1. STATE OF THE ART – THE RELATIONSHIP AND COMPATIBILITY BETWEEN IBE AND BAYESIANISM

Any presentation of the possible compatibility between IBE and Bayesianism and of the ways of articulating it, should start, surprisingly, with van Fraassen's initial diagnosis that the two are actually incompatible (van Fraassen Reference Van Fraassen1989: 169). The reason for starting in this way is that all the subsequent discussions of compatibility (including McCain and Poston's discussion on evidential relevance, which I will deal with in more detail in §2) attempt, in one way or another, to respond to van Fraassen's charges. One such charge, for instance, has been that of the ‘bad lot’ (van Fraassen Reference Van Fraassen1989: 143), holding that, all our attempts to find the best explanation notwithstanding, the right explanation might be outside of the pool of our available hypotheses. It was in response to this charge that Lipton rolled back to interpreting IBE as inferring the probable truth of the best explanation (Lipton Reference Lipton2004: 58), and this cautious move has also been adopted by other IBE theorists (e.g. Niiniluoto Reference Niiniluoto1999).

As far as the theme of the present paper is concerned, it is another of van Fraassen's lines of attack against IBE which stands out: explanatory considerations can play no role in the context of Bayesian conditionalisation, on pain of drawing unwarranted inferences. If the posterior probabilities of more explanatory hypotheses were given ‘bonus points’ post-conditionalisation, due to their superior explanatory content, this would violate the demands of Bayesian rationality and lead to Dutch-Book results – a set of bets guaranteed to make one lose money in all scenarios (Van Fraassen Reference Van Fraassen1989: 169).

An interesting answer to this irrationality charge came from Okasha (Reference Okasha2000), followed by Lipton (Reference Lipton, Hon and Rakover2001) and Lipton (Reference Lipton2004).Footnote ⁵ Lipton and Okasha argued that associating explanatory elements to Bayesian reasoning, in the sense of taking these explanatory features into account after the posterior probabilities have been calculated, is actually putting the cart before the horse (Okasha Reference Okasha2000: 702–4; Lipton Reference Lipton2004: 106–17). The right way to construe the ‘friendly companionship’ needs to be tighter than merely taking into account the explanatory features of hypotheses after conditionalisation. These explanatory features should play a part in the conditionalisation itself, in the sense that explanatory considerations should influence the assignment of priors and/or likelihoods.

It is commonplace that, in the framework of IBE, the explanatory value of hypotheses is standardly cashed out using several virtues such as simplicity, scope, theoretical unity and individualisation, entailing, respectively, that a more explanatory hypothesis is simpler, covers a greater part of the evidence, converges with previous knowledge, and provides a mechanism or a fine-grained description of the causal enchainment(s) in question, respectively. If one or more of these features or virtues sets a hypothesis higher than its competitors, then, before applying Bayes' theorem to obtain the posterior probability (p(h/e) = p(h)p(e/h)/p(e)), one could assign to the more explanatory hypothesis either a higher prior (p(h)) (say, if it converges more to previous knowledge than its rivals) and/or likelihood (say, if it has a greater scope).

Here is one of Okasha's examples (an example with a medical context, as it happens). Suppose a mother brings her child to a doctor with leg pain complaints. The doctor has at his disposal two hypotheses: the first is that a muscle was strained, the second is that ligaments are torn. After examining the child, he opts for the second hypothesis, because for children of that age straining of muscles is very rare (background knowledge), and because the hypothesis that ligaments are torn best explains the symptoms he notices after examining the child (greater scope and individualisation). In probabilistic terms, this translates to the second hypothesis having a greater prior probability than the first, and to the probability of the evidence conditional on the second hypothesis (the likelihood) being higher than the probability of the evidence conditional on the first hypothesis. After conditionalisation, the posterior probability of the second hypothesis will be rendered higher, with no apparent violation of the Bayesian rationality.

Admittedly, not all hypotheses with a high prior and likelihood are also highly explanatory. But, in turn, all highly explanatory theories should have either a higher prior or likelihood, or both (Okasha Reference Okasha2000: 705). This strategy applies with a vengeance to cases in which scientists come up with radical new hypotheses, because the Bayesian's usual strategy of retorting that ‘today's priors are yesterday's posteriors’ does not apply. In such cases, the ‘Bayesian model is silent’, on Okasha's stern diagnosis (Okasha Reference Okasha2000: 709 et passim).Footnote ⁶ A less drastic observation would be to say that, in the context of new hypotheses being devised, the Bayesian has problems in assigning prior probabilities and likelihoods, and the ‘friendly companionship’ should hold in these cases also, with explanationist features helping to circumscribe the probabilities in question (Lipton Reference Lipton2004: 115–19).

