Inference to the Best Explanation

The Miracle Argument for realism is a special case of inference to the best explanation, hereafter IBE for short. IBE is a pattern of argument that is ubiquitous in everyday life as well as in science.

Before turning directly to this, how does IBE work in general and what does it show? Philosophers assume that IBE, and its intellectual ancestor Peirce's abduc­tion, are non-deductive or inductive or ‘abductive' arguments which are supposed to show that some theory is true. I think the philosophers are wrong on both counts.

Peirce's abduction is supposed to go like this:

The surprising fact, C, is observed.

But if A were true, C would be a matter of course.

Hence,... A is true.

[C. S. Peirce, Collected Papers, 1931-1958, Vol. 5, p. 189.]

This is deductively invalid. We can validate it if we view it as a deductive en- thymeme and supply its missing premise, “Any explanation of a surprising fact is true”. But this missing premise is obviously false. Nor is any comfort to be derived from weakening the missing premise (and the conclusion) by replacing ‘true' with ‘probably true' or with ‘approximately true'—though philosophers have cottage industries devoted to both these projects. It is a surprising fact that marine fossils are found on mountain-tops. One explanation of this is that Martians came and put them there to surprise us. But this explanation is not true, or probably true, or approximately true. Nor should philosophers derive any comfort from saying that although the argument is deductively invalid, it has some sort of merit in some special inductive or abductive logic.

IBE attempts to improve upon abduction by requiring that the explanation is the best explanation we have. It goes like this:

F is a fact.

Hypothesis H explains F.

No available competing hypothesis explains F as well as H does.

Therefore, H is true.

[Lycan 1985, p. 138]

This is better than abduction, but not much better. It is also deductively invalid. We can validate it if we view it as a deductive enthymeme and supply its missing premise, “The best available explanation of a (surprising) fact is true”. But this missing premise is also obviously false. Nor, again, will going for probable truth or approximate truth or some fancy explanationist logic help matters.

There is a way to rescue abduction and IBE. Peirce provided the clue to this. Peirce's original abductive scheme was not quite what we have considered so far. Peirce's original scheme went like this:

The surprising fact, C, is observed.

But if A were true, C would be a matter of course.

Hence, there is reason to suspect that A is true.

[C. S. Peirce, Collected Papers, 1931-1958, Vol. 5, p. 189.] This is invalid, but to repair it we need the missing premise ‘There is reason to suspect that any explanation of a surprising fact is true'. This missing premise is, I suggest, true. After all, the epistemic modifier ‘There is reason to suspect that...’ weakens the claims considerably. In particular, ‘There is reason to suspect that A is true’ may be true even though A is false. If the missing premise is true, then instances of the abductive scheme may be deductively sound. We have not traded obvious invalidity for equally obvious unsoundness.

IBE can be rescued in a similar way. I even suggest a stronger epistemic modifier than ‘There is reason to suspect that namely ‘There is reason to believe (tentatively) that or ‘It is reasonable to believe (tentatively) that What results, with the missing premise spelled out, is:

It is reasonable to believe that the best available explanation of any fact is true.

Hypothesis H explains F.

No available competing hypothesis explains F as well as H does.

Therefore, it is reasonable to believe that H is true.

This scheme is valid and instances it of might well be sound. Inferences of this kind are employed in the common affairs of life, in detective stories, and in the sciences.

Of course, to establish that any such inference is sound, the ‘explanationist’ owes us an account of when a hypothesis explains a fact, and of when one hypothesis explains a fact better than another hypothesis does. If one hypothesis yields only a circular explanation and another does not, the latter is better than the former. If one hypothesis has been tested and refuted and another has not, the latter is better than the former. These are controversial issues, but they are not the most controversial issue. That concerns the major premise. Most philosophers think that the scheme is unsound because this major premise is false, whatever account we can give of explanation and of when one explanation is better than another. So let me assume that the explanationist can deliver on the promises just mentioned, and focus on this major objection.

It is objected that the best available explanation might be false. Quite so—and so what? It goes without saying that any explanation might be false, in the sense that it is not necessarily true. It is absurd to suppose that the only things we can reasonably believe are necessary truths.

