Moreover, it is in this combined process of verification and falsification that the probabilist’s comparison of theories comes to play a central role. I think such a two-stage formulation has the merit of an admirable verisimilitude, and it may open the way to explaining the role of agreement—or disagreement—between fact and theory in the process of verification. At least to historians of science, it is not very persuasive to claim that verification establishes agreement between fact and theory. All historically significant theories have agreed with the facts, but only by and large. There is no more precise answer to the question of whether, or how well, any individual theory corresponds to the facts. But analogous questions can be raised when theories are treated collectively or in pairs. It is entirely reasonable to ask which of two actual and competing theories better fits the facts. For example, although neither Priestley’s theory nor Lavoisier’s theory was in strict agreement with the existing observations, only a few scholars of the time hesitated for more than a decade before concluding that Lavoisier’s theory was more adequate.
Yet this formulation makes the choice between paradigms seem easier and more familiar than it actually is. If there existed only a single series of scientific problems—that is, only one world within which those problems operated, and a single set of standards for their solution—then the competition between paradigms might be settled, more or less routinely, by some procedure such as counting the number of problems solved by each paradigm. In fact, however, these conditions are never fully met. The proponents of competing paradigms are always, at least to some extent, at cross-purposes. Neither side will concede all the nonempirical assumptions the other needs to make its position secure. Like Proust and Berthollet in their dispute over the composition of chemical compounds, they inevitably argue in part through their own paradigms. For in viewing science and its problems, although each side wishes to draw the other over to its own way of seeing, neither can expect its own position to be proved. The competition between paradigms is not the kind of battle that can be resolved by proof.
We have already examined several reasons why the proponents of competing paradigms cannot make full contact with the other side’s viewpoint. Taken together, these reasons have been described as the incommensurability of the normal-scientific traditions before and after a revolution, and here we need only summarize them briefly. First, the proponents of competing paradigms will often disagree about the list of problems that any candidate for paradigm must solve.
Their standards or definitions of science are not the same either. Must a theory of motion be able to explain the cause of the attractive forces acting between particles of matter, or is it enough for a theory of motion simply to reveal the fact that such forces exist? Newtonian mechanics, unlike the theories of Aristotle and Descartes, was widely rejected because it implied the latter answer to that question. And when Newton’s theory was accepted, that question thereby disappeared from science. Yet it is a question that the general theory of relativity may well claim to have solved. Or, in the widespread situation of the nineteenth century, Lavoisier’s chemical theory prevented chemists from posing the question of why metals are so much alike—a question that phlogiston chemistry had raised and even answered. The transition to Lavoisier’s paradigm, like the transition to the Newtonian paradigm, meant the disappearance not only of permissible questions but also of completed solutions. Such disappearance, however, was not permanent. In the twentieth century, questions concerning the properties of chemical substances, along with some answers to them, reappeared in science.
But more than incommensurability is involved here. Since new paradigms are born from old ones, they ordinarily include much of the conceptual and operational terminology and apparatus that the traditional paradigm had previously used. But the new paradigm does not use these borrowed elements in the traditional way. Within the new paradigm, old terms, concepts, and experiments enter into new relations with one another. The inevitable result, though the expression may be inadequate, is what must be called misunderstanding between two competing schools.
