7) H.metzger, Les doctrines chimiques en France du debut du XVII siecle a la fin du XVIII a la fin du XVIII siecle (Paris, 1923_, pp.359__61;Marie Boas, Robert Boyle and Seventheenth-Century Chemistry(Cambridge, 1958), pp.112__5.
8) Leo Konigsberger, Hermann von Helmholtz, trans. Francis A. Welby(Oxford, 1906),pp.65__66.
9) James E.Meinhard, "Chromatorgraphy ; A Perspective", Science, CX (1949), 387__92.
10) For corpuscularianism in general, see the following: Marie Boas, "The Extablishment of the Mecanical Philosophy", Osiris, X(1952), 412__541. On its influence on Boyle's chemistry, see T.S.Kuhn, "Robert Boyle and Structrual Chemistry in the Seventeenth Century", Isis, XLII(1952), 12__36.
V. The Priority of Paradigms
The Priority of Paradigms
To elucidate the relationship between rules, paradigms, and normal science, let us first consider how historians of science distinguish the particular loci of commitment that I have just called accepted rules. A close historical investigation of a given specialty at a given time reveals, in the conceptual, observational, and instrumental applications of its various theories, recurring, quasi-standard illustrations of those theories. These are the paradigms of the scientific community, embodied in textbooks, lectures, and laboratory exercises.
By studying them and by engaging in scientific activity with them, the members of the corresponding scientific community learn their work. Of course, the historian will also discover penumbral areas filled with scientific achievements whose identity remains doubtful, but the core of solved problems and techniques will usually be clear. Though they may in some cases be ambiguous, the paradigms of a mature scientific community can be determined with relative ease.
But the determination of shared paradigms is not the determination of shared rules. That requires a second step, and one of a somewhat different kind. In taking this step, the historian of science must compare the community’s paradigms with one another, and also with the contemporary research reports of the scientific community. In doing so, his object is to discover what isolable elements, explicit or implicit, the members of that community have abstracted from the more global paradigms and deployed as rules for their research. Anyone who has tried to describe or analyze the emergence of a particular scientific tradition must necessarily have sought accepted principles and rules of this sort. As noted in the preceding section, he will almost certainly have succeeded, at least in part. But if his experience is at all like my own, he will have found that the search for rules is far more difficult and less satisfying than the search for paradigms. Some of the generalizations he introduces to describe the beliefs shared by the community will raise no problems. Yet other generalizations, including those presented earlier as examples, will seem strongly shadowed. Expressed in just that way, or in any other way he can imagine, they will almost certainly be rejected by some members of the group he is studying. Nevertheless, some designation is needed for the basis of a research tradition. Therefore the search for a body of rules competent to constitute any given tradition of normal research always becomes a continuing and serious frustration.
Yet by becoming aware of that frustration, it becomes possible to diagnose its source.
Scientists may agree that Newton, Lavoisier, Maxwell, or Einstein produced apparently permanent solutions to a group of remarkable problems, while differing—sometimes without realizing it—about the particular abstract characteristics that make those solutions permanent. In other words, scientists can agree in their identification of a paradigm without agreeing on, or even attempting to obtain, a full interpretation or rationalization of it. The absence of a standard interpretation or of an agreed reduction to rules will not prevent a paradigm from guiding research. Normal science can be determined in part by the direct inspection of paradigms, a process often aided by the formulation of rules and assumptions but not dependent upon them. In fact, the existence of a paradigm need not even imply the existence of any complete set of rules.1) Inevitably, the primary effect of these statements is to raise problems. Without a competent body of rules, what is it that binds a scientist to a particular tradition of normal science? What is meant by the phrase “direct inspection of paradigms”? Partial answers to these questions were developed, though in a very different context, by Ludwig Wittgenstein. Since their content is more basic and more familiar, it will be useful first to examine the form of his argument. Wittgenstein asks: What must we know in order to apply terms such as “chair,” “leaf,” or “game” unambiguously and without provoking dispute?2)
This question is very old, and for the most part we have answered it, whether consciously or intuitively, by saying that we must know what a chair, a leaf, or a game is. That is to say, we must grasp certain attributes possessed in common only by games. But Wittgenstein concluded that, given the way language is used and the sort of world to which we apply it, no such common characteristic need exist. Though discussing certain attributes shared by many games, chairs, or leaves often helps us learn how to apply the corresponding term, there is no bundle of characteristics that can be applied simultaneously to all members of the class, and only to them. Rather, when confronted with an activity previously unobserved, we apply the term “game” because what we see bears a close “family resemblance” to many activities we have already learned to call by that name. In short, for Wittgenstein, games, chairs, and leaves correspond to natural families, each constituted by a network of overlapping and crisscrossing similarities. The existence of such a network sufficiently explains why we succeed in identifying the corresponding objects or activities. Only if the families we name overlapped and gradually merged into one another—that is, only if there were no natural families—would our success in identification and naming provide evidence for common characteristics corresponding to each of the family names we use.
