3.5 Symbolic Arguments

Objective: SWBAT determine if an argument is valid or invalid using truth tables and the standard forms of arguments. SWBAT translate arguements into symbolic form and determine if they are valid or invalid.

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.

Valid or Invalid? If the truth table answer column is true in every case, then the statement is a tautology, and the argument is valid. If the truth table answer column is not true in every case then the statement is not a tautology, and the argument is invalid.

Law of Detachment The argument form symbolically written: Premise 1: Conclusion: Change to the following to create a truth table If [ premise 1 and premise 2 ] then conclusion [ (p g q) ^ p ] g q

Determine Whether an Argument is Valid Write the argument in symbolic form. Compare the form with forms that are known to be either valid or invalid. If the argument contains two premises, write a conditional statement of the form [(premise 1) ^ (premise 2)] g conclusion Construct a truth table for the statement in step 3. If the answer column of the 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 Validity with a Truth Table Determine whether the following argument is valid or invalid. If you score 90% on the final exam, then you will get an A for the course. You will not get an A for the course. You do not score 90% on the final exam.

Example: Determining Validity with a Truth Table Solution: Let p: You score 90% on the final exam. q: You will get an A in the course. In symbolic form the argument is: p g q ~q ~p Construct a truth table.

Example: Determining Validity with a Truth Table Fill-in the table in order, as follows: Column 1 is answer to if p then q p q [(p g q) ^ ~ q] g ~p T F T F T F F T F T T F T 1 3 2 5 4 Since column 5 has all T’s, the argument is valid.

Valid Arguments You do not need to creat a truth table if you identify one of these arguments Law of Detachment Law of Syllogism Law of Contraposition Disjunctive Syllogism

Example: Determine if the following argument is valid. ~p q q r ~p r Valid: Law of Syllogism

Invalid Arguments Fallacy of the Converse Fallacy of the Inverse

Example: Determin the Validity using a standard form p ~q ~q p Invalid: Fallacy of the Converse

Homework P. 147 # 7 – 12 all, 15 -63 (x3)