Section 3.5. Symbolic Arguments. Copyright 2013, 2010, 2007, Pearson, Education, Inc.


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1 Section 3.5 Symbolic Arguments
2 INB able of Contents Date opic Page # July 28, 2014 Section 3.5 Examples 84 July 28, 2014 Section 3.5 Notes 85 July 28, 2014 Section 3.6 Examples 86 July 28, 2014 Section 3.6 Notes 87 July 28, 2014 Practice est #5 88 July 28, 2014 Practice est #5 Workspace
3 What You Will Learn Symbolic arguments Standard forms of arguments 3.53
4 Symbolic Arguments A symbolic argument consists of a set of premises and a conclusion. It is called a symbolic argument because we generally write it in symbolic form to determine its validity
5 Symbolic Arguments An argument is valid when its conclusion necessarily follows from a given set of premises. An argument is invalid or a fallacy when the conclusion does not necessarily follow from the given set of premises
6 Law of Detachment Also called modus ponens. Symbolically, the argument is written: Premise 1: Premise 2: Conclusion: p q p q If [premise 1 and premise 2] then conclusion [(p q) p ] q 3.56
7 o Determine Whether an Argument is Valid 1. Write the argument in symbolic form. 2. Compare the form of the argument with forms that are known to be either valid or invalid. If there are no known forms to compare it with, or you do not remember the forms, go to step If the argument contains two premises, write a conditional statement of the form [(premise 1) (premise 2)] conclusion 4. Construct a truth table for the statement above. 5. If the answer column of the truth table has all trues, the statement is a tautology, and the argument is valid. If the answer column of the table does not have all trues, the argument is invalid
8 Example 1: Determining the Validity of an Argument with a ruth able Determine whether the following argument is valid or invalid. If you watch Good Morning America, then you see Robin Roberts. You did not see Robin Roberts. You did not watch Good Morning America
9 Example 1: Determining the Validity of an Argument with a ruth able Solution Construct a truth table. p q [(p q) ~ q] ~p F F F F F F F F F F F F Since the answer, column 5, has all s, the argument is valid
10 Standard Forms of Valid Arguments Law of Detachment p q p q Law of Syllogism p q q r p r Law of Contraposition p q ~q ~ p Disjunctive Syllogism p q ~ p q
11 Standard Forms of Invalid Arguments Fallacy of the Converse p q q p Fallacy of the Inverse p q ~ p ~q
12 Example 2: Identifying a Standard Argument Determine whether the following argument is valid or invalid. If you are on Facebook, then you see my pictures. If you see my pictures, then you know I have a dog. If you are on Facebook, then you know I have a dog
13 Example 3: Identifying Common Fallacies in Arguments Determine whether the following argument is valid or invalid. If it is snowing, then we put salt on the driveway. We put salt on the driveway. It is snowing
14 Example 4: Identifying Common Fallacies in Arguments Determine whether the following argument is valid or invalid. If it is snowing, then we put salt on the driveway. It is not snowing. We do not put salt on the driveway
15 Example 5: An Argument with hree Premises Use a truth table to determine whether the following argument is valid or invalid. If my cell phone company is Verizon, then I can call you free of charge. I can call you free of charge or I can send you a text message. I can send you a text message or my cell phone company is Verizon. My cell phone company is Verizon
16 Example 5: An Argument with hree Premises Solution
17 Section 3.6 Euler Diagrams and Syllogistic Arguments
18 What You Will Learn Euler diagrams Syllogistic arguments
19 Syllogistic Arguments Another form of argument is called a syllogistic argument, better known as syllogism. he validity of a syllogistic argument is determined by using Euler (pronounced oiler ) diagrams
20 Euler Diagrams One method used to determine whether an argument is valid or is a fallacy. Uses circles to represent sets in syllogistic arguments
21 Symbolic Arguments Versus Syllogistic Arguments Symbolic argument Syllogistic argument Words or phrases used and, or, not, ifthen, if and only if all are, some are, none are, some are not Methods of determining validity ruth tables or by comparison with standard forms of arguments Euler diagrams
22 Example 1: Ballerinas and Athletes Determine whether the following syllogism is valid or invalid. All ballerinas are athletic. Keyshawn is athletic. Keyshawn is a ballerina
23 Example 2: 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
24 Example 3: 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
25 Example 4: Fish and Cows Determine whether the following syllogism is valid or invalid. No fish are mammals. All cows are mammals. No fish are cows
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Section 3.5 Symbolic Arguments What You Will Learn Symbolic arguments Standard forms of arguments 3.52 Symbolic Arguments A symbolic argument consists of a set of premises and a conclusion. It is called
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