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Chapter 8 Overview

Critical Thinking

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Chapter 8 Overview You may think of all the preceding chapters as preliminaries to the detailed and precise task of evaluating arguments. Now it is time to put arguments to the test. The book's remaining chapters will take up deductive arguments, inductive arguments, and then the difficult kinds of arguments concerning moral, legal, and aesthetic matters. We begin with deductive arguments, which we have characterized as being either valid or invalid. Chapters 8–9 present two methods for testing for validity. In the present chapter, we use the logic of categorical statements, which dates back to Aristotle, and is a powerful tool for handling one large group of arguments. Those arguments are distinguished by the form of claims that make up their premises and conclusions—roughly, claims beginning with the words "all" and "some." Chapter 8 first shows how to work with such categorical statements by themselves: translating them into equivalent forms, separating them from superficially identical claims, and so on. Then we look at the standard arrangement of such statements into arguments, called categorical syllogisms. Two methods test syllogisms for validity; either one will let the reader evaluate every standard categorical syllogism. 1. Categorical logic studies the relations among classes or categories of things. a. This theory of logical inference began with Aristotle and developed for over two thousand years since his time. b. Like truth-functional logic (see Chapter 9), it helps in every situation that calls for clarification and analysis. i. Our evaluation of arguments most obviously will depend on logic. ii. Many other situations—legal contracts, logical reasoning tests, and so on—call for the same skills. 2. Categorical claims , which make assertions about groups or categories of things, make up the subject matter of categorical logic. a. We will use categorical claims in their standard forms. A standard-form categorical claim has one of these structures: i. A: All _____ are _____. ii. E: No _____ are _____. iii. I: Some _____ are _____. iv. O: Some _____ are not _____. b. Categorical claims have nouns and noun phrases in the above blanks. i. We call those nouns and noun phrases terms . 1. The first term in a standard-form claim is its subject term , S. 2. The second is its predicate term , P. ii. Only nouns and noun phrases can work as terms. c. Each of these forms of claims can be given a visual illustration in a Venn diagram . i. In each Venn diagram, the two overlapping circles represent the groups or categories named by the subject and predicate term. ii. A shaded area represents an empty class. (Note that this is the opposite of what shaded areas mean in Venn diagrams you may have used in math class.)
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iii. An area with an X represents a class that is not empty: The class contains at least one member. (In this chapter, "some" will mean "at least one.") d. When drawing Venn diagrams for categorical claims, it helps to think of those claims in terms of empty and nonempty classes.
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Chapter 8 Overview - Chapter 8 Overview You may think of...

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