This applies for various other situations in which, although the hypotheses in question are not new, we still have incomplete data or evidence; and various theorists have followed up this path, suggesting that explanatory constraints should be employed to make the transition from subjective to (some sort of) objective Bayesianism and Bayesian interpretation of probabilities. Weisberg (Reference Weisberg2009: 141) has argued that explanatory considerations should be used to constrain ‘a priori’ probabilities, along with objectivist principles such as the Principle of Indifference (in cases in which the background knowledge, and the available evidence, are such that, even if the Principle of Indifference applies, we do not get a unique value of the prior probabilities of hypotheses).Footnote ⁷

Another brand of objective Bayesianism which incorporates explanatory elements is the one proposed by Jon Williamson. Of the three main requirements of his objective Bayesianism (probability, calibration and equivocation), upholding the norm of equivocation (which asks that one's degrees of belief should equivocate as far as possible between the elementary outcomes; Russo and Williamson Reference Russo and Williamson2007: 168), amounts to introducing a classical explanatory constraint, namely simplicity and parsimony. This can be seen by looking at the corresponding account of epistemic causation developed by Williamson. On this account, the norm of equivocation asks that a causal graph be as non-committal as possible about what causes what: ‘A causal graph C is maximally non-committal, from all those in E, if there is no other causal graph D in E which makes fewer causal claims (including both arrows and gaps) than C’ (Wilde and Williamson Reference Wilde, Williamson, Wiedermann and von Eye2016). Williamson's objective Bayesianism leaves enough room to introduce other explanatory elements, and we will shortly come back to his insightful relationship between causation and Bayesianism.

Now, problems for this approach show up because, in certain cases, it might be wrong to use the explanatory virtues to constrain the priors and/or the likelihoods. Here is one example (used originally for different purposes) in Weisberg (Reference Weisberg2009: 129–30). Suppose you find one day your house in disarray, with the lock broken and valuable belongings missing. The first hypothesis that comes to mind is that a burglar broke in, stole the valuables and while searching for them, caused all the mess in the house. But there is another, more complicated hypothesis, and it happens that it is the true one. One burglar did force the lock and entered the house, but happened to encounter in that very moment another burglar who had penetrated through the window. They started to fight, turning everything in the house upside down, until a police officer came in. They both took off, and it is the policeman who decided to take advantage of the situation and take the valuables, planning to cast the blame on the two burglars.

Clearly, the first hypothesis is best explanatory, in terms of simplicity, theoretical unity, etc.; and yet it is the wrong one. Why then pay any attention after all to explanatory values at the level of confirmation? Such examples seem to be devastating, and there is a slight irony in the fact that, after providing the above example (admittedly, for a different purpose, namely in order to show that explanatory considerations might conflict with prior subjective probabilities), Weisberg goes on to argue that such explanatory considerations should contribute to fixing the ‘a priori’ probabilities, in an objective Bayesian framework (Weisberg Reference Weisberg2009: 137–41). It is slightly ironical because his discussion of the fixing of ‘priors’ for objective probabilities does not take into account the main lesson of the burglars' example, namely the fact that in some cases, explanatory values could pick out the wrong hypothesis – and this lesson can still be drawn even if the probabilities in question are further constrained by objectivist principles.

Of course, plausible, insightful replies could be formulated. One plausible reply (which Weisberg also touches upon; Weisberg Reference Weisberg2009: 132–3), would be the following: the mere fact that the hypothesis that scores higher in terms of the explanatory virtues might be false in certain particular cases, does not directly show that those virtues should not be used to constrain the priors and/or likelihoods. It simply shows that the explanatory virtues can be misleading. Compare the analogous reasoning – there can be cases where your total evidence supports the hypothesis that is false as a matter of facts, but it does not follow in such cases that you should not use your total evidence. Thus, based on particular cases, one should not deny the use that explanatory values might have in the assignment of priors and/or likelihoods.

