154 CHAPTER 3 Logic In Section 3.5, we showed how to determine the validity of symbolic arguments using truth tables and comparing the arguments to standard forms. This section presents another form of argument called a syllogistic argument, better known by the shorter name syllogism. The validity of a syllogistic argument is determined by using Euler (pronounced “oiler”) diagrams, as is explained shortly. Syllogistic logic, a deductive process of arriving at a conclusion, was developed by Aristotle in about 350 b.c. Aristotle considered the relationships among the four types of statements that follow. All ________ are ________. No ________ are ________. Some ________ are ________. Some ________ are not ________. Examples of these statements are as follows: All doctors are tall. No doctors are tall. Some doctors are tall. Some doctors are not tall. Since Aristotle’s time, other types of statements have been added to the study of syllogistic logic, two of which are ________ is a ________. ________ is not a ________. Deandre is studying to be a nurse. While reading the program literature, he learns that “All art classes are electives.” He also learns that “Introduction to Theater is an elective.” From these two statements can Deandre conclude that Introduction to Theater is considered an art class? In this section we will examine arguments that consist of statements that contain quantifiers. We learned in Section 3.1 that quantifiers include words such as all, some, or none. LEARNING GOAL Upon completion of this section, you will be able to: 7 Determine the validity of syllogistic arguments using Euler diagrams. Why This Is Important When several sentences containing the words all, some, or none are put together into an argument, we need to be able to determine if the conclusion necessarily follows from the premises. In this section we will study such arguments, and we will be able to see how we can analyze similar arguments that we encounter in our everyday lives. Examples of these statements are as follows: Maria is a doctor. Maria is not a doctor. The difference between a symbolic argument and a syllogistic argument can be seen in the following chart. Symbolic arguments use the connectives and, or, not, if– then, and if and only if. Syllogistic arguments use the quantifiers all, some, and none, which were discussed in Section 3.1. Symbolic Arguments Versus Syllogistic Arguments Words or phrases used Method of determining validity Symbolic argument and, or, not, if–then, if and only if Truth tables or by comparison with standard forms of arguments Syllogistic argument all are, some are, none are, some are not Euler diagrams SECTION 3.6 Euler Diagrams and Syllogistic Arguments Hero Images Inc./Alamy Stock Photo
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