According to Kuhn, an a.n.a.lysis of the characteristics of a crisis period in science demands the competence of the psychologist as much as that of the historian. When anomalies come to be seen as posing serious problems for a paradigm, a period of "p.r.o.nounced professional insecurity" sets in. Attempts to solve the problem become more and more radical and the rules set by the paradigm for the solution of problems become progressively more loosened. Normal scientists begin to engage in philosophical and metaphysical disputes and try to defend their innovations, of dubious status from the point of view of the paradigm, by philosophical arguments. Scientists even begin to express openly their discontent with and unease over the reigning paradigm. Kuhn (1970a, p. 84) quotes Wolfgang Pauli's response to what he saw as the growing crisis in physics around 1924. An exasperated Pauli confessed to a friend, "At the moment, physics is again terribly confused. In any case, it is too difficult for me, and I wish I had been a movie comedian or something of the sort and had never heard of physics". Once a paradigm has been weakened and undermined to such an extent that its proponents lose their confidence in it, the time is ripe for revolution.

The seriousness of a crisis deepens when a rival paradigm makes its appearance. According to Kuhn (1970a, p. 91), "the new paradigm, or a sufficient hint to permit later articulation, emerges all at once, sometimes in the middle of the night, in the mind of a man deeply immersed in crisis". The new paradigm will be very different from and incompatible with the old one. The radical differences will be of a variety of kinds.

Each paradigm will regard the world as being made up of different kinds of things. The Aristotelian paradigm saw the universe as divided into two distinct realms, the incorruptible and unchanging super-lunar region and the corruptible and changing earthly region. Later paradigms saw the entire universe as being made up of the same kinds of material substances. Pre-Lavoisier chemistry involved the claim that the world contained a substance called phlogiston, which is driven from materials when they are burnt. Lavoisier's new paradigm implied that there is no such thing as phlogiston, whereas the gas, oxygen, does exist and plays a quite differen role in combustion. Maxwell's electromagnetic theory involved an ether occupying all s.p.a.ce, whereas Einstein's radical recasting of it eliminated the ether.

Rival paradigms will regard different kinds of questions as legitimate or meaningful. Questions about the weight of phlogiston were important for phlogiston theorists and vacuous for Lavoisier. Questions about the ma.s.s of planets were fundamental for Newtonians and heretical for Aristotelians. The problem of the velocity of the earth relative to the ether, which was deeply significant for pre-Einsteinian physicists, was dissolved by Einstein. As well as posing different kinds of questions, paradigms will involve different and incompatible standards. Unexplained action at a distance was permitted by Newtonians but dismissed by Cartesians as metaphysical and even occult. Uncaused motion was nonsense for Aristotle and axiomatic for Newton. The trans.m.u.tation of elements has an important place in modern nuclear physics (as it did in mediaeval alchemy and in seventeenth-century mechanical philosophy) but ran completely counter to the aims of Dalton's atomistic program. A number of kinds of events describable within modern microphysics involve an indeterminancy that had no place in the Newtonian program.

The way scientists view a particular aspect of the world will be guided by a paradigm in which they are working. Kuhn argues that there is a sense in which proponents of rival paradigms are "living in different worlds". He cites as evidence the fact that changes in the heavens were first noted, recorded and discussed by Western astronomers after the proposal of the Copernican theory. Before that, the Aristotelian paradigm had dictated that there could be no change in the super-lunar region and, accordingly, no change was observed. Those changes that were noticed were explained away as disturbances in the upper atmosphere.

The change of allegiance on the part of individual scientists from one paradigm to an incompatible alternative is likened by Kuhn to a "gestalt switch" or a "religious conversion". There will be no purely logical argument that demonstrates the superiority of one paradigm over another and that thereby compels a rational scientist to make the change. One reason why no such demonstration is possible is the fact that a variety of factors are involved in a scientist's judgment of the merits of a scientific theory. An individual scientist's decision will depend on the priority he or she gives to the various factors. The factors will include such things as simplicity, the connection with some pressing social need, the ability to solve some specified kind of problem, and so on. Thus one scientist might be attracted to the Copernican theory because of the simplicity of certain mathematical features of it. Another might be attracted to it because in it there is the possibility of calendar reform. A third might have been deterred from adopting the Copernican theory because of an involvement with terrestrial mechanics and an awareness of the problems that the Copernican theory posed for it. A fourth might reject Copernicanism for religious reasons.

A second reason why no logically compelling demonstration of the superiority of one paradigm over another exists stems from the fact that proponents of rival paradigms will subscribe to different sets of standards and metaphysical principles. Judged by its own standards, paradigm A may be judged superior to paradigm B, whereas if the standards of paradigm B are used as premises, the judgment may be reversed. The conclusion of an argument is compelling only if its premises are accepted. Supporters of rival paradigms will not accept each others' premises and so will not necessarily be convinced by each others' arguments. It is for this kind of reason that Kuhn (1970a, pp. 93-4) compares scientific revolutions with political revolutions. Just as "political revolutions aim to change politicial inst.i.tutions in ways that those inst.i.tutions themselves prohibit" and consequently "political recourse fails", so the choice "between competing paradigms proves to be a choice between incompatible modes of community life", and no argument can be "logically or even probabilistically compelling". This is not to say, however, that various arguments will not be among the important factors that influence the decisions of scientists. On Kuhn's view, the kinds of factors that do prove effective in causing scientists to change paradigms is a matter to be discovered by psychological and sociological investigation.

There are a number of interrelated reasons, then, why, when one paradigm competes with another, there is no logically compelling argument that dictates that a rational scientist should abandon one for the other. There is no single criterion by which a scientist must judge the merit or promise of a paradigm, and, further, proponents of competing programs will subscribe to different sets of standards and will even view the world in different ways and describe it in different languages. The aim of arguments and discussions between supporters of rival paradigms should be persuasion rather than compulsion. I suggest that what I have summarised in this paragraph is what lies behind Kuhn's claim that rival paradigms are "incommensurable".