It cannot simply be said that the ordinary person who laughed off Einstein’s general theory of relativity because space could not possibly be “curved”—space was not that sort of thing—was wrong or mistaken. Nor were the mathematicians, physicists, and philosophers who tried to develop Einstein’s theory in Euclidean terms wrong.3) What space had meant before was necessarily flat, homogeneous, and uniform, and unaffected by the presence of matter. Had it not been so, Newtonian physics could not have existed. For the transition to Einstein’s universe, the entire conceptual organization whose elements were space, time, matter, force, and so on had to be transformed, and then placed once more upon nature as a whole. Only those who had undergone such a transformation, or had failed to undergo it, could accurately discover what they agreed and disagreed about. Communication across the watershed of revolution can only be partial. As another example, consider those who said Copernicus was mad because he claimed that the earth rotated. They were not simply wrong, nor even greatly wrong. What they meant by “earth” already included the notion of a fixed position. Their earth, at least, could not be moved. Thus the innovation Copernicus brought about was not merely to set the earth in motion. It was an entirely new way of approaching the problems of physics and astronomy, and it necessarily changed the meanings of both “earth” and “motion.”4) Without such changes, the idea of a rotating earth was madness. Once those changes were made and came to be understood, however, both Descartes and Huygens could realize that the motion of the earth was a question without substance as science.5) These examples point to a third and most fundamental aspect of the incommensurable character of competing paradigms. What I can no longer explain adequately is that the proponents of competing paradigms conduct their research in different worlds. One deals with constrained bodies falling slowly, the other with pendulums that continue to repeat their motion. In one, solutions are compounds; in the other, mixtures. One is contained in flat space, the other in curved space. Because they work in different worlds, the two groups of scientists see different things even when they look from the same point of view. This does not mean, however, that they see whatever they please. Both are looking at the world, and the objects they look at have not changed. But in certain areas they see different things, and they see them in different relations. This is why a law that cannot even be proved to one group of scientists may appear intuitively obvious to another. Likewise, this is why, if sufficient communication between them is to be hoped for, one group or the other must undergo the conversion we have called a paradigm shift. Because it is a transition between incommensurables, the transition between competing paradigms is not forced by logic or by value-neutral experience and does not proceed one step at a time. As in a gestalt switch, it must occur all at once—even if not necessarily in a single instant—or not at all.
How, then, do scientists bring about this transposition? Part of the answer is that they often do not bring it about. Copernican theory won only a few converts for nearly a century after his death. Newton’s work was not generally accepted, especially on the Continent, for more than half a century after the publication of the “Principia.”6) Priestley never accepted the oxygen theory, nor did Lord Kelvin accept the electromagnetic theory, and the examples continue. The difficulty of conversion has often been noted by scientists themselves. In a passage of unusually deep insight near the end of his “Origin of Species,” Darwin wrote: “Although I am convinced of the truth of the views given in this volume... I by no means expect to convince experienced naturalists whose minds are stocked with a multitude of facts all viewed, during a long course of years, from a point of view directly opposite to mine. ...But I look with confidence to the future—to young and rising naturalists, who will be able to view both sides of the question with impartiality.”7) And Planck, looking back on his life in his “Scientific Autobiography,” ruefully observed: “A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.”8) These facts and many others like them are so widely known that they need no further emphasis. But they do need reappraisal. In the past, such facts were often taken to show that scientists, being only human, refused to acknowledge their errors despite strict evidence. In these matters, I think neither proof nor error is at issue. The transition from paradigm to paradigm is a conversion experience that cannot be forced. The lifelong resistance of those who adhere to an older tradition of normal science is not a violation of scientific standards, but an indicator of the very nature of scientific research. The source of resistance lies, in the end, in the conviction that the old paradigm will solve all its problems—that nature will fit into the framework provided by the paradigm.
Indeed, as sometimes happens. In revolutionary periods, such conviction cannot but appear stubborn and obstinate. Yet it is also something more. It is precisely that conviction that makes normal science, or the puzzle-solving science, possible. And it is only through normal science that the professional community of science can succeed in developing the potential scope and precision of an older paradigm, and then, at the next stage, in isolating the difficulties through research from which a new paradigm will emerge.
But to say that such resistance is inevitable and legitimate, and to say that paradigm change cannot be justified by proof, does not mean that all argument is irrelevant or that scientists cannot be persuaded to change their minds. Sometimes it takes a generation for the change to occur, but scientific communities have, again and again, continued to convert to new paradigms.
Moreover, these conversions take place despite the fact that scientists are human beings. Some scientists, especially older and more experienced ones, may simply refuse, but most scientists can be approached in one way or another in a manner that shifts their views. After the last resistance has disappeared, conversions will occur a few at a time, until the entire professional community once again conducts its research under a single, but now different, paradigm. We must therefore ask how conversion is induced and how it is resisted.
What sort of answer can we expect to this question? Because it is a question about the techniques of persuasion, or about argument and counterargument in situations where proof is unavailable, our question is a new one, requiring a type of study that has not previously been undertaken. We shall have to be content with a highly partial and impressionistic survey. Moreover, what has already been said accords with the results of such considerations, which maintain that when we ask about persuasiveness rather than proof, there is no single, uniform answer to the question concerning the nature of scientific argument. Scientists come to accept a new paradigm for all sorts of reasons, and usually for several reasons at once. Some of these reasons—for example, the sun worship that helped convert Kepler into a Copernican—lie entirely outside the proper domain of science.9) Others must be determined by the features of the scientist’s life and personality. Even the nationality of an innovator and his teachers, or their already established reputation, can play a considerable role.10) We must therefore learn, in the end, to ask these questions differently.
