1. Introduction

A recently fashionable claim in philosophy of science is that the realism/anti-realism debate ought to be dissolved rather than solved. There is a feeling that the debate is not entirely well-formed, that the disputants are speaking past one another. Motivating this view, Blackburn writes:

He then argues that, when clearly stated, a “surprising ‘quietism’ or pessimism about a metatheoretical position begins to seem attractive” (Reference Blackburn2002, 111). In explaining the success of some piece of science, there is no “getting behind the explanation,” he writes; the best explanation for the success of the hypothesis that the world is round is that the world is round. There is no “further set of data about science (its success) that required something like an independent, sideways explanation” (Reference Blackburn2002, 130). Maddy draws a similar conclusion, urging that we not “add extra-scientific standards of justification to our repertoire” (Reference Maddy2001, 47–48). Adding these extra-scientific standards yields nothing but dead-end debates over realism. Though distinct, Maddy and Blackburn's positions are both descendants of Fine's well-known attempt to dissolve the realism debate (Reference Fine and Leplin1984).

The issue may be clarified by distinguishing what we call retail arguments for realism (arguments about specific kinds of things such as neutrinos, for instance) from wholesale arguments (arguments about all or most of the entities posited in our best scientific theories). Wholesale arguments promise a conclusion that applies to all mature science. Wholesale realism seeks to explain the success of science in general; wholesale anti-realism seeks to explain the history of science in general. Dissolving the debate, we suggest, involves attending to the retail arguments without trying to settle the debate in an all-or-nothing, wholesale manner. Dissolvers want us to answer the question, ‘Are there atoms?,’ by referring to the same evidence scientists use to support the atomic hypothesis; e.g., Einstein and Smoluchowski's Brownian motion theory and the experiments by Perrin in 1908. But they do not want us to answer by appealing to this as an instance of a more general claim, namely, that the theory and experiment of Einstein, Smoluchowski, and Perrin are part of a mature science and the posits of mature science are generally true. We sympathize with potential dissolvers of the realism debate, inasmuch as it concerns wholesale arguments. However, the exact reasons for being a dissolver are often unclear. Why exactly are questions like ‘What explains the reliability and success of science?’ taboo? That it remains unsolved is not a sufficient reason to think that a philosophical problem is illegitimate or even insoluble. We ask and answer plenty of similar questions: ‘Is this mathematical modeling technique reliable?’ ‘What explains the success of bright silver fishing lures?’ ‘Is the eye generally reliable?’ One is left wondering when to solve and when to dissolve.

Here we are concerned to provide a clear reason for believing that the wholesale realism debate should be dissolved, a reason that does not rely on contentious claims about the nature of truth, the status of normative epistemology, and what-have-you.Footnote ¹ We hope that our analysis explains what dissolvers find objectionable—that some debates about scientific realism amount to adamant, futile table thumping—without the baggage of some of their epistemological analyses. We do this by considering the two most powerful wholesale arguments in the literature, the no-miracles argument for scientific realism and the pessimistic induction for anti-realism. The former has been dubbed the “ultimate argument” for realism, and anti-realists from Duhem through Laudan have relied primarily on the latter. Worrall (Reference Worrall1989) recently billed these two arguments as the main considerations for and against realism. They pull in opposite directions with comparable, perhaps even balanced, force. Yet Colin Howson and Peter Lewis have independently suggested that these arguments embody a familiar, seductive fallacy. Howson (Reference Howson2000, 52–54) makes the point about the no-miracles argument;Footnote ² Lewis (Reference Lewis2001) about the pessimistic induction. Interestingly, neither applies the point to both arguments. With each argument we are tricked by a base rate fallacy. If this is correct and the intuitions marshaled by argument are phantoms of that fallacy, then there is much sound and fury in debates over realism that signifies nothing.

In this paper we appeal to the arguments of Howson and Lewis and use them as part of an explanation for why the two most prominent wholesale arguments in the literature seem irresolvable. Though the formal reconstruction of these arguments is artificial in various respects, reconstructing the arguments this way allows us to see a crucial flaw in both. In particular, framed as Howson and Lewis would have it, we can see very clearly why realists and anti-realists have been talking past one another. We then formulate a dilemma for advocates of either argument, answer potential objections to our criticism, discuss what remains (if anything) of these two major arguments, and then speculate about a future philosophy of science freed of these two arguments. In so doing, we connect the point about base rates to the wholesale/retail distinction; we believe it hints at an answer of how to distinguish profitable from unprofitable realism debates. In short, we offer a probabilistic analysis of the feeling of ennui afflicting contemporary philosophy of science.

