An Epistemic Advantage of Accommodation over Prediction

1. Introduction

There are two ways for a piece of data to support a hypothesis. If the hypothesis was designed to fit the data, we say that the hypothesis accommodates the data. If the data fits the hypothesis despite not having been designed to do so, we say that the hypothesis predicts the data. So the difference between accommodation and prediction comes down to a difference between whether the hypothesis was already built to fit the data (accommodation), or whether this fit between hypothesis and data was instead a happy discovery made after the hypothesis had been constructed (prediction).

But what is the significance of this distinction for whether and how much the data confirms the hypothesis? Philosophers of science have defended a variety of answers to that question, ranging from the view that only predicted data could support a hypothesis (e.g. Giere, 1983, 1984) to the view that there is no epistemic difference between prediction and accommodation (e.g. Keynes, 1921; Howson, 1990). Between these extremes, there are a number of more moderate and widely accepted views, here jointly labelled weak predictivism (e.g. Maher, 1988; Lange, 2001; White, 2003; Lipton, 2004; Barnes, 2009). According to these views, the information that a hypothesis predicts rather than accommodates some data is, all other things being equal, symptomatic of some epistemic feature that speaks in favor of the hypothesis. Thus weak predictivists hold that the information that a hypothesis was predicted is an indirect epistemic reason to place more confidence in the hypothesis in so far as this suggests that some such epistemic feature is present in the hypothesis-data pair.

The current paper argues for a form of what I call weak accommodationism, viz. that the information that a hypothesis accommodates rather than predicts some data is, all other things being equal, symptomatic of an epistemic feature that speaks in favor of the hypothesis. An outrageous claim, to be sure, especially given the popularity and plausibility of its ‘converse’ thesis, weak predictivism. But as we shall see, this version of weak accommodationism follows straightforwardly from plausible assumptions about confirmation, uncertainty, and motivations for data fraud. We shall also see that, appearances perhaps to the contrary, weak accommodationism is not in fact incompatible with weak predictivism, for there may be distinct advantages to prediction that aren’t annulled or cancelled by the proposed advantage to accommodation. This, I shall suggest, may partly explain why the accommodation/prediction distinction is generally not deemed as epistemically relevant in science as weak predictivism suggests that it should be. In sum, then, it will be argued that weak accommodationism is true, and furthermore not just compatible with, but indeed complementary to, the ‘converse’ thesis of weak predictivism.

As we shall see, this argument for weak accommodationism is not merely of theoretical interest. The argument shows that the information that a hypothesis accommodated rather than predicted some data provides an epistemic advantage to the hypothesis via establishing reasons to believe in the integrity of the relevant scientist(s). In this way, the argument of this paper goes against a common sentiment among some philosophers of science according to which scientists who design their hypotheses so as to accommodate existing data are viewed with suspicion, even to the point of being compared to pseudoscientists in the Popperian sense (Barnes, 2009, 240). Instead what emerges is a picture on which prediction and accommodation provide different and complementary epistemic advantages, so that an ideal scientific community would plausibly consist in a mixture of ‘predictors’ and ‘accommodators’. This is especially so in sciences that are politically contested or charged, such as climate science, since even the most ardent skeptics of such sciences cannot reasonably claim that the accommodated data has been manipulated or fabricated in order to artificially support the relevant hypothesis. So, for example, the practice of ‘tuning’ of climate models to accommodate available data sets (see, e.g., Steele and Werndl, 2013; Frisch, 2015) is not just a perfectly legitimate source of support for such models, but indeed offers an additional reason to place one’s confidence in these models and the scientists who develop them.

2. Prediction and Predictivism

As I have indicated already, I will be using the terms ‘prediction’ and ‘accommodation’ to mark a distinction in whether a hypothesis supported by some data was designed to fit the data. Thus hypothesis $H$ predicts data $D$ just in case $H$ fits $D$ but $H$ wasn’t designed to fit $D$; and conversely $H$ accommodates $D$ just in case $H$ fits $D$ and $H$ was designed to fit $D$. In this pair of definitions, I am using the admittedly vague term ‘fits’ where others often use ‘entails’. I prefer the former because a hypothesis will often predict or accommodate data even when the hypothesis doesn’t entail the data, as when the hypothesis is inherently statistical and so will at best only assign a certain probability (less than one) to the data.¹ Assuming that you think that accommodation and prediction both carry some evidential weight, you can replace ‘fits’ with ‘confirms’ or ‘supports’ in these definitions. On the other hand, if you think that accommodation (or, alternatively, prediction) is evidentially irrelevant, then you can instead replace ‘fits $D$’ with ‘would have confirmed $H$, if $H$ had predicted (accommodated) $D$’. In this way, ‘fits’ can be replaced without remainder by other terms commonly used in philosophy of science; but I will continue to use it here to simplify the discussion.²