But what if the best explanation of a fact not only might be false, but actually is false. Can it ever be reasonable to believe a falsehood? Of course it can. Van Fraassen has a homely example:

I hear scratching in the wall, the patter of little feet at midnight, my cheese disappears—and I infer that a mouse has come to live with me. Not merely that these apparent signs of mousely presence will continue, not merely that all the observable phenomena will be as if there is a mouse, but that there really is a mouse.

But this means, it is objected further, that being the best available explanation does not prove a hypothesis to be true. Quite so—and again, so what? The explanationist principle—“It is reasonable to believe that the best available explanation of any fact is true”—means that it is reasonable to believe or think true things that have not been proved to be true. Philosophers who think that it can only be reasonable to believe what has been proved will reject the explanationist prin­ciple. Such philosophers accept what I have called the ‘justificationist principle', according to which a reason for believing something must be a reason for what is believed.

Explanationism, or the explanationist principle, stands opposed to justifica- tionism, or to the justificationist principle. As I see it, the rejection of justifica- tionism lies at the heart of Karl Popper's critical rationalism. And explanationism, as I understand it, is part and parcel of critical rationalism. But most philosophers see things differently, accept justificationism, and go in for the usual formulations of IBE, where the conclusion is that the best explanation is true (or probably true, or approximately true). Critics rightly object that such conclusions do not follow. They can be made to follow, but only by adding to the premises an absurd metaphysical principle like “The best available explanation of any fact is true (or probably true, or approximately true)”. Most philosophers, instead of making these absurd meta­physical principles explicit, reply that abduction or IBE has some special merit in some special abductive or non-deductive logic.

But do explanationism and realism go hand-in-hand as well? Why cannot constructive empiricists also accept IBE and put their own gloss upon it? When we consider van Fraassen's mouse hypothesis, truth and empirical adequacy coincide, since the mouse is an observable thing. But when it comes to hypotheses about unobservables, truth and empirical adequacy come apart. Why cannot the con­structive empiricist also accept IBE, but only as licensing acceptance of the best available explanation as empirically adequate, not as true? As Howard Sankey puts it: “The question is why it is reasonable to accept the best explanation as true. Might it not be equally reasonable to accept the best explanation as empirically adequate...?” (2006, p. 118).

My answer to this question is NO. Suppose that H is the best explanation we have of some phenomena. Remember the Truth-scheme: It is true that H if and only if H. Given the Truth-scheme, to believe that H and to believe that H is true are the same. Given the Truth-scheme, to accept that H and to accept that H is true are the same. So what is it to accept that H is empirically adequate? It is not to accept H, for this is the same as accepting that H is true. Rather, it is to accept a meta-claim about H, namely the meta-claim “H is empirically adequate” or equivalently “The observable phe­nomena are as if H were true”. Call this meta-claim H*. Now, and crucially, H* is no explanation at all of the phenomena. The hypothesis that it is raining explains why the streets are wet—but “The phenomena are as if it were raining” does not. Ergo, H* is not the best explanation—H is, or so we assumed. (Actually, all we need assume here is that H is a better explanation than H*.) So given IBE, H* should not be accepted as true.

I wonder which part of this argument those who believe that there is a con­structive empiricist version of IBE will reject. Not IBE—at least, they are pre­tending to accept it. Not, presumably, the Truth-scheme. Not, presumably, its consequence, that to accept H and to accept H as true are the same thing. Not, presumably, the equivalence of “H is empirically adequate” and “The observable phenomena are as if H were true”. Not, presumably, the claim that H is a better explanation of the phenomena than “The phenomena are as if H were true”. What this shows is that realism and explanation go hand-in-hand. If you try to recast IBE in terms of empirical adequacy rather than truth, you end up with something incoherent. You start off thinking that it is reasonable to accept the best explanation as empirically adequate. And you end up accepting something that is no explanation at all.

This does not refute constructive empiricism. It only refutes the idea that con­structive empiricists can traffic in explanation, and in IBE, just as realists do. It is no accident that down the ages acute anti-realists have pooh-poohed the idea that science explains things. Van Fraassen should join Duhem in this, as he already has in most other things.

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