Moreover, it is worth noting that examples such as the burglars’ one seem especially effective when used and directed against one of the most vulnerable of the explanatory virtues, namely simplicity, and we have here a vulnerability that is acknowledged by IBE theorists. Lipton has dubbed the corresponding objection ‘Voltaire's objection’, in connection to Voltaire's diatribe against the best of the possible worlds theory of Leibniz (Lipton Reference Lipton2004: 144–7). Why should the world (and our true hypotheses about its causal structure) be simple? However, one could reply, simplicity is just one of the explanatory virtues. When our explanations are based on mechanisms (which embody simultaneously various explanatory virtues, since mechanisms-based explanations are arguably more theoretically unified, have greater scope and greater individualisation), then it is much harder to reject as ad hoc (or as stemming from some sort of idealist perspective) the inferences to the best explanation that favour the hypotheses backed up by mechanisms, over the hypotheses that are not thus backed up.

Hence, moving on to the friendly companionship between IBE and Bayesianism, to say that, in the realm of medicine, one should increase the likelihoods or priors for those hypotheses which also provide a mechanism, is not prima facie susceptible to Voltaire's objection and is not betraying some sort of straightforward, simple-minded use of the explanatory virtues of IBE.

However, one has to admit that there is still here a bone of contention. Given the intricate nature of these debates and the circumscribed scope that the present paper has, I will focus, for the sake of cautiousness, on what appears to be a less controversial aspect of the Bayesianism/IBE possible collaboration, which I will look at in the next section.

2. RESILIENCE – OF MECHANISMS AND PROBABILITIES

Using mechanisms in order to control the priors or likelihoods is not an uncontroversial move to make for the theorist of medicine. Still, mechanisms (and the criteria for mechanistic evidence) should have some role in the confirmation of causal claims in medicine. But what would this role be? In §1, I mentioned Williamson's objective Bayesianism, as an example of how one could attempt to strengthen the subjective basis of the Bayesian theory with norms that could be derived from (or resemble) explanatory considerations. But Williamson's account is a source of inspiration at this point from yet another point of view, precisely because his account of objective Bayesianism is coupled with an account of causation (in which the requirements of objective Bayesianism have corresponding requirements for circumscribing causal relations).Footnote ⁸ The lesson to be drawn immediately is that the to-and-fro between a theory of subjective credences/objective probabilities and a theory of causation can be illuminating by allowing us, via various analogies, to circumscribe, or rather suggest, characteristics of credences/probabilities that parallel ontic characteristics of causal relations. In other words, such a to-and-fro between the epistemic and ontic levels could be useful heuristically in order to suggest features that our theories of confirmation should possess, in relation to the ontic structure of reality that science uncovers (or, in our particular discussion, in relation to the causal structure that we know to be in place ontically in biology and medicine).Footnote ⁹

Now, what is the main characteristic of mechanisms in medicine and biology as far as the causal relations are concerned? Perhaps a univocal answer to his question cannot be provided, but at least it would be safe to say that one of the main characteristics of mechanisms is that of ‘stabilising’ causal relationships. The idea is present in the founding (Reference Russo and Williamson2007) paper by Russo and Williamson (in which the basis for the equal treatment of mechanisms and population studies was put forward). Moreover, the literature on biological mechanisms abounds in references to the ‘resilience’ of mechanisms (Bechtel and Abrahamsen Reference Bechtel and Abrahamsen2005, Reference Bechtel, Abrahamsen and Hooker2011; Folke Reference Folke2006)Footnote ¹⁰ – where their ‘resilience’ means that they can resist and adapt to variations in inputs and parameters, both internal to the organisms, and external, through different paths of feedback and self-maintenance, such that the causal relations that mechanisms produce are conserved.

Moving on from this ontic level, it just so happens that we have in the literature a related notion on the epistemic side, namely the notion of the ‘resilience’ of probability, developed by Brian Skyrms (Reference Skyrms1977, Reference Skyrms1980). Very briefly put, Skyrms arrived at this notion in an attempt to characterise the probabilities that figure in statistical laws. More precisely, the attempt was to provide a notion of law-like, objective chance (or ‘propensity’ in his own terms) to be distinguished from the mere subjective credence, by pinning down the limited variation of such objective chances in law-like statements or propositions, relative to any other statements, i.e. by pinning down the resilience of the respective probabilities when conditionalised on other statements. The resilience of a proposition q having a probability a, was defined as 1 minus the greatest difference between a and the probability of q, conditional on any truth function of other propositions which is consistent both with q and its negation (Skyrms Reference Skyrms1977: 405; Mellor Reference Mellor1983: 101).