The distinction between prediction and accommodation I am employing here has become known as a heuristic distinction, since it concerns whether the data $D$ was used (as a heuristic) for designing the hypothesis $H$ (see, e.g., Zahar, 1973; Worrall, 1978, 1985; Gardner, 1982). In the early literature on prediction and accommodation, by contrast, it was common to employ a temporal distinction between prediction and accommodation, where $H$ was said to predict $D$ just in case $D$ fits $H$ and $H$ had been constructed prior to obtaining $D$ — and $H$ was said to accommodate $D$ just in case $D$ fits $H$ and $H$ had not been constructed prior to obtaining $D$ (see, e.g., Popper, 1963; Lakatos, 1970). With the benefit of hindsight, the heuristic distinction is clearly preferable. After all, whatever epistemic benefits there are to prediction will also be present in cases where $D$ was obtained before constructing $H$ but $D$ played no role whatsoever in the construction of $H$. For example, Einstein is often taken to have predicted the precession of Mercury’s perihelion from the general theory of relativity since Mercury’s perihelion seemingly played no role in the construction of Einstein’s theory — regardless of the fact that the precession of Mercury’s perihelion was known well before Einstein’s theory. Other ways of drawing the prediction/accommodation distinction have been proposed as well (see, e.g., Barnes, 2009), but following most other recent discussions I will be concerned with the heuristic distinction in what follows.

Predictivism is the general idea that predictions are epistemically superior to accommodation in some way. An extreme form of predictivism, which can rightly be called naive predictivism, holds that only predictions can serve to confirm scientific hypotheses.³ On this view, accommodated data is confirmationally irrelevant. Although naive predictivism seems to have been defended in the past (Giere, 1983, 1984),⁴ these arguments have been shown to be fallacious (Howson, 1990; Collins, 1994). Furthermore, naive predictivism would have truly absurd consequences, as the following case illustrates: Suppose $H$ predicted some data set $D_1,\mathrm{\dots },D_n$, which thus confirms it at some time $t_1$; at $t_2$, $H$ is then modified (never mind why) into another hypothesis $H^{\ast }$ so as to accommodate some additional data $D_{n+1}$ (which may conflict with $H$ or simply lie outside of $H$’s scope) while preserving the previous fit with $D_1,\mathrm{\dots },D_n$.⁵ According to naive predictivism, $H^{\ast }$ could derive no support whatsoever from $D_{n+1}$, nor could it derive any support from $D_1,\mathrm{\dots },D_n$. After all, $H^{\ast }$ would have been designed to fit both $D_{n+1}$ and $D_1,\mathrm{\dots },D_n$. So, according to naive predictivism, $H^{\ast }$ would enjoy no support whatsoever while the clearly less adequate $H$ would be considered strongly supported by $D_1,\mathrm{\dots },D_n$.

A somewhat more plausible form of predictivism is strong predictivism, which holds that although accommodation and prediction can both confirm hypotheses, “prediction is intrinsically superior to accommodation” (Barnes, 2018, §4). I take this to entail that, if $H$ predicted rather than accommodated $D$, then $D$ necessarily confirms $H$ more strongly than it would have otherwise (all else being equal). Strong predictivism is widely criticized in the literature (Howson, 1990; Achinstein, 1994; Barnes, 2005b, 2009; Harker, 2006, 2008). The strongest consideration against it may simply be that it places a rather mysterious epistemic significance on how a hypothesis came into existence. Appealing to the genesis of a hypothesis in determining its epistemic status in this way would apparently require us to look beyond any extant account of epistemic justification or evidential support. After all, current theories of epistemic justification typically hold that an empirical proposition is ultimately supported by perceptual foundations (foundationalism), or else logical, probabilistic or explanatory coherence (coherentism); neither of which includes facts about how a hypothesis was designed or constructed. Thus, unless and until a persuasive explanation or argument for why strong predictivism would be true is presented, strong predictivism does not seem promising.⁶

Naturally, then, philosophers tend to advocate more modest theses regarding the epistemic status of prediction versus accommodation. These theses differ in important respects, but they share a common structure and have thus jointly been labelled weak predictivism.⁷ Weak predictivism holds that the fact that a hypothesis predicts rather than accommodates some data is, all other things being equal, symptomatic of some other epistemic feature that speaks in favor of the hypothesis. Thus weak predictivists hold that it is the likely presence of this other epistemic feature that explains why the information that the hypothesis predicted the data often confirms the hypothesis more strongly than the information that the hypothesis accommodated the data.⁸

Different versions of weak predictivism then differ in what they identify as the relevant epistemic feature of which prediction is taken to be symptomatic.⁹ For example, Maher (1988, 1990, 1993) argues that the information that a hypothesis predicted rather than accommodated data indicates (ceteris paribus) that the hypothesis was constructed by a more reliable method, i.e. by a method is more likely to generate correct hypotheses, which in turn increases the probability of the hypothesis. Lange (2001), by contrast, suggests that predicting hypotheses are less likely to consist of arbitrary conjunctions as compared to accommodating hypotheses, and so that predicting hypotheses are superior (ceteris paribus) in virtue of being sufficiently unified so as to be capable of being confirmed by past successes. For both Maher and Lange — and indeed for any weak predictivist — there is thus an epistemic feature of hypotheses for which prediction serves as a reliable proxy, all other things being equal.¹⁰

An attentive reader may have noticed that I have described weak predictivists as claiming that prediction is symptomatic of some other epistemic feature of hypotheses all other things being equal (or, equivalently, ceteris paribus). This qualifier is needed because any reasonable weak predictivism will have to acknowledge that the link between prediction and the relevant epistemic feature is defeasible. Consider, for instance, Maher’s weak predictivism: Suppose we knew beforehand that the method by which a hypothesis was constructed was not at all reliable, e.g. that the hypothesis had been generated from a completely random process. Then the information that the hypothesis predicted rather than accommodated some data clearly does not indicate that the hypothesis was constructed by a reliable method. In that case, even by Maher’s lights, the information that the data was predicted by the hypothesis doesn’t tell us anything about whether the hypothesis is likely to be correct. So in that specific type of case, prediction would not be superior to accommodation on Maher’s view. An analogous point holds for Lange’s weak predictivism: If we knew already that a hypothesis is a conjunction of utterly arbitrary claims, then the information that the hypothesis predicted rather than accommodated the data cannot successfully indicate that it isn’t gerrymandered, and so shouldn’t boost our confidence in the predicting hypothesis.

It is presumably possible to provide more a informative version of any given weak predictivism by replacing this rather vague qualifier (‘all other things being equal’/‘ceteris paribus’) with a precise description of the conditions under which prediction non-defeasibly indicates that the epistemic feature is in place. Indeed, Maher (1988, 276-280) explicitly provides a list of 12 assumptions from which he derives the result that the information that the hypothesis predicted the data increases the probability that the hypothesis construction method was reliable. These assumptions can effectively be viewed as specifying the conditions under which Maher’s thesis holds unqualifiedly. Since Lange does not derive his thesis from probabilistic assumptions, it is harder to identify exactly what conditions would have to be in place for prediction to non-defeasibly indicate that a hypothesis isn’t an arbitrary conjunction. Presumably, though, these conditions would rule out — perhaps among other things — situations in which we already know whether, or the extent to which, the hypothesis is a gerrymandered arbitrary conjunction. In general, I assume it would be possible to formulate such specific conditions for any version of weak predictivism — effectively replacing the ceteris paribus-qualifier with a more precise description of the range of cases in the thesis is meant to hold unqualifiedly.

I have been dwelling on how to formulate more precise versions of weak predictivism by replacing qualifiers with specific conditions because I shall later suggest that these conditions interact with other conditions in ways that illuminate the overall epistemic advantage of prediction versus accommodation. In the next two sections, I will be arguing that there are conditions under which the information that a hypothesis accommodated rather than predicted the data indicates that it has a specific epistemic feature. Now, it is perfectly possible for both types of conditions to be satisfied simultaneously, in which case there would be epistemic advantages to both predicting and accommodating the data. To be sure, these epistemic advantages would be different for accommodation and prediction respectively, since prediction and accommodation would be indicative of different epistemic features of the hypothesis. It is of course also possible for the conditions for a given weak predictivism to be satisfied while the conditions for weak accommodationism aren’t, in which case prediction would be overall epistemically advantageous. Finally, the converse is also possible, i.e. that the conditions for ‘weak accommodationism’ are satisfied while the conditions for weak predictivism are not, in which case accommodation would be overall epistemically advantageous (see section 5).

3. Anti-Fraud Accommodationism

As noted, I will be arguing that the information that a hypothesis accommodated rather than predicted some data is indicative of a epistemic feature that counts in favor of the hypothesis. I have referred to this as ‘weak accommodationism’, since it is essentially the ‘converse’ of weak predictivism where ‘prediction’ and ‘accommodation’ have switched places.¹¹ Now, the specific version of weak accommodationism for which I will be arguing holds that, ceteris paribus, the information that a hypothesis accommodated rather than predicted some data indicates that the data is more likely to be accurate, which in turn increases the (posterior) probability of the hypothesis. The conditions under which this holds are, roughly, conditions in which one isn’t already certain whether the data has been manipulated or fabricated to fit the hypothesis. Since one could conceivably advocate weak accommodationism of a different variety or for different reasons, I shall refer to this specific thesis as anti-fraud accommodationism.

My argument for anti-fraud accommodationism proceeds straightforwardly in two distinct steps, corresponding to the structure of the thesis itself. The first step establishes that the information that a hypothesis $H$ accommodated rather than predicted some data $D$ does indeed indicate (ceteris paribus) that $D$ is more likely to be accurate. The second step aims to establishes that $D$ being more likely to be accurate increases the probability that $H$ is correct. Let me emphasize that these steps are distinct: the first concerns the connection between a hypothesis being accommodated and the probability of the data; the second concerns how this raises the probability of the hypothesis. In this section, I lay out this argument in an informal manner; in the following section I formalize the argument within a Bayesian framework, appealing specifically to the generalization of Bayesian Conditionalization known as Jeffrey Conditionalization. I thus ask formally-inclined readers to bear with me for the time being and interpret the somewhat colloquial argument in this section in light of its later, more precise, formulation.

