First, if such reasons exist, it must be noted that they are not derived from the logical structure of scientific knowledge. In principle, a new phenomenon can appear without having a destructive effect on any part of past scientific activity. The discovery of life on the moon would be destructive to today’s existing paradigms, for those paradigms tell us things that seem incompatible with the existence of life on the moon; but the discovery of life in some less-known part of the galaxy would not. By the same token, a new theory need not contradict any theory that preceded it. A new theory may deal entirely with phenomena previously unknown, as quantum theory dealt—meaningfully, though not completely—with the subatomic phenomena that were unknown before the twentieth century. Or a new theory may simply be a theory on a somewhat higher level than those previously known, one that links together an entire set of lower-level theories without much alteration. Today the theory of energy conservation provides just such a link among mechanics, chemistry, electricity, optics, the theory of heat, and so on. Besides these, mutually compatible relations between old theories and new theories may also be obtained. All such relations may perhaps be exemplified by the historical processes through which science has developed. If so, the development of science would be fundamentally cumulative. A new kind of phenomenon would merely expose regularity in an aspect of nature where nothing had been seen before. In the evolution of science, new knowledge would replace ignorance rather than replace another, contradictory kind of knowledge.
Of course, science—or perhaps some other, less effective intellectual activity—may have developed in such a wholly cumulative fashion. Many people have believed that it did, and most still seem to think that such cumulativeness is at least the ideal that historical development would have revealed had it not so often been distorted by human beings. There are important reasons for holding this belief. In Section X we shall see how closely the view of science-as-cumulation is intertwined with the dominant epistemology that regards knowledge as a structure built directly by the mind upon unprocessed data. And in Section XI we shall examine the strong support given to just such a view of development by the techniques of effective science teaching.
Yet despite the powerful support for this ideal image, there are increasing reasons to doubt whether it can be an image of science. After the pre-paradigm period, the assimilation of every new theory, and of almost every new kind of phenomenon, has in fact brought about the destruction of an earlier paradigm and conflict among competing schools of scientific thought.
The cumulative piling up of unexpected novelties turns out to be an exception scarcely found in the actual rules of scientific development. Anyone who takes historical fact seriously cannot help thinking that science does not move toward the ideal suggested by our image of its cumulativeness. Perhaps science is a different kind of activity from that.
But if such resistant facts make it difficult for us to believe this, reconsidering the grounds already examined shows that the cumulative accumulation of novelty is not only rare in fact but also improbable in principle. Normal science, which is cumulative in character, achieves its success because scientists are able regularly to select problems that can be solved with conceptual and instrumental techniques approximating those already in existence. This is why excessive concern with useful problems, regardless of their relation to existing knowledge or technique, can easily hinder scientific development. But the person striving to solve a problem defined by existing knowledge and technique is not simply looking around. He knows what he wants to accomplish, and he designs his tools and directs his thinking accordingly. Unexpected novelty, that is, a new discovery, can appear only when his predictions about nature and his instruments prove to be wrong.
The importance of the discovery that results will often be proportional to the degree and stubbornness of the anomalous phenomenon that shows itself as a sign of the discovery. Then, clearly, a conflict will arise between the paradigm that reveals the anomaly and the paradigm that will later turn the anomalous phenomenon into something lawlike. The examples of discovery through paradigm destruction examined in Section VI did not confront us with mere historical accidents. There is no other effective way in which discoveries can arise.
The same argument applies even more clearly to the invention of new theories. In principle, there are only three kinds of phenomena in the presentation of a new theory. The first consists of phenomena already well explained by existing paradigms, and these rarely provide either a motive for theory construction or a point of departure for it. When such phenomena do provide a motive or starting point, as in the three famous predictions discussed at the end of Section VII, the theories that result are seldom accepted. The reason is that nature provides no basis for discrimination. The second class of phenomena consists of those whose nature is indicated by existing paradigms but whose detailed content can be understood only through further theoretical clarification. These are the phenomena on which scientists concentrate much of their research time, but such research aims at clarifying existing paradigms rather than at inventing new ones. Only when these attempts at clarification fail do scientists encounter the third type of phenomena: recognized anomalies, whose characteristic feature is their adamant refusal to be assimilated into existing paradigms. Only this third type of phenomenon becomes the agent of new theories.
