Carnap, Kuhn, and the Philosophy of Scientific Methodology

Carnap, Kuhn, and the Philosophy of Scientific Methodology John Earman

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Introduction

For the past two decades logical positivism has served as a whipping boy. By emphasizing the shortcomings of this failed philosophical, program, the virtues of the new postpositiyist pTi|osop_hy__of_sciencc arc made to seem more lustrous. It is, of course, not surprising to find such polemical devices employed, since they are common to the rhetoric of revolutions, whether political, scientific, or philosophical. Or so the standard assessment would go. What I find askew in this assessment is the notion that a philosophical revolution as opposed to an evolution has taken place. For although I am no apologist for logical positivism, it does sccoiJo jme that many of the themes£fjJT£ so-called postpositivist philosophy of jscicncc arc extensions of ideas found in the writings oLCarnap and other leading logical positivists and logical emplficlstC^But my purpose here is not to contribute to a revisionist history of philosophy. Rather, I aim to pay homage to both Carnap and Kuhn by noting some striking similarities and also some striking differences. These similarities and differences are useful in helping to focus some of the still unresolved issues about the nature of scientific methodology. 2 Logical Positivism, Logical Empiricism,, and Kuhn's Structure of Scientific Revolutions The members of the Vienna Circle often took votes on the issues they debated. While I have no documentary evidence to offer of an

John Earman

aclual vole, I am morally certain of what the rcsull would have been for ihc question, Verification is a relation between what and what? In "x is verified by y,"j&fs presumably a sentence. And it is tempting to lake^jHo be a fact, stale of affairs, or something in ihe world lhal makes AC iruc and can be directly ascertained. But an attempt to compare language and ihe world would have slruck ihe Circle members as of a piece with the metaphysics thai ihe verifiabilily principle of meaning was supposed lo banish. Their alternative was lo lake y lo be another sentence, for then the relationjjctwecn x and y is an . unproblcmalic logical _ rcjation._Th.Í5 move, however, seems lo leave j us in ihc same metaphysical thickel since verificalion would seem to / require thai y is a true sentence, and is not a true sentence one that / corresponds to the facls? The escape lhat some of ihe circle members soughl was a resort to a coherence theory of truth. Eventually, however, Carnap abandoned resort, presumably because of a combinalion of the drawbacks of the coherence account of truth and the allracliveness of ' theory of truth. Bui whal I wish to emphasize here are ihe qualificalions that Carnap put on any talk about comparing stalemenls wilh facls. In "Truth and Confirmation" (1949) he emphasized lhat he preferred lo speak of confronling slatements wilh facts: There has been a good deal of dispute as to whether in ihc procedure scientific testing slatements must be compared with facts or as lo whether such comparisons be unnecessary, if nol impossible. If "comparison of slalerncnl wilh fact" means ihc procedure which we called ihc firsl opcralio^rylhcn it musí be adinillcd lhal ihis procedure is nol only possible, bul even indispensable for scientific testing. Yel il musí be remarked lhal ihc formulation "comparison of statement and fact" is nol unobjeclionable. First, ihe conccpl "comparison" is not quilc appropriate here. Two objecls can be compared in regard lo a properly which m i r r j j a rn rlnrj ~ r them in varia We ihcrefore prefer lo speak of "cwnfronlalihH" ralhcr ihan^compansol Confrontation is understood to consX^jrjJiMnng out as to fact is such as is described in the statement, or, lo express it differently, as lo whether the statement is true to fact. (1949, 125) Carnap then continued with a passage that might have served as an advertisement for Kuhn's Structure of Scientific Revolutions. Furthermore, ihc formulalion in icrms of "comparison," in speaking of "facls" or "realities" easily Icmpts one inlo the absolutislic view according lo

JJ Carnap, Kulin, and the Philosophy of Scientific Methodology

which we arc said to search for an absolulc reality whose nature is assumed as fixed independently of the language chosen for its description. The answer to a question concerning reality however depends not only upon that "reality" or upon the facts, but also upon the structure (and the set concepts) of the language used for the description. In translating one language into another the factual content of an empirical statement cannot always be preserved unchanged. Such changes arc inevitable if the structures of the two languages differ .inessential points. (1949, 125-126)

Here we have two of the key theses oTthe^gostpositivisl" philosophy i of science:, the noncxistcnce of neutral facts and incommensurabilly in the foriTiof''ftiftn^Trof™iriKrrtTanshrtabHfly. NotcTttMrt-tucsc theses were propounded in the mid 1930s/for although I have, for the sake of convenience, quoted from the 1949 version of Carnap's paper, the relevant passage is also in "Wahrhcil und Bewahrung" (1936)./* | Given these Kuhnian themes—or should we rather say Carnapian themes?—one might predict that Carnap would have found Structure philosophically congenial. That this was indeed the case has been documented by Rcisch (1991). Structure was published as part of the International Encyclopedia of Unified Science, of which Carnap was an associate editor. After reading the completed manuscript for Structure, Carnap wrote to Kuhn in April of 1962. The text of the letter is reproduced in Reisch 1991. I will quote from notes written in Carnap's archaic shorthand. Carnap begins with a piece of Darwinian evolution and then adds, concerning Kuhn's thesis, In analogy to this one has to understand the development of scientific theories: not directed to an ideal [true] theory, the one true theory of the world, but evolution as a step to a belter form, by selection of one oul of several competing forms. The selection is made on ihc basis of preference in ihc community of scientists. Many factors, sociological, c u l t u r a l , . . . , are involved. Nol:vwe are approaching irulh, but: we arc improving an instrument

Another important though largely tacit theme of Structure, a holistic view of meaning, can also be seen as emerging from the writings of the logical empiricists in the 1950s. Hcmpel, for example, took to heart Quine's attack on the analytic/synthetic distinction, which may be taken to embody the thesis that there is a sharp distinction to be drawn between two functions of language: one to specify meaning, the other to make empirical assertions. Applying the moral to scientific theories, one arrives at the conclusion that there is no princi-

