A popular way of reasoning—indeed, it is probably the most widely used across all disciplines—is known as inference to the best explanation (IBE). By the end of this essay, you will know exactly how this works.
Let's start with two examples.
First example: Murder!
Mr. Boddy has been murdered, and now we must find the killer.
One hypothesis is:
H1: Professor Plum is the killer.
But another hypothesis is:
H2: Scarlet is the killer.
Both H1 and H2 explain Mr. Boddy's murder. So how shall we decide between them?
Let’s imagine there is some other fact that H2 does not fit, say, Scarlet has a stellar alibi; professor Plum does not. H1 is looking better now. Sure, H2 is still possible. Perhaps Scarlet is pulling off an elaborate hoax. But this seems somehow a worse explanation. It seems overly complicated or contrived. So, if H1 and H2 are the only options, we can reasonably infer H1. The inference does not guarantee H1, but it makes it likely or plausible.
Still, a further explanation remains:
H3: Professor Plum’s doppelgänger from a parallel universe has mastered the art of hopping dimensions; he is murdering, one by one, all other Professor Plums, so that he will be the only one remaining.
This hypothesis does explain the murder of Mr. Boddy. It fits the data, strictly speaking. But H3 is lousy for other reasons. H1 is far simpler, far more coherent with our background knowledge, whereas H3 requires us to believe a whole bunch of new weird stuff about parallel universes and doppelgängers.
The lesson: while two hypotheses may fit the data, the data is not everything.
That is to say, sometimes two hypotheses are both empirically adequate. Here, “empirical” means coming from or related to experience. An empirically adequate hypothesis is one that fits what experience tells us (in this case, that Mr. Boddy has been murdered). When two hypotheses are both empirically adequate, we will need to settle the matter on extra-empirical grounds, that is, on grounds independent of the data we have. The empirical evidence underdetermines a theory choice. How might we handle such cases?
Before answering that, let's consider a second example.
Second example: Heliocentricity
Remember Copernicus? He’s the guy who single-handedly invented heliocentricity—the idea that the earth revolves around the sun. That, at least, is how the story is told by schoolmarms. In fact, heliocentricity was around long before Copernicus. And it was not fully embraced until long after him.
And for good reason. Believe it or not, geocentricity actually fit our observations of the night sky. To make it fit, however, we had to say that, in addition to revolving around the earth, some bodies also make tiny extra revolutions along the way, called epicycles. Imagine something flying around in a big circle, and as it goes, flying in smaller circles, too, like a tumbling butterfly.
In contrast, heliocentricity was able (eventually) to fit our observations without positing epicycles. It gave us, in the end, a simpler explanation. And all else being equal, the simpler explanation is better.
Three steps of IBE
In sum, to construct an IBE, here are the steps:
Step 1: Describe some fact or datum that needs to be explained.
Step 2: Identify the relevant potential explanations.
Step 3: Decide which explanation is the best.
Those are the three steps, but let’s add some vocabulary.
Some vocabulary
The explanandum (plural: explananda) is the thing that needs to be explained—the untimely death of Mr. Boddy, or the order of the planets. The explanans (plural: explanantia) is the thing that does the explaining—the various hypotheses about who killed Mr. Boddy, or the various models of the universe. In building an IBE, we start with the explanandum, round up the explanantia, then decide on the right explanans.
Explanatory virtues
Step 3 is obviously where much of the action is at. But how can we carry it out? How can we decide which explanation is best?
To do this, we must appeal to explanatory virtues. These are the qualities that make an explanation good. I’ve already mentioned two—empirical adequacy and simplicity. But there are several others, none of which are easy to spell out in detail; it’s something people fight over. Even the terms used can vary.
Nevertheless, here are some explanatory virtues nearly everyone would let into the club (including the two already mentioned).
1. Empirical adequacy
An explanation has empirical adequacy to the extent that it accurately describes our observations, or “fits” our experience. In the murder example, each of H1, H2, and H3 are empirically adequate, at least with respect to Mr. Boddy’s death (if we count Scarlet’s alibi as an observation, then H2 is not empirically adequate).
Empirical adequacy can be thought of as the baseline explanatory virtue. Once an explanation has achieved this, we can go on to assess the explanation for other explanatory virtues, such as
2. Simplicity
An explanation is simple to the extent that it doesn’t posit extra stuff. For instance, in the murder example, one major problem with H3 is its lack of simplicity. It forces us to admit the existence of a new person—the doppelgänger—whom we hitherto had no reason to believe exists, not to mention parallel universes and travel between them.
How exactly to measure simplicity, and why it is a virtue, are controversial. But H3 provides an obviously non-simple explanation, one whose lack of simplicity makes it rather shabby as explanations go. Of course, sometimes we should accept non-simple explanations of things. Sometimes we have to posit new entities—electrons in the cloud chamber, say. But if two explanations are equal in all their other virtues—and that ceteris peribus qualifier is important—yet one is simpler, we should prefer that one.
To make this really clear, imagine a further explanation of Mr. Boddy’s death:
H4: Mr. Boddy was killed by a hitherto undiscovered virus that presents as a gunshot wound.
H4 would explain Mr. Boddy’s death, but it lacks simplicity, since it forces us to posit a new virus. Since there are simpler explanations available, we should prefer these.
3. Predictive power
An explanation has predictive power to the extent that it can make predictions that are (a) correct, (b) novel, and (c) specific. In short, predictively powerful explanations tell us what to expect. For instance, consider the discovery of the planet Neptune. In the 19th c., there was a mismatch between the orbit of Uranus and what you would expect from the laws of gravity. This suggested that a further large object is exerting gravitational effects on Uranus. Indeed, that is exactly what Le Verrier thought, a French astronomer. Le Verrier came up with a mathematical model that predicted the exact location of Neptune, which was confirmed by later observation (via telescope----well, duh).
Here, the explanandum is Uranus’ orbit. And the explanans that Le Verrier offers is both the claim that there is a larger body affecting the orbit. But what made his version of this explanans really powerful was that it made precise predictions.
Indeed, imagine someone else offered a rival explanans. Imagine the rival was just as good as Le Verrier’s in all respects except that it didn’t make any prediction about where exactly Neptune would be. It isn’t that it made a false prediction—that would be a different problem, one of empirical adequacy. It’s rather that it doesn’t make any prediction about the location of Neptune. In that case, Le Verrier’s is the better explanation, better because of its predictive power.
A second example from the history of science: Mendeleev’s periodic table was able to predict the atomic mass of elements as well as some of their chemical properties before they had even been discovered.
Ceteris paribus, we should prefer the explanation with greater predictive power.
4. Unification
An explanation is unifying to the extent that it takes seemingly separate things and shows they have an underlying unity. For instance, in the 19th c., it was discovered that electricity and magnetism were at root the same force. This explanation not only made our view of the world simpler (by positing less junk); it also made it deeper. It showed us something more fundamental about the structure of the world.
Summing up
There are other explanatory virtues besides these ones, but this list of four is a good place to start. Ceteris paribus, explanations that have these traits—that are empirically adequate, that are simple, that make predictions, that unify the stuff we see—are preferable to those that don’t.
Still, IBE does not offer absolute certainty. Even a good IBE leaves it open that the conclusion might be false. In this way, it differs from deductively valid arguments. Nevertheless, IBE is often the best tool we have for the job.
I've given examples of IBE from science and forensics. But for an example from philosophy, check out the fine-tuning argument.