Then we should not be concerned with the arguments that actually convert this or that person, but rather with the character of the scientific community that, as a single group, will sooner or later be re-formed. But we shall postpone this problem until the final section, and here examine several types of argument that have proved especially effective in the struggle surrounding paradigm change.
Perhaps the single most powerful claim advanced by the supporters of a new paradigm has been that they can solve the problems that led the old paradigm into crisis. Where it can be justified, this is often the most effective argument possible. In the field where such a claim is made, the paradigm has become known to be in difficulty. That difficulty has been repeatedly explored, and attempts to remove it have repeatedly proved futile. “Crucial experiments”__experiments that can distinguish the two paradigms with particular sharpness__have been recognized and tested even before the new paradigm has been devised. Thus Copernicus came to claim that he had solved the long-troublesome problem of the length of the year; Newton that he had reconciled terrestrial and celestial mechanics; Lavoisier that he had solved the problems of gas identity and weight relations; and Einstein that he had produced an electrodynamics consistent with a revised theory of motion.
Arguments of this kind are especially likely to succeed when the new paradigm displays a quantitative accuracy far superior to that of its old rival. The mathematical superiority of Kepler’s Rudolphine Tables over all calculations derived from Ptolemaic theory was a major factor in astronomers’ conversion to Copernican theory. Newton’s success in the quantitative prediction of mathematical-astronomical observations was probably the single most important reason his theory triumphed over its more reasonable qualitative rivals in that field. In the twentieth century, the revolutionary quantitative successes achieved by Planck’s law of radiation and Bohr’s model of the atom quickly convinced many physicists to accept those theories, even though, from the general perspective of the physical sciences, they created more problems than they solved.11)
But the claim to have solved the problems that produce a crisis cannot, by itself, be very sufficient. Nor can it always be made with propriety. In fact, Copernicus’s theory was no more accurate than Ptolemy’s, and it did not directly contribute to calendar reform. Again, for many years after it was first announced, the wave theory of light was no more successful than its rival, the particle theory of light, in resolving the polarization effects that had been a principal cause of the crisis in optics. Sometimes the looser conduct of research that characterizes extraordinary inquiry will produce a candidate for paradigm that at first is of no help at all with the problem that caused the crisis. When this happens, as it often does, evidence must be drawn from other parts of the field. And in those other areas, if the new paradigm permits the prediction of phenomena that had never been questioned while the old one was current, arguments of especially great persuasive force can be advanced.
For example, Copernican theory suggested that the planets were similar to the Earth, that Venus would display phases, and that the universe must be far vaster than had previously been thought. As a result, sixty years after his death, when the telescope suddenly revealed mountains on the Moon, the phases of Venus, and countless stars that had never before been predicted, those observations attracted many converts__especially non-astronomers__to the new theory.12) In the case of the wave theory, the principal source of the professional community’s conversion was even more active. When Fresnel demonstrated the existence of a white spot at the center of the shadow of a circular disk, the resistance of French scholars collapsed suddenly and almost completely. This was a result Fresnel himself had not even expected, but Poisson, one of his original opponents, had shown that it was an absurd yet necessary consequence of Fresnel’s theory.13) Because of their striking impact, and because it was so clear that they had not been “built into” the new theory from the beginning, arguments like these can be especially persuasive. Einstein, for example, does not seem to have expected that his general theory of relativity would accurately account for the well-known anomaly in the motion of Mercury’s perihelion, and when it actually did so, he felt an immense sense of triumph.14)
All the arguments for new paradigms discussed so far have been based on the relative ability of competing paradigms to solve problems. For scientists, such arguments are generally the most meaningful and persuasive. The examples above should leave no doubt as to the source of their powerful appeal. Yet for reasons to which we shall shortly return, they are not coercive, either individually or collectively. Fortunately, there exists another kind of thinking. These arguments are rarely made wholly explicit, but they appeal to the individual’s sense of what is appropriate or aesthetic__the new theory is said to be “neater,” “more suitable,” or “simpler” than the old. Perhaps such arguments are less effective in science than in mathematics. The initial form of most new paradigms is immature. By the time their aesthetic appeal can be fully developed, the majority of the scientific community has already been persuaded by other means. Nevertheless, the importance of aesthetic considerations can sometimes be decisive. Though the number of scientists drawn to a new theory through such aesthetic factors is small, the paradigm’s ultimate victory may depend precisely on that minority. Had they not adopted the candidate for paradigm for intensely personal reasons, the new candidate might never have developed sufficiently to lead the scientific community as a whole.