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12 John Earmaii

pled way to distinguish those postulates of the theory that may properly be dubbed meaning postulates. It is then but a seemingly short and tempting step to the further conclusion that all the postulates of the theory function to specify the meaning of the constituent terms and thus that any significant change in the theory implies a change in meaning. This route to semantic holism cannot be traced to any of Carnap's writings. Indeed, in his response to HempePs contribution to the Schilpp volume (1963), Carnap attempted to use the notion of the Ramsey sentence of the theory to identify the postulates of the theory that "merely represent meaning relations" (1963a, 965). And in his last book, Philosophical Foundations of Physics (1966), Carnap maiiv tained that "a sharp analytic-synthetic distinction is of supreme im- ' portance for the philosophy of science" (1966, 257).§ There is, however, another Carnapian route to semantic holism, but that route must be traced all the way back to Carnap's attempt in the Aufbau (1928) to explain how scientific objectivity can emerge from a reconstruction that starts from a phcnomcnalistic basis. An exploration of this matter would take me too far afield; I will simply refer the reader to Michael Friedman's (1987) illuminating discussion. 7 Q 3

Carnap's Relativism

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losophy and Logical Syntax" (1935) proclainicd the relativity ol all philosophical theses to language. This relativity was supposed to hold the key to solving, or rather dissolving, traditional philosophical disputes. Suppose, for example, one philosopher asserts, "Numbers are primitive entities," while another proclaims, "Numbers are classes of classes." "They may," Carnap writes, "philosophize without end about the question of what numbers really are, but in this way they will never come to an agreement" (1935, 450). If, however, they are acute enough to recognize Carnap's relativity principle, they will quickly realize that one is asserting, "In Language LI (Peano), numerical expressions are elementary expressions," while the other is maintaining, "In Language L? (Russell) numerical expressions are class expressions of the second order." "Now these assertions are compatible j

Carnap, Kulin, and the Philosophy of Scientific Methodology

with each other and both arc true; the controversy has ceased to exist" (1935, 451). This model for resolving philosophical disputes in • the philosophy of mathematics was supposed by Carnap to be cxtendiblc quite broadly to philosophical disputes, such as phenomenalism versus materialism and the question of whether space-time points have an existence independent of physical events. Some, like Donald Davidson (1973), have found an air of paradox in the fact that saying in one breath (as Carnap thought he could) that 5 is true in L\, LS, Las, • • . but false in L?, ¿4, ... seems to presuppose a neutral metaframe within which all the language frames can be treated.6 Others, like Michael Friedman (1992), have argued that Carnap's relativism is undercut by Godel's incompleteness theorems, which show that no such neutral metaframe is available. My objections are more local and tactical. My first complaint is that Carnap assumes what needs to be proved. According to Carnap's "principle of tolerance," we are free to choose whatever language system we like. The decision is largely a pragmatic affair, turning on such matters as efficiency and fruitfulness for the -purposes at hand. But to apply the slogan of "free to choose" to dissolve, say, the phenomenalism versus materialism debate assumes that a phenomenalistic language has been produced that shows how physical object talk can be reduced to talk about sensa data or, as Carnap preferred, momentary total experiences ("Elementarerlcbnissc"). This, of course, is exactly what Carnap tried to do in the Av/lau. But by his own admission, the attempt has to counted as a failure if, as he originally assumed, the reduction has to proceed via explicit definitions and explicit Iranslalions. Similarly, to apply the "free to choose" slogan to dissolve disputes about the ontplogical status of space-time points assumes that it can be shown how spacetime points can be constructed out of events, such as coincidences of particles. Advocates of relational theories of space and time repeatedly claim that this can be done and even that it has been done. But none of the claims stands up to scrutiny.7 I am emphatically not claiming that materialism is correct or that space-time points construed as irreducible entities are essential to physics. Rather, I am claiming that the dissolution of the traditional disputes on these matters is not as easy as Carnap made it seem.

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M John Earman

Another complaint arises from the breathtaking scope of the intended application of Carnap's dissolving strategy. Among the "philosophical" disputes that Carnap proposed to treat in this way were such matters as whether time is finite or infinite and whether the world is deterministic. There is obviously a very slippery slope here. If the question about the finilude of time is a philosophical question in the relevant sense, then why not the question of whether the world began from a big-bang singularity? And if this latter question is a philosophical question in the relevant sense, then why not other deep questions in cosmology? But more important, one does not have to go down the slope to recognize the implausibihty of Carnap's procedure. Even if one agrees to talk about truth in L rather than truth period, there is no plausibility to the idea that whether time is finite and whether determinism holds are matters to be settled in L by adopting linguistic rules for L rather than by consulting the facts. Carnap, not surprisingly, acknowledged the point. Speaking of the determinism issue, he said, The objection may pcriiaps be raised at this point that the form of physical laws depends upon experimental results of physical investigation, and that it is not determined by a merely theoretical syntactical consideration.' This assertion is quite right, but we must bear in mind the fact that the empirical results at which physicists arrive by way of their laboratory experiments by no means dictate their choice between the deterministic and the statistical' form of laws. The form in which a law is to be slated has to be decided by an act of volition. This decision, it is true, depends upon the empirical results, but not logically, only practically. The results of the experiments show merely ill.il one mode of formulation would be more suitable than another. (1935, 455)

These sentiments resonate with those Carnap expressed three decades later in commenting on Kuhn's Structure. But here the sentiments arc not to the point. The issue is not whether, for Duhemian or other reasons, the results of experiments, say the recent Einstein, Rosen, Podolsky, and Bell type of experiments, fail to dictate the acceptance of indeterministic laws. Rather the issue is whether determinism is a scientific claim to be argued over the way one argues over other deep scientific claims, none of which ever gets definitively settled by the dictates of experimental evidence; or whether determinism is a claim that can be made true by linguistic fiat in L\, Lr,,