For our purposes, it matters less how exactly Skyrms defined numerically the resilience of probabilities. What matters, however, is to follow the close parallel that links analogically the epistemic characteristic of the resilience of probability functions conditional on other evidential statements (which, in the meantime, has become a rather uncontroversial characteristic of the dynamics of credences for Bayesian theorists) with the ontic characteristic of mechanisms, capable of conserving the causal relations they produce, in spite of variations in the internal and external environment.

Given this parallel, the following proposal can be suggested, bearing also in mind that the explanatory function of mechanisms in the framework of IBE is based on the causal relations that mechanisms produce. The suggestion is that the explanatory considerations that could be integrated by a Bayesian theory of confirmation, refer to the evidential contribution of mechanisms to the resilience of Bayesian credences. More precisely, on this proposal, mechanistic evidence can increase the resilience of Bayesian probabilities, where ‘resilience’ means the stability of one's credences in the face of new evidence.

It is worth noting that, beyond the immediate purposes for which Skyrms used the notion of resilience initially, this notion was subsequently applied by Joyce in order to distinguish between the weight and the balance of evidence in a Bayesian framework (Joyce Reference Joyce2005), by Leitgeb in order to differentiate between the quantitative and the qualitative aspect of evidence and belief (Leitgeb Reference Leitgeb2014, Reference Leitgeb2017), and by McCain and Poston, in order to defend the evidential relevance of explanatory considerations (McCain and Poston Reference McCain and Poston2014). Interestingly, Joyce, Leitgeb, and McCain and Poston never linked the resilience of probabilities or credences to the evidence coming from mechanisms, in spite of the evident epistemic/ontic analogy mentioned above. However, McCain and Poston's discussion of evidential relevance – which draws, among others, on Skyrms (Reference Skyrms1980), and Joyce (Reference Joyce2005), and which I will briefly present and discuss in the next section – will be very useful to situate better within the literature (and the current debates) the proposal as to the resilience brought about by evidence of mechanisms. In turn, §4 will go back to the medical context and will flesh out the consequences of the proposal for the medical interplay between mechanisms and medical controlled population studies.

3. MCCAIN AND POSTON'S DISCUSSION OF EVIDENTIAL RELEVANCE

The state of the art discussion in §1 began with van Fraassen's critique of IBE, as providing the reference point for all subsequent discussion on the collaboration between IBE and Bayesianism. This applies also to McCain and Poston's discussion, because they, too, start from a critique advanced in the vein of Van Fraassen, namely Roche and Sober's charge that explanatory considerations are evidentially irrelevant (Roche and Sober Reference Roche and Sober2013: 659). As a matter of fact, Roche and Sober's critique of IBE is just van Fraassen's argument on the irrationality of adding ‘bonus points’ in disguise.

Roche and Sober's aim is to show that explanatory properties do not influence probabilities at all. In order to show that they cannot and should not influence probabilities, they formulate the issue in Bayesian terms. More precisely, they take a hypothesis H, the observations relevant to it O, and formulate the proposition E: if H and O were true, H would explain O. In their terms therefore, E encompasses the explanatory relation between the hypothesis and the observed data. They ask subsequently, as the Bayesian confirmation theory asks, whether Pr(H/E&O) > Pr(H/O) – in other words, whether the explanatory features add anything to the confirmation of H. Their answer is negative – nothing is added, because E is screened-off by O, or in formal terms Pr(H/O&E) = Pr(H/O); ‘the explanatoriness of H is evidentially idle, once the truth of O is taken into account’ (Roche and Sober Reference Roche and Sober2013: 660). Notably, the target of Roche and Sober's screen-off thesis does not concern prior probabilities, but posterior probabilities. The point is that learning E (i.e., that H would explain O if H and O were true) after having already learned O should not lead one to change your credence in H, which was precisely the crux of van Fraassen's irrationality argument.

Roche and Sober's example is, again, a medical one, concerning smoking and lung cancer. They take two scenarios, one in which smoking causes cancer, and another in which, according to Fisher's ancient supposition, smoking and cancer are both due to a common cause. In the first scenario, E is in place, because H explains O. In the second scenario E does not hold, as H does not explain O since both H and O (or the fact corresponding to the respective propositions, as one might want to read them) are the result of the common cause.

