Section 3 6 Euler Diagrams and Syllogistic Arguments

Section 3. 6 Euler Diagrams and Syllogistic Arguments Copyright 2013, 2010, 2007, Pearson, Education, Inc.

What You Will Learn Euler diagrams Syllogistic arguments 3. 6 -2 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Syllogistic Arguments Another form of argument is called a syllogistic argument, better known as syllogism. The validity of a syllogistic argument is determined by using Euler (pronounced “oiler”) diagrams. 3. 6 -3 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Euler Diagrams One method used to determine whether an argument is valid or is a fallacy. Uses circles to represent sets in syllogistic arguments. 3. 6 -4 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Symbolic Arguments Versus Syllogistic Arguments Words or phrases used Symbolic argument Syllogistic argument 3. 6 -5 Methods of determining validity and, or, not, if-then, Truth tables or by if and only if comparison with standard forms of arguments all are, some are, Euler diagrams none are, some are not Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 3: Ballerinas and Athletes Determine whether the following syllogism is valid or invalid. All ballerinas are athletic. Keyshawn is athletic. ∴ Keyshawn is a ballerina. 3. 6 -6 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 3: Ballerinas and Athletes Solution Keyshawn is athletic, so must be placed in the set of athletic people, which is A. We have a choice, as shown above. The conclusion does not necessarily follow from the set of premises. The argument is invalid. All ballerinas, B, are athletic, A. 3. 6 -7 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 4: Parrots and Chickens Determine whether the following syllogism is valid or invalid. No parrots eat chicken. Fletch does not eat chicken. ∴ Fletch is a parrot. 3. 6 -8 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 4: Parrots and Chickens Solution The first premise tells us that parrots and things that eat chicken are disjoint sets—that is, sets that do not intersect. Fletch is not a parrot, the argument is invalid, or is a fallacy. 3. 6 -9 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 5: A Syllogism Involving the Word Some Determine whether the following syllogism is valid or invalid. All As are Bs. Some Bs are Cs. ∴ Some As are Cs. 3. 6 -10 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 5: A Syllogism Involving the Word Some Solution The premise “All As are Bs” is illustrated. 3. 6 -11 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 5: A Syllogism Involving the Word Some Solution The premise “Some Bs are Cs” means that there is at least one B that is a C. 3. 6 -12 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 5: A Syllogism Involving the Word Some Solution The first illustrations shows that the conclusion “Some As are Cs, ” does not follow, the argument is invalid. 3. 6 -13 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Try This: p. 155 #11 3. 6 -14 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 6: Fish and Cows Determine whether the following syllogism is valid or invalid. No fish are mammals. All cows are mammals. ∴ No fish are cows. 3. 6 -15 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Example 6: Fish and Cows Solution The first premise tells us that fish and mammals are disjoint sets. The second tells us that the set of cows is a subset of the set of mammals. The conclusion necessarily follows from the premises and the argument is valid. 3. 6 -16 Copyright 2013, 2010, 2007, Pearson, Education, Inc.

Homework p. 155 #9 – 27 (x 3) 3. 6 -17 Copyright 2013, 2010, 2007, Pearson, Education, Inc.