Although philosophers of science often write as if data can be assumed to be certain and indubitable — the absolute ‘given’ of scientific reasoning — it should be clear that this is at best a useful idealization. In reality, the data that scientists report may be inaccurate due to a variety of reasons, including honest errors, incompetence, and intentional deception. For a given reported data set, one might of course be more and less optimistic that it is accurate — depending, presumably, on the identity of the scientists, their track record, and the nature of the data. And there is certainly room for reasonable disagreement about how common inaccurate data reporting is in general, and thus how far from the truth is the idealization that data is certain and indubitable. Be that as it may, it would certainly be a mistake of rationality to be absolutely certain of reported data, since that effectively amounts to ruling out beforehand the very possibility that the data is inaccurate for some reason.¹²

The type of inaccurate data that will concern us here is that which is due to deceptive reporting, i.e. to data fraud. In particular, two kinds of data fraud will be relevant to the argument below. In data fabrication, the relevant data is entirely invented or made up so as to appear to confirm some theory or hypothesis. In one particularly high-profile case of data fabrication, physicist Jan Hendrik Schön was found in 2002 to have manufactured data of several reported semiconductor experiments that never took place. Having published his ‘results’ in various leading journals in his field, Schoen’s fabrications were discovered only because he made the mistake of constructing data sets with identical ‘noise’, i.e. minor disturbances in some of the electrical signals that were supposedly being measured. Another type of data fraud, data manipulation, is when data that has actually been obtained is distorted so as to appear to confirm the relevant hypothesis — either by changing the values of measurements or (more commonly) by excluding measurements that do not fit the hypothesis.¹³ One egregious example of data manipulation is Andrew Wakefield’s fraudulent study on MMR-vaccination and autism, in which administrating the vaccine was claimed to cause autism in young children. Wakefield was found to have excluded data that didn’t fit his hypothesis and to have altered other data, e.g. by claiming that eight of the 12 children investigated had experienced symptoms of autism within three days of the vaccination, when in fact only one child experienced such symptoms.

Cutting across the distinction between fabrication and manipulation is the distinction between intentional and unintentional data fraud.¹⁴ In the cases mentioned so far, the researchers appear to have reported data that they knew to be inaccurate so as to fit their favored hypotheses. However, there are also well-known cases of inadvertent data fraud, i.e. cases in which scientists have deceived themselves into ‘observing’ non-existent phenomena or results (Broad and Wade, 1982, 107-126). A particularly striking example is the French physicist René Blondlot’s theory of ‘N-rays’, which Blondlot claimed were a type of radiation analogous to X-rays (Nye, 1980). In 1903, Blondlot claimed to have discovered the presence of N-rays through observing electric sparks jumping between two wires that were (allegedly) slightly brighter than one should otherwise been expected. Blondlot’s ‘discovery’ was widely celebrated among other French scientists and earned him the prestigious Leconte Prize in 1904. Over 40 French scientists subsequently reported that they had ‘reproduced’ Blondlot’s observations, claiming to have also seen the increased brightness reported by Blondlot. Although these scientists couldn’t actually have observed this non-existent effect, there is reason to believe that Blondlot himself, and at least some of his followers, did indeed believe themselves to have seen it. If so, this is an example of unintentional data fraud, where the researchers did not just deceive their intended audience but themselves as well.¹⁵

Now consider what we learn about the likelihood of data fraud when we learn that the relevant data $D$ was either predicted or accommodated by the hypothesis $H$. When a scientist has used $H$ to predict $D$, the scientist could have either fabricated or manipulated $D$ so as to make it fit $H$. Indeed, in many cases the predicting scientist has self-interested reasons to do exactly that, for example because reporting on a prediction that is borne out is generally considered a much more significant result than a failed prediction,¹⁶ or because the scientists has some scientific, financial, or otherwise personal, interest in confirming the hypothesis in question. Returning to our three examples, Schön appears to have fabricated data in order to obtain ‘results’ that fit with accepted scientific theories on semiconductors and would be publishable in the leading journals in his field; Wakefield had personal and financial ties to private companies that benefitted directly from casting doubt on the safety of traditional MMR-vaccines; and French scientists considered Blondlot’s ‘discovery’ of N-rays to be a great triumph of a French scientific community whose reputation was on the decline. In all these cases, the reported data was made to fit pre-conceived hypotheses from which predictions had been derived.

In cases of accommodation, by contrast, there is no operative hypothesis $H$ such that the accommodating scientist could have fabricated or manipulated $D$ in order to fit $H$. Thus the scientist could not have the type of self-interested reason they have in cases of prediction to manipulate or fabricate $D$ to fit $H$. This is not to say that it is impossible for a piece of accommodated data to be fraudulent, since a scientist might fabricate or manipulate data for some other reason, e.g. as a form of self-destructive behavior, regardless of whether the data was predicted or accommodated. Moreover, even non-fraudulent data might be inaccurate for various reasons, e.g. because of honest errors in how the data was obtained and registered. So the claim here is not that accommodated data carries no risk of being fraudulent or inaccurate. Rather, the point is that in cases of prediction there is an additional risk of the data being fraudulent, and thus inaccurate, due to scientists’ own motivations for having their predictions confirm the hypotheses that they have already formulated. A scientist could not possibly have similar motivations for fabricating or manipulating the data to fit the hypothesis in cases of accommodation, since there would be no relevant hypothesis $H$ that the scientist has some stakes in promoting. Indeed, since the hypothesis in question has not yet been formulated when the data is obtained in cases of accommodation, the accommodating scientist can simply alter her hypothesis to fit whatever data she gathers, so the accommodating scientists who is seeking a fit between hypothesis and data can always achieve that in a straightforward, non-fraudulent way.

