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Abduction and the Limits of Science, Part 1: Affirming the Consequent

Abductive Reasoning: A Quick Review

In my last article, I introduced abductive reasoning by telling a story about a guy buried in the sand and juxtaposing abductive reasoning against inductive and deductive reasoning. To review: Abductive reasoning is the form of reasoning whereby one reasons from particular observations to statements, theories, et cetera, that explain those observations. Deductive reasoning is the form of reasoning that led teammate 3 to the conclusion that he was wearing a white X. It's also the form of reasoning that led me to the facetious conclusion that Michael Moore writes for TrueU. (Ha, ha, ha, ha! … Why aren't you laughing?)

Anyhow, I went to the trouble of explaining and defining abductive reasoning because it's interesting and important. Why? Because the natural world is interesting and important, scientists spend a lot of their energy explaining the natural world, and abductive reasoning is the form of reasoning whereby scientists formulate their explanations.

Abductive reasoning has its limits, though, and this means science has its limits. In this article and the next, I'm going to say a few things about these limits.

Explanation Explained

But first, what's an explanation? What, exactly, is it to explain something?

This is a complicated question, and I doubt I could give you an exhaustive answer. But in any case, we can gain some understanding of explanation by noting that answers to "Why ... ?" questions are typically viewed as explanations. We can also gain some insight into the difference between good and bad explanations by looking at a few examples.

Consider the answers below in relation to the question, Why does Shaquille O'Neal spend so much time around basketball players?

Answer 1: Because he plays on a pro basketball team.

Answer 2: Because he's one of the best basketball players in the world.

Answer 3: Because he's a pro athlete.

Answer 4: Because Michael Moore wears tube socks.

Answer 1 is clearly a better explanation of why Shaq spends a lot of time around basketball players than Answer 4. Moreover, most people would agree that 1 through 4 are in order from best explanation to worst. What's the difference, then? What makes us think that 1 is better than 2, 2 is better than 3, and 3 is better than 4?

For starters, we're often inclined to think that statement S explains observation O when O follows deductively from S, as is the case in Answer 1.¹ Since one can't play on a pro basketball team without spending a lot of time around other basketball players, Shaq's spending a lot of time around basketball players follows deductively from the statement that he plays on a pro basketball team.

But we're also often inclined to think that statement S explains O when O is likely, given S. Shaq's spending a lot of time around basketball players doesn't follow from his being one of the best basketball players — perhaps one of the world's best spends all of his time helping orphans in India — but it's very likely that one of the world's best basketball players would spend a lot of his time around other basketball players. This is why we're inclined to feel some sense of satisfaction after reading Answer 2.

What makes 2 a better explanation than 3, then? Degree: If O is more probable on S^-1 than on S^-2, then we'll probably be inclined to think that S^-1 is a better explanation than S^-2. While Shaq's spending a lot of time around basketball players is very probable on the statement that he's one of the best in the world, it's not that probable on the bald statement that he's a pro athlete. After all, people make a living playing lots of different sports; if Shaq was a pro figure skater, he'd be a pro athlete; in this case, however, he'd spend all of his time on the ice rather than the basketball court.

Answer 4 isn't just the worst of these explanations; it would be hard to think of a poorer explanation for Shaq's spending a lot of time around basketball players. This is because, so far as we know, 4 is completely irrelevant to the amount of time Shaq spends around basketball players. Not only does Michael Moore's sock selection not entail Shaq's spending a lot of time around basketball players, there's no probabilistic relationship between the two.

In any case, whatever the precise definition of "explanation" is, it's clear that we can generalize the shortcomings of 4 to form the following conclusion about explanation in general: For any statement S and observation O, if S neither entails O nor suggests that O is likely or probable on S, we will not be satisfied with S as an explanation for O.

And we can generalize from our explanation of the superiority of 2 over 3 to this conclusion: For any two statements S^-1 and S^-2, if — everything considered — O is more probable on S^-1 than on S^-2, S^-1 will strike us as a better explanation of O than S^-2.²

A Few Paradigmatic Examples

OK, now back to abductive reasoning which, you'll recall, is the form of reasoning by which one reasons from observations to statements, theories, et cetera, that explain these observations.

