* starting to discuss Chapter 3 - Basic Logical Concepts * in this chapter, we'll discuss 2 kinds of classical logical arguments: * deductive arguments * conclusion is PROVED by the premises * rigorous and inescapable, narrows the scope * impossible to both ASSERT the premises AND DENY the conclusion * inductive arguments * conclusion is PLAUSIBLE or LIKELY because of the premises * can be flawed, but widens the scope * possible to assert the premises and deny the conclusion (you can choose not to believe it) * we'll be discussing both types; here's a STARTING few ways to distinguish them: * terms often found in deductive arguments: * "certainly" "definitely" "absolutely" ...and other words that try to convey logical certainty * some other CLUEs to recognize deductive logic: * the strict necessity test: * if the conclusion follows with strict logical necessity from the premises, then it should always be treated as deductive * the common pattern test: * if the pattern of the argument matches a well-known deductive logic structure or pattern of reasoning, then the argument is deductive * continuing (for a while) to FOCUS on deductive arguments: * FIRST, a few examples: EX. 1 * We are in Arcata. * Arcata is in California. * Therefore, we are in California. EX. 2 * The winner of the race gets the blue ribbon. * Tim got the blue ribbon. * Therefore, Tim won the race. EX. 3 * Either I walked here OR I rode an ox to get here. * I didn't ride an ox to get here. * Therefore, I walked here. * Some CLASSIC COMMON PATTERNS of DEDUCTIVE logic * reminder: a conditional statement has the form: if A, then B ...where A and B are statements. * the COMBO "If A, then B" is a SINGLE statement * a conditional statement by itself is not an argument ...but it sure might be a PART of an argument, one of an argument's components; * If A, then B. the A part is called the ANTECEDENT the B part is called the CONSEQUENT * Modus Ponens ("mode of AFFIRMATION") * PREMISES: * If A, then B. * A is true. * CONCLUSION: * Therefore, B is true. * also called "affirming the antecedent" because A is the antecedent of a conditional 1st premise and the 2nd premise asserts that A is true * Modus Tollens ("mode of DENIAL") * PREMISES: * If A, then B. * B is NOT true. (also: B is false) * CONCLUSION: * Therefore, A must NOT be true. (also: Therefore, A is false) * Also called "Denying the Consequent" -- because B is the consequent in the 1st premise, and the 2nd premise asserts that B is false * Chain Argument * PREMISES: * If A, then B. * If B, then C. * CONCLUSION: * Therefore, if A, then C * 3 conditional statements here! * by the way: syllogism: a 3-statement argument, with 2 premises and a conclusion * the 3 patterns above are called HYPOTHETICAL syllogisms because they involve if statements/conditional statements * be careful, there ARE some NOT valid patterns of this style; NOT VALID: denying the antecedent If A, then B. A is false. Therefore,...? ...no valid conclusion can be made about the value of B NOT VALID: affirming the consequent If A, then B. B is true. Therefore,...? ...no valid conclusion can be made about the value of A * there are some other classic syllogism forms: * categorical - all, none, or some statements * argument by elimination rules out possibilities * mathmetical arguments * argument from definition * MORE on these,and deductive reasoning, on Monday