Now, on the level of strictly observed correlations, we will have, say: Pr(S smoked at least 10,000 cigarettes before age 50 | S got lung cancer after age 50) = c. And Roche and Sober's point is that c is not modified in any way if E is added: Pr(S smoked at least 10,000 cigarettes before age 50 | S got lung cancer after age 50 & if S smoked at least 10,000 cigarettes before age 50 and S got lung cancer subsequently, then the smoking would explain the lung cancer) = Pr(S smoked at least 10,000 cigarettes before age 50 | S got lung cancer after age 50). The explanationist story does not change the probabilities, so it is evidentially irrelevant.

Going back to McCain and Poston's reply, their main point is that, even if the screening off holds, the explanation features are still evidentially relevant. In other words, they concede as much as they can to Roche and Sober as to their screening off claim (although, as we have seen in the previous section, there is space for discussion as to whether explanatory features can influence the priors of the hypotheses in question). However, McCain and Poston contend, there is a sense in which the explanatory story does have an influence on confirmation or prediction, without modifying as such the probabilities. What they influence is the resilience of the Pr function, by making certain of the probabilities more stable, or less volatile, given new evidence, or rather new information (and we shall see shortly why the distinction between evidence and information might be useful).

Again, the rationality of the Bayesian conditionalisation is not violated. Consider once more the probabilities of Roche and Sober, in a simplified form. We first have: Pr (S will get lung cancer/S has smoked i cigarettes to date) > Pr (S* will get lung cancer/S has smoked j cigarettes to date), for all i > j. On a Bayesian analysis of confirmation this inequality implies that S being a heavier smoker than S* is evidence that S has a greater chance of getting lung cancer than S* (or, strictly speaking, that the hypothesis of S getting cancer is more probable than the hypothesis of S* getting cancer). At this point, one can assign different measures of confirmation, and it is commonplace that there is disagreement among Bayesians as to how exactly to frame this measure of confirmation (see for instance Glass Reference Glass2012). McCain and Poston leave this point aside also, and postulate this measure of confirmation be some d.

Now consider the probabilities to which the explanatory element has been added Pr (S will get lung cancer/S has smoked i cigarettes to date & smoking causes cancer) > Pr (S will get lung cancer/S has smoked j cigarettes to date & smoking causes cancer), for all i > j. McCain and Poston's claim is that, even if the degree of confirmation d has not changed by integrating the explanatory story, the frequency data correlating smoking and lung cancer is ‘reinforced’, without being changed. It is not some paradox or a mere play of words, and in order to clarify what this means, McCain and Poston appeal to the useful distinction between balance and weight of evidence, where ‘balance’ is related to the strictly quantitative, numerical aspect of evidence, whereas ‘weight’ is related to the qualitative aspects of evidence.Footnote ¹¹

Simply put, in McCain and Poston's rationale, the explanatory side, while leaving the balance untouched (i.e. the degree of confirmation), adds to the weight of evidence, which is explained in following manner. Suppose one has a two-sided coin, which looks fairly typical, and one assigns a value of 0.5 to the next flip resulting in heads. Suppose next that one flips the coin a million times and it lands heads approximately one-half of the time. What is now the chance, ask McCain and Poston, that the next flip is heads? The answer is the same, 0.5. Pr_t(heads on next flip/k) = 0.5 and Pr_t+e(heads on next flip/k & e) = 0.5, where k is one's background evidence, e is that there have been roughly 1/2 heads among a million flips, Pr_t is one's initial probability assignment and Pr_t+e is the probability assignment after learning only e.

The balance of the probability has remained unchanged; strictly speaking, the probabilities are the same, and the million flips are ‘screened off’. However, e has added to the weight of evidence, in the sense that the one has learned that the two-sided coin is unbiased.Footnote ¹² In other words, the strictly numerical, quantitative aspect reflected by the balance has remained constant; but the qualitative aspect reflected in the weight of evidence has changed. As a consequence Pr_t+e is more resilient in the way it changes in response to new information. Suppose that after the one million flips, the subject gets next an improbable sequence of five heads in a row (I am changing McCain and Poston's example slightly, to make it more similar to the next example they use, which I will present shortly). Due to the resilience of the probability Pr_t+e the credence of the subject that the next is heads should remain 0.5. Citing Joyce's claim that ‘[t]he weight of this evidence is reflected in the tendency for credences to stably concentrate on a small set of hypotheses about the proposition’s objective chance’ (Joyce Reference Joyce2005: 176, italics added), the two authors contend that that the resilience brought in by explanatory stories works in the same way, by fixing the data about the relevant objective chances.

