to defend rationalism fail, that, therefore, no rationalist account of science can succeed. On the contrary, some of the authors think that rationalism can be defended and that such a stance is to be preferred to the anti-rationalist stances taken by Kuhn and Feyerabend. A recent, and we think, good defense of rationalism is to be found in a book by William Newton-Smith, titled The Rationality of Science. A discussion of Newton-Smith’s views is beyond the limited scope of this paper.


Thomas Kuhn’s book The Structure of Scientific Revolutions, first published in 1962, has been very influential. One of Kuhn’s aims in this book is to challenge the view that scientific knowledge grows by the accumulation of facts. It is not the case, says Kuhn, that scientists discover facts which are then added to an ever-increasing stock of knowledge. Nor is it the case that scientists are constantly correcting the errors of past scientists and so moving ever closer to the truth. These assertions of Kuhn’s are in themselves no challenge to the rationalist. It should be clear that neither Popper nor Lakatos support a development-by-accumulation view of science. Nor do they believe that the goal of science is to discover the truth about reality. However, it becomes clear from his elaboration of his views on the growth of scientific knowledge that Kuhn’s account is fundamentally anti-rationalist.

According to Kuhn, an examination of the history of science would show that science proceeds as follows: a period of normal science is followed by a period of extraordinary science and revolution, which is followed by a new period of normal science, and so on. During period of normal science, all members of a scientific community work within the same paradigm. Scientists who share a paradigm will agree on a number of fundamental issues. They will agree, for instance, on what counts as a worthwhile research project and on which the significant problems are that need to be worked on. They will agree on what methods and techniques are to be employed in solving these problems. Scientists who share a paradigm will also share commitment to certain beliefs and values. They will, for instance, agree on the values to be used in judging and choosing between theories. They might agree, for example, that a theory, to be a good one, should be simple, self-consistent, compatible with other currently held theories, fruitful and so on. During periods or normal science, scientists are engaged in problem-solving and their goal is to solve as many of the problems set by the paradigm as possible. Failure to solve a problem will not result in the refutation of the currently held theory. Failure will be attributed to the scientist instead. When even the ablest members of the scientific community cannot solve some problem, an anomaly is revealed. When many anomalies have been revealed, a crisis of confidence in the existing scientific practice will occur and a period of extraordinary science will be initiated. During such a period, scientists work on developing new theories which are able to deal with the anomalies that the old theory faced. Along with each new theory comes a new and different set of commitments. When a scientific community shifts its allegiance to a new theory together with its set of commitments (to a new paradigm, that it) a scientific revolution will have occurred. A new period of normal science then begins, in which scientists are engaged in trying to solve the problems set by the new paradigm. Kuhn’s anti-rationalism is most obvious in his account of the shifts in allegiance that occur during scientific revolutions. Kuhn likens such shifts to gestalt switches. He claims that scientists do not and cannot have any rational reasons for abandoning one theory in favour of a new one. In order to get their fellow scientists to accept a new theory, scientists have to resort to propagandizing. Every theory comes with its own set of commitments, so changing one’s allegiance means coming to hold a new set of values as to what constitutes a good theory. There is, in other words, no paradigm-neutral set of values for judging and choosing between rival theories. So there cannot be rational grounds for favouring one theory over another. Once cannot explain why scientists chose to work on a particular theory by showing that it was the best available theory according to some objective standard for assessing theories. At best one can hope to give a psychological or sociological explanation for a scientific community’s shift in allegiance.

Rival scientific theories, then are incommensurable. They cannot be compared because they are embedded in paradigms which have different sets of commitments. If theories are incommensurable, however, Kuhn is faced with a problem. The problem is to give a satisfactory account of scientific progress. Kuhn can give an account of progress within a paradigm. Kuhn says: “In its normal state …..a scientific community is an immensely efficient instrument for solving the problems or puzzles that its paradigms define. Furthermore, the result of solving those problems must inevitably be progress”. (13) But it is not clear that Kuhn can give an account of progress through revolutions. Does a succession of incommensurable paradigms constitute scientific progress, or is it merely a series of changes in view? Does the change from one theory to an incommensurable alternative constitute progress in the sense that the later theory is better than the earlier in being closer to the goal of science? Kuhn seems to deny that there is a goal in science, He certainly denies that the goal in science is to move even closer to the one true, full, objective account of nature. (14) And he denies that there are any objective criteria for determining which of two rival theories is to be preferred. It seems that Kuhn cannot make sense of inter-paradigmatic progress. Kuhn at one point says: “Revolutions close with a total victory for one of the two opposing camps. Will that group ever say that the result of its victory has been something less than progress? That would be rather like admitting that they had been wrong and their opponents right. To them, at least the outcome of revolutions must be progress, and they are in an excellent position to make certain that future members of their community will see past history in the same way”. (15) But of course, it is not good enough to simply believe that one has made progress. One ought to be able to give good scientists can do. Kuhn is an anti-rationalist because he does not believe in scientific progress (16) and he denies that there are objectively justifiable criteria for choosing theories.


