5.2 Evaluation of Analogical Arguments

Unlike in the case of deduction, we will not have to learn special techniques to use when evaluating these sorts of arguments. It’s something we already know how to do, something we typically do automatically and unreflectively. The purpose of this section, then, is not to learn a new skill, but rather to critically scrutinize a practice in which we already participate. We evaluate analogical arguments all the time without thinking about how we do it. Here, we want to achieve a metacognitive perspective on the practice of evaluating arguments from analogy; that is, we want to examine a type of thinking that we typically engage in without much conscious deliberation. We will identify the criteria that we rely on to evaluate analogical reasoning—criteria that we apply without necessarily realizing that we’re applying them. Achieving such metacognitive awareness is useful insofar as it makes us more self-aware, critical, and therefore more effective reasoners.

Analogical arguments are inductive arguments. They give us reasons that are supposed to make their conclusions more probable. How probable, exactly? That’s very hard to say. How probable was it that Matthew would like The Wolf of Wall Street given that he’d liked the other four Scorsese/DiCaprio collaborations? We don’t know. How probable is it that it’s wrong to eat pork given that it’s wrong to eat dogs and dolphins? We really don’t know. It’s hard to imagine how you would even begin to answer that question quantitatively.

As we mentioned, while it’s often impossible to evaluate inductive arguments by giving a precise probability of its conclusion, it is possible to make relative judgments about strengths and weaknesses. Recall, new information can change the probability of the conclusion of an inductive argument. We can make relative judgments like this: if we add this new information as a premise, the new argument is stronger/weaker than the old argument; that is, the new information makes the conclusion more/less likely.

It is these types of relative judgments that we make when we evaluate analogical reasoning. We compare different arguments—with the difference being new information in the form of an added premise, or a different conclusion supported by the same premises—and judge one to be stronger or weaker than the other. Subjecting this practice to critical scrutiny, we can identify six criteria that we use to make such judgments.

We’re going to be making relative judgments, so we need a baseline argument against which to compare others. Here is an argument that we’ll use as our baseline:

This is a simple argument from analogy, in which the future is predicted based on past experience. It fits the schema for analogical arguments: the new course she has signed up for is designated by ‘c’; the property we’re predicting it has (Q) is that it is a course Alice will get an A in; the analogues are the four previous courses she’s taken; what they have in common with the new course (P1) is that they are also Philosophy classes; and they all have the property Q—Sally got an A in each.

Anyway, how strong is the baseline argument? How probable is its conclusion in light of its premises? We have no idea. It doesn’t matter. We’re now going to consider tweaks to the argument, and the effect those little changes will have on the probability of the conclusion. That is, we’re going to consider slightly different arguments, with new information added to the original premises or changes to the prediction based on them, and ask whether these altered new arguments are stronger or weaker than the baseline argument. This will reveal the six criteria that we use to make such judgments. We’ll consider one criterion at a time.

Criterion 1. Number of Analogues

Suppose we alter the original argument by changing the number of prior Philosophy courses Alice had taken. Instead of Alice having taken four philosophy courses before, we’ll now suppose she has taken 12. We’ll keep everything else about the argument the same: she got an A in all of them, and we’re predicting she’ll get an A in the new one. Are we more or less confident in the conclusion—the prediction of an A—with the altered premise? Is this new argument stronger or weaker than the baseline argument?

It’s stronger! We’ve got Alice getting an A 12 times instead of only four. That clearly makes the conclusion more probable. (How much more? Again, it doesn’t matter.)

What we did, in this case, is add more analogues. This reveals a general rule: other things being equal, the more analogues in an analogical argument, the stronger the argument (and conversely, the fewer analogues, the weaker). The number of analogues is one of the criteria we use to evaluate arguments from analogy.

Criterion 2. Variety of Analogues

You’ll notice that the original argument doesn’t give us much information about the four courses Alice succeeded in previously and the new course she’s about to take. All we know is that they’re all Philosophy courses. Suppose we tweak things. We’re still in the dark about the new course Alice is about to take, but we know a bit more about the other four: one was a course in Ancient Greek Philosophy; one was a course on Contemporary Ethical Theories; one was a course in Formal Logic; and the last one was a course in the Philosophy of Mind. Given this new information, are we more or less confident that she will succeed in the new course, whose topic is unknown to us? Is the argument stronger or weaker than the baseline argument?

It is stronger. We don’t know what kind of Philosophy course Alice is about to take, but this new information gives us an indication that it doesn’t really matter. She was able to succeed in a wide variety of courses, from Mind to Logic, from Ancient Greek to Contemporary Ethics. This is evidence that Alice is good at Philosophy generally, so that no matter what kind of course she’s about to take, she’ll probably do well in it.

Again, this points to a general principle about how we evaluate analogical arguments: other things being equal, the more variety there is among the analogues, the stronger the argument (and conversely, the less variety, the weaker).

Criterion 3. Number of Similarities

In the baseline argument, the only thing the four previous courses and the new course have in common is that they are Philosophy classes. Suppose we change that. Our newly tweaked argument predicts that Alice will get an A in the new course, which, like the four she succeeded in before, is cross-listed in the Department of Religious Studies and covers topics in the Philosophy of Religion. Given this new information—that the new course and the four older courses were similar in ways we weren’t aware of—are we more or less confident in the prediction that Alice will get another A? Is the argument stronger or weaker than the baseline argument?