The relevant upshot here is that data fraud — fabrication and manipulation of data, be it intentional or unintentional — can safely be taken to be considerably less common in cases of accommodation as compared to prediction. That is not necessarily to say that data fraud is common even in cases of prediction; only that it is much more common than in cases of accommodation. So, all other things being equal, one should be less confident that predicted data is accurate as compared to accommodated data. After all, the chances of predicted data being manipulated or fabricated — and thus inaccurate — are considerably higher than for accommodated data. This contrast in how confident one should be about the data in cases of accommodation versus prediction is the epistemic feature that I take accommodation to be an indication of or proxy for. Note that this is not yet to say anything about how confident one should be about the the hypothesis in cases of accommodation versus prediction. So it remains to be argued that this epistemic feature of accommodation — that the relevant data is more likely to be accurate in accommodation than in prediction, ceteris paribus — makes it more likely that the hypothesis is correct.

That is where the next step of the argument comes in. Informally, this step shows that, all other things being equal, the confidence assigned to a hypothesis in light of some data should be greater to the extent that one assigns greater confidence to the data itself being accurate, provided that the data would indeed confirm the hypothesis if it was accurate. A formal proof of this step will be given shortly, but I’ll start by providing the following informal argument. Suppose that by your lights a hypothesis $H$ would be confirmed by some data $D$, so that if you discovered that $D$ is accurate you would increase your confidence in $H$. Now suppose that instead of learning that $D$ is definitely accurate, you learn that $D$ is to a certain extent likelier to be accurate than you previous thought. Then your confidence in $H$ should be somewhere strictly between what it would be if $D$ was and wasn’t definitely discovered to be accurate, since the possibility that $D$ isn’t accurate means your confidence should be lower than it would be if you definitely learned that $D$ is accurate while the possibility that $D$ is accurate means it should be higher than what it would be if you definitely learned that $D$ isn’t accurate. Similarly, if you learned that $D$ is even more likely to be accurate (as compared to the previous case), then your confidence in $H$ should be somewhere strictly between what it should have been in the previous case and what it would have been if you definitely learned that $D$ is accurate. By the same token, if you learned that $D$ is less likely to obtain (as compared to the first case), then your confidence in $H$ should be somewhere strictly between what it should have been in the first case and what it would have been if you didn’t learn anything about $D$. And so forth. The upshot, of course, is that your confidence in $H$ should be proportional to how much you increase your confidence in $D$ in light of what you learn.

With this informal version of the second step in place, I can now summarize the argument for what I am calling anti-fraud accommodationism. In the first step, I argued that because scientists have no reason to commit data fraud in cases of accommodation, whereas they unfortunately do have self-interested reasons to do so in cases of prediction (and have been known to do so in such cases), we should place less confidence in the accuracy of predicted data as compared to accommodated data, all other things being equal. In the second step, I then argued that this difference in how much confidence we should place in the data translates into a difference in how confident we should be about the hypothesis that the data is meant to support. From this we can conclude that, all other things being equal, the information that a hypothesis accommodates rather than predicts some data does serves as an indication of an epistemic feature, viz. the likelihood that the data is accurate, that counts in favor of the hypothesis. Since that is what anti-fraud accommodationism asserts, this concludes my (informal) argument.

4. Derivation with Jeffrey Conditionalization

In order to formalize this argument, we must appeal to some formal framework for inductive reasoning. The dominant one is Bayesianism, a standard version of which can be viewed as the conjunction of the following three theses: First, perfectly rational agents can be represented as having fine-grained opinions known as credences. Second, the credences of such perfectly rational agents satisfy the Kolmogorov axioms of probability, which means that the credences they have at a given time can be represented as (subjective) probabilities. Third, perfectly rational agents are required to update their credences as they obtain new data in accordance with Bayesian Conditionalization, which holds that when you obtain some data, you should set your new credence in any hypothesis equal to your previous credence in that hypothesis conditional on the data.¹⁷ Formally:

Bayesian Conditionalization: When you obtain some data $D$, your new (subjective) probability for any hypothesis $H$, $P_n(H)$, should equal your old probability for $H$ given $D$, $P_o(H|D)$:

Although Bayesian Conditionalization is a powerful tool, there is an important limitation to this rule that turns out to be crucial to my argument in this paper. What if you do not simply ‘obtain’ or ‘learn’ the data $D$ in the intended unqualified sense, but instead merely become more (or less) confident that $D$ holds? Richard Jeffrey (1965) proposed a generalization of Bayesian Conditionalization that handles cases of this sort, a simple version of which can be stated as follows (Jeffrey, 1965, 169):¹⁸

Jeffrey Conditionalization: When your (subjective) probability for some data $D$ changes in any way, your new probability for any hypothesis $H$, $P_n(H)$, should equal a weighing of your old conditional probabilities $P_o(H|D)$ and $P_o(H|\neg D)$ by your new probabilities for the data, $P_n(D)$ and $P_n(\neg D)$:

The idea here is that when there is uncertainty about the data $D$, one should conditionalize on $D$ to the extent that one has credence in $D$ and on $\neg D$ to the extent that one has credence in $\neg D$.¹⁹