Paradigms assign, for every phenomenon except anomalies, a theory-determined place within the scientist’s field of vision.
But if a new theory is to be called forth in order to resolve an anomaly in the relation between an existing theory and natural phenomena, then the successful new theory must somewhere be able to yield predictions different from those derived from the previous one. That difference would not occur if the two were logically compatible. In the process of being assimilated, the second theory must replace the first. Even a theory such as energy conservation, which today appears to be a logical system that relates to nature only through independently established theories, did not historically develop without paradigm destruction. Rather, it emerged from a phase of crisis in which a central element was the conflict between Newtonian mechanics and certain recently formulated consequences of the caloric theory of heat. Only after the caloric theory was abandoned could the law of energy conservation become part of science.1) And only after it had remained part of science for some time could it come to appear as a logically higher-level theory that did not contradict its predecessors. It is difficult to understand how a new theory could appear without such destructive changes in beliefs about nature. Though logical inclusion remains an acceptable view of the relation between successive scientific theories, historically it is improbable.
A century ago, I think I could perhaps have let the case for the inevitability of scientific revolutions rest at this point. Today, however, that is unfortunately impossible, because the view developed above cannot be maintained if the most influential modern interpretation of the nature and function of scientific theory is accepted. That interpretation, closely related to early logical positivism and not categorically rejected by its successors, would restrict the scope and meaning of an accepted theory so that it could not possibly contradict a later theory that makes predictions about the same natural phenomena. The best-known and clearest case illustrating this restricted conception of scientific theory is found in discussions of the relation between modern Einsteinian mechanics and the older mechanics derived from Newton’s Principia. From the standpoint of this study, the two theories are fundamentally contradictory, just as was explained in the relation between Copernicus’s heliocentric system and Ptolemy’s geocentric system. Einstein’s theory can be accepted only by recognizing that Newton’s was wrong. Yet today this remains a minority view.2) We must therefore examine the most influential objections to it.
The gist of these objections can be developed as follows. Relativistic mechanics cannot prove Newtonian mechanics wrong, because Newtonian mechanics is still used with great success by most engineers and is also selectively applied by many physicists. Moreover, the validity of this use of the older theory can be proved from the very theory that replaced it in other applications. Einstein’s theory can be used to show that, in all applications where a small number of limiting conditions are satisfied, the predictions of Newtonian equations will serve as well as our measuring instruments. For example, if Newtonian theory is to provide a plausible approximate solution, the relative velocities of the bodies under consideration must be small compared with the speed of light. If this condition and a few others are satisfied, Newtonian theory appears to be derivable from Einsteinian theory; thus Newtonian theory becomes a special case of Einsteinian theory.
But the objection continues by arguing that no theory can contradict one of its special cases. If Einsteinian science seems to make Newtonian mechanics wrong, that is only because some Newtonians rashly claimed that Newtonian theory gives perfectly accurate results or that Newtonian theory works well even when relative velocities are very high. Since those members of the Newtonian school could have had no evidence to support such claims, they departed from the norms of science when they made them. The claims of Newtonian theory, insofar as it is a truly scientific theory supported by valid evidence, still hold. Only the absurd claims made for that theory—claims that were not part of orthodox science—could be shown wrong by Einstein. If these reckless acts of primitive human nature are excluded, Newtonian theory has never been challenged and cannot be challenged.
Some variant of this sort of argument is quite sufficient to make any theory used by an influential group of competent scientists immune to attack. The flawed phlogiston theory, for example, imposed regularity on a variety of physical and chemical phenomena. It explained why bodies burn—because they are rich in phlogiston—and why metals have far more in common with one another than they do with their ores. Metals were all compound substances in which different elementary earths were combined with phlogiston, and since phlogiston was common to all metals, it conferred upon them their common properties. In addition, phlogiston theory explained the various reactions in which acids were produced by the combustion of substances such as carbon and sulfur. It also explained the decrease in volume that occurs when combustion takes place in a limited volume of air—the phlogiston released by combustion “spoils” the elasticity of the air that absorbs it, just as flame “spoils” the elasticity of a steel wire.3) If these had been the only phenomena that phlogiston theorists used to defend their theory, that theory could never have been challenged. An argument of much the same kind would suffice for any theory that has been successfully applied to some range of phenomena.
