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Introduction. It is commonly thought that the views of scientific theory change put forward by Thomas Kuhn in The Structure of Scientific Revolutions^¹ in 1962 and by Karl Popper (initially in Germany^²) in the 1930s in The Logic of Scientific Discovery^³ are radically opposed to one another^⁴. Popper proposes a static, rational model of theory change: the progression of science happens by the successive refutations (by the method of falsification) of scientific hypotheses. Science, consequently, is a cumulative growth of un-refuted scientific hypotheses, with the proviso that any currently un-refuted theory might be refuted in the future. The progress of science can be understood as issuing from its method, and that method must be based in pure logic, as only pure logic alone can serve to underwrite any theory choice or change. Kuhn's view is that science is to be understood as an historical/social, dynamic entity constrained to progress according to the psycho-social forces internal to science (Kuhn limits his analysis to internal sociological forces constraining science; see Huff (2003, pp. 25-32) for a discussion). As a fundamentally human practice, it must be understood on its own terms and as the product of (often irrational) minds in a shared community, embedded in a particular historical context. It is the context, broadly understood, which governs the true progress of science, not the "logic" of its method, as Popper sees it.

I would like to argue for the following thesis: if we assume that Kuhn's picture of the progress of science is right, then Popper's view in Logic is best understood as describing the stage of scientific practice Kuhn calls "normal science". This thesis, I would argue, implies a somewhat stronger point: that while Popper's and Kuhn's views are significantly different, they are not so different as to be fully incompatible with one another. Under my view, Popper's thesis of the logic of theory change is not in opposition to Kuhn's view of the socio-historical nature of theory change; rather it is an important aspect of what Kuhn terms "normal science". The argument for my position will constitute the present review of Popper's Logic of Scientific Discovery and Kuhn's The Structure of Scientific Revolutions, hopefully compelling the reader to read both works and judge my thesis for themselves.

I will focus my attention to the area of overlap between Popper's and Kuhn's monographs: their models of theory change. First, I will outline each author's position on this issue. My evaluation of these works will be positive: I will show the points of consonance between Popper and Kuhn. Specifically, theory change is to be understood as a process involving both rational/logical elements (Popperian components) and nonrational/irrational psycho-social-economic (Kuhnian) elements. Kuhn's picture of theory change is very broad and allows for Popperian-type theory change as a lower-level stage of change. Popper's analysis seeks to abstract away from the details of actual scientific practice and offers an idealized justificatory scheme for theory change/acceptance. At some points during the course of scientific history, such an idealization finds an example (i.e., in "normal science"); but it is not the whole story of the advent of a Scientific Revolution (which for Kuhn is the complete change of a set of theories, methods and beliefs). The whole story lies in the conjunction of Kuhn's "paradigm" analysis of scientific theory change, and Popper's "falsification of hypotheses" analysis.

1. Popper's View of Theory Change: Logic. Popper's Logic of Scientific Discovery is an all-encompassing and thorough analysis of science as an empirical enterprise with a set of specific methodologies, all of which is supposed to give us knowledge of the external world. "I suggest that it is the task of the logic of scientific discovery, or the logic of knowledge, to give a logical analysis of this procedure; that is, to analyse the method of the empirical sciences" (Popper, 27). Indeed, the task of the Logic is at once to: (i) define science (the falsifiability criterion of demarcation, pp. 34-8); (ii) give an analysis of scientific theories (ch. III); (iii) place science on sound epistemic footing (via deductive logic; pp. 27-30, 39-44 and ch. IV); (iv) spell out a sound empirical methodology (ch. II, V); (v) say exactly how science is an objective epistemic endeavor (pp. 44-8 and ch. V); (vi) discuss theory testing chs. VI, VIII); (vii) detail some criteria of theory preference (i.e., simplicity, etc.; ch. VII); (viii) discuss the role of probability in scientific methodology (ch. VIII); and (ix) ultimately suggest a view of the progress of science (as the growth of more and more true knowledge of the external world).

Popper's primary philosophical concern is with providing the rational, sound epistemic grounds for the rejection of one theory (or hypothesis) for another. He is not concerned with anything but the justification of scientific knowledge as a rational entity. He is therefore uninterested in the motivations any particular scientist might have for proposing an hypothesis, or (for that matter) in the particular historical/social context within which any scientist exists; such matters are external to the logic of scientific knowledge (Popper, 31). Consequently, Popper distinguishes between the psychology of knowledge (matters of fact) and the logic of knowledge (matters of justification or validity), for it is only the latter that can justify science as a sound epistemic practice (Popper, 30). This ground can only one of pure logic. Specifically, science, if it is to be a purely rational entity, must rely on deductive logic alone. Thus, any sound scientific methodology must be a deductive one (Popper, 32-3). He takes his job to be, as a philosopher, to show how the practices of science can be rationally reconstructed (Ibid.). This reconstruction has the virtue that it (purportedly) demonstrates how science is an epistemically sound practice that it minimizes epistemic error while maximizing true knowledge of nature.