Carnap, Kuhn, and the Philosophy of Scientific Methodology ¿35, . . . and false by linguistic fiat in L2, LT, ¿37 ..... and then we just pays our money and takes our choice of language. Again I refuse to give a global answer to this query and favor instead a tactical response. All indications are that the debate over the implications for deterijiinism of the Bell inequalities and the Aspect experiments belongs to the former rather than to the latter. Indeed, indications are that in any language system adequate for the formulation of theories that save the experimentally verifiable quantum statistics, the laws must be indeterministic. 9 I suspect that Carnap's relativism began by his being impressed by the achievements of Frege, Russell, and others in the philosophy of mathematics and was furthered by a misplaced zeal for extending his model for resolving philosophical disputes in this area to a broad area of philosophical and scientific questions. Of course, whatever the origins of Carnap's relativism, it or something like it could perhaps be promoted on the basis of his doctrine that language-neutral facts do not exist. I find it difficult to assess this matter, since I do not find in Carnap's writing a helpful explanation of this In the following section I will comment on the related doctrine of Feycrabcnd, Hanson, and Kuhn that observation is theory laden. In closing this section, I note that Carnap displayed a consistency on the matter at hand — not the consistency that is the hobgoblin of little minds but the magnificent consistency of a grand visionary. In his contribution to the Schilpp volume for Carnap, Herbert Fcigl (1963) sketched a mind-body identity theory that he was later to elaborate in his famous essay "The 'Mental' and the ThysicaF"(1958).'° Clearly, the politically correct thing for Carnap was to endorse Fcigl's approach. Instead, he wrote, "it seems preferable to me to formulate the question [of mind-body identity] in the metalanguage, not as a factual question about the world, but as a question concerning the choice of language. Although we prefer a different language, we must admit that a dualistic language can be constructed and used without coming into conflict with cither the laws of logic or with empirically known facts" (1963b, 885-886). 4 Kuhn's Relativism Kuhn resists being labeled a relativist. I use the label here to refer to three doctrines of Structure: the theory ladenncss of observation, the

]G John Earnian

¡ncomnicnsurability of theories, and (lie denial that there is a llicoryindcpcndcnl notion of truth. Part of what was meant by the theory ladcnncss of observation is embodied in the thesis that what we see depends upon what we believe, a thesis open to challenge (see Fodor 1984). I am concerned rather with the related thesis of the nonexistence of a neutral observation language in which different theories can be compared. My response is once again tactical. That is, without trying to adjudicate the general merits of the thesis, I claim that things aren't so bad for actual historical examples. Even for cases of major scientific revolutions, we cari find, without having to go too far downward toward something like foundations for knowledge, an observation base that is neutral enough for purposes at hand. A nice example is provided by Allan Franklin (1986, 110-113), who shows how to construct an experiment that is theory-neutral enough between Newtonian and special-relativistic mechanics to unambiguously decide between the predictions of these theories for elastic collisions. The two theories agree on the procedure for measuring the angle between the velocity vectors of the scattered particles, and the two theories predict differ- ~ ent angles. A ^b More generally, I claim that in the physical sciences there is in principle always available a neutral observation base in spatial coincidences, such as dots on photographic plates, pointer positions on dials, and the like. If intcrsubjective agreement on such matters were not routine, then physical science as we know it would not be possible. 1 reject, of course, the posilivistic attempt to reduce p'hysics to such coincidences. And I readily acknowledge that such coincidences by themselves are mute witnesses in the tribunal for judging theories. But what is required to make these mute witnesses articulate is not a Gcstalt experience but a constellation of techniques, hypotheses, and theories: techniques of data analysis, hypotheses about the operation of measuring instruments, and auxiliary theories that support bootstrap calculations of values for the relevant theoretical parameters that test the competing theories. But I again assert that to the extent that this process cannot be explicitly articulated but relies on some sui generis form of perception, the practice is not science. This is not to say, however, that the vulgar image of science as a blindly impartial enterprise is correct, for the articulation uncovers assumptions to

/ 17 Carnap, Kulin, and the Philosophy of Scientific Methodology

which different scientists may assign vcfy different, degrees of confidence. But this sense in which different scientists can (mislcadingly) be said to "see" different things when looking at the same phenomenon is one with which a probabilistic or Bayesian epistemology—the kind of epistemology which the later Carnap came to advocate—must cope on a routine basis, even in cases far away from the boundaries of scientific revolutions. How these differences are resolved is part of the Bayesian analogue of Kuhn's problem of community decision on theory choice. Kuhn's problem will be encountered in the following section, and the Bayesian analogue will be discussed in sections 8 and 9. The matter of incommensurability is much more difficult to discuss for two reasons. First, it is tied to difficult issues about meaning and reference that I cannot broach here. Second, issues about incommensurability present amorphous and shifting targets. In Structure, for example, incommensurability was a label for the entire constellation of factors that lead proponents of different paradigms to talk past one another. In recent years Kuhn has come around to a more Carnapian or linguistic formulation in which incommensurability is equated with untranslatability. More specifically, the focus has shifted from paradigms to theories, and two theories are said to be incommensurable just in case "there is no common language into which both can be fully translated" (Kuhn 1989, 10). I have no doubts about Kuhn's claims that theories on different sides of a scientific revolution often use different "lexicons," that differences in lexicons can make for a kind of untranslatability, and that in turn this explains why scientists reading out-of-date texts often encounter passages that "make no sense" (1989, 9). But I deny that there is incommensurability/untranslatability that makes for insuperable difficulties for confirmation or theory choice (a phrase I don't like for reasons to be given below) in the standardly cited cases of scientific revolutions such as the transition from Newtonian to special-relativistic mechanics and the subsequent transition to general relativity. Newtonian, special-relativistic, gcncral-relativistic, and many other theories can all be formulated in a common language, the language of differential geometry on a four-dimensional manifold, and the crucial differences in the theories lie in the differences in the geometric object fields

