TESTING INFERENCE TO THE BEST EXPLANATION

IGOR DOUVEN TESTING INFERENCE TO THE BEST EXPLANATION ABSTRACT. Inference to the Best Explanation has become the subject of a lively debate in the philosophy of science. Scientific realists maintain, while scientific antirealists deny, that it is a compelling rule of inference. It seems that any attempt to settle this debate empirically must beg the question against the antirealist. The present paper argues that this impression is misleading. A method is described that, by combining Glymour s theory of bootstrapping and Hacking s arguments from microscopy, allows us to test IBE without begging any antirealist issues. 1. INTRODUCTION Defenses of scientific realism typically rely on Inference to the Best Explanation (IBE), a rule of inference governed by the idea that explanatory success is a (not necessarily unfailing) mark of truth. The status of this rule is unclear, however, and has been disputed by antirealists. There is certainly room for dispute, given that IBE takes us beyond what follows logically from the data and is thus not deductively valid. The rule may still be reliable, of course, in the sense that it mostly leads from true premises to true conclusions. But if a defense of scientific realism by means of IBE is meant to convince the antirealist, then pointing to the mere possibility that the rule is reliable will not do; scientific realists will have to show, or at least make plausible, that it actually is. For IBE to be reliable, there must be a positive correlation between explanatoriness and truth (or a derivative notion, such as approximate truth). Assuming a standard conception of truth, such a correlation is not apriori. Thus, if it can be done at all, the reliability of IBE must be established empirically. As will be seen below, the fact that realists and antirealists differ over what can be empirically established seems to implicate that any test of IBE must necessarily beg the question against the antirealist. My aim in the present paper is to show that this impression is misleading. I shall describe how, by combining Glymour s account of bootstrap confirmation and Hacking s well-known arguments from microscopy, we can test IBE without begging any antirealist issues. The paper is organized as follows. Section 2 scrutinizes van Fraassen s influential critique of IBE which, if it were successful, would render futile Synthese 130: 355 377, 2002. 2002 Kluwer Academic Publishers. Printed in the Netherlands.

356 IGOR DOUVEN the whole project of testing IBE. Section 3 briefly rehearses Hacking s arguments from microscopy and interprets them in terms of IBE. Section 4 starts by outlining the essential features of Glymour s theory of bootstrapping and then describes in some detail how this can be put to use in testing IBE. Section 5 anticipates and tries to answer some objections against the bootstrap test devised for IBE. 2. VAN FRAASSEN ON INFERENCE TO THE BEST EXPLANATION Above we have only roughly characterized IBE as a rule being governed by the idea that explanatoriness is truth conducive. As illustrated by the various distinct, more precise formulations one finds in the literature, the latter idea can be fleshed out in quite diverse ways. If van Fraassen is right, however, it is quite immaterial how precisely IBE is articulated. For, he claims, IBE cannot be a recipe for rational change of opinion (van Fraassen 1989, 142) whatever its exact formulation. As we shall see now, this is vastly overstated. 1 Van Fraassen first criticizes what could be called the standard or textbook version of IBE (throughout this paper IBE will be used to refer to the general idea that explanatoriness is truth conducive, and IBE to refer to the following articulation of that idea): IBE Given evidence E and potential explanations H 1,...,H n of E, infer to the (probable/approximate) truth of the H i that explains E best. Against IBE, van Fraassen (1989, 142ff) points out that in order to make this rule rationally compelling it is insufficient to assume that, in general, the H i that explains the evidence best is true, or probably/approximately true, provided the truth, or at least one approximately true theory, is among the hypotheses H 1,...,H n. For the rule to be reliable, it must be that the latter condition is always or mostly fulfilled, i.e., it must be that the truth, or an approximately true theory, is generally to be found among the hypotheses we have actually come up with. Else IBE may well lead us to believe the best of a bad lot (van Fraassen 1989, 143). Since only rarely will we have considered all potential explanations of the evidence, for that further premise to be true some sort of privilege seems required, namely that, whenever we consider possible explanations of the data, we are somehow predisposed to come up with the truth/an approximately true theory. What could justify this assumption? Van Fraassen does more than just challenge the realist to show that we are privileged in the required way;

TESTING INFERENCE TO THE BEST EXPLANATION 357 he also argues that, at least from a realist perspective, it must aprioribe rather implausible to suppose we are thus privileged (van Fraassen 1989, 144). Various authors have objected against this so-called argument of the bad lot. Instead of trying to meet the argument head-on, most of these authors have sought to reduce it to absurdity by arguing that, if it were conclusive, it would show far too much. For, they think, in that case the argument would undermine scientific realism and antirealism alike, thereby leaving no option on the table. To be a bit more specific, their claim is that only by presupposing a kind of privilege not essentially different from that which IBE seems to require can the antirealist avoid his position to issue in a blanket scepticism (cf. Devitt 1991; Lipton 1991; Kitcher 1993; Psillos 1996). Thus it appears that we must be privileged, and that even the antirealist will have to acknowledge as much, whether we are able to account for that privilege or not. However, for reasons given in Ladyman et al. (1997), I believe this strategy to be misguided and to depend on a serious misrepresentation of at least van Fraassen s brand of antirealism. 2 A more constructive response to the argument of the bad lot has been given by Lipton (1993). He believes that the challenge of showing that the truth is always or mostly among the hypotheses considered, can be met without having to assume some form of privilege. His argument turns on the possibility of generating a set of theories, given the ones we have so far thought of, that necessarily includes the truth. Suppose H 1,...,H n are all the available theories for a certain domain. Then define H n+1 as i H i (i = 1,...,n). Clearly the truth about the domain must be among the theories H 1,...,H n+1.soifibe works provided the truth is among the available hypotheses as van Fraassen is willing to concede in the context of his argument we apparently can make it work without exception. Unfortunately, this procedure for closing off the class of available hypotheses can be quite misleading. 3 For although there may be many hypotheses H j that imply H n+1 and, had they been formulated, would have been evaluated as being a better explanation for the data than the best explanation among the H i s (i = 1,...,n), H n+1 will in general be hardly informative; in fact, in general it will not even be clear what its empirical consequences are. 4 We may thus assume that qua explanation it will be ranked quite low (if it will be ranked at all, which would seem nonsensical in case it is unclear what empirical consequences it has). Hence, scientists who rely on IBE and follow this procedure may be expected to mostly decide that the truth is not to be found among the common contraries of the theories they have actually thought of. Though this may sometimes, or

358 IGOR DOUVEN even mostly, be true, the procedure evidently does not provide any warrant for such a conclusion. 5 It appears, then, that the argument of the bad lot is not easily countered. However, it is only a first step in van Fraassen s critique of IBE, and the remainder of that critique is much more problematic. In this remainder, he starts by concluding from the argument of the bad lot that, if IBE can be made to work at all, it must be in the form of a probabilistic rule akin to Bayes rule, but different from the latter in that it explicitly factors in explanatory considerations. There is in principle an infinity of such rules, but van Fraassen purports to show, by means of Lewis dynamic Dutch book argument (as reported in Teller 1973), that any such probabilistic version of IBE must be incoherent. Thus his conclusion that there cannot be a viable rule of inference based on explanatory considerations. But, first, elsewhere I have tried to explain that the question whether or not a probabilistic rule whether Bayes rule or another is coherent, is not a question that can be answered independently of considering what other epistemic and decision-theoretic rules are accepted along with it; coherence is a property that pertains to packages of such rules, not to rules for belief change in isolation (cf. Douven 1999). I there also describe a coherent package of rules including a probabilistic version of IBE. 6 Secondly, though IBE can be given a (coherent) probabilistic formulation, it does not follow from the argument of the bad lot that it must be given such a formulation. That would only be so if it had been shown that that argument undermines each and every version of IBE not of that sort. And van Fraassen has not done so. In effect, van Fraassen could not have shown this, for there exist many non-probabilistic versions of IBE clearly invulnerable to the argument of the bad lot. This argument capitalizes on a peculiar asymmetry in IBE.The rule gives license to an absolute conclusion that a given theory is true on the basis of a comparative premise, viz., that the particular theory is the best explanation of the evidence relative to the other theories available (cf. Kuipers 2000, 171). There are two immediate ways to avoid this asymmetry: One can have the rule require an absolute premise, 7 or have it sanction, given a comparative premise, only a comparative conclusion. Both these options can in turn be realized in more than one way. The resulting symmetric versions of IBE, whatever their exact formulation, will not require the assumption of an implausible privilege on our part that IBE requires. Of course the argument of the bad lot would still be significant if it turned out that the versions of IBE obtained by following any of the justmentioned strategies were too weak to serve realist purposes. Although in

TESTING INFERENCE TO THE BEST EXPLANATION 359 that case the argument would still fail to cast doubt on the general possibility of there being a reliable non-probabilistic rule of IBE, it would cast doubt on the possibility of there being a reliable non-probabilistic version of IBE that could be of help to the realist. However, while not every possible symmetric version of IBE may suffice for the realist, some certainly do. By way of proof, let me quickly demonstrate this for one particular symmetric version of IBE, to wit: IBE* Given evidence E and potential explanations H 1,...,H n of E, if H i explains E better than any of the other hypotheses, infer that H i is closer to the truth than any of these others. 8 It is not hard to see that IBE* in any case allows us to hold on to a position interestingly stronger than van Fraassen s constructive empiricism. According to van Fraassen (1980, 12), science aims to give us not true but merely empirically adequate theories, i.e., roughly, theories true of the observable part of the world. 9 Now, it may be that aiming at truth is too ambitious a goal, but if IBE* is a reliable rule of inference, then we are definitely underplaying our hand if we aim no higher than at empirical adequacy. For if IBE* is reliable, then the goal that is minimally within the reach of science is to bring us ever closer to the truth, even on a theoretical level (I am assuming that in general scientists are able to think up hypotheses explanatorily superior to the one(s) already available). Quite clearly, this is a weaker position than scientific realism as it is commonly characterized; commonly scientific realists claim that we have good reason to believe that contemporary scientific theories are (approximately) true, not just that they are closer to the truth than their predecessors were (which does not imply that the former are close to the truth at all). But those realists not satisfied with the just-mentioned convergent realism, should not immediately despair if it turns out that no stronger version of IBE than IBE* can be coherently maintained; it may well be possible to defend a full-blooded scientific realism by means of IBE*, too. As a moment s reflection shows, this rule licenses an inference to the unqualified truth of the absolutely best or perfect explanation. That is to say, if one is sure that, however many other potential explanations for the data may have gone unconsidered, none can equal the best of those that have been considered, then it makes no difference whether one applies IBE or IBE*. (Of course the same holds if one is sure that the truth is among the available hypotheses.) Consequently, if one is able to show that full-blooded scientific realism is a perfect explanation for the observed predictive accuracy of science or the success of scientific methodology or whatever (i.e., that no unborn hypothesis can even equal scientific realism as an explanation for these

360 IGOR DOUVEN facts), then it suffices to show that IBE* is a reliable rule of inference in order to defend the stronger version of scientific realism as well. 3. HACKING S ARGUMENTS FROM MICROSCOPY Many of us feel an intuitive tension between results from twentieth-century microscopy and an antirealism such as van Fraassen s, according to which our epistemic access is restricted to that part of reality that can be observed with the unaided senses. Thus Miller (1987, 465) urge[s] anyone who thinks disbelief in unobservables is always a rational option to get a microscope and acquire data. And Giere (in Callebaut (ed.) 1993, 171) thinks that in order to see that antirealism is just bizarre, we only have to look at electron microscope pictures of chromosomes, of DNA we have pretty nice pictures of DNA. But an intuitive tension is no argument, and it seems that an argument is required if the antirealist is to concede that we have pretty nice pictures of DNA. In his (1981), Hacking proffers two arguments from coincidence for the more general claim that what we see through certain types of microscopes is veridical, i.e., that the entities apparently disclosed by these instruments are there as imaged (136) and not artifacts. Hacking s first argument points to the fact that when we study blood cells both by means of a low-resolution electron microscope and by means of a fluorescent microscope, the visual outputs we get from these microscopes are typically very similar. This, Hacking claims, gives reason to believe that these outputs reveal real structures, for It would be a preposterous coincidence if, time and again, two completely different physical processes produced identical configurations which were, however, artefacts of the physical processes rather than real structures in the cell (1981, 144f). The second argument the argument of the grid uses another example from the practice of microscopy. In this practice, tiny metal grids are used to fix upon whatever it is that is being studied. These grids are produced by photographically reducing large-scale line drawings, and then depositing metal on the reduced lines. When one looks at the result of this process through a microscope any kind of microscope one sees exactly the grid that was drawn with pen and ink. To entertain the thought that the large scale grid was shrunk into some non-grid which when viewed using 12 different kinds of microscopes still looks like a grid one must, Hacking says, believe in a gigantic conspiracy of 13 totally unrelated physical processes (1981, 147). Thus he concludes: To be an antirealist about that grid you would have to invoke a malign Cartesian demon (ibid.). 10

TESTING INFERENCE TO THE BEST EXPLANATION 361 Hacking is well aware that there is a prima facie similarity between these arguments and the explanationist defenses of scientific realism that all claim that, unless scientific realism is true, we must believe that the success of science and/or of scientific methodology is due to an enormous coincidence (cf., for instance, Putnam 1975; Boyd 1981; 1984). However, according to Hacking, his arguments, unlike those defenses of scientific realism, do not depend on IBE. With respect to the example of the blood cells, he says that it is no explanation of this to say that some definite kind of thing... is responsible for the persistent arrangement of dots (1981, 146). But to this Reiner and Pearson (1995, 64) object that, still, it is an explanation of the observed phenomena to say whether those phenomena are due to a real entity, or to an artifact. Other commentators have been equally unwilling to accept Hacking s contention that his arguments do not rely on IBE (cf. van Fraassen 1985, 298; Devitt 1991, 112). I do not want to suggest that there is no room for other interpretations of Hacking s arguments. 11 If these arguments can succeed without reliance on IBE or any other inferential principle which is controversial in the eyes of the antirealist, then so much the better for realism. What I want to show in the next section is that, if as I suspect Hacking s critics are right that his arguments from coincidence are essentially IBE arguments, they can still play a decisive role in the realism debate (though one might suppose that in that case they cannot, given that one of the parties to the debate does not accept IBE). Two comments before we turn to our test: The hypothesis that modern microscopes are veridical is certainly not the only explanation for the data cited in Hacking s arguments. For instance, another explanation for the fact that through our microscopes we see the grid exactly as it was earlier drawn, is that in the process of producing the grid, the grid structure gets distorted but aberrations of the microscopes compensate for this. Contrary to what Hacking implies, this is not necessarily an appeal to a Cartesian demon; the explanation might be given some plausibility by telling a story about the various instruments involved having a history of co-calibration (Seager 1995, 462; cf. also van Fraassen 1985, 298). But if we agree with Lipton (1991, 63) that the best explanation is the loveliest one, i.e., the one that, overall, does best on such criteria as simplicity, informativeness, and elegance (Lipton 1991, 71, 114 122), then, I submit, it is undeniable that the hypothesis that our current microscopes are veridical furnishes the best explanation for the data Hacking reports. In fact, it seems that there can hardly be a lovelier explanation for those data. If this is correct, then Hacking s arguments establish that the various modern types of microscopes are veridical not only relative to IBE but also relative to IBE*.

362 IGOR DOUVEN (One might object that explanatory loveliness is a subjective notion, and that in particular the foregoing judgement of what constitutes the best explanation in the cases at hand may only receive acclaim from realists. Note, however, that this is not a problem if one seeks to investigate the reliability of IBE empirically, as we do. Even if the objection is correct insofar as it claims loveliness to be subjective, 12 it merely shows that the question that needs answering is this: Is there a correlation between truth or relative truth-closeness and explanatory loveliness, where the latter is understood as loveliness by realist lights?) The second comment concerns a terminological point. For van Fraassen, observable strictly applies to what can be seen with the naked eye. It might therefore cause confusion if we said that it follows from Hacking s arguments (relative to certain versions of IBE) that through the introduction of certain instruments the realm of the observable has been extended, for, clearly, it is not true that because of these instruments more things have become observable to the naked eye. A better way of putting the conclusion of these arguments, I suggest, is to say that what is and what is not observable with the naked eye marks, pace van Fraassen, no significant epistemological distinction; we are justified in treating at least what we see by means of our microscopes as being epistemically on a par with what we see with the unaided eye. Or, equivalently, we can say that, if correct, Hacking s arguments show that if it wasn t already, then part of the unobservable has become epistemically accessible due to advances in microscopy. 4. BOOTSTRAPPING INFERENCE TO THE BEST EXPLANATION We seem to face an insurmountable difficulty when it comes to empirically evaluating IBE. Evidence for the reliability of this rule will have to consist of successful applications of it, that is, applications that led us to accept (approximately) true theories or, in case we are testing IBE in the version IBE*, applications that led us to choose theories that were closest to the truth, relative to the rivals these theories had at the moment they were chosen. Note, now, that for each version of IBE, there is a weaker, empiricist 13 variant that reads just like it but has an empirically adequate theory or the observational truth where the former has the truth (e.g., infer that the best explanation is empirically adequate, or infer that the best explanation is closer to the observational truth than any of the available alternative hypotheses cf. Fine 1991, 83). To test some version of IBE, then, it will not do to point to successful applications that only involved observables (so the, in this context, oft-cited example of

TESTING INFERENCE TO THE BEST EXPLANATION 363 the discovery of Neptune is of no help). In order to be able to distinguish between a realist version of IBE and its empiricist variant, that is, in order to establish that, if some version of IBE is reliable, it is really the realist reading of it, and not just its attenuated variant, that is reliable, we must be able to determine whether particular applications of that version of IBE led to theories that are (to some extent) true at a theoretical level, or whether they just led to theories that are (to some extent) empirically adequate. But how are we to show, in a way that does not already presuppose realism, that a theory is indeed true, or closer to the truth than its rivals, or whatever the given (realist) version of IBE says it is, and not merely empirically adequate casu quo closer to the observational truth than its rivals? Using at this point IBE to infer a theory s truth from its instrumental success would obviously render the test circular. And if there were some rule other than IBE that would permit us to make the mentioned inference, then it is hard to see why there should still be a call for IBE. Thus, it seems there can be no evidence of the required sort that does not beg the question against the antirealist. 14 It is tempting to think that Hacking s just-considered arguments offer a way out of this seeming impasse. Suppose for the nonce that the antirealist can be convinced of the conclusion of these arguments. We then can all agree that in the recent history of science, there have occurred shifts in the boundary between what is and what is not epistemically accessible. But in that case there certainly can be evidence of a non-question-begging sort that is specific enough to discriminate between, on the one hand, the realist versions of IBE and, on the other, their empiricist counterparts. For instance, suppose that at a certain point in the history of science, hypothesis H was accepted because it was judged to offer the best explanation for certain phenomena by postulating a particular, unobservable mechanism, and suppose further that, thanks to a boundary shift that has occurred in the meantime, we have gained epistemic access to part of the unobservable sufficient to confirm that H is not just instrumentally reliable but also (approximately) true a mechanism underlies these phenomena which closely fits H s description of the underlying mechanism or that H is closer to the truth about the underlying mechanism than any of the hypotheses it competed with. Clearly, such a discovery would distinctively lend support to IBE casu quo IBE*. We could thus test IBE by searching in the history of science for evidence of the kind described, i.e., by searching for cases where (i) in the history of science a hypothesis was accepted because it was deemed to be the best explanation of the then available potential explanations, and (ii) we are now able to ascertain by means of some of our

364 IGOR DOUVEN microscopes whether the hypothesis is approximately true, casu quo closer to the truth than the other potential explanations. The suggestion that boundary shifts of the kind described may bear on the realism debate is neither a surprising nor an original one. For instance, Harré (1986; 1988) argues for his own type of realism by pointing to a number of examples of entities that were once postulated on purely theoretical grounds and that, due to technical advances in scientific instrumentation, later were (allegedly) discovered to exist. Bird (1998) even explicitly relates the relevance of such technical advances to an empirical justification of IBE. To the problem noted in the first paragraph of this section that we can only check the reliability of IBE in cases in which the conclusion is strictly about observables he responds as follows: This would be a powerful argument [against the possibility of an empirical vindication of IBE] if that which was once unobservable remained thus evermore. But that is not the case. Inferences to the existence of unobservables have later been verified by direct observation once observational techniques have improved. We can now observe microbes and molecules, the existence of which was once a purely theoretical, explanatory hypothesis. (Bird 1998, 160) However, that the boundary between the epistemically accessible and the epistemically inaccessible is historically contingent, is something both Harré and Bird take entirely for granted. The antirealist cannot be expected to follow suit. But so far I can hardly claim to have done better than Harré or Bird. I have only pointed out how IBE can be tested in a non-questionbegging way provided the antirealist can be convinced of the conclusion of Hacking s arguments. But as we saw, Hacking s arguments may well themselves hinge on IBE. So it seems that to become convinced of their conclusion one must already believe that IBE is a reliable rule of inference, which, of course, the antirealist does not. Apparently, we are still at an impasse. Here, Glymour s (1980a) theory of bootstrap confirmation may come to the rescue. This theory has been widely discussed in the past two decades. It will therefore suffice to rehearse its core idea, passing over the details. 15 We have long been familiar with the fact that evidence generally accrues to a hypothesis only relative to one or more auxiliaries. Hence the basic confirmation relation is necessarily a relativized, ternary one: Evidence E confirms hypothesis H with respect to theory T.However,whatGlymour in his book argues is that the indispensability of auxiliaries in testing hypotheses by no means impedes absolute, unrelativized confirmation; under certain conditions, we can go from relative to absolute confirmation. Schematically, the core idea of his new theory of confirmation can be put as follows. Let T ={H 1,...,H n }, and suppose that for each H i T there

TESTING INFERENCE TO THE BEST EXPLANATION 365 are H j1,...,h jk T such that (1) evidence E confirms H i with respect to H j1,...,h jk, 16 and (2) there are possible data E that would, were they actual, disconfirm H i with respect to H j1,...,h jk. Then not only does E confirm T with respect to T, bute confirms T, period. As Glymour (1980a, 127) explains, the second condition is meant to ensure that assuming certain hypotheses in T in testing some (other) hypothesis in T does not guarantee that the latter is confirmed whatever the data and thus that the test is not trivial (we shall hence call (2) the nontriviality condition). Observe that this gloss actually suggests that we can make do with a somewhat weaker condition than (2) (or than the corresponding condition iv of Glymour s (1980a, 130f) formal presentation of the bootstrapping idea). For the gloss only seems to demand that there be possible evidence such that, were it actual, it would not confirm the hypothesis under investigation relative to the auxiliaries taken from the same theory, not that there be possible disconfirming evidence for the hypothesis. Nevertheless, in the following we will assume condition (2) as stated above. Before putting Glymour s account to use in a test for IBE, let me by means of a still rather abstract example elucidate that account a bit further. 17 The example displays the various steps involved in obtaining a positive bootstrap test result for a theory that (just as the theory involving IBE to be described below) consists of two hypotheses, H 1 and H 2, from data D: 1. D confirms H 1 relative to H 2. 2. D confirms H 2 relative to H 1. 3. D confirms H 1 & H 2 relative to H 1 & H 2. 4. D confirms H 1 & H 2. Here we have a positive bootstrap test for H 1 & H 2 from D provided there are possible data D which disconfirm H 1 relative to H 2 as well as possible data D which disconfirm H 2 relative to H 1 ; only if this non-triviality condition is met is the step from 3 to 4, i.e., the step from merely relative confirmation to absolute confirmation, legitimate. 18 How exactly can we apply all this in order to test IBE? Consider the theory T ={V,R},whereV and R are the following hypotheses: V What we see through our microscopes is veridical. R IBE/IBE* 19 is a reliable rule of inference. In the previous section, we saw that the data cited in Hacking s arguments from microscopy confirm V with respect to R. And if the advocates of IBE are lucky, historical research will furnish data which confirm R with respect to V. Hence, in that case, jointly the data confirm T with respect

366 IGOR DOUVEN to T itself. If it can then be shown that neither the assumption of R in testing V nor the assumption of V in testing R trivializes the respective tests, it may be concluded, following Glymour s bootstrapping account of confirmation, that the data confirm T. But it is easy to show that in both tests the non-triviality condition is met. The occurrence of very dissimilar visual outputs in the cases referred to in Hacking s first argument and/or the observation of something quite unlike a grid in his second argument would have disconfirmed V relative to R. There is no incompatibility between the occurrence of such observations and the assumption that IBE/IBE* is a reliable rule of inference. So, assuming R in testing V does not trivialize the test. Similarly, the assumption that certain types of microscopes are veridical does not and cannot guarantee that we will find in the history of science that theories that at one point were accepted as providing the best explanation for the evidence available at that time, mostly gave a better description of what was later revealed (as, given the auxiliary, we may say) by means of a microscope than any of the competing theories deemed to be explanatorily inferior. Surely if V is assumed, then we are (temporarily) committed to the claim that at least all those entities figuring in contemporary theories exist that can apparently be seen by means of modern microscopes. However, that does not preempt the question whether or not these entities were once introduced for theoretical reasons. Indeed, historical research might reveal that, for instance, most entities now accepted in microbiology have their place in our theories because they were detected (or believed to be detected) by working microscopists, and that many of the putative entities that were postulated by biologists before, say, the electron microscope became available were later discarded when data obtained by means of microscopes implied (or seemed to imply) that entities of a sort quite different from those earlier postulated are responsible for the phenomena the latter were thought to explain. In short, depending on what the historical data are, it will be possible to confirm (or disconfirm) T, i.e., it will be possible to confirm, in tandem, the hypothesis that our microscopes are veridical and the hypothesis that IBE is reliable. 20 5. ANTICIPATED OBJECTIONS I have suggested a method for testing a theory comprising the hypothesis that IBE is a reliable rule of inference in a way that I claimed to be non-question-begging. But I expect there to be objections to this test and, especially, to the latter claim. I shall now turn to these and begin

TESTING INFERENCE TO THE BEST EXPLANATION 367 by considering some general worries related to the use the test makes of bootstrapping. 5.1. The Proposed Test is of Limited Significance at Best, for it Relies on Bootstrapping, a Theory that is of Doubtful Standing One evidently cannot find the outcome of the test whatever it may be more telling than one finds Glymour s theory plausible. And that theory has, admittedly, been severely criticized. This is not the place to defend bootstrapping against every assault on it to be found in the literature. Yet I do want to stress that most of the critique it has received appears to have been evoked by what, at bottom, is only an accidental feature of the theory s original exposition. Glymour originally presented his theory as an emendation of Hempel s positive instance account of confirmation. One presumption his theory, as initially presented, borrowed from the latter was that confirmation relations can be characterized purely syntactically. Arguably, the vast majority of the objections that have been levelled against Glymour s theory are either directly or indirectly concerned with showing that the foregoing presumption is false. However, since bootstrapping is not tied to a Hempelian format, 21 these objections do not really affect the theory s core idea as sketched in the previous section. In fact, it seems that so far no reasons have been put forward to doubt this idea. Of course, someone might still be able to show that the theory is fundamentally wrong. But until then, there are no grounds for doubting the significance of the presented testing procedure for IBE. 5.2. Glymour (1980, 76f, 140) Emphasizes the Importance of Testing Each Hypothesis of a Given Theory in a Variety of Ways. And in the Case of V and R it is Not Clear that there are Ways Other than the One Described in the Previous Section in which They Can be Tested, or at Least None that Do Not Beg Antirealist Issues Testing in a variety of ways is supposed to guard against spurious confirmation, which may arise from the fact that in testing one hypothesis with respect to another an error in one may compensate for an error in the other. Though I do not want to contest this point, variety of testing cannot be a requirement for confirmation. First, confirmation is not verification: Bootstrap confirmation of a hypothesis may give reason to believe the tested hypothesis, even if it does not exclude the falsity of the hypothesis (if not, then most or all of the examples of bootstrap confirmation Glymour gives in his book fail to be genuine examples of such confirmation). Second, testing a hypothesis in as many ways as we like will not rule out the possibility that the hypothesis is false: All hypotheses involved may be

368 IGOR DOUVEN false yet compensate for each other s errors. That testing a hypothesis in a variety of ways can possibly give more reason to believe the hypothesis than if it is tested in just one or two ways is quite another matter. So, while it must be recognized that we would be better off if there were more ways of testing V and R than the one outlined above, this does not mean that no significance should be given to a result obtained from our test. 5.3. The Proposed Test for IBE Presupposes the Reliability of IBE, and Thus Is Circular Let me start by noting that the worry that the test is circular is more than understandable. The test builds on arguments each of which has a premise the antirealist flatly denies: Hacking s arguments assume on our reading of them the reliability of IBE; the shifting boundary argument for the reliability of IBE (hinted at by Bird, among others) assumes that modern microscopes are veridical. It now may seem that only by a miracle could a combination of these arguments not be question-begging. Yet I have claimed that in effect only Glymour s theory of confirmation is needed to avoid circularity (or perhaps I should say that Glymour s theory can make miracles happen). Exactly how bootstrapping helps avoid circularity is brought out nicely by our schematic example of a positive test result for the theory consisting of hypotheses H 1 and H 2 given in the previous section. In that example, bootstrapping is clearly seen to act as a kind of mechanism for discharging assumptions. In step 3 of the example we still only have a case of relative confirmation, because we still have two uncancelled premises. Thus at that stage the test is not telling for anyone who does not already accept both H 1 and H 2. But the bootstrap step from 3 to 4 shows that we do not have to end up with relative confirmation; under certain circumstances (namely, if the non-triviality condition is met) we can cancel exactly those assumptions that make 3 a case of relative confirmation only, and thereby obtain absolute confirmation of our hypotheses. Put differently, under certain circumstances the sub-tests carried out in steps 1 and 2 take in each other s wash. Now someone who at the beginning of the test is unwilling to accept H 1 and/or H 2 cannot dodge the test s conclusion by arguing that it relies on assumptions he or she does not accept: These assumptions have been cancelled! In the particular case of our test for T there seems to be a more concrete and easier way to see that the charge of circularity is misguided. If the reliability of IBE were really presupposed in that test, then R would have to follow from the test even without the fieldwork in the history of science having been carried out. But this is clearly not the case. In fact, nothing in the way the test has been set up makes it even likely that IBE will

