F Composition and Division

The fallacy of composition consists in inferring that what is true of a part must be true of the whole. Of course, parts and wholes sometimes do have the same properties.

Every page in a newspaper is flammable, and so is the newspaper as a whole. But not every property is like this. We commit the fallacy of composition when we jump to a conclusion about the whole without considering whether the nature of the property in question makes it reasonable. The radio in my car was made by Motorola, but that does not imply that Motorola made my car as a whole. Every snowflake on my lawn is star-shaped and fell from the sky, but the snowball I make has neither of those properties.

The fallacy of division is the mirror image of composition: It is the inference that what is true of the whole must be true of the parts. The fact that my car gets 25 miles to the gallon does not mean that the radio gets 25 miles to the gallon—a statement that hardly even makes sense. The fact that my car was made by General Motors does not mean that GM made every part.

Composition Inferring that the whole must have a property (merely) because one or more parts have the property Whole

Part(s)

Inferring that the parts must have a property (merely) because the whole has the property Division

Whole

Part(s)

As the diagram suggests, composition has a certain similarity to hasty generaliza-tion. But hasty generalization applies to individual things and the general classes to which they belong, whereas composition applies to the parts of an individual thing and that individual thing as a whole. To see the difference, consider again the radio in my car. The radio is a member of the general class of audio equipment. It would be hasty to general-ize that all audio equipment is made by Motorola, just because my car radio is. That is a different error from composition: inferring that Motorola made my car just because it made the radio. In the same way, the fallacy of division has a certain similarity with accident, but the latter involves a hasty application of a generalization about a class of things, whereas division is an inference from an individual thing to its parts.

The fallacies of composition and division can also occur in thinking about groups as well as individual things—when we are treating the group as a single whole. Suppose, for example, that every member of a college football team is a senior. We obviously can-not infer that the football team itself is a senior; that would be composition. Conversely, the team has properties as a team (e.g., a budget of $X from the college) that do not ap-ply to individual players; inferring that the left guard Harold has a budget of $X would be a case of division. The same distinction applies to statements about general classes.

Compare the statements:

1. Human beings are animals.

2. Human beings evolved 100,000 years ago.

The first is a general statement about humans. It applies to each and every one of us. If we have the additional premise that X is a human being, we can validly infer that X is an animal. But 2 is a statement about the human species as a whole, as a single biological unit. It does not apply to individual humans as members of the species. The fact that the species evolved 100,000 years ago does not imply that you or I evolved—came into existence—back then.

It isn’t likely that anyone would make the absurd inferences I have used so far to illustrate composition and division. So let us turn to cases in which these fallacies are more likely to be committed. One case is the use of statistics. Compare the statements:

3. American steel companies are profitable.

4. The average American steel company is profitable.

Statement 3 is like 1 above, a generalization about each instance of a class. You could therefore infer that any given company is profitable. But an average is a statistical fact

5.3 Fallacies of Context 125

about a class as a whole. So 4 does not support the inference that a given company is profitable, and we would commit the fallacy of division if we made that inference. The controversial issue of racial differences in intelligence provides another example of the same error. If such differences do exist, they are differences in the average IQ of racial groups. To infer that a given individual in one group is more intelligent than another individual in another group, just because his group’s average is higher, would be a fal-lacy of division. Averages are computed from the scores of individuals who are distrib-uted along the whole continuum of intelligence, so the group average tells us nothing about any individual.

People also commit the fallacy of composition with statistical information. Treat-ment for Treat-mental disorders is less expensive per-person than treatTreat-ment for cancer. But it would be composition to infer that total spending on mental disorders is less than total spending on cancer treatment. That depends on the number of patients who seek treat-ment for these conditions. As it happens, there are many more people being treated for mental disorders than for cancer, so that total spending is roughly the same.

Political issues are another area in which these fallacies occur. A society is made up of individual people. What is true of individuals may or may not be true of society as a whole, and vice versa, so we have to be careful to avoid composition and division. For example, a newspaper editorial argues for government economic planning by asking,

“Why is planning considered a good thing for individuals and business but a bad thing for the national economy?” The fact that individuals need to plan how they are going to earn a living and spend their income does not imply that society as a whole should plan how wealth should be produced and distributed throughout the economy. Whether national planning is a good idea depends on a host of other questions, such as whether government planners are capable of performing this task, and whether they have the right to supersede the decisions that individuals and businesses make about how to use their resources. Because the editorial ignores these issues and makes a simple inference to parts to the whole, the argument is a case of composition.

SUMMARY

False alternative: excluding relevant possibili-ties without justification.

Post hoc : using the fact that one event pre-ceded another as sufficient evidence for the conclusion that the first caused the second.

Hasty generalization: inferring a general proposi tion from an inadequate sample of particular cases.

Accident: applying a generalization to a special case in disregard of qualities or circumstances that make it an exception to the generalization.

Slippery slope: arguing against a proposed action or policy by claiming, with insufficient evidence, that it will lead to a series of increas-ingly bad consequences.

Composition: inferring that a whole has a prop-erty merely because its parts have that propprop-erty.

Division: inferring that a part has a prop-erty merely because the whole has that property.

❋ 1. Don’t go down to River Road.

I was down there once and got mugged. They’re all thieves down there.

2. If she loved me, she would have called me back tonight. She didn’t, so she must hate me.

3. Flowers require soil, water, and sunlight to grow. Foxglove grows in the shade, so it must not be a flower.

❋ 4. Although I’m happy about the raise I got today, I’m also a little worried. The last time I got a raise my car got stolen the next morning.

5. Tell your representative that you don’t want health care reform! If the health care reform is passed, private insurance companies won’t be able to compete with the public option. With the private compa-nies out of the picture, individuals will only be able to turn to the public option, and then it will be up to the government to decide whether we should live or die.

6. I’m sure this outfit will look great.

It’s got leopard print, zebra print, plaid, and polka dots, and I like each of those patterns.

❋ 7. On the basis of the rambling speech Madeleine gave at the school assembly last week, I would say she’s not a good public speaker.

8. How can you say that you washed the car? Did you wash every part—

under the hood, around the muf-fler, under the seats?

9. One should always keep appoint-ments. So even though Joe is an

hour late, we should continue to wait for him.

❋ 10. Congressman Jones denies that he’s a liberal, so he must be a conservative.

11. Twenty-five years after graduation, Harvard alumni have incomes much higher than that of the aver-age college graduate. A Harvard education must be the road to riches.

12. Everyone on the Dream Team is the best player in his position, so the Dream Team is the best team around.

❋ 13. If their band accepts this main-stream record deal, they’ll be sell-ing out! Next they’ll get corpo-rate sponsors for their tour, and then we’ll be hearing their songs redone as commercial jingles for toothpaste.

14. A pile of stones will topple if it is not stacked vertically. So it is impossible to build a stone arch.

15. Either Tom was telling the truth when he said his grade average was 3.7 or he was lying. But he wasn’t telling the truth, since his average is actually 3.6, so he was lying.

❋ 16. It’s good to put water in your body, so it must be good to put water in your lungs.

17. I’ve seen my daughter’s teachers underestimate her ability in math and science. This just goes to show that educators in America are sexist.

18. Stock prices fell dramatically 2 years ago, after Congress raised tariffs, and they just raised tariffs

EXERCISE 5.3

Identify which of the fallacies discussed in this section—false alternative, post hoc, hasty generalization, composition, division—is committed in the statements below.