J8 John Earman

postulated and the manner in which these fields relate to such things as particle orbits. This language is anachronistic and so may not be the best device to use when trying to decide various historical disputes." But it does seem to me to be an appropriate vehicle for framing and answering the sorts of questions of most concern to working physicists and philosophers of science. For example, on the basis of the available evidence, what is it reasonable to believe about the structure of space and time and the nature of gravitation? This is not to say that the common language makes for an easy answer. It is indeed a difficult business, but it is a business that involves the same sorts of difficulties already present when testing theories that lie on the same side of a scientific revolution. Finally, so that there can be no misunderstanding, let me repeat: I am not claiming (hat what I call a common language provides what Kuhn wants. It docs not show, for example, that the Newtonian and the Einstcinian can be brought into agreement about what is and is not a "meaningful" question about simultaneity. But what I do claim is that these residual elements of incommensurability do not undermine standard accounts of theory testing and confirmation. 12 My response to worries about the applicability of the notion of truth to whole theories is similarly local and tactical. In the Postscript to the second edition of Structure, Kuhn writes, "There is, I think, no theory-independent way to reconstruct phrases like 'really there'; the notion of a match between the ontology of a theory and its 'real' counterpart in nature now seems to me illusive in principle" (1970, 206). I need not demur if "theory" is understood in 'a very broad sense to mean something like a conceptual framework so minimal that without it "the world" would be undifferenliated Kantian ooze. But I do demur if "theory" is taken in the ordinary sense, i.e., as Newton's theory or special-relativity theory or general-relativity theory.13 For scientists are currently working in a frame in which they can say, correctly I think, that the match between the ontology of the theory and its real counterpart in nature is better for the special theory of relativity and even better for the general theory. Of course, to get to this position required two major coneptual revolutions. How such revolutions affect theory choice, or as I would prefer to say, theory testing and confirmation, remains to be discussed.

]9 Carnap, Kuhn, and the Philosophy of Scientific Methodology

5

Kuhn's Account of Scientific Revolutions

Carnap, as we have seen, found Kuhn's Structure congenial. But many • philosophers of the younger generation, including those who prided themselves on having gone beyond the crudities of logical positivism, professed shock and dismay at Kuhn's account of the displacement of an old paradigm by a new one. For those readers who do not have a copy of Structure to hand, here are some of the purple passages: Like the choice between competing political institutions, that between competing paradigms proves to be a choice between incompatible modes of community life. . .. When paradigms enter, as they must, into a debate about paradigm choice, their role is necessarily circular. Each group uses' its own paradigm to argue in that paradigm's defense. (P. 94) As in political revolutions, so in paradigm choice—there is no standard higher than the assent of the relevant community. To discover how scientific revolutions arc effected, we shall therefore have to examine not only the impact of nature and logic, but also the techniques of persuasive argumentation within the cjuilc special groups that constitute the community of scientists. (P. 94) The proponents of competing paradigms practice their trades in different worlds. . . . Practicing in different worlds, the two groups of scientists sec different things when they look from the same point in the same direction. (P. 150) In these matters neither proof nor error is at issue. The transfer of allegiance from paradigm to paradigm is a conversion experience that cannot be forced. (P. 151) Before they can hope to communicate fully, one group or the other must experience the conversion that we have been calling a paradigm shift. Just because it is a shift between incommensurables, the transition between competing paradigms cannot be made a step at a time, forced by logic and neutral experience. Like a gcslalt switch, it must occur all at once (though not necessarily at an instant) or not at all. (P. 150) Many readers saw in these passages an open invitation to aralionality if not outright irrationality. Thus Imre Lakatos took Kuhn to be saying that theory choice is a matter of "mob psychology" (1970, 178), while Dudley Shapcre read Kuhn as saying that the decision to adopt a new paradigm "cannot be based on good reasons" (1966, 67).

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Kulin in turn was equally shocked by such criticisms. In the Postscript to the second edition of Structure (1970), he professed surprise that readers could have imposed such unintended interpretations on the above quoted passages. I will leave aside the unfruitful question of whether or not Kuhn ought to have anticipated such interpretations and will concentrate instead on what, upon reflection, he intended to say. Kuhn's own explanation in the Postscript begins with the commonplace that "debate over theory-choice cannot be cast in a form that resembles logical or mathematical choice" (1970, 195). But he hastens to add that this commonplace does not imply that "there are no good reasons for being persuaded or that these reasons are not ultimately decisive for the group" (1970, 195). The reasons listed in the Postscript are accuracy, simplicity, and fruitfulness. The later paper "Objectivity, Value Judgments, and Theory Choice" (1977) added two further reasons: consistency and scope. And as Kuhn himself notes, the final list does not differ (with one notable exception to be discussed later) from similar lists drawn from standard philosophy-ofscicnce texts (see also Kuhn 1983). These soothing sentiments serve to deflate charges of arationality and irrationality, but at the same time they also serve to raise the question of how Kuhn's views are to be distinguished from the orthodoxy that Structure was supposed to upset. The answer given in the Postscript contains two themes, which are elaborated in "Objectivity." First, the items on the above list are said to "function as values" that can "be differently applied, individually and collectively by men who concur in honoring them" (1970, 199). Thus, "there is no neutral algorithm for theory choice, no systematic decision procedure which, properly applied, must lead each individual in the group to the same decision." Second, it (supposedly) follows that "it is the community of specialists rather than the individual members that makes the effective decision" (1970, 200). I think that Kuhn is correct in locating objectivity in the community of specialists, at least in the uncontroversial sense that intersubjective agreement among the relevant experts is a necessary condition for objectivity. But how the community of experts reaches a decision when the individual members differ on the application of shared values is a mystery that to my mind is not adequately resolved by

