1.5 Exercising Logic

Inductive reasoning is the process of drawing an inference, or conclusion, from known facts. The nineteenth-century British scientist, educator, and essayist, Thomas Henry Huxley, submits an example:

In the foregoing explanation, Huxley shows that induction is the mental progression from known facts (hard, green apples are sour) to a theoryAn inference, or conclusion, that explains the facts.—an inferenceA conclusion drawn from facts, the result of inductive reasoning. that explains the facts (all hard, green apples are sour). The thought process that moves from what is known to what is inferred is called an inductive leapThe thought progression from what is known to what is inferred..

How careful must we be in taking this inductive leap? The answer depends on what is at stake. If an entire agricultural industry depends on the sale of apples, then one would want to test the theory that all hard, green apples are sour by seeking a wider sampling. If very little is at stake—for instance, your personal choice of apples—such wide-ranging testing of the theory is probably not necessary.

How does one evaluate the validity of a theory? One quality of a valid theory is that it explains, ideally, all the facts. A less valid theory is one that explains only some of the facts and leaves other facts unaccounted for.

We employ inductive reasoning every day. For example, you may be wondering whether you should buy a ticket to a concert. To arrive at a thesis, you must sort through the facts: How much money do I have in the bank? How much of it is already earmarked? How much money must I set aside for basic needs, like food, before my next payday? Am I willing to sacrifice a luxury, like my daily espresso? Once you have examined the facts, you are ready to take that inductive leap to a thesis: Yes, I should buy that ticket.

Throughout your college career and beyond, you will employ inductive reasoning. You may be asked to interpret statistics in your psychology class or estimate the probability of life on other planets in your astronomy class. You might evaluate the risk of calorie-overloading if you eat in the college dining hall or predict the consequences of majoring in theater and dance rather than business. These predicaments are solved by examining the available facts and drawing an inference from them.

Deductive reasoningThe thought progression from a general rule to a specific conclusion., unlike inductive reasoning, progresses from a general rule to a specific conclusion. Deductive reasoning can be demonstrated by a syllogismA set of premises and a conclusion that combine to form a logical argument., which begins with a major premiseThe first step in constructing a syllogism, usually a general rule., proceeds to a minor premiseThe second step in constructing a syllogism, usually a fact., and arrives at a conclusion. The conclusion is a combination of the major and minor premises. All the parts of a syllogism must fit together precisely. The following is an example:

Not all syllogisms are valid, however, as the next example shows:

The preceding syllogism is not valid because the premises do not preclude the possibility that other animals besides mice eat cheese. One could change the word All in the major premise to Only and have a sound syllogism, in which all the parts fit together precisely, but not a valid one, as the major premise—Only mice eat cheese—is not true.

A syllogism in which one of the premises is implicit is called an enthymemeA syllogism in which a premise is not explicitly stated.:

One does not need the major premise to be stated in this enthymeme; it can be only one thing: All unhealthy things should be illegal. Is this, then, a valid syllogism? Is it predicated on a valid major premise? Most of us would answer no. Clearly, we cannot make all unhealthy things illegal, or we would have to start punishing people with sunburns for having stayed out in the sun too long. One can prove beyond a reasonable doubt that smoking cigarettes is unhealthy, but that evidence alone will not suffice in convincing an astute, skeptical reader who is versed in the art of supplying missing premises that smoking cigarettes should be illegal.

Like inductive reasoning, deductive reasoning is part of daily life—something we employ unconsciously. For example, you may be looking for a roommate. In choosing among three possible roommates, you might begin with a rule: My roommate must be a nonsmoker. You go on to a fact: Jane is a smoker. Then you arrive at a conclusion: Therefore Jane cannot be my roommate. More likely, the thought process goes something like this: I need a roommate who is female, a nonsmoker, quiet, and neat. Jane smokes, Sally likes to party too much, and Allison talks on the phone incessantly, but she fulfills all the other criteria. Of the three, therefore, Allison is the best choice.

Deductive reasoning is not simply a personal life skill, however; it is also an academic, professional, and political skill. When Thomas Jefferson wrote the Declaration of Independence, he began with a major premise: “Whenever any form of government becomes destructive,…it is the right of the people to alter or to abolish it, and to institute a new government.” Jefferson’s minor premise was that the British government had become destructive, and his conclusion, therefore, was that the American people had a right to abolish the British government and institute a new government. Jefferson’s logic must have been persuasive; it led to the American Revolution and the establishment of the United States of America.

A thesis, very often the statement of a theory that explains the facts, is most often the result of both inductive and deductive reasoning. Of course, the problems you are solving in college and in your career will be more complex than choosing apples or roommates. The principles of sound reasoning remain the same, though, no matter how complicated the material. And a valid, supportable thesis is most likely the result of careful reasoning.