A two-sided coin being flipped one million times does not really amount to an explanatory story (although in an enlarged sense of explanation, it could be reckoned with this way, if it is taken to explain that the coin is not biased and that is why the chance of heads remains 0.5). Hence, McCain and Poston provide another example, in which the explanatory story is neatly delineated, and which is all the more useful because it will help us see the transition to mechanisms and the quality of evidence.

In the new example, we have Sally and Tom being informed that there are 1,000 x-spheres in an opaque urn. Sally, but not Tom, knows that blue and red x-spheres must be stored in exactly equal numbers because the atomic structure of the x-spheres is such that if there are more or less blue x-spheres than red, the atoms of all of the x-spheres will spontaneously decay resulting in an enormous explosion. Now, a random sampling of ten x-spheres without replacement provides five blue and five red spheres, which are replaced in the urn. Given the data, both Sally and Tom should assign Pr (blue|random draw) = 0.5. However, whereas Tom only has at disposal the frequency data, Sally also has an explanation for why the probability of drawing a blue x-sphere at random is .5. Yet, this evidential difference does not show up, given the initial data, which prompts both to assign Pr (blue|random draw) = 0.5. Suppose, however, that 10 more x-spheres are drawn at random and they are all blue. Given her knowledge about the atomic structure of the x-spheres, Sally's rational credence in blue given a random draw remains the same – Pr _Sally+E (blue|random draw) = .5, where this is her revised probability, upon learning the result of the new draw, E. Yet Tom's rational credence changes significantly. Whereas Pr _Tom (blue|random draw) = .5 for the initial round of testing, Pr _Tom+E (blue|random draw) = .75 when he learns about E. So, Tom's probability function is more volatile in the face of the new information. Sally's probability function is more resilient.

In the terms of Joyce (Reference Joyce2005), adopted by McCain and Poston, Sally's credence stably concentrate s on the hypothesis that the objective chance of blue x-spheres is 0.5. Moreover, at this point, one could recall Lipton's insightful observation that a serious problem for Bayesians is that they cannot distinguish which is the relevant evidence (Lipton Reference Lipton2004: 116).Footnote ¹³ One would thus be tempted to add that the 10 more x-spheres which are drawn at random and are all blue, while constituting information, do not constitute relevant evidence. It is a line of thought that McCain and Poston do not adopt explicitly, although it might well lie in the back of their specific use of the term ‘information’, and of their repeated differentiation between frequencies, epistemic and non-epistemic, objective chances and epistemic probabilities. At any rate, McCain and Poston conclude that explanatoriness is evidentially relevant even when the screening off condition holds, by increasing the total weight of evidence.

We can see that our proposal with respect to mechanisms and resilience, is consistent with, and naturally strengthens, McCain and Poston's rationale as to how explanatory aspects are evidentially relevant. In a sense, our proposal is the natural continuation of the series of suggestions made by Skyrms, Joyce, and McCain and Poston. If (a) one needs to take into account the phenomenon of resilience of probabilities (as Skyrms urges); (b) resilience is an important symptom of the weight and quality of evidence, to be distinguished from its balance (as Joyce has maintained); and (c) it is the explanatory features that increase the weight of evidence and the resilience of probabilities (as we have just see McCain and Poston arguing), then it would only be natural to take the evidence of mechanisms as the main type of evidence that can increase the resilience of probabilities. It is mainly mechanisms that explain, and they do so in virtue of stabilising causal relations – which is an ontic phenomenon that parallels the epistemic phenomenon of ‘resiluence’ for Bayesian probabilities.

One could even claim, with respect to McCain and Poston's discussion that, in their examples, the evidence brought about by mechanisms is almost tacitly present. In the example with the x-spheres for instance, it is mechanistic evidence which is at stake in the difference between the resilience of the probability functions of the two participants at the experiment. When reading such examples, the notion of mechanistic evidence is, as it were, on the tip on the tongue; yet, the notion just remains unarticulated by McCain and Poston. We can now close the circle and return to the mechanistic evidence and the criteria for its quality provided in Clarke et al. (Reference Clarke, Gillies, Illari, Russo and Williamson2014a).