In case you're inclined to doubt that abductive reasoning plays an essential role in scientific explanation, run the following example statements by professors in the disciplines listed and ask if they're typical of the kinds of arguments made in these disciplines:³

Physics:
If the universe is expanding, then the electromagnetic waves produced by starlight will be redshifted; the electromagnetic waves produced by starlight are redshifted; therefore, the universe is expanding.

Geology:

If a valley was formed by a glacier, then it will probably exhibit lateral and terminal moraines, and an overall U shape; many of the valleys in Colorado's Ten Mile Range are U-shaped and exhibit lateral and terminal moraines; therefore, glaciers formed many of the valleys in Colorado's Ten Mile Range.

Biology:
If two species share a recent evolutionary ancestor, then, upon examining them, we should observe many morphological similarities; we observe many morphological similarities between gibbons and orangutans; therefore, gibbons and orangutans share a recent evolutionary ancestor.

Chemistry:
If a composite contains boron, its spectral signature will contain a red spectral line, an orange spectral line and a yellow spectral line; the spectral signature of this composite contains a red spectral line, an orange spectral line and a yellow spectral line; therefore, this composite contains boron.

In each of these examples, the conclusion explains the observation, and does so either by rendering the observation likely or rendering it necessary. Also, in each of these examples the reasoning proceeds from the observation to the conclusion — i.e., from the observation to a statement that explains the observation. But abductive reasoning is that form of reasoning in which one reasons from an observation to a statement that explains that observation. (This is why it's often referred to as inference to the best explanation.) Hence the arguments in the examples above are all instances of abductive reasoning.

Affirming the Consequent

OK, now that we know what abductive reasoning is, plus a few things about explanation in general, and have at our disposal some paradigmatic examples of abductive reasoning in the sciences, we're finally in a strong position to take a look at the limits of science in general.

For starters, let's examine the logical structure of the arguments scientists make in support of their theories. Consider the following argument forms:

Modus ponens
If P, then Q.
P.
Therefore, Q.

Modus tollens
If P, then Q.
Not Q.
Therefore, not P.

An argument is valid if the truth of its premises guarantees the truth of its conclusion. Modus ponens and modus tollens are both valid.⁴ This is obvious upon considering examples like the following:

If Shaq is on a horse, then Shaq is on a mammal; Shaq is on a horse; therefore, Shaq is on a mammal. If Shaq is on a horse, then Shaq is on a mammal; Shaq isn't on a mammal; therefore, Shaq isn't on a horse.

Now consider the following argument form, which is universally recognized as logically fallacious, yet bears obvious formal similarities to modus ponens and modus tollens:⁵

Affirming the consequent
If P, then Q.
Q.
Therefore, P.

At first blush, this argument may appear to be valid, but within the context of concrete examples, it's clearly not. Consider:

If Shaq is on a horse, then Shaq is on a mammal; Shaq is on a mammal; therefore, Shaq is on a horse.

If all we know is that Shaq's on a mammal, we can't rationally conclude that he's on a horse. For all we know, he might be on a camel, or a mouse, or a San Antonio Spur. The truth of the statement that Shaq is on a mammal does not, then, guarantee the truth of the statement that he's on a horse.

But now, notice that all of the examples of abductive reasoning in the sciences that I described in the previous section exhibit exactly the same form as this argument. All of them start with a conditional — if a, then b; all of them then assert the consequent of the conditional — b; and all of them conclude by asserting the conditional's antecedent — a. This, however, is the exact form of the logical fallacy, Affirming the consequent

C O F F E E  S H O P

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What reason do we have for thinking scientific explanations are true if they are using logically fallacious arguments?

Join the discussion!

To reason abductively, then, is to commit a logical fallacy. Yet abductive reasoning is the form of reasoning by which scientists argue for their explanations of the natural world. This leaves us with a tough and interesting question: If scientists arrive at their explanations via logically fallacious arguments, what reason do we have for thinking their explanations are true?

I'll cover more about this topic in part 2.