# 14.3: Deductive Reasoning

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The second type of reasoning is called deductive reasoning, or deduction, a type of reasoning in which a conclusion is based on the combination of multiple premises that are generally assumed to be true. It has been referred to as “reasoning from principle,” which is a good description. It can also be called “top-down” reasoning. However, you should not think of deductive reasoning as the opposite of inductive reasoning. They are two different ways of thinking about evidence.

First, formal deductive reasoning employs the syllogism, which is a three-sentence argument composed of a major premise (a generalization or principle that is accepted as true), a minor premise (an example of the major premise), and a conclusion. This conclusion has to be true if the major and minor premise are true; it logically follows from the first two statements. Here are some examples. The most common one you may have seen before.

All men are mortal. (Major premise: something everyone already agrees on)

Socrates is a man. (Minor premise: an example taken from the major premise.)

Socrates is mortal. (Conclusion: the only conclusion that can be drawn from the first two sentences.)

Major Premise: All State College students must take COMM 1110.

Minor Premise: Brittany is a State College student.

Conclusion: Brittany must take COMM 1110.

Major Premise: All dogs have fur.

Minor Premise: Fifi is a dog.

Conclusion: Fifi has fur.

Of course, at this point you may have some issues with these examples. First, Socrates is already dead and you did not need a syllogism to know that. The Greek philosopher lived 2,400 years ago! Second, these seem kind of obvious. Third, are there some exceptions to “All Dalton State College students must take COMM 1110”? Yes, there are; some transfer students do not, and certificate students do not. Finally, there are breeds of dogs that are hairless. Some people consider them odd-looking, but they do exist. So while it is true that all men are mortal, it is not absolutely and universally true that all State College students must complete COMM 1110 or that all dogs have fur.

Consequently, the first criterion for syllogisms and deductive reasoning is that the premises have to be true for the conclusion to be true, even if the method is right. A right method and untrue premises will not result in a true conclusion. Equally, true premises with a wrong method will also not result in true conclusions. For example:

Major premise: All dogs bark.

Minor premise: Fifi barks.

Conclusion: Fifi is a dog.

You should notice that the minor premise is stated incorrectly. We know other animals bark, notably seals (although it is hard to think of a seal named “Fifi”). The minor premise would have to read “Fifi is a dog” to arrive at the logical conclusion, “Fifi barks.” (Also, there are dog breeds that do not bark.) However, by restating the major premise, you have a different argument.

Major premise: Dogs are the only animals that wag their tails when happy.

Minor premise: Fifi wags her tail when happy.

Conclusion: Fifi is a dog.

Another term in deductive reasoning is an enthymeme. This odd word refers to a syllogism with one of the premises missing.

Major premise: (missing)

Minor premise: Daniel Becker is a chemistry major.

Conclusion: Daniel Becker will make a good SGA president.

What is the missing major premise? “Chemistry majors make good SGA presidents.” Why? Is there any support for this statement? Deductive reasoning is not designed to present unsupported major premises; its purpose is to go from what is known to what is not known in the absence of direct observation. If it is true that chemistry majors make good SGA presidents, then we could conclude Dan will do a good job in this role. But the premise, which in the enthymeme is left out, is questionable when put up to scrutiny.

Major premise: Socialists favor government-run health care.

Minor premise: (missing)

Conclusion: Candidate Fran Stokes favors government-run health care.

The missing statement in the minor premise, “Fran Stokes is a socialist,” is left out so that the audience can make the connection, even if it is erroneous. Consequently, it is best to avoid enthymemes with audiences and to be mindful of them when used by persuaders. They are mentioned here to make you aware of how commonly they are used as shortcuts. Enthymemes are common in advertising. You may have heard the slogan for Smucker’s jams, “With a name like Smucker’s, it has to be good.”

Major premise: Products with odd names are good products. (questionable!)

Minor premise: “Smucker’s” is an odd name.

Conclusion: Smucker’s is a good product.

To conclude, deductive reasoning helps us go from known to unknown and can lead to reliable conclusions if the premises and the method are correct. It has been around since the time of the ancient Greeks. It is not the flip side of inductive but a separate method of logic. While enthymemes are not always errors, you should listen carefully to arguments that use them to be sure that something incorrect is not being assumed or presented.

14.3: Deductive Reasoning is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by Kris Barton & Barbara G. Tucker (GALILEO Open Learning Materials) .