A scientific revolution corresponds to the abandonment of one paradigm and the adoption of a new one, not by an individual scientist only but by the relevant scientific community as a whole. As more and more individual scientists, for a variety of reasons, are converted to the new paradigm, there is an "increasing shift in the distribution of professional allegiances" (Kuhn, 1970a, p. 158). If the revolution is to be successful, this shift will spread so as to include the majority of the relevant scientific community, leaving only a few dissenters. These will be excluded from the new scientific community and will perhaps takes refuge in a philosophy department. In any case, they will eventually die.

The function of normal science and revolutions.

Some aspects of Kuhn's writings might give the impression that his account of the nature of science is a purely descriptive one, that is, that he aims to do nothing more than to describe scientific theories or paradigms and the activity of scientists. Were this the case, then Kuhn's account of science would be of little value as a theory of science. Unless the descriptive account of science is shaped by some theory, no guidance is offered as to what kinds of activities and products of activities are to be described. In particular, the activities and productions of hack scientists would need to be doc.u.mented in as much detail as the achievements of an Einstein or a Galileo.

However, it is a mistake to regard Kuhn's characterisation of science as arising solely from a description of the work of scientists. Kuhn insists that his account const.i.tutes a theory of science because it includes an explanation of the function of its various components. According to Kuhn, normal science and revolutions serve necessary functions, so that science >c.u.mulative progress characteristic of inductivist accounts of science. According to the latter view, scientific knowledge grows continuously as more numerous and more various observations are made, enabling new concepts to be formed, old ones to be refined, and new lawful relationships between them to be discovered. From Kuhn's particular point of view, this is mistaken, because it ignores the role played by paradigms in guiding observation and experiment. It is just because paradigms have such a pervasive influence on the science practised within them that the replacement of one by another must be a revolutionary one.

One other function catered for in Kuhn's account is worth mentioning. Kuhn's paradigms are not so precise that they can be replaced by an explicit set of rules, as was mentioned above. Different scientists or groups of scientists may well interpret and apply the paradigm in a somewhat different way. Faced with the same situation, not all scientists will reach the same decision or adopt the same strategy This has the advantage that the number of strategies attempted will be multiplied. Risks are thus distributed through the scientific community, and the chances of some long-term success are increased. "How else", asks Kuhn (1970c, p. 241), "could the group as a whole hedge its bets?"

The merits of Kuhn's account of science.

There is surely something descriptively correct about Kuhn's idea that scientific work involves solving problems within a framework that is, in the main, unquestioned. A discipline in which fundamentals are constantly brought into question, as characterised in Popper's method of "conjectures and refutations", is unlikely to make significant progress simply because principles do not remain unchallenged long enough for esoteric work to be done. It is all very well painting a heroic picture of Einstein as making a major advance by having the originality and courage to challenge some of the fundamental principles of physics, but we should not lose sight of the fact must either involve those characteristics or some others that would serve to perform the same functions. Let us see what those functions are, according to Kuhn.

Periods of normal science provide the opportunity for scientists to develop the esoteric details of a theory Working within a paradigm, the fundamentals of which they take for granted, they are able to perform the exacting experimental and theoretical work necessary to improve the match between the paradigm and nature to an ever-greater degree. It is through their confidence in the adequacy of a paradigm that scientists are able to devote their energies to attempts to solve the detailed puzzles presented to them within the paradigm, rather than engage in disputes about the legitimacy of their fundamental a.s.sumptions and methods. It is necessary for normal science to be to a large extent uncritical. If all scientists were critical of all parts of the framework in which they worked all of the time then no detailed work would ever get done.

If all scientists were and remained normal scientists, a particular science would become trapped in a single paradigm and would never progress beyond it. This would be a serious fault, from the Kuhnian point of view. A paradigm embodies a particular conceptual framework through which the world is viewed and in which it is described, and a particular set of experimental and theoretical techniques for matching the paradigm with nature. But there is no a priori reason to expect that any one paradigm is perfect or even the best available. There are no inductive procedures for arriving at perfectly adequate paradigms. Consequently, science should contain within it a means of breaking out of one paradigm into a better one. This is the function of revolutions. All paradigms will be inadequate to some extent as far as their match with nature is concerned. When the mismatch becomes serious, that is, when a crisis develops, the revolutionary step of replacing the entire paradigm with another becomes essential for the effective progress of science.

Progress through revolutions is Kuhn's alternative to the that it took two hundred years of detailed work within the Newtonian paradigm and one hundred years of work within theories of electricity and magnetism to reveal the problems that Einstein was to recognise and solve with his theories of relativity. It is philosophy, rather than science, that comes closest to being adequately characterised in terms of constant criticism of fundamentals.

If we compare the attempts by Kuhn and by Popper to capture the sense in which astrology differs from a science, it is Kuhn's account that is the more convincing, as Deborah Mayo (1996, chapter 2) has convincingly argued. From a Popperian perspective, astrology can be diagnosed as a non-science either because it is unfalsifiable, or because it is falsifiable and shown to be false. The first will not work because, as Kuhn (1970b) points out, even in the period during the Renaissance when astrology was practised seriously, astrologers did make predictions that were falsifiable, and indeed were frequently falsified. But this latter fact cannot be taken as sufficient to rule out astrology as a science lest physics, chemistry and biology are ruled out on similar grounds, for, as we have seen, all sciences have their problems in the form of problematic observations or experimental results. Kuhn's response is to suggest that the difference between say astronomy and astrology is that astronomers are in a position to learn from predictive failures in a way that astrologers are not. Astronomers can refine their instruments, test for possible disturbances, postulate undetected planets or lack of sphericity of the moon and so on and then carry out the detailed work to see if such changes can remove the problem posed by a failed prediction. Astrologers, by contrast, do not have the resources to learn from failures in the same way. But the "resources" that astronomers have and astrologers lack can be interpreted as a shared paradigm that can sustain a normal science tradition. Kuhn's "normal science", then, serves to identify a crucial element of a science.