2. The No-Miracles Argument

Some scientific theories are astonishingly successful. Classical thermodynamics has made correct predictions about all manner of substance for almost two centuries; meanwhile, quantum electrodynamics successfully predicts an electron's magnetic moment to more than one part in a billion. The no-miracles argument claims that if these theories did not latch on to the world in some way—that is, if they were not approximately true—then this success would be nothing short of miraculous. Some theories are too good not to be true.

The argument might be formalized in this way: For any theory x, let Sx stand for the expression ‘x is successful’ and let Tx stand for the expression ‘x is true.’ Let ¬A be the negation of A and let Pr(A∣B) be the probability of A conditional on B. We may now gloss the argument in this way for some current theory: [1] The theory h is very likely successful. [2] If h were true, it would be very likely to be successful. [3] If h were false, it would not be likely to be successful. [4] Therefore, there is a high probability that h is true. Formalizing this version of the argument yields:

For instance, assume the values .9, .95, and .05 for Pr(Sh), Pr(Sh∣Th), and Pr(Sh∣¬Th) respectively; then, Pr(Th∣Sh) = .997. The reconstruction is crude, but it is sufficient to frame much of the action surrounding no-miracles reasoning. One can, as Howson (Reference Howson2000, 45) does, complain that it is silly to think that there is a well-defined outcome space, probability distribution, etc. We sympathize but do not want to decide the matter on a technicality. One can also, as Howson does, point out that ‘gruesome’ hypotheses short circuit the argument, for there are an infinity of these that will make the same predictions as our successful theories. But we don't think most realists see the no-miracles argument as solving the problem of induction; rightly or wrongly, that problem is being bracketed here (assumed ‘solved’ or ‘unresolvable’). The crux of the debate then becomes assessing—often in a qualitative way—the relevant probabilities. Many anti-realists have directed their objections at forms of (3). Larry Laudan, for instance, notes that many past theories which were successful proved in the fullness of time not to be true; in effect, Laudan is chipping away at (3), recommending a higher value for Pr(Sh∣¬Th) by considering the history of science.

3. The Pessimistic Induction

Reflections on the history of science motivate the anti-realist argument. Considering past theories, we observe that many once successful theories are now believed to be false, e.g., caloric theory. We sample the successful theories of the past and find that many or most of them were false. We generalize and, by induction on these cases, evaluate Pr(¬Tx∣Sx) as being rather high for an arbitrary theory x. This holds for our present successful theories; hence we should think that they, too, will turn out to be false.Footnote ³ Contemporary discussions of this argument begin with Laudan (Reference Laudan1981), who writes:

If Laudan can show that $\mathrm{Pr}\,(\neg Th\mid Sh) =\frac{6}{7}$ , then—on the further assumption that Pr(Sh) = 1—it follows that $\mathrm{Pr}\,(Th) =\frac{1}{7}$ . This is the pessimistic induction. It invites us to conclude that the probability of some present, successful theory being true is rather low.Footnote ⁴

4. The Fallacy

To see the point clearly, consider a case removed from the giddy heights of realism. Suppose that there is some disease that in the course of time inevitably produces unique and readily identifiable symptoms. Imagine that there is some reliable test for this disease that can identify people infected with it who have not yet developed symptoms. Let Dx stand for ‘x has the disease’ and let Px stand for ‘x tests positive for the disease.’ Now suppose that if someone has the disease, then they are sure to test positive; that is, assume Pr(Px∣Dx) = 1. Suppose further that if someone is not infected there is some small chance that they will nonetheless test positive; that is, there is a chance that a positive test result will be a false positive. (In the language of significance tests, a false positive is a Type II error.) Let that chance of a false positive be five percent, i.e. Pr(Px∣¬Dx) = .05. Now suppose a patient a tests positive for the disease. What is the probability that she actually has it?

It is tempting to say that Pr(Da∣Pa) = .95 or at least to assign a high value to Pr(Da∣Pa). We can construct the inference so as to be formally analogous to the no-miracles argument as we formulated it above: From Pr(Pa) = 1, Pr(Pa∣Da) = 1, Pr(Pa∣¬Da) = .05, infer Pr(Da∣Pa) ≫ 0. As any elementary statistics text will remind us, however, we must consider the sample from which this patient was drawn. Suppose, among the people tested, the disease is rare. If only 1 in 1000 people has the disease, then given the assumptions above we should expect about 51 in 1000 to test positive. Of those 51 who test positive, only 1 will actually have the disease. Thus, the chance that this patient who tests positive has the disease would be 1 in 51; Pr(Da∣Pa) = .02. Thinking that Pr(Da∣Pa) must be rather high is the false positives fallacy, a form of base rate neglect. Footnote ⁵

Now return to the no-miracles argument. Setting worries about (3) aside, there is an additional premise hidden in this formulation of the argument: h is, by stipulation, some current theory of a mature science. Let $\mathstrut{\cal H} $ be the set of present candidate theories. Now the no-miracles argument takes this form for all x:

The argument revised in this way is still valid, but its soundness should tug less at our intuitions. Premise (5) will hold only if any arbitrary member of the population is likely to be successful. On the assumption that success is a reliable indicator of truth, this is tantamount to assuming that any arbitrary member of the population is likely to be true. If $\mathrm{Pr}\,(Tx\mid x\in \mathstrut{\cal H}) $ is low (and how can we know if it is not?), then (5) fails and the conclusion does not follow.

We might attempt to assess (5) by inspecting the pool of theories, $\mathstrut{\cal H} $ . We defined $\mathstrut{\cal H} $ as the set of candidate theories, but what theories were candidates for our present mature sciences? It is impossible to count up or even fairly sample all the theories that were considered for our mature sciences, and so it is impossible to evaluate whether (5) obtains.

The realist may insist that $\mathstrut{\cal H} $ is the set of theories actually professed by our mature sciences and, thus, that we can assess (5) in a straightforward way: sample the overt declarations of mature sciences and check their success. Yet this would be a biased sample, since theories in mature sciences were chosen (in no small part) because they were successful. Any theory $x\in \mathstrut{\cal H} $ would probably be successful, just on account of its membership in $\mathstrut{\cal H} $ . Thus, (6) would hold trivially and not on account of any connection between success and truth; (7) would simply be false, since almost all $x\in \mathstrut{\cal H} $ would be successful, whether true or not. The realist would thus avoid base rate neglect, but at the cost of sample selection bias.

Suppose realists win the point that success-to-truth inference is reliable, even that it is as reliable as our hypothetical diagnostic test. If true theories are rare enough—that is, if $\mathrm{Pr}\,(Tx\mid x\in \mathstrut{\cal H}) \ll 1$ —then Pr(Tx∣Sx) may be very low indeed. The no-miracles argument turns on neglecting this base rate.

The same goes for the pessimistic induction. The anti-realist hoped to show Pr(¬Th∣Sh) ≫ 0 on the basis of the historical record. Mindful of base rates, we should be careful to include the sample population explicitly in formulating the argument. Let the set of past scientific hypotheses be $\mathstrut{\cal H} _{p}$ . Suppose that historical enquiry does show that, for an arbitrary member of $\mathstrut{\cal H} _{p}$ , $\mathrm{Pr}\,(\neg Tx\mid Sx) =\frac{6}{7}$ ; that is, suppose that

If (9) were true, it would not have a direct bearing on the reliability of the success-to-truth inference as expressed in Pr(Th∣Sh). Past successful theories might typically be false because most successful theories are false (Pr(¬Tx∣Sx) ≫ 0), but they might typically be false instead because most past theories were false $(\mathrm{Pr}\,(Tx\mid x\in \mathstrut{\cal H} _{p}) \ll 1) $ .Footnote ⁶ If the latter, then the realist may insist that the population of past theories $\mathstrut{\cal H} _{p}$ was a different kettle of fish than the population of present theories $\mathstrut{\cal H} $ . On that assumption, (9) is compatible with the realists' desire to infer truth from the success of present theories, expressed as (8).

Pressing the point against the realist directly would require showing that the proportion of true to false theories is now about the same as it has always been; i.e. that

The realist will contest (10), of course, and insist that the $\mathrm{Pr}\,(Tx\mid x\in \mathstrut{\cal H} _{i}) $ increases through history. The anti-realist will probably deny that we have any way of evaluating (10), since evaluating it would presume we could determine matters of truth. Lewis suggests how a new induction might address this problem:

Indeed, it is unlikely that there is any neutral way to count up past theories. Mindful of change over time and inter-personal variation, how many theories of Newtonian mechanics were there?

