Inductive Reasoning

Forms of reasoning aren't abstract contrivances, they come from ordinary experience. Inductive reasoning is the natural human tendency to generalize from such experience — to infer conclusions from a body of specific evidence or individual instances. If, when I go grocery shopping, the price of food is a little higher than last time, I'll tend to infer that inflation is in progress and that I can expect even higher prices later. The evidence of individual price hikes contributes to and supports my general conclusion. What happens, however, if when I continue shopping and several weeks later discover that most prices haven't changed or that some have actually declined? My evidence no longer supports the same conclusion, but leads me to a revised one the rate of inflation may be slowing, too.

Inductive reasoning indicates probabilities—sometimes extremely strong ones—but does not offer absolute or perfect proof. We can only conclude what is likely to be true, using the best evidence we can find. When we reason inductively, then, we must be careful not to overgeneralize or go beyond what the evidence can support. When we qualify or limit our inferences, we help to avoid such unwarranted generality. Sometimes our information can support a fairly broad statement. "It seems clear that the days of low-budget feature films are over, given audience tastes for expensive productions and special effects." It is more likely, however, that most inductive conclusions need at least some limits. "Although the days of low-budget feature films appear to be over, some new filmmakers are trying to resurrect the tradition."

It's not always easy to know when we have enough evidence to support an inductive conclusion. Most of the time, common sense must be our guide. If I poll people to see who's likely to win the coming election, my sample must be large enough to be representative. If I see one high-speed auto collision, however, I can probably infer without seeing dozens of them that they're lethal.

The quality of our evidence, as much as its quantity, will determine whether the argument is convincing. If our information is accurate, reliable, able to be checked, and if we have enough to support a carefully limited conclusion, chances are we'll have a convincing case, or a convincing general statement that we can apply to a deductive argument.

Here's how an essay based on inductive reasoning might be organized:

I.. Introduction (and thesis/claim)

II. Evidence in support of claim (Topic 1)

III. Evidence in support of claim (Topic 2)

IV. Evidence in support of claim (Topic 3)

5. Conclusion (or thesis/claim at the end)

Deductive Reasoning

When we reason deductively, instead of starting with data and generalizing from them, we start with general principles or assumptions and apply them to specific situations. Deductive reasoning relies on a logical form called the syllogism, which dictates the relationship among premises (the assumptions we start with), the specific case at hand, and conclusions. If the premises are true and in a valid relationship with one another, the conclusion we draw from them will be true and valid — impossible to refute. Unlike induction, deductive reasoning, with the syllogism, can give us complete certainty in our arguments.

What is the proper or valid relationship between the premises in a syllogism? The minor premise, the specific instance, must be contained within the general class or group of instances expressed by the major premise:

Major premise: All citizens have specific rights and responsibilities.

Minor premise: I am a citizen.

Conclusion: I have specific rights and responsibilities.

If I accept the two premises, and if the minor premise is an instance of the major, then the conclusion follows logically and convinces us because it's the only one possible. For deductive arguments to work, we must grant that the premises are true and in valid form. If we don't accept the premises, we won't accept the conclusion.

The major premise of a syllogism is a "given", we accept it without proof, as an assumption. In some cases, the assumption is a generality derived from observation or evidence, an inductive conclusion: "Wearing safety belts reduces the risk of injury in most auto accidents." In others, the assumption is a matter of belief or value, something we grant as true or self-evident: "We must always oppose injustice." In either type, we apply the generality to an individual situation in order to derive our conclusion.

Sometimes, however, we may join our major and minor premises incorrectly, or the premises themselves may be faulty. Then our arguments may be invalid, untrue, or both. What, for instance, is wrong with this syllogism?

Major premise: All rock stars are drug abusers.

Minor premise: My friend Nick is a rock star.

Conclusion: My friend Nick is a drug abuser.

Here, the major premise is obviously false, it's an unqualified generalization and can't be supported. (Drugs may be a problem in the rock world, but certainly not all rock stars abuse drugs.) My friend Nick may or may not use drugs, but I haven't proved anything with this argument, even though its form is valid, because I've started with an untrue premise.

What's wrong with this one?

Major premise: Distance runners are physically fit.

Minor premise: I am physically fit.

Conclusion: I am a distance runner.

Here, all the statements are true, but the argument is invalid because the premises aren't logically related—the minor premise isn't an instance of the major generality. The conclusion, therefore, has nothing to do with the premises.

Finally, what's wrong here?

Major premise: All businessmen are crooks.

Minor premise: I am a crook.

Conclusion: I am a businessman.

The argument is both untrue and invalid. Most businessmen aren't crooks, and even if they were, and I were one, too, that wouldn't make me a businessman (unrelated premises again).

When using deductive reasoning, then, remember to (1) word your major assumptions so that your reader can accept them as true, and (2) make sure that your specific instances are covered by the generality. If you can defend both the truth and validity of your arguments, your conclusions will be soundly reasoned and forcefully convincing.

Here's how an essay based on deductive reasoning might be organized:

I. Introduction (and thesis/claim)

II. Deductive support (general assumptions)

III. Deductive support (examples of the general case)

IV. Deductive support (refute counterarguments against II and III)

5. Conclusion (or thesis/claim at end)