TESTING INFERENCE TO THE BEST EXPLANATION 369 be vindicated. For what it s worth, my own prior for finding confirming evidence for IBE is roughly equal to my prior for finding disconfirming evidence for it. But this response is too quick, for it leaves open the possibility that the test is what Psillos (1999, 82), following Braithwaite, calls rule-circular (as opposed to premise-circular). The foregoing only shows that IBE is not assumed as a premise in the test (i.e., that the test is not premise-circular). But it could still be rule-circular by using IBE to derive a conclusion (about the reliability of IBE) from the premises. Psillos makes a case for rulecircularity; according to him it is, unlike premise-circularity, not vicious. While that may be correct, this discussion is irrelevant to our test, for that is neither premise- nor rule-circular. Where in the test could IBE be used? If historical research yields the data the friends of IBE hope for, then one might argue that our theory T is true because it constitutes the best explanation for those data in conjunction with the data Hacking s arguments mention. But this is certainly not part of the test proposed in this paper. We can assess T in the light of the data using any confirmation theory to which bootstraps can be consistently attached, like for instance Hempel s theory or Bayesian confirmation theory. 22 The only other place where the use of IBE might be suspected is the part of the test concerned with testing V. But here R, saying that IBE is reliable, is merely assumed as an auxiliary. From R it then follows deductively that in general the best available potential explanation for the data is true (/approximately true/closer to the truth than other available potential explanations/...)(foribecanonlybereliableifthebestexplanationis,in general, true or... etc.). From this in turn it follows again logically that V, being the best or even the perfect explanation for the data in Hacking s arguments, is (very likely) true. Thus each of the steps can proceed purely deductively; at no point need IBE be used. 23 5.4. One of the Main Advantages Glymour Claims his Theory to Have over Hempel s Theory of Instance Confirmation is that the Former Allows the Confirmation of Theoretical Hypotheses, Something that Was Not Possible on the Latter Account. But then It Seems that by Using Bootstrapping to Test IBE We Have Already Smuggled in Realism. If So, Our Test Evidently Begs the Question against the Antirealist As van Fraassen already in his (1980, 221f) remarks, there is nothing essentially realist in Glymour s theory. More precisely, according to him bootstrapping itself is entirely neutral with respect to the question whether a positive test result should be interpreted realistically i.e., as giving

370 IGOR DOUVEN reason to believe the tested theory or antirealistically, i.e., as only giving reason to believe in the theory s empirical adequacy. 24 And thus using Glymour s bootstrapping theory does not automatically bring on board scientific realism. 5.5. But the Answer to the Previous Objection Seems to Suggest that, without Begging the Question against van Fraassen, Our Bootstrap Test Can at Most Provide Support for the Theory that Says that both V and R are Empirically Adequate This is not so. As is clear from van Fraassen s discussion of Glymour s theory, his reasons for believing that bootstrap testing cannot properly confirm hypotheses but only give reason to believe in their empirical adequacy have nothing special to do with Glymour s theory itself, but are simply his general reasons for believing that truth can never be warrantably attributed to theories beyond their observational consequences. That is to say, these reasons stem entirely from the well-known argument from underdetermination: Given that (i) each scientific theory has empirically equivalent rivals, and that (ii) in determining whether some theory is true or not we have only its empirical consequences to go on, we are never in a position to say whether a theory is true. However, as various critics have noted, if premise (ii) is assumed without argument, it begs the question against the realist, who believes that other factors besides empirical fit most notably, explanatory power can help determine the truth-value of a theory. 25 Clearly, van Fraassen s critique of IBE discussed in section 2 purports to undermine the latter realist tenet, and thereby to buttress (ii), but we have seen that it fails to do so. So, at this stage in the debate the antirealist can at most challenge the realist to show that explanatoriness is indeed a mark of truth (or relative truth-closeness). And the test outlined here is explicitly devised to meet this challenge. It may well fail, or someone may still be able to show a priori that premise (ii) is true, but van Fraassen cannot now object to our test on grounds related to his argument from underdetermination. 6. CONCLUSION This paper has argued that, appearances to the contrary notwithstanding, IBE can be tested in a fashion that does not beg any antirealist questions. Can anything concrete be said about what outcome a test as proposed can be expected to have? Without speculating, we can only note the following. The argument of the bad lot gives us aprioriscant reason to expect IBE to work. But note, first, that the argument does not show that the rule