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Carnap, Kuhn, and ihc Philosophy of Scicnlific Mclhodology

Structure or by subsequent writings. My strategy will be to explore these and related issues from the perspective of Carnap's cpistcmology. 6 Carnap and Kuhn: Incommensurability? The passage Reisch (1991) quotes from Carnap's letter to Kuhn and the passage from Carnap's shorthand notes I quoted in section 2 would seem to indicate that Carnap and Kuhn were in substantial agreement as regards paradigm choice. This is surely the case when "paradigm" is interpreted to mean something like a linguistic framework. At this level Carnap would agree, indeed, would insist, on the need to choose, and he would hold that the choice is'a pragmatic one whose dynamics may well involve the sorts of factors emphasized in Kuhn's account. But when the focus shifts to theories, as it does in • Kuhn's later writings, the disagreement begins. In the first place, Kuhn's list of criteria for theory choice is conspicuous for its omission of any reference to the degrees of confirmation or probabilities of the theories. This is not an oversight, of course, but derives both from explicit doctrines, such as the nonexistence of a theory-neutral observation language, and the largely tacit but pervasive anti-inductivism of Structure. Needless to say, this shunning of confirmation theory is most un-Carnapian. But even more anomalous from Carnap's perspective is Kuhn's emphasis on theory choice or acceptance, for in Carnap's version of epistemology, theories arc not chosen or accepted but only probabiIified. M Carnap's writings in the 1940s and 1950s portray him as espousing a "logical" conception of probability. But by the late 1950s and early 1960s, he clearly favored a view that can be termed tempered personalism: probability is rational degree of belief.15 I will have more to say on this matter in section 8, but in the meantime I will present Carnap as a tempered Bayesian personalist. A shotgun marriage of Kuhn and Carnap could be arranged by taking Carnap to supply the probabilities, Kuhn to supply the values or utilities, and then applying the rule of maximizing the expected utility to render a decision on theory choice.16 But like most shotgun marriages, this one would be a mistake. For Carnap it would be a mistake because it would involve the pretense that the accepted the-

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ory is certain even though one's degree of belief in the theory may be less than one, perhaps substantially so. For Kuhn it would also be a mistake, since the efficacy of his values does not depend on the truth of the theories, so estimates of the probable truth of the theories is irrelevant to Kuhnian theory choice. Part of the wrangle here derives from the unfortunate phrase "theory choice." Scientists do choose theories, but on behalf of Carnap, I would claim that they choose them only in the innocuous sense that they choose to devote their time and energy to them: to articulating them, to improving them, to drawing out their consequences, to confronting them with the results of observation and experiment. Choice in this sense allows for a reconciliation of Bayes and Kuhn, since this choice is informed by both Baycsian and Kuhnian factors: probability and the values of accuracy, consistency, scope, simplicity, and fruitfulncss. Alas, this reconciliation is rather shallow. Once we are clear that the sort of choice involved in "theory choice" is a practical one, there is nothing sacred about the list of items on Kuhn's list of values. Other values, such as getting an NSF grant or winning the Nobel Prize, can and do enter. Further, the kind of choice in question allows a scientist to be bigamous, since he can choose to work on two or more theories at once, and it allows him to be fickle, since he can oscillate back and forth. The kind of choice Structure envisioned was much more permanent; indeed, the impression given there is that normal science is not possible without tying Catholic bonds to a theory, bonds that can only be broken by leaving the Church, i.e., by creating a revolution. Is there no way to bridge the gap between Carnap and Kuhn on this issue? To see how baffling the Bayesian finds the notion of theory acceptance, consider the case of Einstein's general theory of relativity (GTR), arguably the leading theory of gravitation and thus the top candidate for acceptance. Marie, a research worker in the field familiar with all of the relevant experimental findings, does some introspection and finds that her degree of belief in GTR is p. Case 1: p is 1, or so near 1 as makes no odds. Here there is a natural sense in which the Bayesian can say that Marie accepts GTR. Such cases, however, arc so rare as to constitute anomalies. Of course, one

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Carnap, Kuhn, and llic Philosophy of Scientific Mclhodology

can cite any number of cases from the history of science where scientists seem to be saying for their pet theories that they set p = 1. Here I would urge the need to distinguish carefully between scientists as advocates of theories versus scientists as judges of theories. The latter role concerns us here, and in that role scientists know, or should know, that only in very exceptional cases does the evidence rationally support a full belief in a theory. Let us move on to case 2. Case 2: p is, say, .75. Subsequently Marie decides to "accept" GTR on the basis of her probability assignments and the values she attaches to GTR and its competitors. What could this mean? Subcase 2a. When she accepts GTR, Marie changes her degree of belief from .75 to 1. This is nothing short of folly, since she has already made a considered judgment about evidential support and no new relevant evidence occasioning a rejudgment has come in. Suitcase 2b. When she accepts GTR, Marie docs not change her degree of belief from .75 to 1, but she acts as z/all doubt were swept away in that she devotes every waking hour to showing that various puzzling astronomical observations can be explained by the theory, she assigns her graduate students research projects that presuppose the correctness of the theory, she writes a textbook on gravitational research that is devoted almost exclusively to GTR, etc. But at this point we have come full circle back to a sense of theory acceptance that is really a misnomer, for what is involved is a practical decision about the allocation of personal and institutional resources and not a decision about the cpistcmic status of the theory. This rather pedantic diatribe on theory acceptance would be best forgotten were it not for its implications for our picture of normal science. As we have seen, theory "choice" or "acceptance" can refer cither to adopting an epislemic attitude or to making a practical choice. In the former case there is no natural Bayesian explication of theory acceptance save in the case where the probability of the theory is one. Since scientists as judges of theories are almost never in a position to justify such an acceptance, the Bayesian prediction is that rarely is a theory accepted in the epistemic sense. Similarly, when theory choice is a matter of deciding what theory to devote one's lime and energy to, the Bayesian prediction is that in typical situations