The complementary part of Kuhn's account, "scientific revolutions", would seem to be of considerable merit too. Kuhn used the notion of a revolution to stress the non-c.u.mulative nature of the advance of science. The long-term progress of science does not merely involve the acc.u.mulation of confirmed facts and laws, but, on occasions also involves the overthrow of one paradigm and its replacement by an incompatible new one. Kuhn was certainly not the first to make this point. As we have seen, Popper himself stressed that scientific progress involves the critical overthrow of theories and their replacement by alternative ones. But, whereas for Popper the replacement of one theory by another is simply the replacement of one set of claims by a different set, there is much more to a scientific revolution from Kuhn's point of view. A revolution involves not merely a change in the general laws but also a change in the way the world is perceived and a change in the standards that are brought to bear in appraising a theory. As we have seen, the Aristotelian theory a.s.sumed a finite universe that was a system in which each item had a natural place and function, an important detail being the distinction between the celestial and the terrestrial. Within that scheme reference to the function of various items in the universe was a legitimate mode of explanation (for example, stones fall to the ground to reach their natural place and restore the universe to its ideal order). After the scientific revolution of the seventeenth century, the universe is an infinite one with items in it that interact by way of forces governed by laws. All explanations are by way of an appeal to those forces and laws. Insofar as empirical evidence played a role in the Aristotelian and Newtonian theories (or paradigms), in the former the evidence of the unaided senses operating under optimum conditions was regarded as fundamental, whereas in the latter, evidence acquired by way of instruments and experimentation was fundamental and often preferred over the direct deliverances of the senses.

Kuhn is undoubtedly correct, as a matter of descriptive fact, to note that there are such things as scientific revolutions that involve a change, not just in the range of claims made but also in the kind of ent.i.ties that are a.s.sumed to make up the world and the kinds of evidence and modes of explanation that are deemed appropriate. What is more, once this is acknowledged, then any adequate account of scientific progress must include an account of how the changes made in the course of a revolution can be construed as progressive. Indeed, we can draw on Kuhn's characterisation of science and pose the problem in a particularly acute way. Kuhn insisted that what counts as a problem can change from paradigm to paradigm, and also that the standards of adequacy that are brought to bear on proposed solutions to problems also vary from paradigm to paradigm. But if it is the case that standards vary from paradigm to paradigm, then what standards can be appealed to in order to judge that a paradigm in better than, and so const.i.tutes progress over, the paradigm it replaces? In precisely what sense can science be said to progress through revolutions?

Kuhn's ambivalence on progress through revolutions.

Kuhn is notoriously ambiguous on the basic question we have posed and which his own work serves to highlight. After the publication of The Structure of Scientific Revolutions Kuhn was charged with having put forward a "relativist" view of scientific progress. I take this to mean that Kuhn proposed an account of progress according to which the question of whether a paradigm is better or not than one that it challenges does not have a definitive, neutral answer, but depends on the values of the individual, group or culture that makes the judgment. Kuhn clearly was not comfortable with that charge and, in the PostScript that he added to the second edition of his book he attempted to distance himself from relativism. He wrote (1970a, p. 206), "later scientific theories are better than earlier ones for solving puzzles in the often quite different environments to which they are applied. That is not a relativist's position, and it displays the sense in which I am a convinced believer in scientific progress". This criterion is problematic insofar as Kuhn himself stresses that what counts as a puzzle and a solution to it is paradigm-dependent and also insofar as Kuhn (1970a, p. 154) elsewhere offers different criteria such as 'simplicity, scope and compatibility with other specialties'. But even more problematic is the clash between the non-relativist claim about progress and the numerous pa.s.sages in Kuhn's book that read as an explicit advocacy of the relativist position, and even as a denial that there is a rational criterion of scientific progress at all.

Kuhn likens scientific revolutions to gestalt switches, to religious conversions and to political revolutions. Kuhn uses these comparisons to stress the extent to which the change of allegiance on the part of a scientist from one paradigm to another cannot be brought about by rational argument appealing to generally accepted criteria. The way in which the diagram on p. 6 changes from a staircase viewed from above to a staircase viewed from below is a modest example of a gestalt switch, but it serves to emphasise the extent to which such a switch is the very ant.i.thesis of a reasoned choice, and religious conversions are typically considered to be an a.n.a.logous kind of change. As far as the a.n.a.logy with political revolutions is concerned, Kuhn (1970a, pp. 93-4) insists that those revolutions "aim to change political inst.i.tutions in ways that those inst.i.tutions themselves prohibit" so that "political recourse fails". By a.n.a.logy, the choice "between competing paradigms proves to be a choice between incompatible modes of community life" so that no argument can be "logically or even probabilistically compelling". Kuhn's insistence (1970a, p. 238) that the way in which we are to discover the nature of science is "intrinsically sociological" and is to be accomplished by "examining the nature of the scientific group, discovering what it values, what it tolerates, and what it disdains", also leads to relativism if it transpires that different groups value, tolerate and disdain different things. This, indeed, is how proponents of the sociology of science currently in vogue commonly interpret Kuhn, developing his views into an explicit relativism.

In my view, Kuhn's account of scientific progress as it appears in the second edition of his book, complete with PostScript, contains two incompatible strands, one relativist and one not. This opens up two possibilities. The first is to follow the path taken by the sociologists mentioned in the previous paragraph and to embrace and develop the relativist strand in Kuhn's thought, which among other things involves carrying out the sociological investigation of science the need for which Kuhn alluded but never responded to. The second alternative is to ignore the relativism and rewrite Kuhn in a way that is compatible with some overarching sense of progress in science. This alternative will require an answer to the question of the sense in which a paradigm can be said to const.i.tute progress over the one it replaces. I hope it will be clear by the end of the book which option I regard as the most fruitful.

Objective knowledge.

"The transition between competing paradigms ... must occur all at once (though not necessarily in an instant) or not at all." I am not the only one to have found this sentence from Kuhn (1970a, p.150) puzzling. How can a paradigm change take place all at once, but not necessarily in an instant? I do not think it is difficult to find the source of the confusion embodied in the problematic sentence. On the one hand, Kuhn is aware of the fact that a scientific revolution extends over a considerable period of time involving much theoretical and experimental work. Kuhn's own cla.s.sic study of the Copernican Revolution (1959) doc.u.ments the centuries of work involved. On the other hand, Kuhn's comparisons between paradigm change and gestalt switches or religious conversions make immediate sense of the idea that the change takes place "all at once". I suggest that Kuhn is, in effect, confusing two kinds of knowledge here, and it is important and helpful to spell out the distinction.

