MODELS OF SCIENTIFIC EXPLANATION AND
INFERENCE TO THE BEST EXPLANATION

We’ve all read footnotes that say something along the lines of ‘This topic is relevant to our discussion, but cannot be adequately addressed in this article due to space constraints’. In my article ‘Which Models of Scientific Explanation Are (In)Compatible with IBE?‘, I discuss a topic that is usually only mentioned in these kinds of footnotes.

Explanationists defend inference to the best explanation (or IBE) as a rational form of inference. However, they rarely tell us what constitutes an explanation, nor do they address the issue of how IBE relates to the models of scientific explanation defended and discussed by philosophers of science. Often, explanationists defend IBE by providing intuitive examples where the best explanation seems to be the most likely. Consider the following scenario: My partner is at a local pub watching their football team play a derby. They come home looking very grumpy. I infer that their team lost the derby. Why do I make this inference? Because the hypothesis that their team lost the derby is the best explanation for why my partner is as grumpy as they are.

Personally, I don’t find these examples persuasive. Why think the inference is an instance of IBE rather than a case of Bayesian conditionalization? I want the explanationist to tell me what constitutes a good explanation so that I may know whether the qualities that make something a good explanation also make it likely. However, after giving examples like these, explanationists do not provide an account of explanation. Rather, they often proceed by assuming that the correct account of explanation, whichever one that may be, will support IBE. Even explanationists who acknowledge the need to defend an account of explanation that supports IBE often relegate that task to future work. Similarly, philosophers of science who develop and defend various models of explanation are rarely concerned with whether their favoured model is compatible with IBE. Wesley Salmon and Nancy Cartwright are the exceptions here; they have developed models of explanation and have rejected IBE on the basis of their favoured models of explanation.

In my article, I address this under-explored issue. I survey some of the leading models of scientific explanation and ascertain which are, and which are not, compatible with IBE. I begin by distinguishing between Bayesian interpretations of IBE and non-Bayesian (or ampliative) interpretations of IBE. On Bayesian interpretations of IBE, a hypothesis’s status as a good explanation of the evidence manifests in the Bayesian priors, namely, the probability of the hypothesis, P(H), the probability of the evidence given the hypothesis, P(E|H), and the probability of the evidence, P(E). On ampliative interpretations of IBE, a hypothesis’s status as a good explanation of the evidence provides probabilistic boosts beyond Bayesian conditionalization. I restrict my discussion of IBE and models of scientific explanation to Bayesian interpretations of IBE. This is because any model of scientific explanation is trivially compatible with ampliative IBE. To my knowledge, no model of scientific explanation prohibits boosting one’s credence in a hypothesis beyond the probability of that hypothesis given the evidence when the hypothesis is the best explanation of the evidence.

For Bayesian interpretations of IBE, things are not so simple. According to Bayesian explanationists, explanatory goodness is conducive to Bayesian confirmation or inference. That means a given body of evidence needs to make the best explanation probable or more probable than it would otherwise be. Thus, I argue that IBE requires two things from a model of scientific explanation. First, the positive correlation requirement: The model needs to tell us that explanatory goodness is positively correlated to likelihood. Roughly, a hypothesis is a good explanation if it is positively correlated to its own probability, P(H), the probability of the evidence given the hypothesis, P(E|H), or both. If a model does not satisfy this requirement, then it tells us that explanatory goodness is not conducive to Bayesian confirmation or inference. Second, the epistemic accessibility requirement: The model needs to tell us that explanatory goodness is often more epistemically accessible than assignments of Bayesian priors. That is, the direction of inference goes from the hypothesis’s status as a good explanation to the hypothesis’s probability and likelihood, not the other way around.

Thus, I lay out the following criteria: A model of scientific explanation supports IBE if and only if the model entails that explanatory goodness is positively correlated to the probability of the hypothesis, P(H), or the probability of the evidence given the hypothesis, P(E|H), and explanatory goodness is more epistemically accessible than assignments of Bayesian priors. A model of explanation is merely compatible with IBE if and only if it is merely consistent with the positive correlation requirement and the epistemic accessibility requirement. A model of explanation is incompatible with IBE if and only if it entails the denial of the positive correlation requirement or the epistemic accessibility requirement. Now, the work may begin.

I spend much of the article discussing five of the most influential models of scientific explanation in the literature: Philip Kitcher’s unificationist account, Peter Railton’s deductive-nomological-probabilistic model, Salmon’s statistical-relevance model and his causal-mechanical model, and Bas van Fraassen’s erotetic account.

I will avoid going into the details here. However, I argue that Kitcher’s unificationist account supports IBE. On this account, an explanation is good to the extent that it unifies seemingly independent phenomena. This account entails that explanatory judgements are more epistemically accessible than probability assignments and that explanatory goodness is positively correlated to likelihood.

Railton’s deductive-nomological-probabilistic model and Salmon’s statistical-relevance model are incompatible with IBE because each entails that explanatory goodness is not positively correlated to likelihood. On both of these accounts, we can have a perfectly good explanation that does not make the event-to-be-explained probable or even one that decreases the probability of the event-to-be-explained. This means that on both of these accounts, we can have a perfectly good explanation that is improbable given the evidence or made less probable by the evidence it purports to explain.  Van Fraassen’s erotetic account satisfies the positive correlation requirement. On his view, a good explanation must increase the probability of the event-to-be-explained. However, it makes explanatory evaluations the result of probability assignments. So, it is incompatible with IBE because it entails that explanatory goodness is not epistemically accessible except through ascertaining probabilities.

Finally, Salmon’s causal-mechanical model is merely compatible with IBE. This model fulfils the epistemic accessibility requirement but says nothing about whether explanatory goodness is positively correlated to likelihood. If the causal-mechanical model is paired with Salmon’s views on causation, the result will be incompatible with IBE because Salmon allows for probability-decreasing causes. If paired with a view of causation where causes are always probability-increasing, the result will support IBE.

To sum up, I’ve investigated five of the most influential models of scientific explanation. One of them supports IBE, three of them are incompatible with IBE, and the last is merely compatible with IBE. So, many philosophers of science seem to conceive of explanation in a way that does not support IBE.

Next I outline several possibilities we might investigate as a result of my findings. Perhaps one group of philosophers—either philosophers of science or explanationists—has seriously misinterpreted how scientists use the concept of explanation. An empirical study may be helpful to ascertain whether practicing scientists align more closely with philosophers of science or with explanationists on this issue.

A second possibility is that maybe philosophers of science and explanationists mean different things in their use of the term ‘explanation’. That is, maybe they do not use the term univocally. This is difficult to verify, in part because explanationists rarely give us an account of explanation when they defend IBE. Hopefully, by showing that many accounts of explanation are incompatible with IBE, I have given explanationists reason to start developing their own accounts of explanation. If not, I hope to have challenged the assumption often made that the correct account of explanation will support IBE.

A third possibility is that the ampliative interpretation of IBE deserves a closer look. Many explanationists object to the ampliative interpretation of IBE because it is inconsistent with Bayesianism. If that is considered a weakness of the ampliative interpretation, then perhaps the fact that it is the only interpretation of IBE that is compatible with any model of explanation should be considered a virtue.

My findings may also have implications for areas of philosophy that employ explanatory arguments. For instance, it may be worth asking what account of explanation is assumed in arguments such as the explanatory gap argument in philosophy of mind, the no-miracles argument in the realism versus anti-realism debate, and so on. In short, it’s worth investigating those arguments that seem to employ IBE to determine which—if any—model of explanation is at work.