The locus of theory change is to be found in science's methodology, the core of which is the deductive technique known as modus tollens. Science is supposed to proceed by the derivation of predictions from theoretical systems (systems that include conjectural hypotheses), and the subsequent attempted falsification of the inferred prediction by means of crucial experiments (Popper, 76-7; 86-8). It is important to point out that in order to successfully test a theory, two things must be true: (a) the theory you are testing must be a complete theoretical system and (b) the test must be severe enough. By a complete theoretical system, Popper means an axiomatized system (Popper, 71ff), in the mathematical sense (e.g., Euclid's axiomatic system of geometry). "The attempt is made [when axiomatizing] to collect all the assumptions [of a theory] which are needed, but no more, to form the apex of the system" - these are the axioms (Ibid.)^⁵.

Let t be a theoretical system, which is a collection of basic laws and assumptions, including statements about particular initial conditions. From this system, one can derive as a consequence some prediction p. A prediction is a specific statement of fact about the world that is either true or false, where this is to be determined by experimentation and observation. To falsify t is to show, on the basis of a crucial experiment (or class of such experiments), that p is false which in turn logically implies that t is false. In other words, "I p is derivable from t, and if p is false, then t is also false" (Popper, 76).

The degree to which one has falsified an entire body of theory depends on exactly what is contained in t, the theoretical system. This t might be a lower-level system contained within a larger theoretical system, T^⁶. For example, one might propose a low-level hypothesis within the context of terrestrial mechanics, say about the period of a water clock. Suppose that this prediction about the period is off by a statistically significant amount (say, by 40%). And also suppose that this is a repeatable result, and that other results have been confirmed by independent researchers. What follows? If the hypothesis about the period of water clocks is made from axioms at the highest level of your theoretical systems (say, directly from Newton's second law of motion), then you have a potential instance of falsification for those axioms directly. If, however, your inferred prediction comes just from the water-clock theoretical system, and bears only a weak relationship with the highest axioms of your system (the laws of Newtonian mechanics alone), then you have a potential falsification of just the axioms of that sub-system, not the entire theoretical system. To successfully refute a whole system, T, all such subsystems t will produce predictions which contradict experience and which consequently imply the falsity of T.

Under this view, science as a whole is just a body of un-falsified theoretical systems. The progress of science is cumulative under this view. All individual hypotheses or theoretical systems are conjectural and hypothetical in nature until falsified according to the method outlined above. Science then is the process of proposing new hypotheses, constructing theoretical systems, and then subjecting the systems to experimental tests whose purpose ultimately is to refute (falsify) a theoretical system. As time marches on, and as scientists propose theories, all and only those theories which have not been falsified survive. Science, at any one time, is just the collection of these un-refuted theories of nature.

2. Kuhn's View of Theory Change: Structure. Scientific theory change is the progression of paradigms. A scientific paradigm, roughly, is the collection of shared beliefs and assumptions (methodological, epistemological and metaphysical). It "is a network of commitments - conceptual, theoretical, instrumental, and methodological ?" (Kuhn, 42). The paradigm, found in the current science textbooks, laboratories, and university science curricula, provides a rough theoretical "guidebook" for the practitioner: the paradigm constrains the theoretical research that constitutes the activity of "normal science", the time when the reigning theories are worked out in detail, and where the major puzzles it suggests (puzzles of the fit between the theory and all relevant/known phenomena) are tackled. A paradigm "give[s] form to the scientific life. ? [I]t functions by telling the scientist about the entities that nature does and does not contain and about the ways in which those entities behave" (Kuhn, 109). With the directive of the paradigm in place, science progresses. "So long as the tools a paradigm supplies continue to prove capable of solving the problems it defines, science moves fastest and penetrates most deeply through confident employment of those tools" (Kuhn, 76).

The paradigm defines a certain class of phenomena that serves as the focus of its researchers. Their job is threefold: (1) to determine the significant facts to be studied, (2) to match the facts with theory (i.e., to fit the phenomena into the paradigm) and (3) to articulate (as a consequence of the first two projects) the theory more precisely (Kuhn, 33-4). This implies the existence of certain puzzles, some instrumental in nature, others conceptual and mathematical, and some experimental. For example, it was the job of any astronomical theory in antiquity to account at least for all observed data. Indeed, the Ptolemaic astronomical system was constructed to "save the appearances", as well as to be consistent with the reigning philosophical belief that only uniform circular motion could underwrite those appearances^⁷. It was a "puzzle" for ancient natural philosophers to explain, given the dominant philosophical paradigm^⁸, to fit the appearances into an explanatory framework that was fully consistent with the paradigm's demands (stillness of the earth, geocentrism, circular motion, uniform motion, the inherent rationality of the universe, naturalistic explanations of nature as opposed to deity-based ones, etc.). The Ptolemaic system was one theory of celestial phenomena that succeeded, indeed the only largely successful one at the time, even though other systems were proposed (notably Aristarchus's (ca. 310-230 BCE) heliocentric model).

