Subjective Views of Kuhn

Peter Achinstein Johns Hopkins University

In response to a charge of subjectivism, Kuhn in his Postscript emphasizes the importance of “values” (accuracy, simplicity, explanatory power, etc) that are shared by scientists generally. However, Kuhn adds, these values are applied differently by different scientists. By employing a comparison with partially subjective views of Carnap on conªrming evidence, this paper raises questions about Kuhn’s position on values by considering ways it might be interpreted as subjective and ways it may not. Many philosophers of science have wrestled with the question of whether there is a universal scientiªc method, i.e., a set of rules for discovering or testing scientiªc hypotheses. The rules are universal because they hold for all sciences and all times. Examples might include rules of the sort that Descartes proposed (his 21 rules) in Rules for the Direction of the Mind, or the 4 rules of reasoning that begin the third book of Newton’s Principia. Two major ªgures in 20th century philosophy of science, Karl Popper and Paul Feyerabend, whose deaths occurred within a year or two of Kuhn’s, offered strikingly different answers to the question of whether universal rules exist. Popper’s answer I take to be a resounding, “Yes,” at least to the question of whether there are such rules in the case of scientiªc testing or justiªcation. (Rules of discovery, he believed, are another matter.) Popper’s method of corroboration—his version of hypothetico- deductivism—is, I believe, intended to be a universal scientiªc method for testing hypotheses. Feyerabend, although a student of Popper, offered a very different answer: There are no universal rules of discovery or testing. Doing science, Feyerabend said in one of his typically provocative moments, is like mak- ing love or waging war. There are some useful hints, some rules of thumb,

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but in general, to quote his most notorious principle, “anything goes.” Anarchism, while it may not be a workable political strategy, yields the best science, and is the best philosophy of science, he used to say. With Popper on the extreme right and Feyerabend on the extreme left, where does Kuhn ªt on this spectrum? One might be tempted to say that Kuhn acknowledges the existence of methodological rules, but they are not universal. They are paradigm-speciªc. The paradigm supplies rather speciªc rules for what sort of hypotheses are worth testing, e.g., ones that do not violate conservation of energy, or that do not postulate action at a distance or velocities greater than that of light. And the paradigm supplies speciªc rules for how to test such hypotheses. On the other hand, in his Postscript written for the second edition of The Structure of Scientiªc Revolutions, Kuhn emphasizes the importance of what he calls scientiªc values as an essential part of the “disciplinary matrix,” a term that replaces “paradigm” (Kuhn 1970a, p. 182ff.). Kuhn mentions values such as accuracy, consistency, scope, simplicity, fruitfulness, explanatory power, and plausibility. These are values employed in determining what theory or hypothesis to accept, or to promote, or at least to take seri- ously and explore. There are passages in Kuhn suggesting that these values are shared by very different scientiªc communities, that they are shared over time, and indeed that this is the reason why all scientists can, in an important sense, be thought of as forming a single community (Kuhn 1970a, “Postscript,” p. 184). So is Kuhn here allied with Popper? Is he a universalist? I don’t think so. Nor is he an anarchist either. Instead, he is delightfully paradoxical. He speaks of values shared within a scientiªc community and shared even by different communities. But he also says that these shared values are frequently applied differently even by scientists within the same community. Although the criterion of “accuracy” is pretty stable from one application to another, “judgments of simplicity, consistency, plausibility, and so on often vary greatly from individual to individual” (Kuhn 1970a, “Postscript,” p. 185). “In short,” Kuhn writes, “though values are widely shared by scientists and though commitment to them is both deep and constitutive of science, the application of values is sometimes considerably affected by the features of individual personality and biography that dif- ferentiate the members of the group” (Kuhn 1970a, p. 185). So while you and I may both agree that the simplest hypothesis is to be preferred, pro- moted, tested ªrst, or whatever, we may disagree substantially over what counts as simple. And this disagreement, I take it, may be unresolvable by argumentation, but only explainable by reference to causal features of temperament, training, and so forth. Moreover, to complicate matters further, in determining which of two theories to prefer, promote, or pursue,

