Inference to the Best Explanation Cannot Be Reduced to Likelihoods

Some think that inference to the best explanation (hereafter, IBE) is a unique inferential methodology, distinct from deduction and induction. In this blog, I examine and evaluate a reductionist move, wherein IBE is taken to be nothing more than an assessment of likelihoods (i.e., 'Pr(E|H)', where 'E' is some evidence and 'H' some hypothesis). More precisely:

• Reduction to Likelihoods (RL): an inference to H on the grounds that it is the best explanation for E is nothing more than an assessment of the likelihood ratio, Pr(E|H)/Pr(E|~H), wherein the ratio is taken to be equal to some value greater than 1.

Something like RL is defended by Gilbert Harman [1]. An additional and related attitude towards IBE that I've often encountered goes something like this: "Why even bother with IBE, given that we can just assess likelihoods? IBE is both unnecessary and of no practical value now that we have the probability calculus." I'll call this the irrelevance objection (IO) to explanatory reasoning. IBE is irrelevant, says IO, if we can assess likelihoods. Both RL and IO take it that likelihoods (and Bayes's theorem in general) are doing the real inferential work. 

As it seems to me, both RL and IO are misguided. The reason is that we are often not in a position to discern the value (comparative or absolute) of 'Pr(E|H)/Pr(E|~H)'. In virtue of what are we able to say that 'Pr(E|H) > Pr(E|~H)', or vice-versa? RL and IO simply take it for granted that an analysis of likelihoods (comparative or otherwise) is epistemically accessible, independent of other non-probabilistic considerations. However, this is dubious. While likelihood ratios are useful for assessing confirmation when we already have a grasp of what the likelihoods are, Bayesian resources are of no avail when the likelihoods are the very values in question. In such cases, it seems, we must rely on criteria we take to be epistemically relevant (perhaps instrumentally relevant) for assessing likeliness. Epistemic considerations of some sort must guide our thinking about the values of the likelihoods we're assessing. As many would argue, explanatory virtues can play this role [2]. 

On this matter, Peter Lipton is worth quoting at length:

[Thinking of IBE as Inference to the Likeliest Explanation] would push Inference to the Best Explanation towards triviality. We want a model of inductive inference to describe what principles we use to judge one inference more likely than another, so to say that we infer the likeliest explanation is not helpful. To put the point another way, we want our account of inference to give the symptoms of likeliness, the features an argument has that lead us to say that the premises make the conclusion likely. A model of Inference to the Likeliest Explanation begs these questions...Inference to the Best Explanation is an advance only if it reveals more about inference than that it is often inference to the likeliest cause. It should show how judgements of likeliness are determined, at least in part, by explanatory considerations [3].

I think Lipton is absolutely right. To avoid these problems, Lipton explicates IBE as inference to the loveliest explanation, where H is more lovely than its competitors if it brings more understanding [4]. One may disagree with this account, wishing to offer some alternative story of what IBE is, but the main point is this: some account of IBE that does not construe explanatory inference as Inference to the Likeliest Explanation is needed. Both RL and IO fail on this account, either making IBE trivial (in the case of RL) or failing to appreciate the need for epistemic/instrumental virtues that guide our thinking about likeliness (in the case of both RL and IO). 

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[1] See Plutinsky, "Four Problems of Abduction: A Brief History" (2011).

[2] For a good paper on how explanatory virtues serve as guides for thinking about probability values within a Bayesian framework, see McGrew, "Confirmation, Heuristics, and Explanatory Reasoning" (2003). 

[3] Lipton, Inference to the Best Explanation (1991; 2nd edition).

[4] In the end, Lipton's full account of IBE turns out to be inference to the loveliest, potential, causal, contrastive explanation.