Inference to the Best Explanation (IBE) has a curious status within analytic philosophy. Many acknowledge its pervasiveness in our cognitive activity, but, especially in the arcane game of epistemology, others find it of dubious value. The collection of essays under review reflects this ambivalence but does not do a great deal to resolve it.

Crudely speaking, it did not take long for western philosophy to achieve some sort of grasp of deductive reasoning, where conclusions are conditionally guaranteed by their premises. But it didn’t do much for the other modes of reasoning that people use. The traditional contrast between deduction and induction tended to portray induction on the model of its enumerative version (collect lots of As that are B and conclude all As are Bs), which is arguably a philosopher’s invention rather than anything a rational person would adopt (see Peter Godfrey-Smith, “Induction, Samples, Kinds“). Be that as it may, enumerative induction offers a picture of only a tiny portion of our non-deductive thinking.

While people like Descartes and Newton propounded “rules” for scientific investigation, and later J.S. Mill offered his methods for causal investigations, it seems to be Peirce who first explicitly tied (scientific) explanation to a mode of reasoning distinct from deduction or induction, a mode he baptised abduction. As Cheryl Misak notes in chapter 2 in our collection, Peirce’s abduction belongs to the realm of discovery rather than establishing provisional truth: you have some facts, abduction is meant to provide an explanation of them, so you then investigate whether that explanation holds, using “varieties of induction and statistical inference” (p. 29). A problem here is that there seem to be no rules for inventing explanations, so Peirce’s three-way classification of logic breaks down (what he appeals to is in fact deductive: P entails and would explain the facts, so let us investigate whether P, but there is no rule that provides P in the first place). Subsequent philosophers have taken explanatory considerations as relevant to the justification, or less tendentiously, good sense, of some of our non-deductive conclusions (v. Douven, Igor, “Abduction“, The Stanford Encyclopedia of Philosophy (Summer 2017 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/sum2017/entries/abduction/>).

Before turning to the book under review, let me note two more problems for philosophical engagement with IBE. It is obviously concerned fundamentally with (best) explanations, so it would be helpful if we had a story to tell about explanation. But this being philosophy, of course we don’t. The book does not deal much with this problem, relying on our intuitive ability to detect better or worse explanations, and on what seems to me a defensible thought that while more is required of a good explanation than that what is to be explained, the explanandum, follows deductively from laws (and possibly initial conditions), that is at least one desideratum that explanations aspire to.

The second problem does get considerable discussion in the book. It arises from the fact that IBE tells you what it is sensible to accept in the light of your evidence, and that Bayesianism also tells you what it is sensible to do in the light of (new) evidence. Since these are different advisors with often different advice, what are you to do? (Bayes’ theorem tells you how to adjust your degree of belief, credence, in a claim when given a piece of evidence [let me suppose evidence e for a hypothesis h, we can write the value of the credence in question as Pr(h|e)]; it produces an answer from your degrees of belief in three other claims: the prior degree for the claim (Pr(h)), the prior degree for the evidence (Pr(e)), and the degree of belief in the evidence given the claim, which is labelled its likelihood (Pr(e|h)). Pr(h|e) = Pr(e|h) x Pr(h)/Pr(e). It doesn’t mention anything about h‘s explaining e.)

This question occupies much of the first section of the book. Igor Douven kicks off by comparing the mathematically precise formulations offered by Bayesianism with the slippery characterisations of IBE, concluding that regarding it as no more than a slogan  – assess hypotheses at least partly on the basis of their explanatory virtues (p. 7) – is not such a bad idea. He reaches that conclusion via showing that one can formulate precise versions of IBE à la Bayes and that, in the very artificial situations in which people study the utility of probabilistic rules for updating credences, such IBE rules perform as well as Bayes’ own, and zero in on the true hypothesis somewhat faster (he summarises results for various rules on pp. 21-22).

