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Deductive Reasoning Study Guide (page 3)

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Updated on Sep 19, 2011

Conditionals

A conditional deductive argument expresses the same reasoning in a different way. The first premise states that if something is true of A, then something is true of B: If you spill the lemonade, then the table will get sticky. In the second premise, the "if " in A either happens or it doesn't: You spill the lemonade, or You do not spill the lemonade. The conclusion then states that, as a result, B happens or does not: The table will get sticky, or The table will not get sticky.

Let's look at some examples:

      If you attend Camp HiLow, you will lose weight. (If A, then B)
      You attend Camp HiLow. (A)
      You lose weight. (B)
      If Jason stays after class to speak with his professor, he will miss the bus. (If A then B)
      Jason did not stay after class to speak with his professor. (not A)
      Jason did not miss the bus. (not B)
      If we do not earn the money, we will miss the concert. (If not A, then B)
      We earned the money. (A)
      We did not miss the concert. (not B)

Tip

Conditional "if … then" statements are used when predicting what might happen. if the cold front stalls over our area, then we're in for another day of possible thunderstorms.

How Deduction Can Be Misused

People sometimes use deductive arguments incorrectly, deliberately, or by accident. The better you are at spotting such arguments, the less likely you are to accept them as true. Remember, a deductive argument is invalid if either or both of the premises are not true or if the wrong conclusion is reached even though the premises are true. In the next lesson, you learn more about these untruths, called logical fallacies, but for now, here's an example:

      All Americans wear sneakers. (major premise)
      Harold is an American. (minor premise)
      Therefore, Harold wears sneakers. (conclusion)

Since not all Americans wear sneakers, the major premise is false. That makes the conclusion, and therefore the deductive argument itself, invalid.

In this case, the wrong conclusion is reached:

      Many Americans wear sneakers.
      Harold is an American.
      Therefore, Harold wears sneakers.

In Short

Deductive reasoning takes two premises, which may be rules, laws, principles, or generalizations, and forms a conclusion based upon them. In order to be valid, a deductive argument must have premises that are true and a conclusion that logically follows from those premises, without trying to go beyond them. When you understand how these arguments work, you will know how to construct your own strong arguments. You will also avoid being influenced or persuaded by faulty deductive reasoning.

Skill Building Until Next Time

  • Find a deductive argument in print. Put it in the form of a diagram, listing the major premise, minor premise, and conclusion. Is it valid? If not, why?
  • The next time you need to persuade someone to do something, such as eat at your favorite restaurant instead of theirs or see the movie you prefer, argue for your choice using deductive reasoning.

Exercises for this concept can be found at Deductive Reasoning Practice Exercises.

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