If I say "I know the date on which I wrote this particular paragraph and you do not", I am referring to knowledge that I am aquainted with and that resides in my mind or brain, but which you are not aquainted with and is absent from your mind or brain. I know Newton's first law of motion but I do not know how to biologically cla.s.sify a crayfish. Again, this is a question about what resides in my mind or brain. The claims that Maxwell was unaware that his electromagnetic theory predicted radio waves and that Einstein was aware of the results of the Michelson-Morley experiment involve this same usage of "know" in the sense of "being aware of". Knowledge is a state of mind. Closely connected with this usage, in the sense that it is also to do with the states of mind of individuals, is the issue of whether or not, and the degree to which, an individual accepts or believes a claim or set of claims. I believe that Galileo made a convinving case for the validity of the use of his telescope, but Feyerabend did not. Ludwig Boltzmann accepted the kinetic theory of gases but his compatriot Ernst Mach did not. All these ways of talking about knowledge and claims to knowledge are about the states of mind or att.i.tudes of individuals. It is a common and perfectly legitimate way of talking. For want of a better term I will call what is talked of here knowledge in the subjective sense. I will distinguish it from a different usage which I refer to as knowledge in the objective sense.

The sentence "my cat lives in a house that no animals inhabit" has the property of being contradictory, while the sentences "I have a cat" and "today a guinea pig died" have the property of being consequences of the statement "today my white cat killed someone's pet guinea pig". In these examples, the fact that the sentences have the properties I attribute to them, in some common sense, is obvious, but this need not be so. For example, a lawyer in a murder trial may, after much painstaking a.n.a.lysis, discover the fact that one witness's report has consequences that contradict those of a second witness. If that is indeed the case, then it is the case whether the witnesses in question were aware of it or believed it or not. What is more, if the lawyer had not discovered the inconsistency, it may have remained undiscovered, so that no one ever became aware of it. Nevertheless, it would remain the case that the statements were inconsistent. Propositions can have properties that are distinct from what individuals might be aware of. They have objective properties.

We have already encountered, in chapter 1, an instance of the distinction between subjective and objective knowledge. I drew a distinction between the perceptual experiences of individuals, and what they might believe as a consequence of them, on the one hand, and the observation statements that they might be taken to support on the other. I made the point that the latter are publicly testable and debatable in a way that the former are not.

The maze of propositions involved in a body of knowledge at some stage in its development will, in a similar way, have properties that individuals working on it need not be aware of. The theoretical structure that is modern physics is so complex that it clearly cannot be identified with the beliefs of any one physicist or group of physicists. Many scientists contribute in their separate ways and with their individual skills to the growth and articulation of physics, just as many workers combine their efforts in the construction of a cathedral. And just as a happy steeplejack may be blissfully unaware of the implication of some ominous discovery made by labourers digging near the foundations, so a lofty theoretician may be unaware of the relevance of some experimental finding for the theory on which he or she works. In either case, objective relationships exist between parts of the structure independently of whether individuals are aware of that relationship.

Historical examples from science that ill.u.s.trate this point are easy to find. It is frequently the case that unexpected consequences of a theory, such as an experimental prediction or a clash with another theory, are discovered by subsequent work. Thus Poisson was able to discover and demonstrate that Fresnel's theory of light had the consequence that a bright spot should be visible at the centre of the shadow side of a suitably illuminated opaque disc, a consequence of which Fresnel had been unaware. Various clashes between Fresnel's theory and Newton's particle theory of light, which it challenged, were also discovered. For example, the former predicted that light should travel faster in air than in water, whereas the latter predicted the reverse.

I have ill.u.s.trated a sense in which knowledge can be construed as objective by talking of the objective properties of statements, especially statements of theoretical and observational claims. But it is not only such statements that are objective. Experimental set-ups and procedures, methodological rules and mathematical systems are objective too, in the sense that they are distinct from the kinds of things that reside in individual minds. They can be confronted and can be exploited, modified and criticised by individuals. An individual scientist will be confronted by an objective situation - a set of theories, experimental results, instruments and techniques, modes of argument and the like - and it is these that the scientist must use in order to attempt to modify and improve the situation.

I do not intend my use of the term "objective" to be evaluative. Theories that are inconsistent or which explain little will be objective according to my usage. Indeed, such theories will objectively possess the properties of being inconsistent or explaining little. Although my usage of "objective" derives from and follows closely that of Karl Popper (see especially his 1979 text, chapters 3 and 4), I do not wish to follow him in getting involved in the tricky question of the precise sense in which these objective properties exist. Statements do not have properties in the sense that physical objects do, and spelling out the mode of existence of such linguistic objects, as well as other social constructions such as methodological rules and mathematical systems, is a tricky philosophical business. I am content to make my points at a commonsense level, using the kinds of examples I have used. This is sufficient for my purpose.

Much of Kuhn's talk of paradigms fits well into the objective side of the dichotomy I have introduced. His talk of the puzzle-solving tradition within a paradigm and the anomalies confronted by a paradigm, and also the way in which paradigms differ in involving different standards and different metaphysical a.s.sumptions, are all cases in point. Accepting this mode of talk, it is quite meaningful, in Kuhn's terms, to formulate our basic question concerning the sense in which a particular paradigm can be said to be an improvement on its rival. This is a question about the objective relation between paradigms.

However, there is this other mode of talking at work in Kuhn's book which is situated on the subjective side of my dichotomy. This includes his talk of gestalt switches and the like. Talking of the switch from one paradigm to another in terms of gestalt switches, as Kuhn does, creates the impression that the viewpoints on either side of the switch cannot be compared. The change from one paradigm to another is identified with the change that takes place within a scientist's mind or brain when he or she changes allegiance from one to the other. It is this identification that leads to the confusion embodied in the sentence from Kuhn introduced at the beginning of this section. If our concern is the nature of science and the sense in which science can be said to progress, as Kuhn's seems to be, then my suggestion is that all the talk of gestalt switches and religious conversions be removed from Kuhn's account and that we stick to an objective characterisation of paradigms and the relationship between them. Much of the time Kuhn does precisely this, and his historical studies are a mine of important material for helping to elucidate the nature of science.