Since Jeffrey Conditionalization can handle cases in which the data is uncertain, it is arguably superior to Bayesian Conditionalization as a general rule for evidential updating.²⁰ After all, as we have seen, one should never treat data as absolutely certain. Indeed, the need to use Jeffrey Conditionalization rather than good-old Bayesian Conditionalization is especially apparent when we contrast accommodation and prediction, since predicted data should (ceteris paribus) be treated as more uncertain than accommodated data, due to the fact that scientists have no self-interested reasons to manipulate or fabricate accommodated data whereas they unfortunately often do have such reasons in the case of predicted data. So if we wish to analyze the epistemic significance of accommodation versus prediction, we should clearly prefer Jeffrey Conditionalization, where differences in the certainty of data can be represented, to Bayesian Conditionalization, where such differences have been idealized away. The question, then, is how a rational agent using Jeffrey Conditionalization should update her credences in cases of accommodation versus cases of prediction.

To start, recall that I am seeking to show that accommodation has one important epistemic advantage over prediction, not that accommodation is overall more epistemically advantageous than prediction. Indeed, as I will emphasize in the next section, I am happy to acknowledge that prediction often has epistemic advantages over accommodation, e.g. along the lines suggested by Maher (1988) and Lange (2001). But in order to isolate the specific feature of accommodation that interests me here, I must start by comparing cases of prediction and accommodation in which these advantages to prediction — whatever they may be — are not present.²¹ (Recall that proponents of weak predictivism acknowledge that there are such cases, since they concede that prediction is only superior to accommodation when all other things are equal.) Of course, I will not assume that accommodation has any advantages over prediction either, beyond the difference in how probable the data should be taken to be in each type of case. Rather, I will simply restrict the argument to cases in which prediction and accommodation are on a par with regard to how much confirmation is conferred on a hypothesis $H$ by predicted data, $D_P$ versus accommodated data, $D_A$; and likewise for their respective negations $\neg D_P$ and $\neg D_A$. Formally:

I will also restrict the argument to cases in which the hypothesis would be confirmed by the data to some extent, i.e. in which the subjective probability of the hypothesis is higher conditional on the data than on the data’s negation. This is just to say that the data, if it were discovered to be accurate, would have some positive epistemic relevance to the hypothesis. To deny this is to say that the data would either be completely irrelevant to the hypothesis, or else disconfirm that hypothesis. Since that is not the sort of case in which the data can be said to ‘fit’ the hypothesis, I take this condition to follow from the definitions of ‘prediction’ and ‘accommodation’. Formally:

Finally and most significantly, we represent the fact that one should be less certain about the accuracy of predicted data as compared to accommodated data by an inequality in the (posterior) probabilities assigned to each type of data after obtaining it:²²

In support of this condition, I have argued in the previous section that scientists cannot be motivated to manipulate or fabricate data to fit their preferred hypothesis in cases of accommodation, whereas that is unfortunately not so in cases of prediction. Of course, it is still possible that a piece of accommodated data is inaccurate, e.g. due to honest errors or incompetence. But that is equally true of predicted data. The difference is that in the case of predicted data, there is an additional risk of the data being inaccurate due to scientists’ own interest in having their predictions confirm the hypotheses they or their colleagues have already formulated. It is this contrast between accommodation and prediction that justifies the third and final condition (although as I discuss below, I do acknowledge that (3) isn’t satisfied in certain non-typical cases).

With conditions (1)-(3) in place, a straightforward derivation using Jeffrey Conditionalization can now be given for assigning a higher subjective probability to $H$ in the case of accommodation as compared to prediction:

A formal proof of this entailment is mathematically straightforward and provided in the Appendix. It should also be easy to see how the proof proceeds at an intuitive level: By Jeffrey Conditionalization, one should roughly speaking update by conditionalizing (i) on $D$ to an extent that matches one’s current credence in $D$, and (ii) on $\neg D$ to an extent that matches one’s current credence in $\neg D$. Given (3), one’s current credence in $D$ should be higher in cases of accommodation than in cases of prediction, so one should conditionalize to a greater extent on $D$ (and to a lesser extent on $\neg D$) in cases of accommodation than in cases of prediction. By (2), conditionalizing on $D$ raises the probability of $H$ more than conditionalizing on $\neg D$, so — given that all other things are equal, as per condition (1) — it follows that updating by Jeffrey Conditionalization in cases of accommodation raises the probability of $H$ more than it does in otherwise identical cases of prediction.

5. Discussion and Loose Ends

I have argued that, ceteris paribus, the information that a hypothesis accommodates rather than predicts some data confers a specific epistemic advantage on the hypothesis in virtue of increasing our rational confidence in the data itself. In this penultimate section, I address two important questions about this thesis: First, how commonly, and under what conditions, is the ceteris paribus-clause satisfied in such a way that accommodation in fact confers this epistemic advantage on a given hypothesis? Second, assuming that anti-fraud accommodationism and some version of weak predictivism are both true, how (if at all) can one tell, in a given case, whether prediction or accommodation is more epistemically advantageous all things considered?