Kuhn sees this period of science, when it is engaged in (1) - (3) above, and when it is puzzle solving, as the period of so-called normal science. Indeed, normal science is puzzle-solving in this sense (Kuhn, 35ff). During this phase of science, knowledge is cumulative, and each successful solution gets added to the accepted body of theoretical knowledge.

When certain puzzles of normal science become persistent and resist solution within the confines of the reigning paradigm, this compels the researcher to find new explanations to deal with these anomalies (Kuhn, 68). Indeed, as Kuhn point out, since Ptolemy's system never adequately predicted the precession of the equinoxes and the precise planetary positions, this in part^⁹ compelled the adoption of the Copernican system (Ibid.). This period of the breakdown of the paradigm, the inability of researchers to adequately solve the paradigm's puzzles, is the period of crisis. Crisis, which signals the degeneration of normal science, is the necessary precondition for a scientific revolution. "Scientific revolutions are inaugurated by a growing sense ? that an existing paradigm has ceased to function adequately in the exploration of an aspect of nature to which that paradigm itself had previously led the way" (Kuhn, 92).

A paradigm shift is total and non-cumulative, since the rejection of a paradigm entails the rejection of fundamental categories with which a researcher sees the world. "Scientific revolutions are here taken to be those non-cumulative developmental episodes in which an older paradigm is replaced in whole or in part by an incompatible new one" (Kuhn, 92). Rejecting Aristotelianism, for example, would mean (among other things) the rejection of the Aristotelian understanding of: essences, the so-called "four causes", and so on. The world, consequently, is seen differently and through other conceptual categories. "Successive paradigms tell us different things about the population of the universe and about the population's behavior" (Kuhn, 103). All knowledge that had accumulated under one paradigm becomes invalid and (literally) false of the world.

3. The Compatibility of Popper's and Kuhn's Views. I have tried to emphasize a major difference between the views of Popper and Kuhn that becomes the ground for showing that the two views are actually compatible. The general difference between Popper and Kuhn is that Popper is concerned with the logic of scientific methodology, the falsification of scientific hypotheses individually (theoretical systems collectively), and the logico-rational reconstruction of any branch of science as an axiomatic system. Kuhn, however, focuses on the socio-historical context of scientific theories, normal science, the period of crisis and the eventual rejection of a paradigm which is constitutive of a scientific revolution.

Kuhn's analysis, then, is necessarily more general. His view tries to account for the seemingly radical difference between modern science, on the one hand, and ancient science, on the other (Kuhn, 2-3). In other words, Kuhn's motivation is this: when theorizing about the change from one scientific system to another, one needs to account for the history of science, which necessarily will include an understanding of the internal logic of science (Popper's primary concern). In this sense, Kuhn's study is a sociological theory of the advance of science from antiquity to the present^¹⁰. Popper's account, while honest about its a-historical nature, is wholly inadequate to explain why it is that science looks so different than it did in antiquity. Popper's view has it that science is what it is today because of the successful refutation of past theories. Since Popper does not view theories as being necessarily embedded in a larger sociologic milieu, wherein is located a whole battery of assumptions intimately tied to any theory, Popper must think of some knowledge remaining with us throughout the ages, while some other knowledge being dismissed. However, if Kuhn is right, then any science-as-accumulation view will ultimately fail, given that what changes are paradigms and that implies a radical conceptual gestalt shift.

But this reading of the severity of the difference between Popper and Kuhn is too drastic: Popper's view, that science progresses by successive refutations of theories and that knowledge is cumulative, if limited to the domain of Kuhn's normal phase of science, suffices to provide a rough picture of the operation of such normal scientific research. As Kuhn points out, normal science is in part the testing of theories, by checking their fit with observation. Furthermore, it is not unreasonable to suppose that Popper's view must be so constrained: since Popper's view is a-historical in nature (concerned as it is with the idealized internal logic of science), then it would be unwise to try to generalize it throughout history, unless one can support such a generalization with a copious amount of historiographic detail. Popper has not supplied any such historical support for the generality of his model, so it therefore must be limited in its applicability. I am arguing that Popper's view be limited to the period of science when the paradigm and all its theoretical structure is more or less in a "finished" form (analogous to what Popper would call an axiomatized theoretical system); that is, Popper's view is valid only for Kuhn's vision of normal science. And it is during the period of normal science that knowledge cumulatively increases - a necessary feature of Popper's view of the progress of science. And since I find it reasonable to limit the validity of Popper's view to normal science, it follows that progress and the growth of knowledge steadily increase during normal science. However, under my interpretation, this Popperian accumulation of science necessarily comes to an end, as a scientific revolution entails the rejection of that body of accumulated knowledge nurtured during normal science. This implies the incommensurability of successive paradigms.