We can now offer a diagnosis of the feeling of futility in the realism debates. By pointing to apparently successful but false theories, anti-realists responding to the no-miracles argument seek to increase Pr(¬Th∣Sh). By restricting the pool of theories under consideration to those that meet various strict conditions like maturity, novelty, and so on, realists responding to the pessimistic induction seek to lower the value for Pr(Sx∣¬Th). (That is, they are essentially replacing S with new, more stringent conceptions of success, S*.) One is working on the likelihood, the other on the probability. Cases might shift the above probabilities/likelihoods, but it won't matter all that much. It won't matter that much because to connect the likelihood with the probability there is a third crucial ingredient, the base rates of S and T in the population, and these aren't talked about—for good reason.

5. A Dilemma

Perhaps the most natural counter-argument is to suppose that the base rates or priors are determined in some way. Let's consider whether this might be so. In the case of our imagined disease, the problem of false positives need not undermine the usefulness of the test. If some group has been exposed to the disease, we might have good reason to think that many of them have it—for instance if the disease is highly contagious and all members of the group were exposed to it. Even without such knowledge, we might quarantine anyone who tests positive. If only 1 in 1000 has the disease, then we should expect quarantine to inconvenience 50 healthy people. However, this would contain the disease, and it would certainly be better than inconveniencing 999 healthy people as we would if we quarantined potential victims without testing. So, the test may still be a useful thing. It may also be that we have superior but more expensive tests. We could then save money by testing only 51 people rather than all 1000 with the expensive test. Also, we know that infected people will ultimately eventually break out with symptoms, giving us an independent way of checking to see if a positive result was a false positive.

The realist will be hard-pressed to save the success-to-truth inference in these ways. Selecting successful theories may increase the probability that we will have a true one, just as quarantining people who test positive increases the proportion of people under consideration who have the disease from 1 in 1000 to 1 in 51. Success of course is a good thing. Yet the true theories will not break out with any other symptoms—they will merely continue to be true. Nor are there further tests. This is a crucial point. The realist gambit is in a way posing further tests and looking for symptoms of a theory's truth. For example, they look for empirically successful theories that ‘break out’ with novel predictions, maturity, unification, etc. Granting realist claims, whittling down the pool like this will increase the positive probability shift. Settle on a definition of success, though, and we still need to know base rates; unless we know them, these shifts are useless for helping advance the no-miracles argument. The realist is faced with a dilemma: Either there is a way of knowing the approximate base rate of truth among our current theories or there is not. If there is, then we must have some independent grounds for thinking that a theory is very likely true; yet if we had such grounds, the no-miracles argument would be superfluous. If there is not, then the no-miracles argument requires an assumption that some significant proportion of our current theories are true; yet that would beg the question against the anti-realist.

Anti-realists, meanwhile, can keep finding successful false theories. By finding more and more of them, they can eventually drive the realist to make a choice between giving up the reliability of the success-to-truth inference and making the base rate of true theories very low. If Laudan found hundreds and hundreds of successful but false theories, this ought to make the realist squirm a bit. Even so, as reflection on the above numbers shows, realists can always find a value of the base rate that suits their purposes. More importantly, given the tremendous controversy over merely a handful of cases (aether, phlogiston, the wave theory of light, caloric, etc.), it is unlikely that a sufficient number of uncontroversial successful-but-false theories would ever be found to even slightly nudge a realist cognizant of the base rate fallacy.

Of course, if the base rates are interpreted as prior probabilities in a subjective Bayesian framework, the problem can be avoided. If some interval of values can be deemed the subjectively ‘reasonable’ priors, then—as Dorling (Reference Dorling1992) shows—the Bayesian can be a realist or an anti-realist. Given certain priors and evidence, Bayesians will be committed to realism about particular entities; given other priors, Bayesians will be committed to anti-realism. But notice that these are retail arguments about particular entities. In Dorling's cases, there may well be some plausible set of priors available, priors that realists and anti-realists could have agreed on before all the evidence came in. In the present wholesale case, however, where the entire fate of realism or anti-realism seems bound up with the priors, we can't imagine how one could find a reasonable set of priors.