Again, it is stronger. Unlike the last example, this tweak gives us new information both about the four previous courses and the new one. The upshot of that information is that they’re more similar than we knew; that is, they have more properties in common. To P1 = ‘is a Philosophy course’ we can add P2 = ‘is cross-listed with Religious Studies’ and P3 = ‘covers topics in Philosophy of Religion’. The more properties things have in common, the stronger the analogy between them. The stronger the analogy, the stronger the argument based on that analogy. We now know not just that Alice did well not just in Philosophy classes—but specifically in classes covering the Philosophy of Religion; and we know that the new class she’s taking is also a Philosophy of Religion class. We can be much more confident predicting she’ll do well again than we were when all we knew was that all the classes were Philosophy; the new one could have been in a different topic that less interesting to her.

General principle: other things being equal, the more properties involved in the analogy—the more similarities between the item in the conclusion and the analogues—the stronger the argument (and conversely, the fewer properties, the weaker).

Criterion 4. Number of Differences

An argument from analogy is built on the foundation of the similarities between the analogues and the item in the conclusion—the analogy. Anything that weakens that foundation weakens the argument. So, to the extent that there are differences among those items, the argument is weaker.

Suppose we add new information to our baseline argument: the four Philosophy courses Alice did well in before, were all courses in the Philosophy of Mind; the new course is about the history of Ancient Greek Philosophy. Given this new information, are we more or less confident that she will succeed in the new course? Is the argument stronger or weaker than the baseline argument? Clearly, the argument is weaker. The new course is on a completely different topic than the other ones. She did well in four straight Philosophy of Mind courses, but Ancient Greek Philosophy is quite different. We can be less confident that she’ll get an A than we were before.

If we add more differences, the argument gets even weaker. Supposing the four Philosophy of Mind courses were all taught by the same professor (the person in the department whose expertise is in that area), but the Ancient Greek Philosophy course is taught by someone different (the department’s specialist in that topic). Different subject matter, different teachers: now we are even less optimistic about Alice’s continued success.

Generally speaking, other things being equal, the more differences there are between the analogues and the item in the conclusion, the weaker the argument from the analogy.

Criterion 5. Relevance of Similarities and Differences

Not all similarities and differences are capable of strengthening or weakening an argument from analogy, however. Suppose we tweak the original argument by adding the new information that the new course and the four previous courses all have their weekly meetings in the same campus building. This is an additional property that the courses have in common, which, as we just saw, other things being equal, should strengthen the argument. But other things are not equal in this case. That’s because it’s very hard to imagine how the location of the classroom would have anything to do with the prediction we’re making—that Alice will get an A in the course. Classroom location is simply not relevant to success in a course. (And there is no backstory to support its relevance.) Therefore, this new information does not strengthen the argument. Nor does it weaken it; we’re not inclined to doubt Alice will do well in light of the information about the location. It simply has no effect at all on our appraisal of her chances.

Similarly, if we tweak the original argument to add a difference between the new class and the other four, say, that while all four of the previous classes were in the same building, while the new one is in a different building, there is no effect on our confidence in the conclusion. Again, the building in which a class meets is simply not relevant to how well someone does.

Contrast these cases with the new information that the new course and the previous four are all taught by the same professor. Now that strengthens the argument! Alice has gotten an A four times from this professor—all the more reason to expect she’ll receive another one. This tidbit strengthens the argument because the new similarity—the same person teaches all the courses—is relevant to the prediction we’re making—that Alice will do well. Who teaches a class can make a difference in how students do—either because they’re easy graders, or because they’re great teachers, or because the student and the teacher are in tune with one another, etc. Even a difference between the analogues and the item in the conclusion, with the right kind of relevance, can strengthen an argument. Suppose the other four philosophy classes were taught by the same teacher, but the new one is taught by a Teaching Assistant—who just happens to be her boyfriend. That’s a difference, but one that makes the conclusion—that Alice will do well—more probable.

Generalization is difficult: It’s important to pay careful attention to the relevance of any similarities and differences to the property in the conclusion; the effect on strength varies, depending on the situation.

Criterion 6. Modesty/Ambition of the Conclusion

Suppose we leave everything about the premises in the original baseline argument the same: four Philosophy classes, an A in each, new Philosophy class. Instead of adding to that part of the argument, we’ll tweak the conclusion. Instead of predicting that Alice will get an A in the class, we’ll predict that she’ll pass the course. Are we more or less confident that this prediction will come true? Is the new, tweaked argument stronger or weaker than the baseline argument?

It’s stronger. We are more confident in the prediction that Alice will pass than we are in the prediction that she will get another A, for the simple reason that it’s much easier to pass than it is to get an A. That is, the prediction of passing is a much more modest prediction than the prediction of an A.

Suppose we tweak the conclusion in the opposite direction—not more modest, but more ambitious. Alice has gotten an A in four straight Philosophy classes, she’s about to take another one, and we predict that she will do so well that her professor will suggest that she publish her term paper in one of the most prestigious philosophical journals and that she will be offered a three-year research fellowship at the Institute for Advanced Study at Princeton University. That’s a bold prediction! Meaning, of course, that it’s very unlikely to happen. Getting an A is one thing; getting an invitation to be a visiting scholar at one of the most prestigious academic institutions in the world is quite another. The argument with this ambitious conclusion is weaker than the baseline argument.

General principle: the more modest the argument’s conclusion, the stronger the argument; the more ambitious, the weaker.