Студопедия — Deduction
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Deduction






Deduction is the reverse of induction. Instead of formulating a conclusion after considering pieces' of evidence, you start with an observation that most people accept as true and then show how certain conclusions follow from that observation. For example, to convince a friend to study harder, you begin with the assumption that a profitable career requires a good education; proceed to argue that for a good education students must study diligently; and conclude that, as a result, your friend should spend more time with the books. Poli­ticians who assert that we all want to act in ways beneficial to future genera­tions, then point out how the policies they favor will ensure that outcome, argue deductively.

As with induction, you have several options when organizing a deductive argument. You might begin with the position you intend to prove, with a ques­tion that will be answered by the argument, or with a synopsis of the argu­ment. The body of the paper works out the implications of your assumption. In the conclusion you could directly state (or restate, in different words) your position, suggest the consequences of adopting or not adopting that position, or pose a question that is easily answered after reading the argument. Here is a short example of deductive argument:

The recent spot-checks of our rooms by the dorm's head advisor are an unacceptable invasion of privacy. This practice should stop immediately.

The United States Constitution prohibits searches by police officers unless these officers have adequate reason. That is why the police need a search warrant before they can search any home. If they fail to obtain one, a case that ends up in court will likely be thrown out. Our right to privacy, then, can't be violated without due cause.

If the police can't search our homes without good reason, why should our head advisor spot-check our rooms for signs of wrongdoing?

Sammy Borchardt

A common and powerful form of deduction called reductio ad absurdum (to reduce to absurdity) is used to attack an opponent's position by showing that its consequences are absurd if carried to their logical end. To counter the position that the government should impose no restrictions on the public's right to bear arms, you might point out that, carried to its logical extreme, such a policy would allow individuals to own bazookas, cannons, and nuclear bombs. This absurd result makes it clear that certain restrictions should apply to our right to bear arms. The question then becomes where we should draw the ownership line.

Often, a deductive argument is built around a categorical syllogism, a set of three statements that follow a fixed pattern to ensure sound reasoning. The first statement, called the major premise, names a category of things and says that all or none of them shares a certain characteristic. The minor premise notes that a thing or group of things belongs to that category. The conclusion states that the thing or group shares the characteristics of the category. Here are two examples:

Major premise: All persons are mortal.

Minor premise: Sue Davis is a person.

Conclusion: Therefore, Sue Davis is mortal.

Major premise: No dogs have feathers.

Minor premise: Spot is a dog.

Conclusion: Therefore, Spot does not have feathers.

Note that in each case both major and minor premises are true and the conclusion follows logically.

Syllogisms frequently appear in stripped-down form, with one of the premises or the conclusion omitted. The following example omits the major premise: "Because Wilma is a civil engineer, she has a strong background in mathematics." Obviously the missing major premise is as follows: "All civil engineers have strong backgrounds in mathematics."

Syllogistic Argument at Work. A syllogism can occur anywhere in an essay: in the introduction to set the stage for the evidence, at various places in the body, even in the conclusion in order to pull the argument together. Here is an example that uses a syllogism in the introduction:

In 1966, when the Astrodome was completed in Houston, Texas, the managers concluded that it would be impossible to grow grass indoors. To solve their problem, they decided to install a ruglike synthetic playing surface that was fittingly called Astroturf. In the ensuing years, many other sports facilities have installed synthetic turf. Unfortunately, this development has been accompanied by a sharp rise in the number and severity of injuries suffered by athletes-a rise clearly linked to the surface they play upon. Obviously, anything that poses a threat to plaver safety is undesirable. Because synthetic turf does this, it is undesirable and should be replaced by grass.

Denny Witham

To support his position, the writer then notes that turf, unlike grass, often becomes excessively hot, tiring players and increasing their chances of injury; that seams can open up between sections of turf and lead to tripping and falling; that players can run faster on artificial turf and thus collide more violently; and that the extreme hardness of the turf leads to torn ligaments and tissues when players slam their toes into it.

Avoiding Misuse of Syllogisms Two cautions are in order. First, make sure any syllogism you use follows the proper order. The writer of the following passage has ignored this caution:

And that's not all. Newton has stated openly that he favors federally funded abortions for the poor. Just the other day, the American Socialist party took this same stand. In my book, Newton's position puts him squarely in the Socialist camp. I strongly urge anyone supporting this man's candidacy to reconsider....

Restated in syllogistic form, the writer's argument goes like this:

Socialists favor federally funded abortions for the poor.

Newton favors federally funded abortions for the poor.

Therefore, Newton is a Socialist.

The last two statements reverse the proper order, and as a result the syllogism proves nothing about Newton's politics: he may or may not be "in the Socialist camp."

Second, make sure the major premise of your syllogism is in fact true. Note this example:

All conservatives are opposed to environmental protection.

Mary is a conservative.

Therefore, Mary is opposed to environmental protection.

But is every conservative an environmental Jack the Ripper? In some commu­nities, political conservatives have led fights against air and water pollution, and most conservatives agree that at least some controls are worthwhile. Mary's sympathies, then, may well lie with those who want to heal, rather than hack, the environment.

Exercise 1. Which of these syllogisms is satisfactory, which have false major premises, and which is faulty because the last two statements reverse the proper order?

1. All singers are happy people.

Mary Harper is a singer.

Therefore, Mary Harper is a happy person.

2. All cowards fear danger.

"Chicken" Cacciatore is a coward.

Therefore, "Chicken" Cacciatore fears danger.

3. All cats like meat.
Towser likes meat.
Therefore, Towser is a cat.

4. No salesperson would ever misrepresent a product to a customer.
Sabrina is a salesperson.

Therefore, Sabrina would never misrepresent a product to a customer.







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