Nor can we imagine how one could find the objective ratio of true theories among all past theories. We might admit that in principle there is such a ratio, but there is in practice no way to ascertain it. And if there were, there would then be no need to make either argument in the first place.

6. Doing Justice to Intuitions

The fallaciousness of the no-miracles argument and the pessimistic induction may come as no surprise. Worrall suggests that they might better be called “considerations” for and against realism. Although not valid arguments, they reveal a deep realist intuition and a deep anti-realist intuition (Worrall Reference Worrall1989, 101).Footnote ⁷ What do the considerations amount to? Well, any story about science and its history had better allow for the fact that sometimes scientists have thought highly of theories that later turned out false; and any story about science had better reflect the fact that science sometimes makes very detailed predictions that are confirmed with beautiful precision.

Yet one may feel an urge to say more than this. Even after the exposure of the fallacy, the two ‘arguments’ may still prime us to feel realist or anti-realist impulses. Whether we should acknowledge these impulses as probative intuitions is another matter.

One may object: ‘There must be something wrong with the foregoing discussion! Debates that so many smart people have taken seriously can't be predicated on such an elementary fallacy.’ Yet there is evidence that people are prone to commit the false positives fallacy. Psychologists have been aware of the phenomenon at least since Meehl and Rosen's classic paper (Reference Meehl and Rosen1955), and it has been demonstrated experimentally by Tversky and Kahneman (Reference Tversky, Kahneman, Kahneman, Slovic and Tversky1982) and others following after them. It is not confined to the psychologist's subject of choice, the college undergraduate; Casscells, et al. (Reference Casscells, Schoenberger and Graboys1978) demonstrate its prevalence among physicians. There is no reason to expect that philosophers would be immune.

The propensity to commit this fallacy explains why these two ‘considerations’ have rhetorical force even after their logical force has been shown lacking. Just as we are susceptible to optical illusions after we understand them for what they are, we may continue to be susceptible to these logical illusions. We should not try to do justice to the intuitions, except in the sense that the court may do justice to a killer. This diagnosis, if it is correct, means that the major considerations for and against realism come to naught.

We have argued so far that the no-miracles argument and the pessimistic induction are instances of the same fallacy, that research suggests that educated people are apt to commit this fallacy, and thus that the intuitive appeal of the no-miracles argument and the pessimistic induction should not be taken as a sign that they have any probative force. This does not entail that there is no issue between realism and anti-realism. Nevertheless, one wonders what debates about realism would be like without appeals to either of these attractive but fallacious arguments. We return to this train of thought in Section 8.

7. Reformulations

Following Howson and Lewis, we've formulated both arguments as statistical inferences of a particular kind. Perhaps the point is merely an artifact of a deficient formulation of the argument?

The no-miracles argument might be reconstructed as a likelihood inference (cf. Sober Reference Sober and Savage1990). As we've already noted, this could provide some incremental confirmation of a theory's truth. That is, learning that a theory is successful gives us a reason to revise upwards the probability that it is true. Nevertheless, nothing guarantees that the resulting probability will be high enough to merit belief. Recall the hypothetical disease: The probability that an arbitrary person has the disease is .001; testing positive shifts this upward to .02. Yet the realist seems to think that the probability of the truth of theories is close to 1 or at least that it's greater than .5. An argument purely in terms of likelihoods cannot secure this conclusion.

The realist might object that the no-miracles argument is not fallacious when supplemented with an appropriate auxiliary assumption. As argued above, however, suitable assumptions (e.g., that there is a significant proportion of true theories in $\mathstrut{\cal H} $ ) either beg the question or render the no-miracles argument redundant. The realist is still free to suggest that the supplemented no-miracles argument is valid and that he the realist thinks it is sound. It then joins inductive defenses of induction and abductive defenses of inference to the best explanation. Here we enter murky waters and cannot do justice to the subtleties of the discussion in the literature (see Howson Reference Howson2000, chap. 10; Lipton Reference Lipton and Derksen1994; Psillos Reference Psillos1999).

