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Abduction and the Limits of Science, Part 2: Simplicity and Explanatory Power

What This Article's All About

In my last article, I showed that scientific explanation involves an inextricable reliance upon a logically fallacious form of reasoning called Affirming the Consequent. To review: In order to explain the natural world, scientists must engage in abduction; abductive reasoning is formally identical to the logical fallacy Affirming the Consequent; thus, in order to explain the natural world, scientists must engage in logically fallacious reasoning.

In this article, I'm going to say a bit more about the limits of science, and I'm going to do so by further unpacking the limits of abduction.

As I stated in my last article and the one before it, abductive reasoning involves reasoning from some observation to a statement, theory, et cetera, that explains that observation; this is why abduction is often referred to as "inference to the best explanation."

Even a basic, cursory account of abduction (such as the one I just offered you) should leave you with the following questions: How do we determine which of several competing explanations is the best explanation? And even in cases where it's obvious which explanation is the best, why think the "best" explanation is actually true? Obviously, we'll have to employ some criteria to determine which explanation is the best; isn't it possible that these criteria would lead us to embrace an explanation that's false?

Those are the questions I'm going to deal with in this article.

Sutherland Did It

Consider the following scenario: You and a friend drive to a nearby field to throw a Frisbee; when you get there, you're surprised by the fact that the field is covered in water and consequently too wet to use. Taken aback by the amount of water on the field, you and your friend find yourselves debating various explanations for this fact.

You point out that, if it rained really hard, then the field would be really wet; you conclude that it must have rained really hard. Your friend points out that if the sprinklers had been on all night the field would be really wet. He also draws your attention to the fact that the parking lot isn't that wet and points out that heavy rain would dump just as much water on the parking lot as it would on the field. You counter with the observation that water always runs downhill in combination with the observation that the field is downhill from the parking lot; "the water ran off of the parking lot and onto the field," you say; then you point out that there are very dark clouds nearby and that these clouds are much more probable on the heavy rain theory than the sprinkler theory.

Suddenly, a man wearing black sunglasses and a black suit pulls up in a black Lincoln Town Car and tells you in hushed tones that it did rain, a little, and the sprinklers were on, but only for five minutes. The real reason the field is so wet is that Donald Sutherland hates you and he sabotaged your Frisbee session by spending hours and hours with his accomplice, Gary Wasserfeld, hosing down the field.

The rain theory, the sprinkler theory and the Donald Sutherland theory all entail the field being really wet. But the field being really wet entails none of these theories. Neither do the other observations mentioned above. In fact, they entail no theory at all; they entail only consequences — specifically, the consequences of the field being wet, the parking lot being above the field, etc. In what sense, then, would the observations listed above suggest that one of the theories is better than the others?

There is no straightforward, purely logical way to get from an observation or set of observations to a theory. And, as we shall see, there is also no straightforward, purely logical way to determine from an observation or set of observations which of several competing theories is the best.

Explanatory Power

Perhaps, then, we can determine which theory is the best, not by working from the observations back to the theories, but by working from the theories to the observations via prediction and seeing which theory predicts the highest number of the things we observe.

Suppose, for example, that we've observed natural phenomena P^-1 through P^-10, and suppose we're locked in heated debate over three competing explanations of phenomenon P^-1. Moreover, suppose that, whereas theory 1 entails everything we've observed (i.e., P^-1 through P^-10), theory 2 entails only P^-1 through P^-8, and theory 3 entails only P^-1 through P^-4. In this case, we might be inclined to conclude that theory 1 is the best explanation for P^-1. But if the true explanation is always the best explanation, then it's clear that this inclination might lead us astray.

Again, think about the field and the three theories we had to explain it — the sprinkler theory, the rain theory and the Donald Sutherland theory. Also, suppose that, in addition to the fact that the field is really wet, the fact that the parking lot is above the field and the fact that there are dark clouds nearby, we've observed that everything is a little wet for miles around, that everyone is indoors, and that the field has more water on it than a nearby drainage ditch that's lower than it.

Which of our three theories predict these observations?

The rain theory predicts that people will probably be indoors and that everything will probably be wet for miles around, whereas the sprinkler theory doesn't. On the other hand, the sprinkler theory predicts that the field will probably have more water than the nearby drainage ditch, whereas the rain theory doesn't. But the Donald Sutherland theory predicts all of these things, since light rain implies both that everything would be a little wet and that people would probably be indoors, and since Donald Sutherland soaked only the field, not the nearby drainage ditch.

We've mentioned six observations; if we count, we'll see that the Donald Sutherland theory accounts for six of them, that the rain theory accounts for five of them, and that the sprinkler theory accounts for four of them. If the "best" explanation is the explanation which explains the highest number of our observations — that is, if the best explanation is the most powerful explanation — then the Donald Sutherland theory is obviously the best. But why think that the most powerful explanation is the true explanation?

Simplicity

Now suppose that the mysterious man in the black car drives by again and explains that the dark clouds on the horizon never came near the field and are therefore completely unrelated to the fact that everything is wet, explains that Donald Sutherland flooded the drainage ditch too, but it's so full of cracks that it can't contain any water, and explains that everyone is indoors because they're all in front of the TV watching American Idol. Also, suppose we include all of this new information as part of the Donald Sutherland theory.

As we noted above, the Donald Sutherland theory is more powerful than the rain theory and the sprinkler theory. But it's rather unwieldy, isn't it? Compared to the rain theory and the sprinkler theory, wouldn't trying to explain the world with theories like this one resemble walking into the backcountry with a huge box of tools instead of just taking your Leatherman® Surge™ multi-tool? If your job required you to make use of different theories, wouldn't you prefer theories like the rain theory and the sprinkler theory to theories like the Donald Sutherland theory?

If the "best" explanation is the explanation that's easiest for us to wield — i.e., if it's the simplest — then the Donald Sutherland explanation is obviously not the best. But what if it's actually true? It's awfully strange, no doubt, but strange things sometimes happen. Sometimes, the events we want explained aren't caused by law-like processes that can be elegantly articulated in a few words or expressed as a tidy equation.

In any case, the point is, only on the unwarranted assumption that the world and its phenomena are always simple (rather than complicated, unpredictable and complex) can we put much confidence in the claim that a true explanation will always be a simple explanation.

Tidy Conclusion

C O F F E E  S H O P

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What do you do if the best explanation is not necessarily the true explanation?

Join the discussion!

So, if by "best" we mean either simple or powerful (or perhaps a combination of simple and powerful), then it's not clear that the best explanation of some phenomenon will be the true explanation of that phenomenon. But perhaps we can determine which explanation is the best some other way. Perhaps, for example, we can subject our theories to a process of elimination; perhaps we can demonstrate — via experimentation — that all but one of them are false and thereby conclusively demonstrate which of them is the best.