Paul Feyerabend is also an avowed anti-rationalist. Like Kuhn, Feyerabend thinks that rival scientific theories are incommensurable. His reasons for thinking this is that he thinks that the meanings of all the terms in a theory depend on the theoretical context in which the terms are embedded. It follows that a change in the theoretical context would alter the meaning of all the terms. That is, theory change generates meaning change. For example, the change from classical to relativistic mechanics is an instance of theory change and so, if Feyerabend is right, it involves a meaning change. But if the meanings of all the terms in these two theories differed, then these two theories would not be comparable. They would not stand in any logical relation to one another, and even if they contained the same linguistic signs (terms) they would really be talking at cross-purposes, because these signs would have different meanings in the two theories. It would not be possible to make judgments about the relative merits of the two theories. For instance, one could not say that relativistic mechanics is a better approximation of the truth than is classical mechanics. Much has been written on the subject of incommensurability due to meaning variance, but it is beyond the scope of this paper to consider the issues arising from these discussions.

Perhaps a more interesting challenge to a rationalist account of the scientific enterprise is Feyerabend’s attack on scientific method. Feyerabend says: “The idea of a method that contains firm, unchanging, and absolutely binding principles for conducting the business of science meets considerable difficulty when confronted with the results of historical research. We find then, that there is not a single rule, however plausible, and however firmly grounded in epistemology, that is not violated at some time to other. It becomes evident that such violations are not accidental events, they are not results of insufficient knowledge or of inattention which might have been avoided. On the contrary, we see that they are necessary for progress” (17) Feyerabend’s strategy for showing that there is not and should not be a fixed method in science is to isolate two methodological rules that he thinks philosophers defend. He argues that for both rules there is an equally plausible but incompatible counter-rule. He then argues that an examination of the history of science shows that there were times at which scientists acted in accordance with one or other of the counter-rules, and not in accordance with one of the (purportedly) standard methodological rules. Moreover, Feyerabend wishes to claim that if these scientists had been bound by the standard rules, they would have made the wrong theory choices. They would not have chosen the best available of the alternative theories. Feyerabend’s conclusion is that scientists should not be bound by methodological rules at all. He says: “there is only one principle that can be defended under all circumstances and in all stages of human development. It is the principle: anything goes”. (18) Feyerabend wants to argue that because sometimes we would be led astray by our methodological rules we should, therefore, do without any such rules. But this skeptical conclusion does not follow. It may still be preferable to be guided by a set of fallible methodological rules that not to be guided by rules at all. One should of course be aware of the fact that one’s rules are fallible. Feyerabend’s attack on scientific method seems in any case to be misguided. He attacks the view that there is a fixed, unchanging, binding set of methodological rules, which supposedly provides an algorithm for choosing between rival theories. But it is doubtful whether any contemporary philosopher of science would thing of methodological rules as providing such an algorithm. More importantly, there is not reasons for someone who wishes to defend a rationalist view of science to think of scientific method in this way. It is possible to think of methodological rules as inductive rules, as rules which indicate which theories are more likely to prove successful. And moreover, it is possible to think that we can make discoveries about scientific method just as much as we can make discoveries in science.

We have tried to indicate in the preceding sections of this paper how various philosophers stand with regard to questions such as “Can there be progress in science?”; “Are there rationally justifiable criteria for choosing between rival theories?” and “Is there such a thing as scientific method?”. Although we have favoured a rationalist account of science, we have not argued for such an account. However, it was not our intention to argue for one or another answer to the above questions, but merely to indicate some of the possible answers that have been offered. Moreover, we do not wish to suggest that these are the only, or even the most important, questions that engage contemporary philosophers of science.