It might be better to reconstruct the argument such that the chances and miracles are not expressed as probabilities.Footnote ⁸ It is common to say that the no-miracles argument is not a probabilistic argument at all, but instead an inference to the best explanation (IBE). Critics of IBE complain that the argument is viciously circular—anti-realists doubt that IBE is in fact a reliable inferential method, so it can't be used to defend realism. Defenders of the argument respond that there is ‘good’ circular and ‘bad’ circular, that if the argument is only as bad as deductive defenses of deductions it is not so bad. The upshot of these debates seems to be that defenders of IBE view the IBE no-miracles argument as having the rhetorical force to make the hearer believe what the hearer believes. Perhaps, as Lipton (Reference Lipton and Derksen1994) argues, these ‘sermons to the choir’ have a legitimate purpose, but they cannot settle debates over realism.Footnote ⁹ As such, we do not see how the no-miracles argument can be meaningfully saved by another formulation.

What about the pessimistic induction? One might defend it as a classical statistical inference: If the theories are drawn at random from the history of science, then we may infer from the theories sampled to the population of all scientific theories. The question, of course, is whether it's appropriate to think of scientific theories as balls in an urn. For a classical statistical inference, the draws from the urn must be independent and identically-distributed. Cases offered for the pessimistic induction are not drawn in this way, since they all come from the past. This is analogous to pouring half of the balls from the original urn into a second urn and taking random draws only from this second urn. It will only be legitimate to generalize from the second urn to the original urn if the distribution of balls in the second urn is the same as the distribution in the original. The analogous assumption in the historical case is that the distribution of true theories in the past is the same is the distribution of true theories in the present and future—that is, it is just the contested assumption about base rates. So we don't see how even a completely random sampling of past theories could resolve the problem.

We can imagine IBE formulations of the pessimistic induction: the absence of any robust connection between success and truth might be offered as the best explanation for the eventual failure of past successful theories. This is a tantalizing suggestion. We leave it undeveloped, since we doubt that any anti-realists would be charmed by such a schizophrenic defense of anti-realism in the first place.

Perhaps there is some formulation of one or the other argument that escapes these worries. We note simply that the obvious formulations do not. Consider, then, a realist who finds realism appealing because of a pre-theoretic intuition that the success of science could not be a miracle. Is it plausible to think that her intuition harkens to some elusive formulation of the argument? Isn't it more plausible to think that she has the obvious version of the argument in mind, especially since the fallacy in the obvious version is one that even educated people are prone to commit? The same holds for an anti-realist who finds anti-realism appealing on account of the history of science. Since he has a psychological propensity to neglect base rates in a way that would make the obvious version of the argument convincing for him, then why think his intuitions anticipate some as-yet-undiscovered argument?

8. Imagining a Future

Imagine, if you will, what the literature on scientific realism would be like if we set aside no-miracles arguments and pessimistic inductions. As we mentioned at the outset, the no-miracles arguments and pessimistic induction are wholesale arguments, in that the conclusions are supposed to hold for all (or most) of the theories of our present, mature sciences. If we eschew these two arguments, we might look for some other wholesale motivation to settle realism debates en masse or instead for retail arguments that resolve questions only about particular kinds or individuals.

9. Conclusion

We can now answer the question with which we began. The question of why scientific methods succeed is, in a sense, just as legitimate as the question of why silver fishing lures succeed in catching fish. There is nothing wrong with the philosopher wanting an answer to the broader question. Because one can imagine a full continuum of cases where base rates are knowable to a varying degree, one can see that the distinction between wholesale and retail is a matter of degree and not kind. We concede that there is no sharp distinction between the wholesale and the retail. Nevertheless, good retail arguments for realism are on one side of the spectrum and wholesale arguments occupy an extreme position on the other side. The lunge for totality in wholesale arguments suggests that they will need statistical considerations about all or most theories and also that there will not be any independent methods for estimating the relevant base rate. Without independent methods for estimating crucial base rates, there is little to do but make arguments that beg the question. Wholesale realism debates persist not due to mere stubbornness, but because there is no reason for opponents to agree. The more modest reach of the narrower retail question allows for arguments that are non-statistical or for broad agreement in estimating base rates. These debates are profitable because there is reason to agree.

We suggest that the great hope for realism and anti-realism lies in retail arguments that attend to the details of particular cases. It is unlikely that either side will win every argument; it seems more likely that realism and anti-realism are options to be exercised sometimes here and sometimes there.Footnote ¹⁶ This equivocal victory for each might be uncomfortable for realists and anti-realists alike, but so be it.