Similar moves are made by Jonah Schupbach in the third chapter where he first elucidates a notion of explanatory power (to make the explanandum unsurprising), sets out some conditions it should satisfy and argues that there is only one form of measure (operating like Bayes’ with probabilities of hypotheses and evidence) that succeeds. His formula measures comparative power: this hypothesis explains better than those. He shows that when a hypothesis has greater power than others, “the hypothesis judged to provide the best explanation will have the greatest corresponding likelihood of any explanatory hypothesis considered…. Holding all else constant, the greater a hypothesis’s corresponding likelihood, the greater its probability given e” (p. 48). If our best explanatory hypothesis is at least as plausible (apart from e‘s consideration) as its competitors then IBE’s advice will coincide with Bayes’.

Bayesianism proposes a highly idealised epistemic context (logical omniscience; exact values for the various credences [actually having anything like such credences]; among other issues). Schupbach reports computer simulations that show that when reasoners are assumed to have accurate prior probabilities, IBE performs almost as well as Bayes in arriving at the correct hypothesis, but when, more realistically, their priors are inaccurate, IBE, which only attends to likelihoods, may become more reliable than standard probabilistic reasoning (p. 55). So one response to the Bayes issue is to think that, lacking the accurate probabilities required for Bayes, ordinary human reasoners are more than adequately provided for by IBE’s quick and dirty heuristic. That is also the upshot, as the editors see it, of Alexander Bird’s discussion in chapter 7. (But a good deal of Bird’s paper focusses on problems within Bayesianism, what I called its highly idealised assumptions. Perhaps the same can be said for Timothy McGrew’s short chapter 15, which argues for adopting “Cromwell’s rule” within Bayesian operations so as to avoid dogmatism: let Pr(h|e) = 1 if and only if e logically implies h. One important point McGrew makes, almost in passing, is that a rational person would not always simply plug in their credences to Bayes’ theorem when they acquire new evidence: they might think the taken-for-granted circumstances are not what they seemed. Or they might cast around for new ideas. But these are problems for Bayes, not IBE.) In a way it is also close to the aim of Leah Henderson in chapter 16: “when the structure of scientific theories is taken properly into account, a Bayesian model of the preference for better explanations can be provided, making only assumptions which are quite natural and independent of any explanatory concerns” (p. 248). The Bayesian God sees that what humans prefer for explanatory reasons is underwritten by whatever probabilities it operates with.

Several chapters discuss what epistemologists should make of IBE. They exemplify the somewhat idiosyncratic nature of current epistemology:

·         is IBE a fundamental form of reasoning? (No: Richard Fumerton, chapter 5, Kareem Khalifa and others, ch. 6; Yes: the editors, ch. 8);

·        can IBE be justified? (Yes and No: Adam Carter and Duncan Pritchard, ch. 9; Yes, Ali Hassan, ch. 10);

·         how does IBE fare against scepticism? (ok: James Beebe, ch. 11; badly: Ruth Weintraub, ch. 12, Susanna Rinard, ch. 13).

These writers trade in intuitions about warrant and what we can recognise a priori. They mostly assume that they know what induction is, though on a couple of occasions Harman’s belief that what people call induction (when it is a sensible thing to do) is really another instance of IBE is noted but not properly discussed.

One of the most interesting of these discussions is James Beebe’s chapter 11, which argues that the workings of standard sceptical hypotheses (dreaming, brain-in-a-vat, etc.) themselves employ key IBE notions (rather than what he labels the “quasi-logical” mechanisms mostly used to analyse them), so those notions cannot be impugned in general when anti-sceptics use IBE in offering a response to scepticism.

Two papers have not yet been mentioned: William Roche’s heavily mathematical chapter 14 on one of Hempel’s paradoxes and how “screening off” rather than explanatory power might be a key part of the solution to it, and Elizabeth Fricker’s very long and dense final chapter vindicating what has always seemed right to me, that when the question of accepting testimony arises for rational decision, the solution is to look for the best explanation of the fact of its having been given – not what explains p but what explains the fact that this witness testifies that p.

So what to make of this collection? It presents a picture of some of the work that is going on relating to IBE, a few reports of minutiae that might better have been put in a journal, and some more comprehensive discussions, but aimed at cognoscenti rather than a newcomer to the field. It is the sort of book good libraries should have and that some graduate students may need to consult. It is not a game changer.

 

© 2018 Ed Brandon

 

Ed Brandon is, by training, a philosopher, and now is retired from working in a policy position in the University of the West Indies at its Cave Hill Campus in Barbados.