The way in which one historically existing paradigm might be said to be better than the rival that it replaces is distinct from the question of the ways in which, or the reasons why, individual scientists change their allegiance from one to the other, or come to be working in one or the other. The fact that individual scientists in their scientific work make judgments and choices for a variety of reasons, often influenced by subjective factors, is one thing. The relationship between one paradigm and another, perceivable most clearly with the benefit of hindsight, is another. If some distinctive sense in which science progresses is to be identified, it is the latter kind of consideration that will yield the answer. That is why I am dissatisfied with Kuhn's attempt, in his 1977 text (chapter 13), to combat the charge of relativism by focusing on "value judgment and theory choice".

Further reading.

The key source is, of course, Kuhn's The Structure of Scientific Revolutions (1970a). In "Logic of Discovery or Psychology of Research" (1970b) Kuhn discusses the relationship between his views and Popper's and replies to some of his critics in "Reflections on My Critics" (1970c). A valuable collection of Kuhn's essays is his 1977 text. A detailed discussion of Kuhn's philosophy of science is Hoyningen-Huene (1993), which contains a detailed bibliography of Kuhn's work. Lakatos and Musgrave (1970) contains a number of interchanges between Kuhn and his critics. For appropriations of Kuhn's ideas by sociologists see, for example, Bloor (1971) and Barnes (1982). For an account of the construction of meaning in science that exemplifies the position outlined in the first section of this chapter, see Nersessian (1984).

CHAPTER 9:.

Theories as structures II: Research programs.

Introducing Imre Lakatos.

Imre Lakatos was a Hungarian who moved to England in the late 1950s and came under the influence of Karl Popper who, in Lakatos's own words "changed [his] life" (Worrall and Currie, 1978a, p. 139). Although an avid supporter of Popper's approach to science, Lakatos came to realise some of the difficulties that faced Popper's falsificationism, difficulties of the kind we have considered in chapter 7. By the mid-1960s Lakatos was aware of the alternative view of science contained in Kuhn's The Structure of Scientific Revolutions. Although Popper and Kuhn proposed rival accounts of science, their views do have much in common. In particular, they both take a stand against positivist, inductivist accounts of science. They both give priority to theory (or paradigm) over observation, and insist that the search for, interpretation and acceptance or rejection of the results of observation and experiment take place against a background of theory or paradigm. Lakatos carried on that tradition, and looked for a way of modifying Popper's falsificationism and ridding it of its difficulties, among other ways by drawing on some of the insights of Kuhn while totally rejecting the relativist aspects of the latter's position. Like Kuhn, Lakatos saw the merit in portraying scientific activity as taking place in a framework, and coined the phrase "research program" to name what were, in a sense, Lakatos's alternatives to Kuhn's paradigms. The primary source for an account of Lakatos's methodology is his 1970 text.

Lakatos's research programs.

We saw in chapter 7 that one of the main difficulties with Popper's falsificationism was that there was no clear guidance concerning which part of a theoretical maze was to be blamed for an apparent falsification. If it is left to the whim of the individual scientist to place the blame wherever he or she might wish, then it is difficult to see how the mature sciences could progress in the coordinated and cohesive way that they seem to do. Lakatos's response was to suggest that not all parts of a science are on a par. Some laws or principles are more basic than others. Indeed, some are so fundamental as to come close to being the defining feature of a science. As such, they are not to be blamed for any apparent failure. Rather, the blame is to be placed on the less fundamental components. A science can then be seen as the programmatic development of the implications of the fundamental principles. Scientists can seek to solve problems by modifying the more peripheral a.s.sumptions as they see fit. Insofar as their efforts are successful they will be contributing to the development of the same research program however different their attempts to tinker with the peripheral a.s.sumptions might be.

Lakatos referred to the fundamental principles as the hard core of a research program The hard core is, more than anything else, the defining characteristic of a program. It takes the form of some very general hypotheses that form the basis from which the program is to develop. Here are some examples. The hard core of the Copernican program in astronomy was the a.s.sumption that the earth and the planets...o...b..t a stationary sun and that the earth spins on its axis once a day. The hard core of Newtonian physics is comprised of Newton's three laws of motion plus his law of gravitational attraction. The hard core of Marx's historical materialism would be something like the a.s.sumption that major social change is to be explained in terms of cla.s.s struggle, the nature of the cla.s.ses and the details of the struggle being determined, in the last instance, by the economic base.

The fundamentals of a program need to be augmented by a range of supplementary a.s.sumptions in order to flesh it out to the point where definite predictions can be made. It will consist not only of explicit a.s.sumptions and laws supplementing the hard core, but also a.s.sumptions underlying the initial conditions used to specify particular situations and theories presupposed in the statement of observations and experimental results. For example, the hard core of the Copernican program needed to be supplemented by adding numerous epicycles to the initially circular orbits and it was also necessary to alter previous estimates of the distance of the stars from earth. Initially the program also involved the a.s.sumption that the naked eye serves to reveal accurate information concerning the position, size and brightness of stars and planets. Any inadequacy in the match between an articulated program and observation is to be attributed to the supplementary a.s.sumptions rather than the hard core. Lakatos referred to the sum of the additional hypotheses supplementing the hard core as the protective belt, to emphasise its role of protecting the hard core from falsification. According to Lakatos (1970, p. 133), the hard core is rendered unfalsifiable by "the methodological decisions of its protagonists". By contrast, a.s.sumptions in the protective belt are to be modified in an attempt to improve the match between the predictions of the program and the results of observation and experiment. For instance, the protective belt within the Copernican program was modified by subst.i.tuting elliptical orbits for Copernicus's sets of epicycles and telescopic data for naked-eye data. The initial conditions also came to be modified eventually, with changes in the estimate of the distance of the stars from the earth and the addition of new planets. Lakatos made free use of the term "heuristic" in characterising research programs. A heuristic is a set of rules or hints to aid discovery or invention. For example, part of a heuristic for solving crossword puzzles might be "start with the clues requiring short-word answers and then proceed to those requiring long-word answers". Lakatos divided guidelines for work within research programs into a negative heuristic and a positive heuristic. The negative heuristic specifies what the scientist is advised not to do. As we have already seen, scientists are advised not to tinker with the hard core of the program in which they work. If a scientist does modify the hard core then he or she has, in effect, opted out of the program. Tycho Brahe opted out of the Copernican program when he suggested that only the planets, but not the earth, orbit the sun and that the sun orbits the earth.