One area in the history and philosophy of science which has recently been the focus of much debate, is the questions of whether scientific theories should be given a realist interpretation or an anti-realist interpretation. Anti-realism incorporates a number of different positions such as phenomenalism, operationism, conventionalism, fictionalism, constructive empiricism. What these philosophical positions have in common, is there opposition to realism. Very generally, realism proposes the existence of a reality that underlines all experience and exists independently of it. Consequently, a realist sees the aim of science as the discovery of the reality underlying the phenomena which he perceives. He believes that the theoretical statements of a scientific theory are true, generalized, descriptions of reality and, that they are true independently of a theorizer. He believes that the entities to which theoretical statements make reference actually exist in the real world.

Thus the statements in scientific theory are true or false because of the way the world is, rather than because of the way it is subjectively experienced or linguistically (theoretically) described. So the scientific realist is directing this research towards a true account of how the world actually is. Hence, when the realist accepts a theory, he accepts it as true: to accept a theory is, for the realist, to believe it to be true.

By contract, in an anti-realist interpretation of theories, truth is not a criterion which influences theory choice. Indeed, anti-realist philosophers of science accept the impossibility of knowing which hypotheses are true and which are false i.e which make reference to entities which do exist and which make reference to fictious entities. Consider, for example, the theory of the luminiferous ether. In the nineteenth century almost all scientists believed that the ether did exist despite the fact that attempts to perceive it were unsuccessful. However, today the ether is regarded as no more than one of the numerous myths in the history of science and the question of its existence is no longer even raised.

So, rather than concern themselves with the truth of scientific hypotheses, anti-realists choose their theories on the basis of the theoretical economy, simplicity and utility of the hypotheses i.e they employ pragmatic criteria and look upon theories not as true representations of the way the worlds is, but rather as heuristic devices for facilitating scientific research. Scientific theories may be seen as powerful tools; they are the instruments of research. The entities to which the statements or hypotheses of a theory refer should be plausible, but the point is that they are mere constructs, works of the imagination or convenient fictions. They have no existence independently of the theorizer.

There are some extreme forms of anti-realism, for instance phenomenalism and Machian positivism which deny more than the possibility of hypotheses and theories being true or false or the possibility of theoretical terms making reference to actually existing entities. They emphasise the claim that theories are merely temporary, they are constantly replaced by better theories; thus our current theories are regarded as dispensable, having no more than psychological value. Facts alone are the objects of scientific knowledge and as such they should be indentifiable once and for all i.e they should be unchanging. These facts are defined as whatever can be perceived. Scientific knowledge is about what we can perceive or experience and the ultimate components of our experience are sensory elements or sensations. Sensations should be regarded as the ultimate phenomena and the only true scientific knowledge is knowledge of things, we can only have knowledge of the sequence and ordering of our sensations. Thus, for instance laws of nature such as Newton’s three laws of motion, should be regarded as nothing more than an economical summery of past experience.

Despite the fact that proponents of this position do not consider theories to be the basis of knowledge, they are not completely redundant. Theories are useful to be extent that they provide a shorthand for facts by recording and ordering past experience. So, theories help us to organise our experience in such a way that we can use this information as the basis for scientific prediction, and prediction is almost universally accepted as one of the primary goals of science.

Ant anti-realist interpretation of science is a particularly attractive philosophical position to adopt in periods of scientific crisis. During such period there may be no universal consensus as to which of two or more competing theories most adequately accounts for, and explains, the available scientific data. Where the competing theories, say T1 and T2, make reference to different theoretical entities, a realist interpretation of the theories would result in contradiction as it would force one to accept the existence of the entities referred to by T1 as well as the entities referred to by T2. If these entities were different to the extent of being mutually incompatible, then accepting both theories under a realist interpretation would lead one to contradiction. However, if an anti-realist interpretation is adopted and the entities referred to by the theories are regarded just as convenient fictions, then there is no reasons why one set of fictions should be most convenience under certain circumstances while a different set be better suited to different circumstances. An anti-realist interpretation of theories this resolves the immediate conflict between incompatible theories.

For this, it is just a small step to see that it the realist is to be able to maintain his position consistently, then he must be able to show that, in general, theories are not underdeterminded. This means that the realist must be able to show that it is not possible for there to be two theories explaining an intersecting range of phenomena where these two theories are logically incompatible i.e where they refer to different entities, yet where they are empirically underdeterminded i.e where they are equally well confirmed by all we could, in principle, ever know. The possibility of there being such theories would force the realist into contradiction so he is bound to try and deny the possibility of two such theories arising. This is a topic which is elicting much research in the philosophy of science at present.