Something of the same sort may well hold for the various research problems and techniques that arise within a single tradition of normal science. What they have in common is not that they satisfy some set of rules and assumptions—some explicit, or even fully discoverable set—that gives the tradition its character and its hold upon the scientific mind. Rather, they are related, through resemblance and modeling, to one part or another of the scientific corpus already recognized by the community in question among its established achievements. Scientists conduct research from models acquired through education and through continued exposure to the literature, often without quite knowing, or needing to know, what characteristics have given those models the status of paradigms for the community.
For that reason, scientists do not need a complete bundle of rules. The coherence displayed by the research tradition in which they participate may not even imply the existence of an underlying body of rules and assumptions that could be uncovered by further historical and philosophical inquiry. The fact that scientists usually do not ask or dispute what legitimates a particular problem or solution at least intuitively leads us to suppose that they know the answer. But it may also indicate that neither the question nor the answer seems relevant to their research. Paradigms may be prior to, more binding than, and more complete than any bundle of research rules that can be explicitly abstracted from them.
Thus far this point of view has been entirely theoretical. Paradigms may determine normal science without the intervention of discoverable rules. I now wish to emphasize its clarity and importance by offering several reasons for believing that paradigms do in fact operate in that way. The first reason, already discussed rather fully, is the extreme difficulty of discovering the rules that have guided a particular tradition of normal science. This difficulty is almost exactly like the one the philosopher faces when he tries to say what all games have in common. The second reason, in fact a necessary consequence of the first, is rooted in the nature of scientific education. As should already be clear, scientists never learn concepts, laws, and theories abstractly and in themselves.
Rather, these intellectual tools are encountered from the outset at a historically and pedagogically prior stage, in which they appear together with, or through, their applications. A new theory is always announced together with its application to some concrete domain of natural phenomena. Without such applications, it would not even be an acceptable candidate theory. Once accepted, those same applications, or other examples of application, appear together with the theory in the textbooks from which future scientists will learn their work. They are included in textbooks not merely as decoration, or even as documentary evidence. On the contrary, the process of learning a theory depends on applied study, which includes the actual solving of problems both with pencil and paper and by means of instruments in the laboratory. For example, when a student studying Newtonian mechanics learns the meanings of terms such as “force,” “mass,” “space,” and “time,” he usually does so by observing and taking part in the application of these concepts to problem-solutions, and far less from the incomplete, though sometimes helpful, definitions given in the textbook.
Such a process of learning through actual calculation or practice continues throughout the transmission of professional specialization.
As a student proceeds from the freshman course at university to the stage of the doctoral dissertation, the problems given to him become increasingly complex, and some arise that are not supported by precedent. Yet such problems, like those that will be dealt with regularly in the subsequent life of an independent scientist, continue to be closely modeled upon achievements previously made. One might suppose that, somewhere along that path, the scientist intuitively abstracts the rules of the game for himself, but there is little reason to believe so. Many scientists can readily and ably discuss the particular individual hypotheses inherent in their current concrete research topic, but when it comes to characterizing the established foundations of their field or its valid problems and methods, they are little better than non-specialists. If scientists do master such abstract conceptualization, they demonstrate it chiefly through their ability to carry out research successfully. But that ability can be understood without recourse to hypothetical rules of the game.
These consequences of scientific education establish the argument that paradigms provide guidance for research not only through conceptualized rules but also by serving directly as models. Normal science can proceed without rules only insofar as the relevant scientific community accepts without question certain problem-solutions that have already been achieved. Therefore, when a paradigm or model is felt to be in jeopardy, rules will become important, and the characteristic indifference to rules will disappear. Moreover, that is precisely what actually happens. In particular, we have examined several instances in which pre-paradigm periods are ordinarily marked by frequent and serious debates over legitimate methods, problems, and standards of problem-solution—standards that serve to define schools rather than to bring about agreement—and such debates played an even more important role in the development of seventeenth-century chemistry and early nineteenth-century geology.3) Furthermore, such debates do not vanish all at once simply because a paradigm emerges.
Although they are almost nonexistent during periods of normal science, debates regularly recur immediately before and during scientific revolutions—that is, in periods when a paradigm comes under attack and is then replaced.