The key to answering the first question is condition (3), according to which accommodated data should be assigned a higher (posterior) probability than predicted data. The justification for this condition was that scientists have self-interested reasons to manipulate or fabricate predicted data, whereas the same isn’t true for accommodated data. While I have argued that this is typically the case, there are also cases in which this consideration is defeated. If you already knew for certain whether the data was manipulated or fabricated, then information which bears on whether the relevant scientists had reasons to manipulate or fabricate the data shouldn’t effect your rational confidence that it was. Consider, in particular, the special case in which you gathered the relevant data yourself. In that case, you can presumably be more-or-less certain that the data wasn’t (or was!) manipulated or fabricated, so it would make practically no difference to the probability of the data whether you predicted or accommodated it.²³ Accordingly, the epistemic advantage of accommodation over prediction to which anti-fraud accommodationism appeals would not be present in cases of this sort.²⁴

On the other hand, whenever one isn’t already rationally certain whether the data was manipulated or fabricated, then the conditions for there being an epistemic advantage to accommodation over prediction would be satisfied. I think it’s fair to say that these conditions will typically be satisfied, since it is really only in the special case in which you gathered the data yourself that it would plausibly be rational to be close to absolutely certain that the data hasn’t been manipulated or fabricated. According to a recent meta-analysis of various previous surveys on research misconduct, 2% of scientists admit to “fabricating, falsifying or modifying data”, and 14% claim to have knowledge of it by their colleagues (Fanelli, 2009). Since these surveys rely on self-reporting of misconduct and knowledge thereof, there is reason to think they underestimate the true extent of data fraud. In any case, these numbers are high enough that it would certainly be a mistake to exclude beforehand the possibility that the predicting scientist has manipulated or fabricated the data they report (except perhaps when that scientist is you). Hence it is fair to say that there is typically an epistemic advantage to accommodation over prediction.

Indeed, there is reason to think that scientists are themselves conscious of the possibility that an apparently successful prediction is based on data fraud. Consider, for instance, the controversy over Gregor Mendel’s (1866) work on inheritance, in which Mendel proposed and argued for his laws of segregation and independent assortment (Franklin, 2008). The controversy concerns whether the observations reported by Mendel are ‘too close’ to the frequencies one would expect from the laws he proposed. For example, Mendel’s laws predicted that certain mutually exclusive phenotypes in peas, e.g. being green versus yellow, would occur with probability ratios of 3:1 in a second generation of breeding. In other words, each pea would be three times more likely to be yellow than green. This would lead us to expect that the observed frequency of dominant to recessive phenotypes will lie somewhere reasonably close to a 3:1 ratio. In fact, Mendel reported an observed frequency of almost exactly that ratio, viz. 3.01:1 (Mendel, 1866, 12).

The fact that the observations Mendel reported fit his theories’ predictions so remarkably well aroused skepticism from W.F.R. Weldon, who became convinced that Mendel had manipulated his data (even while acknowledging that Mendel’s theories were both important and substantially correct). Another eminent statistician, R.A. Fisher (1936), performed a detailed statistical analysis of Mendel’s data and concluded that it provides evidence that “the data of most, if not all, of the experiments have been falsified so as to agree closely with Mendel’s expectations” (Fisher, 1936, 132).²⁵ Whether or not Weldon’s and Fisher’s accusations are in fact accurate, they show clearly that scientists themselves at least sometimes consider data fraud to be a live possibility in cases of prediction.²⁶

The second question I promised to address in this section concerns what the epistemic advantage to accommodation over prediction entails about whether prediction or accommodation is more epistemically advantageous all things considered. Suppose — as I believe is plausible — that some version of weak predictivism is true.²⁷ Then there are some ceteris paribus-conditions under which the information that the data was predicted rather than accommodated confers an epistemic advantage on the corresponding hypothesis. Recall, for example, that in Maher’s version of weak predictivism, these conditions specify that one isn’t already certain whether the method of hypothesis-construction was reliable. Call any such condition $C_P$.²⁸ And call the corresponding condition for anti-fraud accommodationism $C_A$. In order to answer the question of whether accommodation or prediction is more epistemically advantageous overall in a given case, we consider which of these conditions are satisfied:

1. If neither $C_P$ nor $C_A$ is satisfied, there is no epistemic advantage to either prediction or accommodation, so neither is more epistemically advantageous overall.

2. If $C_P$ is satisfied but $C_A$ isn’t, there is some epistemic advantage to prediction but no advantage to accommodation, so prediction is more epistemically advantageous overall.

3. If $C_P$ isn’t satisfied but $C_A$ is, there is no epistemic advantage to prediction but some advantage to accommodation, so accommodation is more epistemically advantageous overall.

4. If both $C_P$ and $C_A$ are satisfied, there are (different) epistemic advantages to both prediction and accommodation, and no obvious way to tell which (if either) type of epistemic advantage is stronger.

For our purposes, the most interesting set of cases are those in the third category, where $C_A$ is satisfied but $C_P$ isn’t. Whenever one knows that one is dealing with such a case, one should be more confident that the relevant hypothesis is correct if one also knows that it was constructed to accommodate the data than if one knows that the hypothesis was used to predict the data. So in such cases the common thought that prediction is superior to accommodation should not just be rejected but indeed reversed. Suppose for example that Maher’s version of weak predictivism is correct (and that other versions of weak predictivism are not). In that case, $C_P$ includes as a necessary condition that one doesn’t already know for certain whether the method by which the hypothesis was constructed was reliable. Thus, in any circumstances in which one does know for certain whether the method by which the hypothesis was constructed was reliable (so $C_P$ isn’t satisfied), but one doesn’t know for certain whether the data was manipulated or fabricated (so $C_A$ is satisfied), one should prefer the hypothesis to have accommodated rather than predicted the data. The point generalizes to any other version of weak predictivism: Whenever the typicality conditions set forth by the weak predictivist aren’t satisfied, but the corresponding typicality condition for anti-fraud accommodationism is satisfied, accommodation is epistemically superior to prediction — not just in one respect, but all things considered as well.