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it may turn out that each has some virtues the other lacks, and that scientists, even from the same community, weight these virtues differently. Kuhn emphasizes that the criteria for selecting theories “function not as rules, which determine choice, but as values which inºuence them” (Kuhn 1977, p. 331). The idea seems to be that rules, at least if clearly for- mulated, are, or are supposed to be, applied by different people in the same way under the same circumstances. It wouldn’t do if the rule that you must stop your car at a red light could be interpreted by different people in a very different manner. But for Kuhn, values can be variably applied, and that is ªne and dandy. Moreover, Kuhn thinks this is sufªcient to avoid the charge of subjectivity levelled against him by a number of critics. Responding to Schefºer, e.g., Kuhn writes, “it is emphatically not my view that ‘adoption of a new scientiªc theory is an intuitive or mysti- cal affair, a matter for psychological description rather than logical or methodological codiªcation’” (Kuhn 1970b, “Reºections on My Critics,” p. 261). Kuhn insists that there are good reasons for adopting one theory over another, and these reasons are of the sort philosophers of science typically describe involving accuracy, scope, simplicity, explanatory power, and so on. So where does Kuhn end up on the spectrum between Popper, the universalist, and Feyerabend, the anarchist. Like Popper, he wants to promote certain values common to scientists generally, from one period to another. He wants to say that scientists generally favor theories satisfying these values. Appeals to these values constitute good reasons for preferring the theories. And it is the acceptance of such values that is at least part of what it is to be a scientist. Like Feyerabend, however, he wants to reject the idea that scientists proceed in accordance with some ªxed and universal set of rules which determine what hypothesis it is reasonable to accept. Let me put this another way which may be more helpful. All three of the philosophers I have mentioned talk about values such as simplicity, consistency, explanatory power, and empirical conªrmation (even though Feyerabend at one point calls them “verbal ornaments”). Now there are several views about such values. On one, there are objective rational constraints on how they are to be interpreted and applied in particular circumstances. On another, opposing view, there are no objective rational constraints. What one takes to be simple, consistent, explanatory, or conªrmatory, is a personal matter, or perhaps is decided by voting or power politics. I will attribute that view to Feyerabend, at least in his more provocative moments. As for the rational constraint view, I see two versions: one is a strict constraint view. This is the idea that how a value is applied is strictly con- strained by usage, or deªnition, or practice, so that in accordance with this

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usage or deªnition or practice, although there might be borderline cases, what counts, or is to count, as simple, consistent, explanatory, or empiri- cally conªrmed, is quite generally determined in individual applications. I think that is Popper’s view, or something close to it. The second rational constraint view is weaker. It is that usage or deªnition or practice furnish at least some constraints on how scientiªc values are to be interpreted and applied. Not just any theory a scientist or a community calls simple or conªrmed is really so. But these constraints, however universal, do not completely determine how scientiªc values are to be interpreted and applied. Scientists associated with the same practice can still differ considerably over whether, or to what extent, some theory is simple, conªrmed, explanatory, etc. I suspect this weak constraint view is Kuhn’s view, or something close to it. If this is Kuhn’s view, there is an interesting similarity between this and the view of someone most people take to be one of Kuhn’s major op- ponents, viz. Rudolf Carnap, the arch-logical positivist. In his Continuum of Inductive Methods published in 1952, 10 years before Kuhn’s most fa- mous work, Carnap sought to explicate the idea of the degree to which a theory is conªrmed or supported by the evidence. He began by setting down all the objective, rational, universal constraints he could think of for this concept, resulting in 11 axioms. However, these axioms do not determine a unique concept of conªrmation, but rather an inªnity of them. Which concept does one choose, and how is the choice to be made? Carnap proposed that both subjective and objective factors be used. The subjective factors—the ones that can vary from one individual scientist to another—include familiarity and ease of operating with the concept. The main objective factor is success in using that concept, by which Carnap means how frequently highly conªrmed hypotheses turn out to be true or yield true predictions. Carnap’s appeal to success in using a particular concept of conªrmation as a criterion for selecting it strikes me as circular. It is justifying an inductive method by appeal to induction. If we drop this and keep Carnap’s other criteria then we have a view of conªrmation that involves some constraints (Carnap’s 11 axioms) and some subjectivity. So, on the basis of the same evidence and background information and partially constraining axioms, you can say that a certain hypothesis is highly conªrmed by the evidence while I can say that the conªrmation is much less. You can say that the degree of conªrmation is .96, and I can say it is .69. And we can both be reasonable and even correct. That is, in your conªrmation system, which is determined in part by subjective factors, the degree of conªrmation is .96, in mine it is .69.