The transition from Newtonian mechanics to quantum mechanics gave rise to many debates, some of which still continue, concerning the nature and norms of physics.4) There are still people alive who remember that similar debates were produced by Maxwell’s electromagnetic theory and by statistical mechanics.5) And earlier still, the assimilation of Galilean and Newtonian mechanics recorded a particularly famous series of controversies with the Aristotelians, Cartesians, and Leibnizians over the proper standards of science.6) When scientists do not agree on whether the fundamental problems of their field have been solved, the search for rules acquires a function it does not ordinarily possess. While a paradigm remains secure, however, it can function without agreement about rationalization, or even without any thought of rationalization at all.
I shall conclude this section by explaining a fourth reason why paradigms occupy a position prior to shared rules and assumptions. In the introduction to this essay, I suggested that small-scale revolutions as well as large-scale ones can occur; that some revolutions affect only the members of a subdivided specialty; and that, for such a group, even the discovery of a new and unexpected phenomenon can be revolutionary. In the next section I shall present selected examples of revolutions of that kind, but it is still far from clear how they can exist. If normal science is as rigid as this, and if the scientific community is as closely interwoven as the preceding discussion has implied, how can a change of paradigm affect only a small subgroup?
Judging from what has been discussed so far, it might be inferred that normal science, as the integrated activity of a single system, must share the fate of all paradigms. Yet in science this is clearly very rare, or has perhaps never happened at all. When one surveys every field as a whole, science seems instead to possess a rather loose structure, with little coherence among its various parts.
There is, however, no contradiction here with ordinary observation. Rather, replacing rules with paradigms will make the diversity of scientific fields and subspecialties easier to understand. Explicit rules, when they exist, are customarily common to very broad groups of scientists, but paradigms need not be. For example, those who work in fields as far apart as astronomy and plant taxonomy are educated through exposure to different achievements described in entirely different books.
And even those who begin by studying many of the same books and achievements in identical or closely related fields may, in the process of specialization, acquire substantially different paradigms.
As one example, consider the vast and diverse scientific community made up of all physical scientists.
Today every member of such a group learns, for instance, the laws of quantum mechanics, and most of them apply those rules at some point in their research or teaching. But not all of them learn the same applications of those laws, and therefore they are not all affected in the same way by actual changes in quantum mechanics. On the road toward specialization, some physical scientists are exposed only to the basic principles of quantum mechanics. Others study in detail the paradigmatic applications of those principles to chemistry; still others study their applications to solid-state physics, and so on. What quantum mechanics means to each scientist is determined by what courses he has taken, what books he has read, and what literature he studies. Thus, although a change in the laws of quantum mechanics would be revolutionary for all these groups, a change that affects only this or that paradigmatic application within quantum mechanics becomes revolutionary only for the members of a particular subdivided specialty. For the remaining specialties, and for those who study other physical sciences, such a change need not be a revolution at all.
To put it plainly, quantum mechanics (or Newtonian mechanics, or electromagnetic theory) is a paradigm for many scientific groups, but it is not the same paradigm for all of them.
It can therefore simultaneously determine several traditions of normal science that overlap without having the same breadth. A revolution that occurs in one of these traditions will not necessarily spread to the others.
A brief account of the effects of specialization will further reinforce this general series of points. A researcher, wishing to learn something about what scientists thought atomic theory was, asked an eminent physicist and a famous chemist whether a single atom of helium was, or was not, a molecule. Both answered without hesitation, but their answers were not the same. For the chemist, an atom of helium was a molecule, because from the standpoint of the kinetic theory of gases it behaved like a molecule. For the physicist, on the other hand, a helium atom was not a molecule, because it did not exhibit a molecular spectrum.7) The two men were talking about the same particle, but each was viewing it through his own distinctive research training and activity. Their experience in problem-solving had taught them what a molecule must be. Without doubt, their experiences had much in common; in this case, however, those experiences did not tell the two specialists the same thing. As the discussion proceeds, we shall discover what consequences paradigmatic differences of this kind can produce in certain cases.
“Notes”
1) Michael Polanyi developed a very similar theme admirably by arguing that scientists’ success depends largely on “tacit knowledge,” that is, knowledge acquired through practice and not capable of being explicitly expressed. See his Personal Knowledge (Chicago, 1958), especially chapters v and vi.
2) Ludwig Wittgenstein, Philosophical Investigations, trans. G. E. M.
Anscombe (New York, 1953), pp. 31–36. Wittgenstein, however, says little about the kind of world required to support the naming process he outlines.
Some of the views that follow, therefore, are not taken from him.
3) For chemistry, see H. Metzger, Les doctrines chimiques en France du début du XVII à la fin du XVIII siècle (Paris, 1923), pp. 24–27, 146–49; Marie Boas, Robert Boyle and Seventeenth Century (Cambridge, 1958), chapter 2.