The positive heuristic of a program, that which specifies what scientists should do rather than what they should not do within a program, is more difficult to characterise specifically than the negative heuristic. The positive heuristic gives guidance on how the hard core is to be supplemented and how the resulting protective belt is to be modified in order for a program to yield explanations and predictions of observable phenomena. In Lakatos's own words (1970, p. 135), "the positive heuristic consists of a partially articulated set of suggestions or hints on how to change, develop, the 'refutable variants' of the research program, how to modify, sophisticate, the 'refutable' protective belt". The development of the program will involve not only the addition of suitable auxiliary hypotheses but also the development of adequate experimental and mathematical techniques. For instance, from the very inception of the Copernican program it was clear that mathematical techniques for combining and manipulating epicycles and improved techniques for observing planetary positions were necessary. Lakatos ill.u.s.trated the notion of a positive ir heuristic with the story of Newton's early development of his gravitational theory. Here, the positive heuristic involved the idea that one should start with simple, idealised cases and then, having mastered them, one should proceed to more complicated, and more realistic, cases. Newton first arrived at the inverse square law of attraction by considering the elliptical motion of a point planet around a stationary point sun. It was clear that if the program was to be applied in practice to planetary motions then it would need to be developed from this idealised form to a more realistic one. But that development involved the solution of theoretical problems and was not to be achieved without considerable theoretical labour. Newton himself, faced with a definite program, that is, guided by his positive heuristic, made considerable progress. He first took into account the fact that the sun as well as a planet moves under the influence of their mutual attraction. Then he took account of the finite size of the planets and treated them as spheres. After solving the mathematical problem posed by that move, Newton proceeded to allow for other complications such as those introduced by the possibility that a planet can spin, and the fact that there are gravitational forces between the individual planets as well as between each planet and the sun. Once Newton had progressed that far in the program, following a path that had presented itself as more or less necessary from the outset, he began to be concerned about the match between his theory and observation. When the match was found wanting he was able to proceed to non-spherical planets and so on. As well as the theoretical program , the positive heuristic contained an experimental one. That program included the development of more accurate telescopes, together with auxiliary theories necessary for their use in astronomy, such as those providing adequate means for allowing for refraction of light in the earth's atmosphere. The initial formulation of Newton's program already indicated the desirability of constructing apparatus sensitive enough to detect gravitational attraction on a laboratory scale (Cavendish's experiment).

The program that had Newton's laws of motion and his law of gravitation at its core gave strong heuristic guidance. That is, a fairly definite program was mapped out from the start. Lakatos (1970, pp. 140-55) gives an account of the development of Bohr's theory of the atom as another example of a positive heuristic in action. An important feature of these examples of developing research programs, stressed by Lakatos, is the comparatively late stage at which observational testing becomes relevant. This is in keeping with the comments about Galileo's construction of his mechanics in the first section of chapter 8. Early work in a research program is portrayed as taking place without heed or in spite of apparent falsifications by observation. A research program must be given a chance to realise its full potential. A suitable sophisticated and adequate protective belt must be constructed. In our example of the Copernican program, this included the development of an adequate mechanics that could accommodate the earth's motion and an adequate optics to help interpret the telescopic data. When a program has been developed to the stage where it is appropriate to subject it to experimental tests, it is confirmations rather than falsifications that are of paramount significance, according to Lakatos. The worth of a research program is indicated by the extent to which it leads to novel predictions that are confirmed. The Newtonian program experienced dramatic confirmations of this kind when Galle first observed the planet Neptune and when Halley's comet returned as predicted. Failed predictions, such as Newton's early calculations of the moon's...o...b..t, are simply indications that more work needs to be done on supplementing or modifying the protective belt.

The main indication of the merit of a research program is the extent to which it leads to novel predictions that are confirmed. A second indication, implicit in our discussion above, is that a research program should indeed offer a program of research. The positive heuristic should be sufficiently coherent to be able to guide future research by mapping out a program. Lakatos suggested Marxism and Freudian psychology as programs that lived up to the second indicator of merit but not to the first, and contemporary sociology as one that lives up to the first to some extent but not the second (although he did not back up these remarks with any detail). In any event, a progressive research program will be one that retains its coherence and at least intermittently leads to novel predictions that are confirmed, while a degenerating program will be one that loses its coherence and/or fails to lead to confirmed novel predictions. The replacement of a degenerating program by a progressive one const.i.tutes Lakatos's version of a scientific revolution.

Methodology within a program and the comparison of programs.

We need to discuss Lakatos's methodology of scientific research programs in the context of work within a program and in the context of the clash between one research program and another. Work within a single research program involves the expansion and modification of its protective belt by the addition and articulation of various hypotheses. Any such move is permissible so long as it is not ad hoc in the sense discussed in chapter 6. Modifications or additions to the protective belt of a research program must be independently testable. Individual scientists or groups of scientists are open to modify or augment the protective belt in any way they choose , provided these moves open up the opportunity for new tests and hence the possibility of novel discoveries. By way of ill.u.s.tration, let us take an example from the development of the Newtonian program that we have employed several times before and consider the situation that confronted Leverrier and Adams when they addressed themselves to the troublesome orbit of the planet Ura.n.u.s. Those scientists chose to modify the protective belt of the program by proposing that the initial conditions were inadequate and suggesting that there was an as yet unidentified planet close to Ura.n.u.s and disturbing its...o...b..t. Their move was in accordance with Lakatos's methodology because it was testable. The conjectured planet could be sought for by training telescopes on the appropriate region of the sky. But other possible responses would be legitimate according to Lakatos's position. For instance, the problematic orbit could be blamed on some new type of aberration of the telescope, provided the suggestion was made in a way that made it possible to test for the reality of such aberrations. In a sense, the more testable moves that are made to solve a problem such as this the better, because this increases the chances of success, (where success means the confirmation of the novel predictions ensuing from a move). Moves that are ad hoc are ruled out by Lakatos's methodology. So, in our example, an attempt to accommodate Ura.n.u.s's problematic orbit by simply labelling that complex orbit as the natural motion of Ura.n.u.s would be ruled out. It opens up no new tests and hence no prospect of novel discoveries.