4. EVIDENCE OF MECHANISMS AND THE RESILIENCE OF CREDENCES

We have seen in the previous section that McCain and Poston ground their argument in favor of the resilience of probability functions on the distinction between weight and balance, where weight is related to the qualitative aspect of evidence, which arguably cannot be captured in pure probabilistic terms. Now, a crucial piece in the puzzle of how to apply in a medical context the rationale of the resilience of probability functions, is that the criteria of mechanistic evidence advanced in Clarke et al. are related precisely to this qualitative aspect. As mentioned in the Introduction, these criteria are means to assess and provide a hierarchy for the quality of medical mechanistic evidence. They take into account traits such as independent methods, different research groups, proportion of features found, knowledge of analogous mechanisms, and robustness, defined in terms of being reproducible across a wide range of conditions. Each of these traits plays a role in terms of pluses and minuses, and in the pre-confirmation stage they are used for grading the ‘quality’ of evidence.

Take for instance the case in which the mechanistic evidence comes from two different teams reporting two mechanistic features, using the same research methodology. This evidence will be graded higher than the evidence of two mechanistic features provided by a single team, but will be graded lower than evidence coming from two different teams reporting two mechanistic features using different methodologies; in turn, the latter evidence will be graded lower than evidence coming from two different teams reporting three mechanistic features using different methodologies, and so on.

Now, if the quality of mechanistic evidence is traced back to the balance/weight distinction, then we can see immediately the way to apply to our medical context the proposal concerning the resilience of probabilities brought about by mechanistic evidence. The way to apply it would be to say that, for the medical correlations obtained from the controlled population studies, the corresponding Pr function should be more resilient, to the degree to which the criteria of Clarke et al. for mechanistic medical evidence are satisfied. In other words, on this rationale, the quality of medical mechanistic evidence will be reflected in the resilience of the Pr function from the controlled population studies, which will be higher for those hypotheses for which we also have mechanistic evidence obtained using different methodologies, different research teams, with more mechanistic features found, etc.

Take again the example of smoking and lung cancer, as discussed by Roche and Sober. In plain terms, according to them, the mechanism linking smoking and lung cancer does not have any relevance for the correlation between smoking and cancer, no matter whether Fisher's supposition was adequate or not. This might be right, but, using again the plain language of causation, it is evident that the mechanism in question has relevance for whether smoking does cause lung cancer or not (and whether any intervention or manipulation can intervene beneficially). It sounds almost like a truism, and denying this truism is a direct consequence of what Roche and Sober say.

It is this causation worry which underlies McCain and Poston's distinction between frequency and non-epistemic chance, and finally their reasoning as to the resilience of probability functions when backed up by explanatory considerations. It was also this causation worry which triggered the first formulation of the thesis that evidence of mechanisms should be placed alongside (and on the same footing as) evidence from controlled studies, in the original (Reference Russo and Williamson2007) article of Russo and Williamson. More precisely, in that article it was claimed that, in the absence of evidence of the existence of a medical mechanism, one cannot rule out that a correlation, however rigorously established on a population level, could be spurious (Russo and Williamson Reference Russo and Williamson2007: 159) and the claim of ruling out spuriousness is repeated in the more recent Clarke et al. (Reference Clarke, Gillies, Illari, Russo and Williamson2014a: 343).

My suggestion then as to the criteria of mechanistic evidence advanced in the same Clarke et al., is that these criteria can do more than that, in combination with the evidence of correlation from population studies. It is perfectly acceptable to say that the existence of a mechanism helps establish (or even establishes) that a medical correlation is non-spurious. But mechanisms also explain causal relations, and ontically, they stabilise causal relationships (by offering a degree of protection against interfering factors, using various feed-back paths, etc.). Moreover, beyond the simple existence of a mechanism, this explanatory relation is all the more direct, the more the criteria of mechanistic evidence of Clarke et al. are fulfilled. How could this explanatory relation of mechanisms be put to work at the level of confirmation? At the very least, I propose, it is in making more resilient the probability functions resulting from a Bayesian interpretation of the acclaimed RCTs of EBM, in direct correspondence or dependence with the Clarke et al. criteria.

Suppose that a medical study S provides evidence that for the hypothesis H₁ that C₁ causes E, with a strong resulting balance – e.g., that P(E|C₁) = 0.7 > P(E) = 0.1. Hence we have that P(E|C₁ S) = 0.7. Now, some future evidence (study T) might cast doubt on this causal relation, and thus we would have, say, P(E|C₁ S T) = 0.3, where 0.3 would be a compromise between 0.7 and 0.1 = P(E). The evidence of the study T would favor another hypothesis H₂, according to which it is C₂, and not C₁, which causes E.

