### 3.3 Deductive & Inductive Reasoning

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• Math Help

Logic is a fascinating and important topic. In this chapter, you are being given only a brief survey of logic. Even so, the examples and exercises are intended to show you the importance of using logic to analyze arguments in order to determine whether the reasoning is valid.

In Aristotle's type of categorical syllogism, a syllogism is of the following form.

 • Premise: All B are A All men are mortal. • Premise: All C are B All Greeks are men. • Premise: All C are A All Greeks are mortal.

The premises and conclusion must be of the form "All A are B," "Some A are B," "No A are B," or "Some A are not B." The difference between this form and the modern "If P, then Q" form is one of wording. For instance, the above syllogism can be rewritten as follows.

 • Premise: If a being is a man, then the being is mortal. • Premise: If a being is a Greek, then the being is a man. • Conclusion: If a being is a Greek, then the being is mortal.

As you study Section 3.3, remember that the goal of the section is to give you a brief introduction to a classic topic. If you find the topic interesting, there are many ways in which you can learn more about logic, syllogisms, logical reasoning, and fallacies. You might even consider taking an entire course on logical reasoning. You could also search the Internet and find an introductory book on the subject.

• Consumer Suggestion

Stephen Hawking is one of the world's leading scientists in both physics and cosmology. Among his 194 publications, he has written many bestselling books, including his most recent, The Grand Design, which was published in 2010.

He also created a series with the Discovery Channel entitled "Into the Universe with Stephen Hawking." You can view video clips and learn more by visiting the Discovery Channel.

• Checkpoint Solution

Here is one possible syllogism.

 • Premise: Any physical theory is always provisional in the sense that it is only a hypothesis; you can never prove it. • Premise: Any theory of gravity is a physical theory. • Conclusion: You can never prove any theory of gravity.

This is surprising, isn't it ... especially when you consider that it is being said by a person who is considered to be one of the most brilliant physicists who ever lived.

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