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# Deductive Reasoning Study Guide (page 2)

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### Major Premise

A major premise is a statement of general truth dealing with categories rather than individual examples. It relates two terms:

All women were once girls.
Athletes are in good shape.

The subject of the major premise (women, athletes, professors) is called the antecedent; the verb phrase (were once girls, are in good shape, hold advanced degrees) is known as the consequent.

### Minor Premise

A minor premise is a statement that deals with a specific example of the major premise:

My mother is a woman.
Tiger Woods is an athlete.
Dr. Shiu is a professor.

The minor premise either affirms the major premise, or denies it. When it affirms, part of the minor premise equates with the subject, or antecedent, of the major premise. When it denies, part of the minor premise does not equate with the consequent. For example:

Children like top 40 music.
Charles is a child.

In this case, the minor premise (Charles is a child) affirms the major premise by stating that it is something equal to the major premise (child).

Children like top 40 music.
Charles does not like top 40 music.

In this case, the minor premise denies the major premise by asserting that something is not the same as the consequent ("does not like" as opposed to "like").

## Conclusions

Deductive arguments are those in which the truth of the conclusion is thought to be completely guaranteed and not just made probable by the truth of the premises. So if the argument is valid, the truth of the conclusion is contained within the truth of the premises. But, the conclusion must follow logically from and not go beyond or make assumptions about the premises.

Here is an example of a conclusion that follows the premises:

Banks make money by charging interest.
My bank charges me interest.
My bank makes money.

Note that the conclusion has no additional information, and does not make assumptions or inferences about the premises. It is a valid conclusion.

Here is an example of a conclusion that goes beyond the truth of the premises:

Ernest Hemingway wrote some great books.
Ernest Hemingway wrote For Whom the Bell Tolls.
For Whom the Bell Tolls is a great book.

Why is this conclusion invalid? Because the major premise states that some of Hemingway's books are great. The conclusion assumes that For Whom the Bell Tolls falls into that group, when there is no evidence in the premises that this is true.

#### Tip

Did you realize that you use deductive reasoning to prove math facts are accurate?

## Two Forms of Deductive Argument

Deductive arguments are expressed in two common ways: syllogisms and conditionals.

### Fact or Opinion?

As you learned in Lesson 8, you have to know the difference between a fact and an opinion. A fact is an objective statement that can be proven to be true, such as, "Saturn is one of the planets in our solar system." You can research to prove that Saturn is, indeed, a planet in our solar system. Is that statement always true? If the answer is yes, then it's a fact.

An opinion is a subjective statement based on personal beliefs. For example, "Saturn is the most beautiful planet in the solar system." This is a personal belief and open to debate. Other people might think Venus is the most beautiful planet, or Jupiter. The word beautiful is subjective, and tells you this is someone's opinion.

### Syllogisms

A syllogism is made up of two premises and a conclusion. The first premise describes a group, A, and a characteristic of that group, B: All vegetarians do not eat meat. The second premise places a person or thing, C, either within A or not within B: Gordon is a vegetarian. The conclusion states that C is B: Gordon does not eat meat.

A negative in a syllogism follows the same form. The word not in the second premise signals the negative. All vegetarians do not eat meat. Gordon is not a vegetarian. Gordon eats meat.

Here are a few examples of positive and negative syllogisms:

Smart people do not believe in UFOs. (All A are not B)
Lee does not believe in UFOs. (C is not B)
Lee is smart. (C is A)
The greatest jazz artists were all improvisers.
Miles Davis was an improviser.
Miles Davis was a great jazz artist.

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