Other issues which are currently being raised in the debate between realism and anti-realism, focus on the indispensability of theoretical terms in theories and on the inferences which scientists make from competing exaplanations of phenomena to the best explanation of those phenomena. Many realists philosophers of science argue that if the theoretical terms in scientific hypotheses and theories are indispensable then this constitutes sufficient evidence to accept the existence of the entities to which the indispensable terms refer. It then becomes simply a methodological problem to isolate those terms which are indispensable. This position has been countered by certain anti-realists who deny that theoretical terms are indispensable. A paradigmatic example of such an anti-realist manoevre wound be Hartry Field’s Science Without Numbers. (20) In this book, Field claims that it is possible to eliminate numbers from mathematics and science and he shows how he believes this could be done. In other words he counters the view that numbers are indispensable theoretical entities; consequently he argues against a realist interpretation of them. If his position is tenable, then it may be possible to argue analogously against the indispensability of other theoretical entities.

The case against a realist interpretation of theories is, however, by no means conclusive. Realists espouse the view that the inferences that theorists make when they accept a certain explanation of the phenomena to be the best explanation, can only be justified from the starting point of realism. So, when all the evidence points towards there being phenomena which are “something like electrons” causing certain things to happen, it is only a realist standpoint that can support the inference to the hypothesis that there actually are electrons causing the events and, consequently, that such electrons really do exists and not just products of the theorist’s imagination. The anti-realist by contrast would not want to make this assumption, and his theoretical stance would not require the assumption. It is arguments such as those sketched above that have induced contemporary realist philosophers such as Hillary Putnam to defend the claim that a realist position is the only one which can successfully explain how science progresses effectively.


What has been outlined above are certain epistemological issues in the philosophy of science. One aspect that has not been mentioned, though, is the sort of material that is used by philosophers of science in their presentation of arguments to defend their diverse positions. This material, which it is presented in a philosophical reasoning, is drawn exclusively from the history of science. It is precisely in this way that the philosophy of science and the history of science are inextricably linked and are mutually supportative. Ad Imre Lakatos so aptly wrote: “Philosophy of science without history of science is empty; history of science without philosophy of science is blind.” (21)

The history of science provides the source material which arguments in the philosophy of science draw their content. A position in the philosophy of science is only defensible once it can be shown to have actual historical evidence in support of it. In other words it must be possible to illustrate and support abstract philosophical claims as to how science progresses or how theories should be interpreted by drawing on actual episodes from the history of science. Clearly, on an issue such as the debate between realism and anti-realism, the evidence support of the different positions is not obviously in favour of either one position. Philosophers of different persuasions draw on different evidence to substantiate their view. Consequently, the debate has not yet been conclusively settled. It is the history of science which adds substance to the philosophy of science, thereby preventing it from being empty.

The importance of the philosophy of science for the history of science is perhaps not as readily apparent as the importance of the history of science for the philosophy of science. Nonetheless, the influence of philosophy on history should not be underestimated and is worthy of discussion.

It is the philosophers of science who, from scientific theories and sociological analyses, are able to provide a rational reconstruction of the growth of scientific knowledge. More importantly, it is the philosophy of science which makes explicit, and draws attention to, the theoretical framework from within which scientific theories evolve and develop. This provides essential information as to the presuppositions and assumptions underlying past as well as currently adopted scientific theories.

Such information is useful in explaining why some theories were more successful than others and also why some theories, despite their being false or making a very small contribution to scientific knowledge, were retained dogmatically and supported vehemently while others which marked a breakthrough for human learning were greeted with such skepticism. One has simply to contrast theories such as Aristotle’s geocentric cosmological system, accepted without serious questioning for centuries with Darwin’s theory of evolution which faced decades of unrivalled skepticism before it was fairly considered and cautiously accepted.

The philosophy of science also provides an analysis of the methods of research, of the adequacy of scientific explanation, of the degree of evidence required in support of a theory and of other related questions, thereby providing the background against which the credibility of scientific theories can be assessed. The philosophy of science is necessary in so far as it provides an interpretation of scientific theory as well as an evaluation of it. It is in this sense that the history of science without the philosophy of science is blind.

From the above it should be clear just how closes related and interlinked the history of science, and philosophy of science are, and how any adequate study of one is only possible of conducted concurrently with a study of the other. The two disciplines run parallel and should never be studied in isolation.