John l'.arnian

where members of the community assign different utilities to such devotions, they will make different choices. Thus from either the cpistcmic or practical-decision perspective, the Bayesian prediction is diversity. This prediction is, I think, borne out by actual scientific practice. In section 9 below I will argue that insofar as normal science implies a shared paradigm, the paradigm need not and in fact often is not so specific as to include a particular ("accepted") theory. I will also hazard a proposal for a minimal sense of "shared paradigm" that yields a less strait-jacketed image of normal science and that also diminishes without obliterating the difference between normal and revolutionary science. By way of closing this section and introducing the next, I will consider a final way of reconciling Kuhn and Carnap on theory choice. Radically new theories, so the story goes, carry with them different linguistic/conceptual frameworks. Thus, even seriously lo entertain the new theory involves the decision to adopt, if only tentatively, the new framework, and this decision is for Carnap a pragmatic one that involves the sorts of factors emphasized in Kuhn's account of paradigm replacement. In response I would repeat what I have already said in section 4: major scientific revolutions such as the transition from Newtonian to special-relativistic physics- and thence lo general relativity needn't be seen as forcing a choice between incommensurable linguistic/conceptual systems, since it is often possible lo fit ihc possibilities into a larger scheme thai makes llic theories commensurable lo the extenl lhal confirmalion questions can be posed in terms of an observation base lhal is ncuiral enough for assessing ihe relalive confirmation of the theories. However, ihe rccognilion of ihe larger possibility set can produce a drastic change in probability values, a change best described in Kuhnian terms. 7 Revolutions and Belief Shifts A mild form of scientific revolution occurs with ihe inlroduclion of a new llieory lhal articulates possibilities thai lie wilhin ihe boundaries of ihe space of iheories to be taken seriously but that, because of the failure of actual scientists to be logically omniscienl, had previously been unrecognized as explicil possibilities. The more radical form of revolulion occurs when ihe space of possibilities itself needs

25 Carnap, Kuhn, and ihc Philosophy of Scicnlific Methodology

to be significantly altered to encompass the new theory. In practice the distinction between the two forms of revolution may be blurred, perhaps even hopelessly so, but I will begin discussion by pretending that we can perform a separation of cases. Even the mild form of revolution may induce a non-Bayesian shift in belief functions. By non-Bayesian I mean that no form of conditionalizalion, whether strict or Jeffrey or some natural extension of these, will suffice to explain the change. For conditionalizing (in any recognizable sense of the term) on the information that just now a heretofore unarliculated theory T has been introduced is literally nonsensical, because such a conditionalization presupposes that prior to this time there was a well-defined probability for this information and thus for T, which is exactly what the failure of logical omniscience rules out. We can try to acknowledge the failure of logical omniscience by means of Abner Shimony's (1970) device of a catch-all hypothesis Hf, which asserts in effect that something, we know not what, beyond the previously formulated theories T\, Tz, . . . , TT is true. Now suppose that a new theory T is introduced and that as a result the old degrce-of-bclief function Pr is changed to Pr'. The most conservative way the shift from Pr to Pr' could take place is by the process I will call shaving off, namely, Pr(T,) =.Pr'(Ti) for i = 1, 2, . . . , q and Pr'(T) = r > 0 and Pr'(//e) = Pr(//c) - r. That is, under shaving off, Hf serves as a well for initial probabilities for as yet unborn theories, and the actual introduction of new theories results only in drawing upon this well without disturbing the probabilities of previously formulated theories. Unfortunately, such conservatism eventually leads to the assignment of ever smaller initial probabilities to successive waves of new theories until a point is reached where the new theory has such a low initial probability as to stand not much of a fighting chance. Certainly shaving off is a factually inadequate description of what happens in many scientific revolutions, especially of the more radical type. Think of what happened following the introduction of Einstein's special theory of relativity (STR) in 1905. Between 1905 and 1915 little new empirical evidence in favor of STR was recorded, and yet the probability of competing theories, such as those of Lorentz and Abraham, set in classical space and time, fell in the estimates of

26 John Earman

most of the members of the European physics community, and the probability subtracted from these electron theories was transferred to Einstein's STR. The probabilities of auxiliary hypotheses may also be affected, as illustrated by the introduction of the general theory of relativity (GTR). When Einstein showed that GTR accounted for the exact amount of the anomalous advance of Mercury's perihelion, the hypothesis of an amount of zodiacal matter sufficient to affect Mercury's perihelion dropped dramatically in the estimates of most of the physics community (see Earman and Glymour 1991). In using the term "non-Bayesian" to describe such nonconditionalization belief changes, whether of the conservative shaving-off type or some more radical form, I do not mean to imply that the changes are not informed by Bayesian considerations. Indeed, the problem of the transition from Pr to Pr' can be thought of as no more and no less than the familiar Bayesian problem of assigning initial probabilities, only now with a new initial situation involving a new set of possibilities and a new information basis. But the problem we arc now facing is quite unlike those allegedly solved by classical principles of indifference or modern variants thereof, such as E. T. Jayncs's maximum-entropy principle, where it is assumed we know nothing or very little about the possibilities in question. In typical cases the scientific community will possess a vast store of relevant experimental and theoretical information. Using that information to inform the redistribution of probabilities over the competing theories on the occasion of the introduction of the new theory or theories is a process that, in the strict sense of the term, is\o?Slipnal: it cannot'be accomplished by some neat formal rules or, To use Kuhn's term,_bvan algorithm. On the otherjjand, the process is far from beirígjrrationaí>> since it is informecf by reasons. But the reasons, as Kuhn Tias~crrfphasized, come in the form ofpersuasions rather than proof. In Bayesian terms, the reasons are marshaled in the guise of ptausiblTily arguments. The deployment of plausibility arguments is an art form for which there currently exists no taxonomy. And considering the limitless variety of such arguments, it is unlikely that anything more than a superficial taxonomy can be developed. Einstein, the consummate master of this art form, appealed to analogies), symmetry considerations, thought experiments, heuristic principles such as the principle of equivalence, etc. All of these considerations, I am sug-