TESTING INFERENCE TO THE BEST EXPLANATION 371 could not possibly work. Hence empirical investigation may show that it works after all. Of course if it does, we are not thereby able to explain how we hit (mostly) upon the true hypothesis casu quo an approximately true hypothesis, as in that case we apparently would. But that is another matter: We may be privileged even if it currently is rather implausible to believe we are. Secondly, and more importantly, from van Fraassen s argument nothing follows for what were called symmetric versions of IBE, such as IBE*. For the latter, it was seen explicitly that it is strong enough to defend (some version of) scientific realism. Quite clearly, nothing said here gives any guarantee or even an indication that testing IBE, in whatever version, will pay off for the realist. My aim, however, was more modest, namely to show that IBE is testable. And I hope to have shown that it is. ACKNOWLEDGEMENTS I owe a great debt to Theo Kuipers, who provided extensive comments on several earlier versions of this paper, and saved me from a number of serious mistakes. I am also indebted to Dennis Dieks, Ernan McMullin, Stathis Psillos, Jaap van Brakel, Bas van Fraassen, and two anonymous referees for this journal for helpful comments on previous versions, and to Otávio Bueno, Henk de Regt, Leon Horsten, Hans Koeze, James Ladyman, and Uskali Mäki for helpful discussions on the subject matter of this paper. Versions of this paper were presented at the 2000 annual BSPS conference held in Sheffield and at the Universities of Amsterdam (Free University), Nijmegen, and Rotterdam; I am grateful to the audiences for critical questions and remarks. NOTES 1 I will only be concerned with van Fraassen s critique specifically directed at IBE. It should be noted, however, that van Fraassen also has a more general argument for the claim that explanatory considerations cannot have any positive epistemic import. But although Lloyd (in Callebaut (ed.) 1993, 178) calls it the key problem that van Fraassen raises for realism (which according to her no one in any of the thousands of varieties in the realist camp has even dealt with ), this more general argument seems not hard to rebut. The argument starts from the premise that it is part of the meaning of explanation that if one theory is more explanatory than another, the former must be more informative than the latter (cf. in particular van Fraassen 1983b, Sect. 2). Now according to van Fraassen it is an elementary logical point that a more informative theory cannot be more likely to be true [and thus] attempts to describe inductive or evidential support through features that require information (such as Inference to the Best Explanation ) must either contradict themselves or equivocate (1989, 192). The elementary logical point, he claims, is most

372 IGOR DOUVEN [obvious]... in the paradigm case in which one theory is an extension of another: clearly the extension has more ways of being false (1985, 280). However, the problem with this argument is that in any other kind of case the elementary point is not obvious at all. In particular, it is not obvious in the kind of case in which appeal to explanatoriness as a factor of theory appraisal seems to be crucial to the realism issue, that is to say, it is not obvious in those cases in which we are confronted with empirically equivalent rivals. For instance, it is entirely unclear in what sense Special Relativity has more ways of being false than Lorentz version of the æther theory (which is inconsistent with, yet demonstrably empirically equivalent to, SR). And yet it seems that SR is superior, qua explanation, to Lorentz theory. (If van Fraassen were to object that SR is not really more informative than Lorentz theory, or at any rate not more informative in the appropriate sense whatever that is then we should certainly refuse to grant the premise that in order to be more explanatory a theory must be more informative.) See Leeds (1994, Sect. 2) for an excellent discussion of van Fraassen s general argument against explanatoriness as a confirmational virtue. 2 See Psillos (1999, Ch. 9) for a response. I reply to this in my (2001). 3 There is also a formal difficulty, namely that, unless each H i is finitely axiomatizable, i H i is not well-defined. It must be noted, however, that this problem does not arise on a model-theoretic conception of theories; H n+1 in that case stands for the complement of the union of H 1,...,H n, where the latter are to be identified with classes of models or possible worlds. 4 In a Bayesian setting, the fact that the conjunction of the negations of the actually formulated hypotheses (or the catch-all, as Bayesians use to call it) is in general, in Salmon s (1990, 275) words, a hypothesis only in a Pickwickian sense, leads to a problem very similar to the one discussed in the text, namely that of the utter intractability of the likelihood [of the evidence] on the catch-all (ibid.). 5 Interestingly, the argument of the bad lot, Lipton s response to that, as well as the present response to Lipton are, in a very rudimentary form, already to be found in van Fraassen (1980, 21f). 6 See Kvanvig (1994), Harman (1997), Leplin (1997), Niiniluoto (1999), and Okasha (2000) for different responses to van Fraassen s critique of probabilistic versions of IBE. 7 For instance by following Musgrave (1988, 239) or Lipton (1993, 96) and require the hypothesis to the truth of which is inferred not only to be the best of the available potential explanations, but also to be satisfactory (Musgrave) or good enough (Lipton); see also Psillos (1999, 79). 8 IBE* is roughly equivalent to a rule proposed and defended by Kuipers; see for instance Kuipers (1984), (1992), (2000). The reason I pick out this rule is that, to the best of my knowledge, it is the only symmetric version of IBE that has been not only suggested but also elaborated in the literature; in his work, Kuipers not only investigates the logical properties of IBE* in some detail, but he also supplies it with a worked-out account of explanation and a detailed analysis of the notion of being closer to the truth (cf. Niiniluoto (1998) for a critical survey of this and other analyses of truth-approximation that have been proposed during the past decades). A feature of IBE* that Kuipers emphasizes and that it is worth mentioning here is that this rule, unlike IBE, also applies to theories that have already been falsified. See for a discussion of Kuipers rule also Zwart (2001) and Douven (2002). 9 Cf. van Fraassen (1980, 1989), and Bueno (1997) for more formal definitions of the notion of empirical adequacy. For more general discussions of van Fraassen s position and