To understand the reason for the importance of these more subjective and aesthetic considerations, it is necessary to remember what paradigm debates are about. When a new candidate for paradigm is first proposed, it can solve only a small number of the problems before it, and most of those solutions are still very inadequate. Until the appearance of Kepler, Copernican theory scarcely improved the predictions of planetary positions made by Ptolemy. When Lavoisier regarded oxygen as “the air itself entire,” his new theory could not at all cope with the problems raised by the increasing number of new gases, a point on which Priestley made a very successful counterattack. Cases like Fresnel’s white spot are extremely rare. Usually, clearly decisive arguments are developed only long after a new paradigm has been developed, accepted, and explored__as with Foucault’s pendulum proving the rotation of the Earth, or Fizeau’s experiment showing that light moves faster in air than in water. Producing them is part of normal science, and their role appears not in paradigm debates but in post-revolutionary textbooks.
Before such textbooks are written, while the debate is still continuing, the situation is very different. Usually the opponents of a new paradigm can confidently argue that, even in the area in crisis, it has little superiority over its traditional rival paradigm. Of course, the new paradigm may handle some problems better and may uncover a few new laws. But it is believed that the old paradigm, just as it had responded to other challenges before, can be articulated so as to meet this challenge satisfactorily. Tycho Brahe’s partially revised geocentric astronomical system and the later revisions of phlogiston theory were both fairly successful.15) Moreover, defenders of traditional theory and procedure can almost invariably select problems that cannot be solved by the new rival paradigm but that present no difficulty at all from their own point of view. Until the composition of water was discovered, the combustion of hydrogen was a powerful argument in favor of phlogiston theory and against Lavoisier’s theory. And even after the oxygen theory had triumphed, it still could not explain the production of inflammable gas from carbon, a phenomenon that the phlogiston school pointed to as strong support for its own view.16) Even in the field in crisis, the balance of argument and counterargument was sometimes truly difficult to judge. And outside that field, the balance would often tip decisively toward tradition. Copernicus destroyed the traditional theory of motion in the terrestrial realm inherited from antiquity without replacing it. Newton likewise destroyed the old traditional explanation of gravity, and Lavoisier produced similar results with respect to the commonality of metals, among many other cases. In short, if candidates for new paradigms had from the beginning had to be judged by hardheaded people who examined only their relative problem-solving ability, science would have experienced only a very few major revolutions. If we add the counterarguments formed by what was earlier called the incommensurability of paradigms on a common standard, science might never have experienced any revolutions at all.
But although it is quite legitimate that paradigm debates are generally treated from such a standpoint, those debates are not truly about relative problem-solving ability. Rather, the heart of the discussion concerns which paradigm will henceforth serve as the guide for research on the many problems that no competing paradigm can claim to have solved completely; and in such circumstances, the decision must be based on future promise rather than past achievement. In the early stages, a person who accepts a new paradigm must often do so without the evidence provided by problem-solving. That is, knowing only that the old paradigm has failed to deal with a small number of problems, he must have faith that the new paradigm will succeed with the many major problems confronting it. A decision of that sort can be made only on the basis of belief.
This is precisely one of the reasons why the preceding
crisis is so important. Scientists who have never experienced a crisis will rarely deny the solid evidence of problem-solving in order to follow what will soon be revealed as a will-o’-the-wisp, and widely recognized as such. But crisis alone is not enough. There must also be some basis for faith in the particular paradigm candidate chosen, even if that basis is not rational or ultimately justified. Something must make at least a few scientists feel that the new proposal is on the right track, and often only personal, obscure aesthetic considerations can do so. People have sometimes changed their beliefs because of such considerations even when most explicit technical arguments pointed in the opposite direction. Neither Copernicus’s astronomical theory nor de Broglie’s theory of matter possessed much by way of meaningful persuasive force when first proposed. Even today, Einstein’s general theory of relativity attracts people chiefly on psychological grounds, an appeal difficult for outsiders to the field of mathematics to feel.