27

t

" •

Carnap, Kuhn, and the Philosophy of Scientific Methodology

gcsting on behalf of the Baycsians, were deployed to nudge assignments of initial probabilities in favor of the theories Einstein was introducing in the early decades of this century. Einstein's success in this regard is no less important than experimental evidence in explaining the reception of his theories. To summarize, Kuhn's purple passages do not seem overblown when applied to revolutions in the strong sense distinguished above. The persuasions that lead to the adoption of the new shape for the possibility space cannot amount to proofs. Certainly for the Bayesian they cannot consist of inductive proofs, since the very assignment of degrees of belief presupposes the adoption of such a space. After a revolution has taken place, the new and old theories can often be fitted into a common frame that belies any vicious form of incommensurability (as I tried to illustrate in section 4 for Newtonian and relativistic theories). But this retrospective view tends to disguise the shake-up in our system of beliefs occasioned by the adoption of the new shape for the possibility space. Baycsianism brings the shake-up to light, albeit in a way that undercuts the standard form of the doctrine. I have no way of knowing whether Carnap would have approved of my Bayesian reading of Kuhn. But I do claim that it is a reading that fits naturally with Carnap's mature views on probability and induction. 8 Objectivity and the Problem of Consensus I have endorsed a Bayesianized version of Kuhn's claim that in scientific revolutions persuasion rather than proof is the order of the day: revolutions involve the introduction of new possibilities; this introduction causes the redistribution of probabilities; the redistribution is guided by plausibility arguments; and such arguments belong to the art of persuasion. This endorsement is confined to the first stage of the revolution, when the initial probabilities are established for the expanded possibility set. The Bayesian folklore would have it that after this first stage, something more akin to proof than persuasion operates. The idea is that an evidence-driven consensus emerges as a result of the Bayesian learning model: degrees of belief change by conditional!-

28 John Earman

/.¡ilion on ilic accumulating evidence of observation and experiment, and the long-run result is to force a merger of posterior opinion for those Baycsian agents who initially assign zeros to the same hypotheses. This folklore can draw on some mathematically impressive merger-of-opinion theorems. But these theorems are of dubious applicability not only to the sorts of cases discussed in Structure but also to examples from normal, as opposed to revolutionary, science. For one thing, the mathematical results are in the form of long-run or limit results that give no information about how long the long run is." If honest theorem proving won't suffice to explain the merger of opinion that, for the Bayesian epistemologist, constitutes the heart of scientific objectivity, then perhaps we can define our way to a solution. That is, why not define "scientific community" in terms of de facto convergence of opinion over a relevant range of hypotheses? The answer is the same as that given by Kuhn in the Postscript to the threatened circularity of taking a paradigm to be what members of the community share while also taking a scientific community to consist of those scientists who share the paradigm. Just as scientific communities "can and should be isolated without prior recourse to paradigms" (Kuhn 1970, 176), so they can and should be isolated without recourse to convergencc-of-opinion behavior. The European physics community in the opening decades of this century can be identified by well-established historical and sociological techniques. One wants to know how and why, for example, this community so identified reached a consensus about Einstein's STR. Nevertheless, there does seem to be at least this much truth to the definitional move: repeated failures to achieve merger of opinion on key hypotheses will most likely lead.to a split in or a disintegration of the community. This is the appropriate place to ask whether Carnap's views on probability are of any help. In a letter dated July 30, 1963, Carnap wrote to Bruno De Finctti, the arch Baycsian personalisl, that he believed that the constraints of rationality extend beyond the requirement of coherence, which entails that degrees of belief must conform to the standard axioms of probability.18 According to Carnap the requirements of rationality do not suffice to single out a unique probability function, but they do significantly constrain the choice of

2!) Carnap, Kuliii, and the Philosophy of Scientific Methodology

a probability funclion. If this were corrccl, ihc liaycsian version of llie problem of scicnlific objectivity would be made correspondingly easier. However, I do not think that Carnap managed to stake out a defensible position, as can be brought out by the question of how one recognizes which probability functions are "rational." Carnap's answer was to appeal to what he variously called "inductive intuilion" and "induclivc common sense." The trouble, of course, is that one person's inductive common sense is another's inductive non-sense. So the appeal to intuition reveals very diffcrenl opinions as lo whelhcr it is rational to learn from experience at all and, if so, at what rate. At this juncture il will be helpful to review a mechanism proposed by Lehrei and Wagner in Rational Consensus in Science and Society (1981) for achieving a group consensus. Their mechanism requires that the members of ihc community change ihcir degrees of belief in accordance wilh a wcighled-aggrcgalion rule. Suppose that at the initial moment, person i has a degree of belief /;, in the theory in question. Each person i is assumed to assign a weight w¡/ ^ 0 to every person _;', which can be taken as an index of i's opinion as to the reliability of/s opinions. According to Lchrcr and Wagner's rule, i then "improves" her inilial opinion />? by changing it to pi = X,w,y/>". If there arc still differences of opinion, the aggregation process is repeated with the /;,' to obtain further "improved" probabilities /;?, etc., until eventually the probabilities for all members fall into line. Lchrcr and Wagner offer a consistency argument for their aggregation rule: "If a person refuses to aggregate, though he does assign a positive weight to other members, he is acting as though he assigned a weight of one to himself and a weight of zero to every other member of the group. If, in fact, he assigns positive weight to other members of the group, ihen he should nol behave as if he assigned zero weight lo them" (1981, 22). This argument has the flavor of "When arc you going to slop beating your wife." I do assign a, positive weight to the opinions of others, but as a liaycsian I do this not by means of weighted aggregation but by conditionalization: I conditionalizc on information about the opinions of my peers, and I notice that the result is a shift in my degrees of belief toward the degrees of belief of those I respect. When I was a young student, these shifts brought . my opinions closely in line with those belonging to people I regarded