But to save theories in this way, their range of application must be restricted to the phenomena already dealt with by the experimental evidence at hand, and to the accuracy of those observations.4) Take one further step here—and that step, once the first has been taken, inevitably follows—and such a restriction prevents the scientist from claiming to speak “scientifically” about phenomena not already observed. Even in its present form, the restriction prevents the scientist from relying on theory in his own research whenever that research enters a field in which theory-grounded scientific activity provides no precedent, or whenever it seeks greater precision. Such prohibitions are not logically exceptional. But the consequence of accepting them would be the end of the research tradition through which science can develop further.
At this point, this point too is virtually tautological. There can be no normal science without commitment to a paradigm. Moreover, such commitment must extend to fields for which there is no perfect precedent, and to degrees of accuracy for which there is no precedent. If it did not, the paradigm could provide no puzzles that had not already been solved. Nor is normal science alone dependent on commitment to a paradigm. If an existing theory binds the scientist only in relation to its existing applications, then there can be no surprise, no anomaly, and no crisis.
Yet these are precisely the signs that point toward an adjustment to extraordinary science. If positivistic restrictions on the legitimate range of application of a theory are taken literally, the mechanism that tells a scientific community which problems may lead to fundamental transformation must cease to function. And when that happens, the scientific community has no choice but to return to something resembling a pre-paradigm state: a situation in which all its members practice science, yet their collective product rarely resembles science at all. Is it really strange that the price of meaningful scientific progress is the responsibility of risking error?
More important, there is a clear logical gap in the positivist argument, one that will lead us directly back to the nature of revolutionary change. Can Newton’s mechanics truly be derived from relativistic dynamics? What would such a derivation look like? Imagine a set of statements, denoted by ^6 15 2^ ^6 15 23^, ... ^6 15 56 1345^, which together concretely embody the laws of the theory of relativity. These statements include variables and parameters representing spatial position, time, rest mass, and so forth. Together with the apparatus of logic and mathematics, from them there can be derived a complete set of statement-forms, some of which can be verified by observation. To prove the propriety of Newtonian mechanics as a special case, one must add to the supplementary statements of ^6 15 56 24^ something like (u/c)^3456 126^<<1, restricting the range of the parameters and variables. This expanded set of statements can then be calculated into a new set, ^6 1345 2^ ^6 1345 23^, ... ^6 1345 56 134^, having the same form as Newton’s laws of motion, the law of gravitation, and so on. Newton’s mechanics has apparently been derived from Einstein’s theory by attaching to it a few limiting conditions.
Nevertheless, at least as the discussion has proceeded to this point, the derivation appears to be sleight of hand.
^6 1345 56 24^ are special cases of the laws of relativistic mechanics, but they are not Newton’s laws. Or at least they are not Newton’s laws unless those laws have been reinterpreted in a way that would have been impossible before Einstein’s work. The variables and parameters that, in Einstein’s set ^6 15 56 24^, represented spatial position, time, mass, and so forth still appear in ^6 1345 56 24^. And there, too, they still designate Einsteinian space, time, and mass. But the physical referents of these Einsteinian concepts are by no means the same as those of the Newtonian concepts bearing the same names. Newtonian mass is conserved. Einsteinian mass can be transformed into energy. Even when relative velocities are low, the two must not be regarded as identical. Unless we change the definitions of the variables in the set ^6 1345 56 24^, the statements we have derived do not become Newton’s laws. If we do change those definitions, then it is difficult to say that we have derived Newton’s laws, at least in the sense in which “derive” is generally accepted today. Our argument has, of course, explained why Newton’s laws seemed to fit so well. In doing so, for example, it has rationalized the behavior of an automobile driver as if he lived in a Newtonian universe. An argument of the same sort is also used to justify teaching geocentric astronomy to observers of the heavens.
But that argument has not yet proved what it was actually supposed to prove. In other words, it has not proved that Newton’s laws are a limited case of Einstein’s laws.
For on the path to that limitation, it was not only the form of the laws that underwent change.
Along with the change in form, we also had to change the fundamental structural elements composing the universe to which those laws apply.