*Some of the ideas in sections I to IV are derived from W. H. Newton-Smith (5) We have benefited greatly from reading this lucid introduction to problems in the philosophy of science.

1 The major works of these philosophers are Popper (6) and (7), Lakatos (3) and (4), Kuhn (2) and Feyerabend (1)

2 A deductively valid argument has the characteristic that if all its premises are true, its conclusion must be true. Hence, one could establish the truth of some claim by showing that it can be derived from true promises according to the rules of logic. An inductive argument, on the other hand, has the characteristic that it is always possible to deny its conclusion, even though one believes all its premises to be true.

3 Popper’s reasons for denying this is that he thinks that the prior probability of a hypotheses is zero. It can then be shown, using Bayes’ Theorem, that no amount of evidence favourable to the hypothesis can serve to increase its probability. That is, even in the face of favourable evidence, the probability of a hypothesis remains at zero.

4 Presumably a conjecture is an educated or enlightened guess. Scientists make their conjectures in the light of the other theories and beliefs they hold.

5 Popper (7), p.55.

6 It may be the case that predictions are not entailed by the conjecture alone, but ore only entailed by the conjecture conjoined with certain other auxiliary hypothese. In this case, should the predicted event fail to occur, it would be the conjuction of the conjecture and the auxiliary hypotheses which would be falsified. But this means that it is always in principle possible to save a conjecture from refutation by making suitable adjustments to the auxiliary hypotheses.

7 Popper (7), p.51, his emphasis.

8 See Popper (8), p. 94 and Popper (7), p.217

9 This criticism of Popper is taken from W. H. Newton-Smith (5), pp. 64-65.

10 Actually, Lakatos allows such research programs can go through degenerating phases. Provided that these are only temporary, Lakatos thinks that scientists would be justified in sticking by the research program. This admission creates difficulties for Lakatos.

11 Lakatos (4), p.191

12 Ibid. p 187

13 Kuhn (2), p.166

14 Ibid, p. 171. Kuhn does, in places, write as though he believed that there is a goal in science, namely to increase the puzzle-solving ability of our theories. (See Kuhn (2), p.206). Later theories are better than earlier ones because they are better instruments for discovering and solving puzzles. The problem with this is that if paradigms define their own problems it is difficult to see how one could see how one could decide which paradigm was better at discovering and solving problems. (Kuhn himself is aware of this. See Kuhn (2), pp. 109 – 110).

15 Kuhn (2), p. 166

16 This is not quite accurate. Kuhn claim in his Postscript to The Structure of Scientific Revolutions that he is a “convinced believer in scientific progress” (Kuhn (2), p.206). However, my point is simply that, his protestations to the contrary notwithstanding, Kuhn cannot consistently believe in scientific progress. Such a belief is incompatible with other of Kuhn’s beliefs, in particular the belief that rival theories are incommensurable.

17 Feyerabend (1) , p.23.

18 Ibid, p.28. Feyerabend’s emphases.

19 Such a view is defended by Newton-Smith in Newton-Smith (5), chapter IX.

20 Hartry Field, Science Without Numbers, Basil Blackwell, Oxford, 1980.

21 Imre Lakatos, “History of Science and its Rational Reconstructions,” in Ian Hacking (ed), Scientific Revolutions, Oxford University Press, Oxford, 1981


(1) Feyerabend, P. Against Method. London: Verso, 1978.

(2) Kuhn, T.S The Structure of Scientific Revolutions. Second edition. Chicago: University of Chicago Press, 1970.

(3) Lakatos, I The Methodology of Scientific Research Programmes. Edited by J Worrall and G. Curries. Cambridge: CUP, 1978.

(4) Lakatos, I Mathematics, Science and Epistemology. Edited by J. Worrall and G Currie. Cambridge: CUP, 1978

(5) Newton-Smith, The Rationality of Science. London: W.H Routledge & Kegan Paul, 1981.

(6) Popper, K. R The Logic of Scientific Discovery. London: Hutchinson, 1972.

(7) Popper, K. R conjecture and Refutations: The Growth of Scientific Knowledge. London: Routledge & Kegan Paul, 1972.

(8) Popper, K R “ The Rationality of Scientific Revolutions” in I. Hacking (ed.) Scientific Revolutions. Oxford: OUP, 1981, pp. 80 – 106.

(9) Field, H Science without numbers. Oxford, Basil Blackwell, 1980.