However, if at the time of doing the study S, one had good, quality evidence M₁ that there is a mechanism of action by which C₁ causes E, then although this mechanistic evidence would make no difference to the original probability obtained after conditionalising on the evidence of S, namely P(E | C₁ S M1) = 0.7, it would make that probability more resilient under the putative future evidence T, such that, say, P(E | C₁ S M₁ T) = 0.65. And having good, quality evidence M₁ in favor of hypothesis H₁ would mean that the Clarke et al. criteria of mechanistic evidence are satisfied, and that the proportion in which they are satisfied makes it far superior to any alternative mechanistic evidence M₂ that may be put forward in favor of rival hypotheses such as H₂.

Take the example of the current controversy as to the role of cholesterol in atherosclerosis.Footnote ¹⁴ Against the widely accepted view that cholesterol has a pathogenic role in atherosclerosis, a number of (rather isolated) scientists and public figures have advanced the hypothesis that cholesterol is actually an innocuous factor. On this innocuousness hypothesis, the observed correlation between cholesterol and cardiovascular diseases is due to some common cause, like lack of physical activity, mental stress, smoking and obesity (Ravnskov Reference Ravnskov2002). Now, in adopting the pathogenetic hypothesis on cholesterol and rejecting the hypothesis on innocuousness, we do not seem to be dealing (only) with the issue of ruling out spurious cases of causation. Moreover, proponents of the innocuous hypothesis seem to be on the track of a mechanism; it is not entirely implausible that mental stress, smoking, obesity and lack of physical activity could induce directly atherosclerotic lesions.

However, when it comes to the application (and fulfillment) of the Clarke et al. criteria, the pathogenetic hypothesis fares far better than the innocuousness hypothesis. The number of research groups and different methodologies used to pin down the pathogenic mechanism of cholesterol far outreaches that used for the opposite hypothesis. What is even more important, the number of discovered features of the pathogenetic mechanism (including thirteen Nobel prize discoveries; see Endo Reference Endo2010) is far superior to the number of mechanistic features backing up the innocuousness hypothesis. Population studies grouping participants with very different characteristics and background (age, race, dietary habitudes, etc.) have shown a high degree of robustness and stability for the pathogenetic hypothesis (Steinberg Reference Steinberg2005a, Reference Steinberg2005b) that contrasts with the fluctuation of results of studies (mostly systematic reviews) in favor of the innocuousness mechanism.Footnote ¹⁵

All in all, the quality of mechanistic evidence for the pathogenic hypothesis is superior to the quality of mechanistic evidence for the innocuousness hypothesis. Since the explanatory role of mechanisms is all the more direct, the more criteria of Clarke et al. are satisfied, we should have at the level of confirmation that the Pr function resulting from a Bayesian interpretation of population studies in favor of the cholesterol hypothesis is more resilient than the Pr function of the innocuousness hypothesis, thus reflecting the far superior quality of mechanistic evidence (no matter what the balance of population studies shows).

Parenthetically, one of the advantages of this resilience approach is that it leaves room for revolutionary theories (and this is one of the reasons I have chosen the example of the cholesterol controversy). Proponents of the innocuousness hypothesis have often complained of being censured and of having limited access to the academic publishing sphere (and this is a complaint which, of course, given the tremendous influence of pharmaceutical companies, might have some grain of truth in it). However, on the resilience approach, theories such as the innocuousness hypothesis still have the door open. It is the case that quality mechanistic evidence should increase the resilience of corresponding hypotheses. It is not the case that, once good mechanistic evidence is brought in, the rival hypotheses and contrary evidence will simply be ignored. But what is asked from such rival hypotheses (beyond the results of population studies) is that they provide quality mechanistic evidence. Given the subtle and penetrating nature of the Clarke et al. criteria, such mechanistic evidence could be judiciously assessed, and promising evidence would (and should) be given appropriate heed. From this perspective, the message to be sent to the proponents of the innocuousness hypothesis would just be – tell us a bit more about your mechanisms, and we will see what we can do about the resilience!

Subsequent work in the application of Bayes nets to mechanisms themselves,Footnote ¹⁶ as well as, as one should hope, developments of McCain and Poston's own proposal, are likely to make this resilience role of mechanisms more explicit. But it is, I suggest, a very fruitful path of research.