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This seems quite subjective.1 But let me spell this out a bit more. For Carnap there is an important relationship between degree of conªrmation and justiªcation of belief. The relationship is this. If the degree of conªrmation of h on e is some number r, and if e is all you know, or all you know that is relevant for h, then you are justiªed in believing h to the degree r. So, for Carnap, it is perfectly okay for there to be two scientists with exactly the same information e, who not only believe h with substan- tial differences of degree, but who are justiªed in doing so. These scientists may rightfully have substantially different degrees of belief in the same hypothesis on the same evidence because they have chosen different systems of conªrmation for reasons that include subjective considerations, such as familiarity and ease of use. Is this the kind of subjectivism—call it partial subjectivism—that Kuhn advocates? I don’t really know the answer. Instead of saddling Kuhn with one particular view, let me consider three different forms of subjectivism concerning conªrming evidence that might possibly be attributed to him. At one end of the spectrum there is simply the idea that different scientists confronted by the same data, and with roughly the same background knowledge, sometimes, even frequently, come to different conclusions about what to believe or how much to believe it. Putting this in terms of conªrming evidence, different scientists sometimes come to different conclusions about whether, or to what extent, the evidence conªrms the hypothesis. This is absolutely minimal subjectivism, although I take it to be at least part of what Kuhn is saying. Perhaps you will say that there is not enough here even to be labeled subjectivism. At the other end of the spectrum there is the idea that not only do scientists with the same background information and the same data sometimes, even frequently, draw different conclusions about whether, or how much, the data support the hypothesis, but that scientists who do so may all be correct or at least reasonable in doing so. The reason is that whether, or to what extent, data support an hypothesis depends in part on subjective “weighting” factors that can vary from one scientist to another. Accordingly, whether, and to what extent, it is reasonable to believe an hypothesis on the basis of some data depends in part on such factors. This I take to be Carnap’s position in The Continuum of Inductive Methods.

1. An even more vigorous subjectivism than Carnap’s is that of the subjective Bayesians for whom the only objective constraint on rational degree of belief is satisfaction of the mathematical rules of probability. I will assume that this is more subjective than Kuhn wishes to be.

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Now let me mention a third, middle position. Let’s distinguish conªrmation on the one hand from actions to be taken on the basis of conªrmation. One might hold the following view. Whether, or the extent to which, some data support an hypothesis is purely objective.2 It does not depend at all on factors that vary from one scientist to another. Suppose, then, that e conªrms h to the degree r. Nothing whatever follows about what actions it is reasonable to engage in concerning hypothesis h. In the sciences, an important question pertaining to action might be whether to “pursue” h, i.e., whether to invest one’s time, energy, and resources in de- veloping consequences of h, testing them, extending h to new areas, and so on. If we treat this as a decision theory problem, we have two factors: probabilities and utilities. The probabilities can be thought of objectively, the utilities subjectively. The mere fact that on the basis of the data the probability (or degree of conªrmation) of h is low or high tells us nothing about whether to “pursue” h. Suppose h concerns the efªcacy of some new drug and e reports a limited study on 15 patients. Even if the degree of conªrmation of h is high, whether it is reasonable to pursue h by testing it on more individuals can depend on factors that can vary from one scientiªc group or even individual to another—for example, on costs, other activities being engaged in, differences in views of how important the research is, etc. Is this third alternative Kuhn’s view? Does this capture his partial subjectivism? It has the advantage of letting him have his cake and eating it too. The view is objective in this sense. It says that whether, or to what extent, data conªrm an hypothesis does not depend on subjective facts. It is also subjective in these two senses. Like the minimalist view it allows scientists to disagree about whether, or to what extent, e conªrms h. People can disagree about objective matters. More importantly, it allows scientists, on subjective grounds, to reasonably take different actions on the basis of an hypothesis, which is conªrmed to some particular degree. Kuhn speaks of “the adoption of a new scientiªc theory.” If “adoption” involves taking certain actions that depend for their rationality on both objective and subjective factors, then this middle position is at least part of Kuhn’s view, if not the whole of it. If it is the whole of it, that is ªne with me. There is objectivism in the sense I like and subjectivism in a sense that does not bother me at all. Is that all there is to it? I have my doubts. The ªrst and third subjective views are not particularly exciting. But Kuhn was exciting, if he was anything. So let’s say his view was more like Carnap’s. And let me delve a bit

