Section 3.5 Symbolic Arguments, Exercises of Law

Download Section 3.5 Symbolic Arguments and more Exercises Law in PDF only on Docsity! Section 3.5 Symbolic Arguments - Guided notes What You Will Learn: Symbolic arguments Standard forms of arguments 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. 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. Law of Detachment Also called modus ponens. Symbolically, the argument is written(insert here) To 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 3. 3. 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. Example : Determining the Validity of an Argument with a Truth Table 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. Solution Let p: You watch Good Morning America. q: You see Robin Roberts. In symbolic form, the argument is p → q ~p ∴ ~p The argument is [(p → q) ⋀ ~q] → ~p. Standard Forms of Valid Arguments Standard Forms of Invalid Arguments In symbolic form, the argument is p → q q ⋁ r r ⋁ p ∴ p Example : An Argument with Three Premises Solution Write the argument in the form (p → q) ⋀ (q ⋁ r) ⋀ (r ⋁ p)] → p. Construct a truth table. Solution The answer is not true in every case. Thus, the argument is a fallacy, or invalid. Section 3.6 Euler Diagrams and Syllogistic Arguments What You Will Learn Euler diagrams Syllogistic arguments 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. Euler Diagrams One method used to determine whether an argument is valid or is a fallacy. Uses circles to represent sets in syllogistic arguments. Symbolic Arguments Versus Syllogistic Arguments Example: Ballerinas and Athletes Example: golfers and rain gear Example: A Syllogism Involving the Word Some Polite police-