For geology, see Walter F. Cannon, “The Uniformitarian-Catastrophist Debate,”
Isis, LI (1960), 38–55; C. C. Gillispie, Genesis and Geology (Cambridge, Mass., 1951), chapters 4–5.
4) On the controversy over quantum mechanics, see Jean Ullmo, La crise de la physique quantique (Paris, 1950), chapter 2.
5) On statistical mechanics, see René Dugas, La théorie physique au sens de Boltzmann et ses prolongements modernes (Neuchâtel, 1959), pp. 158–83, 206–19.
To examine the reception of Maxwell’s work, see Max Planck, “Maxwell’s Influence in Germany,” in James Clerk Maxwell: A Commemoration Volume, 1831–1931 (Cambridge, 1931), pp. 45–65, especially pp. 58–63; see also Silvanus P. Thompson, The Life of William Baron Kelvin of Largs (London, 1910), II, 1021–27.
6) For one example of the struggle with the Aristotelians, see A. Koyré, “A Documentary History of the Problem of Fall from Kepler to Newton,” Transactions of the American Philosophical Society, XLV (1955), 329–95.
On the controversies with the Cartesian and Leibnizian schools, see Pierre Brunet, L’introduction des théories de Newton en France au XVIII siècle (Paris, 1931); A. Koyré, From the Closed World to the Infinite Universe (Baltimore, 1957), chapter 6.
7) The researcher to whom I am indebted for an oral report was James K. Senior. Several related topics are included in his paper, “The Vernacular of the Laboratory.” Philosophy of Science, XXV (1958), 163–68.
VI. Anomaly and the Emergence of Scientific Discoveries
Anomaly and the Emergence of Scientific Discoveries
Normal science, that is, the puzzle-solving activity we have just examined, is a highly cumulative enterprise, extremely successful in its goal of steadily extending the scope and precision of scientific knowledge. In all these respects, normal science fits very accurately the most common image of scientific research.
Yet one standard product of scientific activity is missing here. Since normal science does not aim at novelties of fact or theory, when it is successful, no such novelties are found.
Nevertheless, new and unexpected phenomena have continually been unveiled by scientific research, and radical new theories have again and again been invented by scientists. History even suggests that the scientific enterprise has developed a uniquely powerful technique for producing wonders of this sort.
If this characteristic of science is to be reconciled with what has already been said, then research under a paradigm must be a particularly effective way of inducing paradigm change. That is the work done by fundamental novelties of fact and theory. When such novelties arise by chance in a game governed by one set of rules, their assimilation requires the elaboration of another set of rules. After the new things have been assimilated as part of science, the work done by specialists in the particular field into which those novelties intruded is never quite the same as before.
We must now ask how changes of this kind can occur, first by considering discoveries, or novelties of fact, and then inventions, or novelties of theory. Yet the distinction between discovery and invention, or between fact and theory, becomes an important clue to resolving some of the most central issues. By examining a few discoveries in the remainder of this section, we shall soon find that they are not isolated events, but extended episodes with a regularly recurring structure. Discovery begins with the perception of anomaly—that is, with the recognition that nature has somehow violated the paradigm-induced expectations that govern normal science. It then continues with a more or less extended exploration of the area of the anomaly. And it closes only when the paradigm theory has been adjusted so that the anomalous has become the expected. The assimilation of a new kind of fact requires something more than an additional adjustment of theory, and until that adjustment is completed—until the scientist has learned to see nature in a different way—the new fact is not yet a scientific fact at all.
To see how closely factual and theoretical novelty are intertwined in scientific discovery, let us examine a particularly famous example: the discovery of oxygen. At least three people each made plausible claims to the discovery of oxygen, and it is certain that in the early 1770s several other chemists besides them obtained oxygen-rich air in laboratory vessels without realizing it.1) In the case of pneumatic chemistry, the progress of normal science had very thoroughly opened the way to a breakthrough into sudden development. The first person said to have obtained a relatively pure sample of oxygen gas was the Swedish apothecary C. W. Scheele. We shall disregard his achievement, however, because it was not published until after the discovery of oxygen had been repeatedly announced elsewhere, and thus in the end had no effect on the historical pattern that most interests us here.2) Chronologically, the second person to claim the discovery of oxygen was the English scientist and theologian Joseph Priestley. In the course of his long, regular investigations of the “airs” released from various solid substances, he collected the gas released when the red oxide of mercury was heated. In 1774, he identified the gas thus produced as nitrous oxide, but after further tests, in 1775, he described it as ordinary air containing somewhat less than the usual amount of phlogiston. The third claimant, Lavoisier (A.