30 John lüirmun

as the experts, but as a mature member of the community, I find that such shifts, while still nonnegligiblc, do not conform my opinions lo those of others, at least not on matters where I now regard myself as an expert. And I resist any further attempt to bend my carefully considered opinions. There are two reasons, independent of Bayesianism, to be unhappy with Lehrer and Wagner's proposal and ones like it. The first is that it is descriptively false, as shown by the very example they use to motivate their proposal. In the 1970s Robert Dicke claimed that optical measurements of the solar disk revealed an oblateness large enough to account for 3" to 5" of arc in Mercury's centenary perihelion advance and thus to throw into doubt Einstein's explanation of the advance. When other astrophysicists disagreed with Dicke's conclusions the differences were not smoothed over by producing a consensual probability by means of a weighted aggregation process. The disagreement remains unresolved to this day. The weight of opinion docs seem lo be going against Dicke's inlcrprctation, but this partial agreement is in fact due not to aggregation but to the acquisition of additional evidence. Of course, Lchrcr and Wagner are perfectly aware of these facts, and the descriptive inadequacies of their proposal do not concern them, since they take themselves to be offering a normative proposal. But even in ihcsc terms the proposal should be faulted. It is fundamental lo science thai opinions be evidence-driven. Differences of opinion need not constilutc an embarrassment that needs lo be quashed, for ihesc differences can serve as a spur lo further iheorelical and experimental research, and the new information produced may drive a genuine scientific consensus. The alternative, an atlcmpl lo manufaclure a consensus by a weighted-aggregation procedure, smacks of the "mob psychology" of which Kuhn was criticized. This last point generalizes. Bayesianism and other approaches to scienlific inference as well suggest that unless there is some evidencedriven process that operates on the level of individual scientists to produce a group consensus, ihe consensus will amounl lo something that, if not mob psychology, is nevertheless a social artifact not deserving either of the labels "rational" or "scienlific." Thus, conlrary

Carnap, Kulin, and the Philosophy of Scientific Methodology

to Kuhn's idea, the group cannot decide—it cannot rationally decide to agree if the individuals disagree. I do not see how this conclusion can be escaped unless some yet to be articulated collcctivisl methodology is shown lo be viable. 9 A Partial Resolution to the Problem of Consensus Part of the answer to the Bayesian version of the problem of consensus is that quite often it does not exist and does not need to exist for normal scientific research to take place. Structure warned of the danger of taking textbook science as our image of how real science actually operates, and in particular, it showed how textbook science tends lo make scientific revolutions invisible by painting an overly rosy picture of a smoothly accumulating stockpile of scientific knowledge. But I think that Structure failed to emphasize how textbook science also disguises the diversity of opinions and approaches that flourish in nonrcvolutionary science. If I had the space, 1 would offer as a case study the development of relativistic gravitational research over the last seventy-five-years.19 Textbooks in this area have tended to be books on Einstein's GTR, thus fostering the illusion that GTR has achieved the status of paradigm hegemony. In addition, early textbooks not only downplayed the existence of rival theories but disguised serious difficulties with two of the principal experimental tests of GTR, the red shift and the bending of light. Normal scientific research in this field continued in the face of both a challenge lo the third experimental leg of GTR deriving from Dicke's solar-oblateness measurements and also an ever growing number of rival theories of gravitation. This and similar examples suggest that normal science is possible when the community of experts share a paradigm in the weak sense of agreement on the explanatory domain of the field, on the circumscription of the space of possible theories to be considered as serious candidates for covering the explanatory domain, on exemplars of explanatory success, and on key auxiliary hypotheses. (I am tempted to say that this is the minimal sense of paradigm needed to underwrite normal science, but historians of science probably have counterexamples waiting in the wings.)

John Kai man

One could argue that not having a paradigm in the stricter sense of a shared theory of gravitation has lowered the puzzle-solving efficiency of normal science. One can recall Thornc and Will's (1971) lament thai, faced with a zoo of alternative theories of gravitation, astrophysicists where hamstrung in their model-building activity. While I think that this is a fair observation, I also think that there is more to progress in normal science than puzzle solving. In particular, I would emphasize the conceptual advances derived from the exploration of the space of possible theories, a point that brings me to the second part of my partial answer to the problem of consensus. Again, if I had the space, I would argue that insofar as a consensus is established, it is often due to a process akin to the much maligned idea of eliminativc induction. This process is often accompanied by a proliferation of theories, not as an exercise in Feyerabendian anarchy or Dadaism, but as a means of probing the possibilities and as a preliminary to developing a classification scheme that makes systematic elimination a tractable exercise.20 The elimination is not of the simplcmindcd Sherlock Holmes variety, for it involves Bayesian elements, especially in the assessment of the auxiliary assumptions needed to bring about a confrontation of theory and experiment. Thus the Baycsianizcd version of the problem of consensus remains. And at the present time I do not see any resolution that does not fall back on something like the definitional solution, which I casually dismissed in the preceding section. Such a fallback undermines scientific objectivity in a way that would not have pleased Carnap and, I presume, docs not please K u h n cither. , 10 Conclusion I was a distant student of Carnap and a close student of Kuhn. But the two seemed to me so different in style and concerns that I placed them in different parts of the philosophical firmament. Only now have I begun to appreciate how misguided my placement was and how much philosophy of science can be enriched by considering how the ideas of these two giants interact. I have presented one way to stage the interaction. There are surely better ones. I urge more able hands to take up the task.21

33 Carnap, Kulin, and the Philosophy of Scientific Methodology

Notes Sections 6-9 of this paper arc based on chapter 8 of Earman 1992. I am grateful to Richard Jeffrey and Wcs Salmon for helpful comments on an earlier draft. 1. I will not atlcmpl