While cases in the third category are thus the most intriguing, cases in the fourth category are the most complicated and difficult to generalize about. For cases in this category, whether prediction or accommodation is overall more epistemically advantageous depends partly on factors other than whether the data was predicted or accommodated. Roughly, this is because whether the epistemic advantage to accommodation outweighs the epistemic advantage(s) to prediction in such cases depends on the extent to which a higher probability of accommodated data raises the probability of the hypothesis, which in turn depends on how well the data fits the hypothesis regardless of whether it was accommodated or predicted.²⁹ So the extent to which accommodation provides an epistemic advantage over prediction, and thus whether that advantage is overall greater than that of prediction in a given case, depends on factors that are independent of whether the hypothesis was predicted or accommodated. In some cases, these factors will be such that having the hypothesis predict the data will provide more support for the hypothesis; in other cases, accommodated data will provide more support. Thus a further analysis of this category would presumably have to proceed on a case-by-case basis.

Since $C_P$ and $C_A$ are ceteris paribus-conditions for weak predictivism and anti-fraud accommodationism respectively, most instances of empirical support will presumably fall under category four. In other words, there will normally be epistemic advantages to both prediction and accommodation with no obvious way to tell which advantage is stronger. Although it might in principle be possible to estimate which type of advantage is stronger in a given case, it would surely be unrealistic to expect working scientists to even come close to performing such an analysis in practice. This may explain why working scientists do not in fact seem to have preferred prediction over accommodation in many historical cases (Brush, 1989, 1990, 1993, 1994).³⁰ That is, since any epistemic advantage of prediction over accommodation identified by a given weak predictivism might just as well be outweighed a contrary advantage of accommodation over prediction identified by anti-fraud accommodationism, prediction and accommodation might as well be treated as epistemically on a par for most practical purposes. The exception to this rule would be cases in which it is obvious to scientists themselves that one but not the other of $C_P$ and $C_A$ is satisfied, in which case one would expect scientists to prefer the type of support for which the corresponding condition is satisfied.³¹

6. Conclusion

I have argued that there is a respect in which accommodation is typically epistemically superior to prediction. The information that some data was accommodated rather than predicted by a hypothesis typically indicates (ceteris paribus) that the data is more likely to be accurate, which in turn increases the probability of the hypothesis by Jeffrey Conditionalization. This is not to deny that there may well be other respects in which prediction is epistemically superior to accommodation. If so, there is no general answer as to which type of empirical support, accommodation or prediction, is epistemically superior all things considered. While it is possible to identify a category of cases in which prediction is always superior all things considered, it is also possible to identify a category in which the reverse is true. Moreover, the largest category of cases is arguably one in which there are advantages to both prediction and accommodation, and in which there is no obvious way to tell which type of advantage happens to be stronger. This goes against the long and venerable tradition in philosophy of science of emphasizing the epistemic potency of prediction as against accommodation.

In closing, I would like to emphasize the potential social implications of these considerations. If my argument is sound, it may be misguided for those who engage with the public about scientific matters to focus exclusively on the predictive support for various scientific theories. Consider, for example, the case of climate science. When the support for anthropogenic climate change is communicated to the public, a great deal of emphasis is often placed on the extent to which climate models with anthropogenic forcings have been predictively successful. There is nothing wrong with pointing to successful predictions, of course, and any sound communication strategy ought to include it. However, a more complete strategy might also emphasize the extent to which these models accommodated data that had been collected previously. After all, support through accommodation cannot plausibly be dismissed as based on fabricated or manipulated data, so even the most ardent climate change deniers cannot reasonably dismiss accommodated data as fraudulent. This suggests that a mixed approach, in which the theory’s predictive and accommodative successes are communicated simultaneously, may help to convince some of those who would otherwise remain skeptical.³²

Appendix: Proof of Theorem

Theorem. (1), (2), and (3) jointly entail:

Proof: First we multiply both sides of (3) with the term $\left(P_o(H|D_A)–P_o(H|\neg D_A)\right)$, which is non-negative according to (2):

We then add the term $P_o(H|\neg D_A)$ to both sides:

Algebraic manipulations, omitted here for the sake of brevity, reveal that this is equivalent to:

Since $(1–P_n^A(D_A))=P_n^A(\neg D_A)$ and $(1–P_n^P(D_P))=P_n^P(\neg D_P)$, this simplifies to:

By (1), we can substitute $P_o(H|D_A)$ for $P_o(H|D_P)$, and similarly $P_o(H|\neg D_A)$ for $P_o(H|\neg D_P)$, on the right hand side. This gets us:

By Jeffrey Conditionalization, this is equivalent to $P_n^A(H)>P_n^P(H)$, as desired. ⬜