This necessity of revising the meaning of established and familiar concepts is central to the revolutionary impact of Einstein’s theory. Though subtler than the change from geocentrism to heliocentrism, from phlogiston to oxygen, or from particles to waves, the resulting conceptual transformation is no less decisively destructive of the previously established paradigm. We may well regard it as the prototype of revolutionary reorientations in science. Precisely because it did not introduce additional objects or concepts, the transition from Newtonian to Einsteinian mechanics describes with particular clarity a scientific revolution as a change in the conceptual network through which scientists see the world.
These remarks should be enough to show something that, in another philosophical context, might be taken for granted. At least for scientists, most of the apparent differences between a discarded scientific theory and its successor are real. An outdated theory can always be regarded as a special case of its most recent successor, but only if it is transformed for that purpose. And that transformation can be carried out only with the benefit of hindsight, that is, under the explicit guidance of the newer theory. Moreover, even if such transformation were a legitimate tool for interpreting the old theory, the result of its application would be a theory so greatly restricted that it could do no more than restate what was already known. Such restatement may be useful because of its economy, but it cannot suffice as a guide for research.
Let us therefore take it as given here that the differences between successive paradigms are both necessary and incompatible. If so, can we say more explicitly what sorts of differences they are? The most obvious form of difference has already been described repeatedly. Successive paradigms tell us different things about the constituents of the universe and about their characteristic behavior. In other words, they say different things about questions such as the existence of subatomic particles, the materiality of light, and the conservation of heat or energy. These are substantial differences between successive paradigms, and they require no further illustration. But paradigms differ in more than substance, because a paradigm is related not only to nature but also to the science that sustains the paradigm that produced it. A paradigm is a source of methods, a problem field, and the standards of problem-solving accepted by a mature scientific community at a given time. Thus acceptance of a new paradigm often necessarily brings with it a corresponding redefinition of the science. Some old problems are transferred to another field of science, or else declared entirely “unscientific.” Problems that previously did not exist, or seemed trivial, may with the emergence of a new paradigm become the very archetypes of meaningful scientific achievement. And as the problems change, the standards that distinguish a genuine scientific answer from mere metaphysical speculation, wordplay, or mathematical manipulation often change as well. The tradition of normal science that emerges from a scientific revolution is not merely incompatible with what preceded it; in fact, it is incommensurable with it.
In the actual practice of science, the impact of Newton’s work on the seventeenth-century tradition of normal science is a superb example of the subtle effects of paradigm change. Before Newton was born, the “new science” of the sixteenth century had at last succeeded in rejecting the Aristotelian and Scholastic explanations expressed in terms of the essences of material bodies.
To say that a stone falls to the ground because its “nature” makes it fall toward the center of the universe had come to seem a mere tautological play on words—which previously it had not been.
Thereafter, the entire range of phenomena belonging to sensory appearance—including color, taste, and even weight—came to be explained in terms of the size, shape, position, and motion of the elementary particles of the underlying material substance. To attribute various properties to fundamental atoms was to rely on magical elements and therefore lay outside the bounds of science. Moliere was said to have caught precisely the new inspiration when he mocked the physician who explained that opium acts as a soporific because of its sleep-inducing efficacy. In the late seventeenth century, many scientists preferred to explain that the round shape of opium particles enabled them to soothe the nerves around which those particles moved.5)
In earlier periods, explanations of things by mysterious qualities had been an inseparable element of productive scientific research. Even so, the new commitment in the seventeenth century to mechanico-corpuscular explanation produced powerful results in many fields of science, eliminating from science problems that had long resisted widely accepted solutions and proposing other problems in their place. In mechanics, for example, Newton’s three laws of motion were less the product of striking new experiments than the result of an attempt to re-explain well-known observations in the context of the motion and interaction of primary neutral particles. To give just one concrete example: the mechanico-corpuscular view of nature directed scientific interest toward an entirely new subject of inquiry—the change in the motion of particles through collision.
Descartes declared this problem and proposed the first conjectural solution.
Huyghens, Wren, and Wallis expanded it further, partly through experiments on the motion of colliding pendulum bobs, but chiefly by applying already well-known characteristics of motion to the new problem.
And Newton incorporated the results they obtained into his laws of motion. The equal “action” and “reaction” in the Third Law are the changes in the quantity of motion undergone by both sides in a collision. That same change of motion provides the definition of mechanical force implicit in the Second Law. Thus, as in many other cases in the seventeenth century, the corpuscular paradigm both gave rise to a new problem and played a major part in solving it.6)