Inductive reasoning works in the opposite direction. We reason inductively when we use firsthand observations to form general conclusions. Sometimes, the process of induction is simply referred to as "generalizing." If, after buying milk at a certain grocery store three times and finding it spoiled each time, someone decided never to buy milk at that store again, that person would be reasoning inductively.
Most of us do not consciously decide to reason deductively or inductively to solve problems. Rather, we constantly employ both forms of reasoning at the same time. We gather facts and observations until we can use them to form general conclusions (inductive reasoning), and we use those general conclusions to make judgments about specific situations (deductive reasoning). When we do not have a good understanding of how deductive and inductive reasoning work, however, we can be more easily persuaded by arguments that are weak or misleading. This section will explain how both kinds of reasoning can support claims.
Deductive Reasoning
The basic unit of deductive reasoning is called a syllogism, which can be thought of as a kind of mathematical formula that works with words rather than numbers. In its most basic form, a syllogism contains two premises and a conclusion drawn from those premises:
Major premise (dealing with a category): All dogs have four legs.
Minor premise (dealing with an individual): Rover is a dog.
Conclusion: Rover has four legs.
The major premise asserts that all members of a category share a certain characteristic. In the example above, everyone who belongs to the category of "dogs" shares the characteristic of "four legs." However, the characteristic can apply to other categories, too—for example, cats also have four legs. If we were to represent the major premise above graphically, it would look like this:
The three simple statements in the syllogism above do not include evidence that Rover is actually a dog; thus, we cannot be sure that the syllogism is true. We can say, though, that if all dogs have four legs and Rover is a dog, then Rover must have four legs. This is because the syllogism is sound, meaning that the premises lead infallibly to the conclusion. A syllogism can be completely true yet unsound. It can also be sound yet demonstrably untrue. Consider the following two arguments:
Major premise: Dogs have purple teeth and green fangs. Minor premise: Rover is a dog.
Conclusion: Rover has purple teeth and green fangs. (Sound but untrue: the major premise is false.)
Major premise: Basketball players are tall.
Minor premise: Shaquille O'Neal is tall.
Conclusion: Shaquille O'Neal is a basketball player. (True but unsound: simply being tall does not make Shaquille O'Neal a basketball player; plenty of tall people are not basketball players.)
To see why the example above that uses basketball players and Shaquille O'Neal is unsound, consider how the major premise would look if represented graphically:
Because the category of "Basketball Players" is contained entirely within the characteristic of "Tall People," it is logical to assert that all basketball players are tall. It is also logical to assert that someone who is not tall cannot be a basketball player. However, since a large part of the circle representing "Tall People" lies outside the category "Basketball Players," it is not logical to assert that someone who is tall is also a basketball player. If we substitute a different name for "Shaquille O'Neal," it becomes clear why the syllogism is unsound:
Major premise: Basketball players are tall. Minor premise: Barack Obama is tall.
Conclusion: Barack Obama is a basketball player. (Unsound and untrue)
The following syllogism would also be unsound, because it asserts that if an individual is not in the category named in the major premise (basketball players), he must not have the characteristic in the major premise (tallness):
Major premise: Basketball players are tall.
Minor premise: Barack Obama is not a basketball player.
Conclusion: Barack Obama is not tall. (Unsound and untrue)
To turn the original syllogism into a sound one that asserts that an individual fits the category of the major premise and therefore shares its characteristics, we would need to rewrite it like this:
Major premise: Basketball players are tall.
Minor premise: Shaquille O'Neal is a basketball player.
Conclusion: Shaquille O'Neal is tall. (Sound and true)
A sound syllogism can also assert that an individual who does not share the characteristic in the major premise (in this example, tallness) cannot be part of the category named in the major premise (in this example, basketball players):
Major premise: Basketball players are tall. Minor premise: George Stephanopoulos is not tall.
Conclusion: George Stephanopoulos is not a basketball player. (Sound and true)
Understanding the structure of syllogisms can be helpful in understanding real-world claims. Consider the following hypothetical statement:
When America was attacked, those who sympathized with these attacks and wished our attackers well opposed going to war in Iraq. At the very moment that terrorists were hoping that we would not go to war, Senator Jones gave a speech on the Senate floor opposing the war. It is important that Americans understand that, in these crucial moments, Senator Jones's sympathies lay with the enemy.
Once we eliminate the political hyperbole in this statement, we are left with a fairly straightforward syllogism:
Major premise: People who support terrorism opposed going to war in Iraq.
Minor premise: Senator Jones opposed going to war in Iraq.
Conclusion: Senator Jones supports terrorism.
Whether or not one considers the premises of this argument to be true, the conclusion is unsound: it states that because the minor premise asserts that an individual shares the characteristic in the major premise (opposing going to war), he must therefore belong to the category in the major premise (people who support terrorism).
When you examine an argument, such as the example above or the ones in this book, think critically about its logic and reasoning. If you were to state the argument in a syllogism, would the syllogism be sound? For example, consider this thesis statement offered earlier in the chapter: "Affirmative action is not a useful educational policy because it has not increased minority graduation rates." Arranged in a syllogism, it would look like this:
Major premise: Useful educational policies increase graduation rates.
Minor premise: Affirmative action has not increased minority graduation rates.
Conclusion: Affirmative action is not a useful educational policy.
Since the minor premise claims that an individual (in this case, a specific instance of educational policy, affirmative action) does not share the characteristic in the major premise, the conclusion that it does not belong to the category in the major premise is sound—and, therefore, the argument is sound (which does not necessarily make it true). Applying this logic to your own arguments can help you ensure that your arguments are sound.
Inductive Reasoning
Inductive reasoning does not produce the kind of mathematical certainty that deductive reasoning does, but it can produce conclusions with a very high likelihood of being true. We engage in induction when we gather together bits of specific information and use our own knowledge and experience to make an observation about what must be true. Inductive reasoning uses observations and prior experiences, rather than syllogisms, to reach conclusions. Consider the following chains of observations: