Induction

Induction (from the Latin inducere, “to lead into”) means arranging an argument so that it leads from particulars to universals, using specific cases to draw a conclusion. For instance:

  Regular exercise promotes weight loss.
  Exercise lowers stress levels.
  Exercise improves mood and outlook.
generalization Exercise contributes to better health.

We use induction in our everyday lives. For example, if your family and friends have owned several cars made by Subaru that have held up well, then you are likely to conclude inductively that Subaru makes good cars. Yet induction is also used in more technical situations. Even the scientific method is founded on inductive reasoning. Scientists use experiments to determine the effects in certain cases, and from there they might infer a universal scientific principle. For instance, if bases neutralize acids in every experiment conducted, then it can reasonably be inferred that all bases neutralize acids. The process of induction involves collecting evidence and then drawing an inference based on that evidence in order to reach a conclusion.

When you write a full essay developed entirely by reasons, one after another supporting the main point, then your entire argument is inductive. For instance, suppose you are asked to take a position on whether the American Dream is alive and well today. As you examine the issue, you might think of examples from your own community that demonstrate that the Dream is not a reality for the average citizen; you might study current events and think about the way societal expectations have changed; you might use examples from fiction you have read, such as the novel Tortilla Curtain by T. Corraghessan Boyle or movies such as Boyz N the Hood, where economic pressures limit the characters’ horizons. All of this evidence together supports the inference that the American Dream no longer exists for the average person. To write that argument, you would support your claim with a series of reasons explained through concrete examples: you would argue inductively.

Arguments developed inductively can never be said to be true or false, right or wrong. Instead, they can be considered strong or weak, so it’s important to consider possible vulnerabilities—in particular, the exception to the rule. Let’s consider an example from politics. An argument written in favor of a certain political candidate might be organized inductively around reasons that she is the best qualified person for the job because of her views on military spending, financial aid for college students, and states’ rights. However, the argument is vulnerable to an objection that her views on, for instance, the death penalty or environmental issues weaken her qualifications. Essentially, an argument structured inductively cannot lead to certainty, only to probability.

Let’s look at an excerpt from Outliers by Malcolm Gladwell for an example of how an argument can be structured largely by induction. Gladwell uses various types of evidence here to support his conclusion that “[w]hen it comes to math…Asians have a built-in advantage.”

from Outliers

Malcolm Gladwell

Take a look at the following list of numbers: 4, 8, 5, 3, 9, 7, 6. Read them out loud. Now look away and spend twenty seconds memorizing that sequence before saying them out loud again.

If you speak English, you have about a 50 percent chance of remembering that sequence perfectly. If you’re Chinese, though, you’re almost certain to get it right every time. Why is that? Because as human beings we store digits in a memory loop that runs for about two seconds. We most easily memorize whatever we can say or read within that two-second span. And Chinese speakers get that list of numbers—4, 8, 5, 3, 9, 7, 6—right almost every time because, unlike English, their language allows them to fit all those seven numbers into two seconds.

That example comes from Stanislas Dehaene’s book The Number Sense. As Dehaene explains:

Chinese number words are remarkably brief. Most of them can be uttered in less than one-quarter of a second (for instance, 4 is “si” and 7 “qi”). Their English equivalents—“four,” “seven,”—are longer: pronouncing them takes about one-third of a second. The memory gap between English and Chinese apparently is entirely due to this difference in length. In languages as diverse as Welsh, Arabic, Chinese, English and Hebrew, there is a reproducible correlation between the time required to pronounce numbers in a given language and the memory span of its speakers. In this domain, the prize for efficacy goes to the Cantonese dialect of Chinese, whose brevity grants residents of Hong Kong a rocketing memory span of about 10 digits.

It turns out that there is also a big difference in how number-naming systems in Western and Asian languages are constructed. In English, we say fourteen, sixteen, seventeen, eighteen, and nineteen, so one might expect that we would also say oneteen, twoteen, threeteen, and fiveteen. But we don’t. We use a different form: eleven, twelve, thirteen, and fifteen. Similarly, we have forty and sixty, which sound like the words they are related to (four and six). But we also say fifty and thirty and twenty, which sort of sound like five and three and two, but not really. And, for that matter, for numbers above twenty, we put the “decade” first and the unit number second (twenty-one, twenty-two), whereas for the teens, we do it the other way around (fourteen, seventeen, eighteen). The number system in English is highly irregular. Not so in China, Japan, and Korea. They have a logical counting system. Eleven is ten-one. Twelve is ten-two. Twenty-four is two-tens-four and so on.

5

That difference means that Asian children learn to count much faster than American children. Four-year-old Chinese children can count, on average, to forty. American children at that age can count only to fifteen, and most don’t reach forty until they’re five. By the age of five, in other words, American children are already a year behind their Asian counterparts in the most fundamental of math skills.

The regularity of their number system also means that Asian children can perform basic functions, such as addition, far more easily. Ask an English-speaking seven-year-old to add thirty-seven plus twenty-two in her head, and she has to convert the words to numbers (37 + 22). Only then can she do the math: 2 plus 7 is 9 and 30 and 20 is 50, which makes 59. Ask an Asian child to add three-tens-seven and two-tens-two, and then the necessary equation is right there, embedded in the sentence. No number translation is necessary: It’s five-tens-nine.

“The Asian system is transparent,” says Karen Fuson, a Northwestern University psychologist who has closely studied Asian-Western differences. “I think that it makes the whole attitude toward math different. Instead of being a rote learning thing, there’s a pattern I can figure out. There is an expectation that I can do this. There is an expectation that it’s sensible. For fractions, we say three-fifths. The Chinese is literally ‘out of five parts, take three.’ That’s telling you conceptually what a fraction is. It’s differentiating the denominator and the numerator.”

The much-storied disenchantment with mathematics among Western children starts in the third and fourth grades, and Fuson argues that perhaps a part of that disenchantment is due to the fact that math doesn’t seem to make sense; its linguistic structure is clumsy; its basic rules seem arbitrary and complicated.

Asian children, by contrast, don’t feel nearly the same bafflement. They can hold more numbers in their heads and do calculations faster, and the way fractions are expressed in their languages corresponds exactly to the way a fraction actually is—and maybe that makes them a little more likely to enjoy math, and maybe because they enjoy math a little more, they try a little harder and take more math classes and are more willing to do their homework, and on and on, in a kind of virtuous circle.

10

When it comes to math, in other words, Asians have a built-in advantage.

(2008)

In each paragraph, Gladwell provides reasons backed by evidence. He begins in the opening two paragraphs by drawing in the reader with an anecdotal example that (he assumes) will demonstrate his point: if you speak English, you won’t do as well as if you speak Chinese. In paragraph 3, he provides additional support by citing an expert who has written a book entitled The Number Sense. In the next two paragraphs, he discusses differences in the systems of Western and Asian languages that explain why Asian children learn certain basic skills that put them ahead of their Western counterparts at an early age. In paragraphs 6 and 7, he raises another issue—attitude toward problem solving—and provides evidence from an expert to explain the superiority of Asian students. By this point, Gladwell has provided enough specific information—from facts, experts, examples—to support an inference that is a generalization. In this case, he concludes that “[w]hen it comes to math…Asians have a built-in advantage.” Gladwell’s reasoning and the structure of his argument are inductive.