A second kind of move ruled out by Lakatos's methodology are ones that involve a departure from the hard core. Making such a move destroys the coherence of a program and amounts to opting out of that program. For instance, a scientist attempting to cope with Ura.n.u.s's...o...b..t by suggesting that the attraction between Ura.n.u.s and the Sun was something other than the inverse square law would be opting out of the Newtonian research program.

The fact that any part of a complex theoretical maze might be responsible for an apparent falsification poses a serious problem for the falsificationist relying on an unqualified method of conjectures and refutations. For that person, the inability to locate the source of the trouble leads to unmethodical chaos. Lakatos's methodology is designed to avoid that consequence. Order is maintained by the inviolability of the hard core of the program and by the positive heuristic that accompanies it. The proliferation of ingenious conjectures within that framework will lead to progress provided some of the predictions resulting from those conjectures occasionally prove successful. Decisions to retain or reject an hypothesis are fairly straightforwardly determined by the results of experimental tests. The bearing of observation on an hypothesis under test is relatively unproblematic within a research program because the hard core and the positive heuristic serve to define a fairly stable observation language.

As was mentioned above, Lakatos's version of a Kuhnian revolution involves the ousting of one research program by another. We have seen that Kuhn (1970, p. 94) was unable to give a clear answer to the question of the sense in which a paradigm can be said to be superior to the one it replaces, and so left him with no option but to appeal to the authority of the scientific community. Later paradigms are superior to their predecessors because the scientific community judges them to be so, and "there is no standard higher than the a.s.sent of the relevant community'. Lakatos was dissatisfied with the relativist implications of Kuhn's theory. He sought a standard that lay outside of particular paradigms or, in Lakatos's case, research programs, which could be used to identify some non-relativist sense in which science progresses. To the extent that he had such a standard, it lay in his conception of progressing and degenerating research programs. Progress involves the replacement of a degenerating program with a progressive one, with the latter being an improvement on the former in the sense that it has been shown to be a more efficient predictor of novel phenomena.

Novel predictions.

The non-relativist measure of progress that Lakatos proposed relied heavily on the notion of a novel prediction. One program is superior to another insofar as it is a more successful predictor of novel phenomena. As Lakatos came to realise, the notion of a novel prediction is not as straightforward as it might at first appear, and care is needed to mould that notion into a form that serves the purpose required of it within Lakatos's methodology or, indeed, any methodology that seeks to make significant use of it.

We have already met novel predictions in the context of Popper's methodology. In that context I suggested that the essence of Popper's position is that a prediction is novel, at a particular time, to the extent that it does not figure in, or perhaps clashes with, the knowledge that is familiar and generally accepted at that time. For Popper, testing a theory by way of its novel predictions amounted to a severe test of that theory just because the prediction clashed with prevailing expectations. Lakatos's use of novel predictions in something like the Popperian sense to help him characterise the progressiveness of a research program will not do, as he himself came to realise, and this can be established by means of fairly straightforward counter examples, examples drawn from the very programs that Lakatos freely utilised to ill.u.s.trate his position. The counter examples involve situations where the worth of a research program is demonstrated by its ability to explain phenomena that at the time were already well established and familiar, and so not novel in the Popperian sense.

There are features of planetary motion that have been well known since antiquity, but which were adequately explained only with the advent of the Copernican theory. They include the retrograde motion of the planets and the fact that the planets appear brightest when they are retrogressing, as well as the fact that Venus and Mercury never appear far from the sun. The qualitative features of these phenomena follow straightforwardly once it is a.s.sumed that the earth orbits the sun along with the planets and that the orbits of Mercury and Venus are inside that of the earth, whereas in the Ptolemaic theory they can only be explained by introducing epicycles designed specifically for the purpose. Lakatos joined Copernicus, and I imagine most of the rest of us, in recognising this as a major mark of the superiority of the Copernican over the Ptolemaic system. However, the Copernican prediction of the general features of planetary motion did not count as novel in the sense we have defined it for the straightforward reason that those phenomena had been well known since antiquity. The observation of parallax in the stars was probably the first confirmation of the Copernican theory by a prediction that counts as novel in the sense we are discussing, but that doesn't suit Lakatos's purpose at all, since it did not occur until well into the nineteenth century, well after the superiority of Copernicus over Ptolemy had been accepted within science.

Other examples are readily found. One of the few observations that could be invoked to support Einstein's general theory of relativity was the precession of the perihelion of the orbit of the planet Mercury, a phenomenon well known and accepted long before Einstein's theory explained it. One of the most impressive features of quantum mechanics was its ability to explain the spectra exhibited by the light emitted from gases, a phenomenon familiar to experimenters for over half a century before the quantum mechanical explanation was available. These successes can be described as involving the novel prediction of phenomena rather than the prediction of novel phenomena.

Lakatos came to realise, in the light of some considerations put forward by E. Zahar (1973), that the account of novel predictions in his original formulation of the methodology of scientific research programs needed to be modified. After all, when a.s.sessing the extent to which some observable phenomena supports a theory or program, surely it is a historically contingent fact of no philosophical relevance whether it is the theory or knowledge of the phenomena that comes first. Einstein's theory of relativity can explain the orbit of Mercury and also the bending of light rays in a gravitational field. These are both considerable achievements that support the theory. It so happens that the precession of the perihelion of Mercury was known prior to Einstein's formulation of the theory whereas the bending of light rays was discovered subsequently. But would it make any difference to our a.s.sessment of Einstein's theory if it had been the other way around, or if both phenomena had been known before or both discovered after? The fine details of the appropriate response to these reflections are still being debated, for example by Alan Musgrave (1974b) and John Worrall (1985 and 1989a), but the intuition that needs to be grasped, and which is at work in the comparison of Copernicus and Ptolemy, seems straightforward enough. The Ptolemaic explanation of retrograde motion did not const.i.tute significant support for that program because it was artificially fixed up to fit the observable data by adding epicycles especially designed for the purpose. By contrast, the observable phenomena followed in a natural way from the fundamentals of the Copernican theory without any artificial adjustment. The predictions of a theory or program that count are those that are natural rather than contrived. Perhaps what lies behind the intuition here is the idea that evidence supports a theory if, without the theory, there are unexplained coincidences contained in the evidence. How could the Copernican theory successfully predict all the observable general features of planetary motion if it wasn't essentially correct? The same argument does not work in the case of the Ptolemaic explanation of the same phenomena. Even if the Ptolemaic theory is quite wrong, it is no coincidence that it can explain the phenomena because the epicycles have been added in such a way as to ensure that it does. This is the way in which Worrall (1985, 1989) treats the matter.

