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# Deductive Reasoning Study Guide

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## Lesson Summary

The two operations of our understanding, intuition and deduction, on which alone we have said we must rely in the acquisition of knowledge.

René Descartes, French philosopher, mathematician, scientist (1596–1650)

What is deductive reasoning? It's an argument based on two facts, or premises. If both are true, then it should follow that the conclusion of the argument must also be true. In this lesson, you'll learn how these arguments work and don't work. And you'll discover how to use deductive reasoning to construct your own strong arguments

You're exposed to deductive arguments, both good and bad, every day. In a magazine, you read an ad: "Brand X just can't get clothes clean. But with Cleany-Oh, your clothes are sparkly clean!" On TV, you hear a politician: "Higher taxes put people out of work. We need tax cuts. Tax cuts help to create jobs for people!" At a restaurant, you hear a parent say, "If you don't finish your supper, you won't get any dessert."

Understanding how these arguments work and do not work will help you construct strong arguments and make it easier to get your point across. And you'll know when someone else's argument is weak so you're not influenced by faulty reasoning. You'll also be aware if someone is presenting a strong argument that should influence you.

## What Is Deduction?

Deduction is the process of drawing a specific conclusion from two things that are known, or general premises. All deductive reasoning includes these three parts:

1. a major premise
2. a minor premise
3. a conclusion

For instance, we know that dogs have four legs, and we know that Fido is a dog. Therefore, since A and B are true, we can conclude with certainty that Fido has four legs. From this example, you may see that a deductive argument is sound when the premises are true, and the conclusion logically follows from the premises.

### Qualities of a Deductive Argument

• Has two premises that provide a guarantee of the truth of the conclusion by providing support for it that is so strong that, if the premises are true, it would be impossible for the conclusion to be false.
• Is described by the terms valid and invalid; when the premises are correct, and the conclusion that follows is correct, the argument is said to be valid. If either or both premises are incorrect, the argument is invalid.
• Is based on rules, laws, principles, or generalizations, as opposed to inductive arguments (see Lesson 14), whose major premises are based on observations or experiences.

## Premises

The key to the credibility of a deductive conclusion lies in the premises. Since the conclusion must result from the premises, it is considered invalid if one or both of the premises is proven false. Therefore, the premises must be truthful facts, rules, principles, or generalizations. Just one word can change the premise from fact to fiction, such as the words "all" and "every."

Consider the following example:
All dogs have brown fur.
Spot is a dog.
Spot has brown fur.

The truth is that some dogs have brown fur. The first premise is untrue, which makes the conclusion invalid.

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