2. For a defense of the idea that there are one or more such concepts employed in the sciences, see Achinstein 2001.

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further into this sort of partial subjectivism. On the Carnapian idea, objective rules of conªrmation provide only a partial constraint on what probability or conªrmation function to adopt. To take a simple Carnapian example, suppose that we have studied some sample of objects of a certain type, a fraction m/n of which have some simple property P. Suppose we want to determine the probability, i.e., the degree of conªrmation, that the next object of that type will have P. According to Carnap, what objective rules of conªrmation require is that this probability be a number between the observed relative frequency m/n and what Carnap calls the logical width of the property P, which is a type of a priori probability. To simplify considerably, we toss a coin 100 times, getting 60 heads. Our hypothesis is that the next toss will yield heads. Suppose that “heads” is a simple property whose logical width is 1/2. Then, says Carnap, the objective, rational constraints imply that the probability, or degree of conªrmation, of the hypothesis that the next toss will yield heads, given the results of the 100 previous tosses, is between 1/2, the logical width, and 3/5, the observed relative frequency. Suppose Carnap is right that objective rational constraints do not determine a unique probability or degree of conªrmation for this hypothesis given the evidence, but only a range. For at least some cases, then, such constraints yield inexact probabilities. Now two options seem possible to me. The ªrst is taken by Carnap. It is to say that inexact probabilities or degrees of conªrmation are not as useful to science as exact ones. We must opt for exact ones, but, and this is crucial, the only way we can get them is by introducing an important subjective element. We choose some particular probability function allowed by the constraints on the basis of factors such as familiarity and ease of use—factors that can vary from one person to another. The second option is simply to stay with inexact probabilities or degrees of conªrmation when and if they occur. So if indeed the probability of h is between 1/2and 3/5 that is what we say, period. Or, to take a non-quantitative assessment, if all that rational constraints allow us to say is that an hypothesis is conªrmed to a fairly high degree by the evidence, then that is all we can say. We make our assessment somewhat inexact or vague. But inexactness or vagueness are not the same as subjectivity, nor do they imply or necessarily lead to subjectivity. This second option avoids subjectivism. So is Kuhn a partial subjectivist in the Carnapian mold, i.e., in accordance with the ªrst option? My feeling is that he may well be so, but that this is not the end of the matter. Nor can I say simply that he is a subjectivist in the two unexciting senses noted earlier, i.e., in the sense that scientists frequently disagree about probabilities and that even when they

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agree they may rationally take different actions based on subjective differences. My feeling is that Kuhn may want to say that what I have been call- ing the “rational constraints” can themselves be differently applied by different scientists on subjective grounds. So let us consider a rational constraint. I pick one that Carnap defends. According to Carnap, the larger the sample the closer the probability that the next individual has the property in question gets to the observed relative frequency of that property in the sample. Perhaps Kuhn wants to say this as well. Suppose this is an objective rational constraint that all scientists accept. Still it can be applied differently. Different scientists can de- cide differently about how fast the probability in question approaches the relative frequency in the sample. A bold (or very empiricist) scientist may say it does so very quickly. A conservative (more “a priori”) scientist may say it does so more slowly. So the rational constraints themselves can be applied differently. Now one thing an objectivist can say in response is that boldness (as Popper would say), or being conservative (as George W. Bush might say) are objective constraints in science no less than in politics. That is, the bold scientist believes in boldness because he thinks it is an objective require- ment; likewise for the conservative. And, sticking with boldness, an objectivist can also say that if two bold scientists disagree about probabilities to be inferred from relative frequencies in a sample, at least one of them is wrong. It is not that both are correct and each chooses what probability to infer on subjective grounds such as familiarity or ease of use. Let me put aside this objectivist response and suppose that boldness or conservativeness do not represent objective constraints, but rather different styles of reasoning that vary with temperament. Some scientists are just bolder in their inferences than others, and that is perfectly okay. At least let me take this to be Kuhn’s position. If this is what Kuhn has in mind, then, although it sounds different from Carnap, I am not sure that it is. Suppose the objective rational constraint is the one expressed earlier, viz. that as the sample size increases, the closer the probability that the next item has the property in question gets to the observed relative frequency. For the sake of argument, suppose we adopt Carnap’s view that the probability that the next toss of this coin yields heads is a number between the a priori probability and the observed relative frequency. Finally, suppose we have a relatively small sample of tosses with this coin, say 10, of which 6 result in heads. So, for the sake of argument, rational constraints tell us to infer that the probability of heads on the next toss is between 1/2and 3/5, but they tell us no more than this. The conservative scientist, let us say, will choose a number closer to 1/2, the bold scientist will choose one closer to 3/5. But if neither conserva-

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tivism nor boldness is itself an objective rational constraint, but simply a personally subjective style, and if this is what Kuhn’s position amounts to, then, I think, Kuhn’s position is Carnap’s or something like it. Although the constraint that inferred probabilities approach observed relative frequencies is objective, it allows different rates of approach or convergence. How quickly it is taken to converge is, on this view, a personal subjective matter. In our coin tossing example, whether to choose a probability closer to 1/2or closer to 3/5 varies from one individual to another. An alternative, of course, is to refuse to play this subjective game. That is, in our example it is to refuse to assign a precise probability to getting heads on the next toss, given the size of the sample. If objective rational constraints yield only that the probability is between 1/2and 3/5, then that is all we can and should say. I tend to favor this approach. Two versions are possible. On one, precise objective probabilities always exist, but there are times when our epistemic situations allow us only to assign up- per and lower bounds and there is no reason to make matters more precise. By analogy, if all the police can say when judging the size of the crowd during the rally is that it was between 1500 and 2000 people, then that is all they should say. It seems wrong and unnecessary to pick a number between these and say that the crowd was 1759. On the second version, precise objective probabilities do not always exist; sometimes they are “smeared out.” By analogy, if the size of the crowd was constantly changing then there is no precise number denoted by the expression “the size of the crowd,” even if there is such a number for the average size of the crowd over the time period of the rally or for the size of the crowd at one particular point in time. However, I won’t pursue this here. My claim is only that if Kuhn’s point is that the same scientiªc value can be applied differently by different scientists, and in our conªrmation example if this is to be understood in the sense that unique conªrmation values, or bold vs conservative strategies, are to be chosen at least partly on subjective grounds, then Kuhn’s subjectivism in this regard is akin to Carnap’s. Finally, there are two more radical alternatives that I would like to re- sist attributing to Kuhn. One is to say that a constraint such as the one I have cited is not a necessary condition but simply a rule of thumb. Some- times it is applied, sometimes not, depending on different subjective factors. This sounds like Feyerabend. The second is to say that the constraint is a necessary condition but that it is subject to different interpretations in a more interesting sense than simply one in which the convergence is bolder or more conservative. The claim would be that the very idea of convergence—the very idea that the inferred probability should approach the observed relative frequency as the size of the sample increases—is subject

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to different meanings. That is, the constraint itself is ambiguous. I won’t speculate about what its different possible meanings might be. The idea would be simply that there are different meanings, and which is chosen is a subjective matter. I hope this is not Kuhn’s view. If it is, then Kuhn’s idea that different scientists share common values is not a good description of what he has in mind. They may share common words, but if these words mean different things, then I would say their values are different. Indeed, on the present alternative, Kuhn’s view would seem to amount to Feyerabend’s most extreme view that scientiªc values are mere “verbal ornaments.” So I leave you with three levels of subjectivism one might plausibly attribute to Kuhn. Conªning our attention just to the case of conªrming evidence, the levels are these. First, there is the minimal idea that different scientists, confronted with the same data and the same background information, sometimes, perhaps often, come to different conclusions about whether, or to what extent, the data conªrm or support an hypothesis. Second, there is a middle position, which distinguishes conªrmation on the one hand from actions (such as pursuing and testing hypotheses) on the other. It says that even though whether, or to what extent, the data conªrm the hypothesis is an objective matter, whether it is reasonable to take certain actions with respect to that hypothesis is at least in part subjective. It depends on, and varies with, individual desires and resources. Third, there is the view that objective rational constraints exist but in many cases do not determine a unique probability or degree of conªrmation or strength of evidence. To arrive at such unique judgments, rather than simply leaving the matter somewhat imprecise, decisions need to be made that depend on subjective factors, e.g., conservativeness or boldness in judgments, that can vary from one person to another. This type of subjectivism, which can be found in Carnap as well, is the strong- est and most interesting of the three.

References Achinstein, Peter. 2001. The Book of Evidence. New York: Oxford Univer- sity Press. Kuhn, Thomas S. 1977. The Essential Tension. Chicago: University of Chi- cago Press. ———. 1970a. The Structure of Scientiªc Revolutions. 2nd ed. Chicago: Uni- versity of Chicago Press ———. 1970b. “Reºections on My Critics.” In Criticism and the Growth of Knowledge. Edited by Imre Lakatos and Alan Musgrave. Cambridge, U.K.: Cambridge University Press.

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