In the light of this, we should reformulate Lakatos's methodology so that a program is progressive to the extent that it makes natural, as opposed to novel, predictions that are confirmed, where "natural" stands opposed to "contrived" or "ad hoc". (We shall revisit this issue from a different and perhaps superior angle in chapter 13.)

Testing the methodology against history.

Lakatos shared Kuhn's concern with the history of science. He believed it to be desirable that any theory of science be able to make sense of the history of science. That is, there is a sense in which a methodology or philosophy of science is to be tested against the history of science. However, the precise way in which this is so needs to be carefully spelt out, as Lakatos was well aware. If the need for a philosophy of science to match the history of science is interpreted undiscriminatingly, then a good philosophy of science will become nothing more than an accurate description of science. As such, it will be in no position to capture the essential characteristics of science or to discriminate between good science and bad science. Popper and Lakatos tended to regard Kuhn's account as "merely" descriptive, in this sense, and hence deficient. Popper was so wary of the problem that he, unlike Lakatos, denied that comparison with the history of science was a legitimate way of arguing for a philosophy of science.

I suggest that the essentials of Lakatos's position, as described in his 1978 text, are these. There are episodes in the history of science that are unproblematically progressive and which can be recognised as such prior to any sophisticated philosophy of science. If someone wants to deny that Galileo's physics was an advance on Artistotle's or that Einstein's was an advance on Newton's then he or she is just not using the word science in the way that the rest of us are. To be concerned with the question of how best to categorise science we must have some pre-theoretical notion of what science is in order to formulate the question, and that pre-theoretical notion will include the ability to recognise cla.s.sic examples of major scientific achievements such as those of Galileo and Einstein. With these presuppositions as a background, we can now demand that any philosophy or methodology of science be compatible with them. That is, any philosophy of science should be able to grasp the sense in which Galileo's achievements in astronomy and physics were in the main major advances. So if the history of science reveals that in his astronomy Galileo transformed what were considered to be the observable facts, and in his mechanics he relied mainly on thought experiments rather than real ones, then that poses a problem for those philosophies that portray scientific progress as c.u.mulative, progressing by way of the acc.u.mulation of secure observational facts and cautious generalisations from them. Lakatos's own early version of his methodology of research programs can be criticised for utilising a notion of novel prediction in a way that makes it impossible to grasp the sense in which Copernicus's astronomy was progressive, as I did in the previous section.

With this mode of argument, Lakatos proceeds to criticise positivist and falsificationist methodologies on the grounds that they fail to make sense of cla.s.sic episodes in the progress of science, and argues, by contrast, that his own account does not suffer from the same deficiency. Turning, then, to more minor episodes in the history of science, Lakatos, or a supporter, can pick on episodes from the history of science that have puzzled historians and philosophers and show how they make complete sense from the point of view of the methodology of scientific research programs. Thus, for example, many have been puzzled by the fact that when Thomas Young proposed the wave theory of light in the early nineteenth century it won few supporters, whereas Fresnel's version, devised two decades later, won widespread acceptance. John Worrall (1976) gives historical support to Lakatos's position when he shows that, as a matter of historical fact, Young's theory was not strongly confirmed experimentally in a natural, as opposed to a contrived, way, as Fresnel's was, and that Fresnel's version of the wave theory had a vastly superior positive heuristic by virtue of the mathematical tools he was able to introduce. A number of Lakatos's students or former students carried out studies, appearing in Howson (1976), intended to support Lakatos's methodology in this kind of way.

Lakatos came to see the main virtue of his methodology to be the aid it gives to the writing of the history of science. The historian must attempt to identify research programs, characterise their hard cores and protective belts, and doc.u.ment the ways in which they progressed or degenerated. In this way, light can be shed on the way science progresses by way of the compet.i.tion between programs. I think it must be conceded that Lakatos and his followers did succeed in casting useful light on some cla.s.sic episodes in the history of the physical sciences by studies carried out in this way, as the essays in Howson (1976) reveal. Although Lakatos's methodology can offer advice to historians of science, it was not intended by Lakatos as a source of advice for scientists. This became an inevitable conclusion for Lakatos given the way he found it necessary to modify falsificationism to overcome the problems it faced. Theories should not be rejected in the face of apparent falsifications because the blame might in due course be directed at a source other than the theory, and single successes certainly do not establish the merit of a theory for all time. That is why Lakatos introduced research programs, which are given time to develop and may come to progress after a degenerating period, or degenerate after early successes. (It is worth recalling in this connection that the Copernican theory degenerated for about a century after its early successes before the likes of Galileo and Kepler brought it to life again.) But once this move is taken, it is clear that there can be no on-the-spot advice forthcoming from Lakatos's methodology along the lines that scientists must give up a research program, or prefer a particular research program to its rival. It is not irrational or necessarily misguided for a scientist to remain working on a degenerating program if he or she thinks there are possible ways to bring it to life again. It is only in the long term (that is, from a historical perspective) that Lakatos's methodology can be used to meaningfully compare research programs. In this connection, Lakatos came to make a distinction between the appraisal of research programs, which can only be done with historical hindsight, and advice to scientists, which he denied it was the purpose of his methodology to offer. "There is no instant rationality in science" became one of Lakatos's slogans, capturing the sense in which he considered positivism and falsificationism, insofar as they can be interpreted as offering criteria that can be used for the acceptance and rejection of theo