Even though I find a point of consonance between Popper and Kuhn, I believe both views inadequate. Particularly, the conclusion that we arrived at above, the incommensurability thesis, is particularly odious; as well, I find Popper's lack of historical detail equally troubling. And I find that both authors fail to do justice to the richness of scientific practice as a whole^¹¹.

4. Conclusion and Evaluation. In the end, though I find both Popper's view and Kuhn's view surprisingly and importantly consonant in key respects, I find that both visions of science are rather impoverished views of science as it really is. Popper's view seems too static to account for the entire history of science, and it seems to ignore key internal aspects to the socio-historical context within which any scientific theory exists - aspects which are surely relevant for an explanation of why it is that one theory is considered inadequate and another chosen in its place. Indeed, it seems that the proximate causes of theory change are not considered: philosophical commitments, social pressures, and the shared rules and conventions of a scientific community. Popper's account cannot be the whole story if it is a fundamentally a-historical one.

On the other hand, Kuhn's view suffers the same fundamental problem as Popper's: not enough real detail in the actual practices of scientists is provided, although Kuhn's view can account for the radically different natures of modern science in contrast to, say, Hellenistic science. As well, the suggestion that with successive paradigms there are concomitant "incommensurable ways of seeing the world and of practicing science in it" entails that nothing whatever can survive a paradigm shift or a scientific revolution (Kuhn, 4). This implication is either a tautology or it is just false. It is a tautology in the sense that if a paradigm defines the reference of all terms in one's language, then necessarily (by stipulation) no term can have the same meaning across paradigms. But it seems also that this must be false: surely this is merely a terminological problem, and not a metaphysical one: the world is just the same as it was; now, with a new paradigm in place, my terms just have different meanings (so maybe I will be perpetually confused!). In either case, though, Kuhn's view implies a somewhat absurd philosophical view of the "nature and necessity of scientific revolutions".

Galison, Peter. 1997. Image and Logic: A Material Culture of Miscophysics. Chicago: Chicago University Press.

Huff, Toby. 2003. The Rise of Early Modern Science. Cambridge: Cambridge University Press.

Kuhn, Thomas. 1996. The Structure of Scientific Revolutions. Chicago: University of Chicago Press.

Lindberg, David C. 1992. The Beginnings of Western Science. Chicago: Chicago University Press.

Rorty, Richard. 2000. "Kuhn" in A Companion to the Philosophy of Science edited by W. H. Newton-Smith. Oxford: Blackwell Publishers.

4 At least some philosophers point out that Kuhn's view is a challenge to Popper's view. Rorty (2000) points out that the notion that the logic of science, or any rational reconstruction of that logic, can be studied a-historically - Popper's and some quasi-positivists' views - was directly challenged by Kuhn: "its [Kuhn's Structure] radical repudiation of the idea of such a logic ? made [Kuhn's Structure] the most widely read ? work of philosophy ?. Kuhn's book suggested that decisions between physical theories are no more algorithmically made than are decisions between alternative political policies" - thus pointing out the inherently socio-historical nature of theory change (Rorty, pp. 203-5).

5 There are several adequacy conditions which must be met before a theoretical system is axiomatized, i.e., logical consistency, independence, etc. See Popper 71-2 for details.

7 See Lindberg's (1992) excellent discussion of Hellenistic astronomy in antiquity (see esp. chap. 4). The puzzles for astronomers under the Ptolemaic system were mostly ones of extracting predictions from the Ptolemaic theory. As well, it seems that Ptolemy was himself concerned with working out a more physically plausible account of the heavens, as opposed to a merely adequate mathematical account (Lindberg, pp.104ff), which suggests something of a philosophical/conceptual puzzle.

8 We must be careful not to identify paradigms with scientific theories, since as Kuhn points out "not all theories are paradigms" (Kuhn, 61). Since some theories are not paradigms, we cannot say that paradigms are theories. Indeed, paradigms are often broader, encompassing both methodological and metaphysical commitments (Kuhn, 41; also see Huff, pp. 26-7).

10 Although, and this is one of the weak points of Kuhn's monograph, he does not make a distinction between a history of science and a sociological theory of science. Perhaps he thinks this distinction is obvious or else unimportant?

11 For one such richly detailed account of modern scientific practice, see Galison's Image and Logic.