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Chapter 3

Oct 4 - CH3 - Types of Valid Arguments - L.docx

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University of Ottawa
Mark Brown

Deductive Argument An argument intended to provide logically conclusive support for its conclusion. The defining characteristic of a deductive argument is that it is valid or invalid. If we describe a deductive argument as valid, we mean that if its premises were true, then they would guarantee the truth of the conclusion. As noted: The only combination of premises and a conclusion that a valid argument cannot have is true premises and a false conclusion. If an argument has true premises and a false conclusion, then it is invalid. Also, we have noted that it is the structure or form of some arguments that make them deductive. When arguments have a specific structure or form, then they are valid, as the premises guarantee the conclusion. Today: We want to look at 8 valid argument forms and 2 invalid argument forms. The ultimate goal is to learn how to construct proofs to show how an argument is valid in its entirety. Sentential Form Conjunction (‘and’) = ● Example: Alice rode her bike, and John walked. p ● q Disjunction (‘or’) = v Example: Either Alice rode her bike, or John walked. p v q Negation (‘not’) = ~ Example: Alice did not ride her bike. It is not the case that Alice rode her bike. ~p Conditional (‘if-then’) = → Example: If Alice rode her bike, then John walked. p → q EIGHT VALID ARGUMENT FORMS 1. Modus Ponens (MP) If Spot barks, a burglar is in the house. Spot is barking. Therefore, a burglar is in the house. If p, then q. p. Therefore, q. P→ Q P ------- Q Variations of MP: ~P → ~Q ~P ------- ~Q ~P → Q P → ~Q P ~P P P → Q --------- --------- -------- Q ~ Q Q 2. Modus Tollens (MT) If p, then q. Not q. Therefore not p. Example: If you work in a bar, you’re over 19. You’re not over 19. So, you must not work in a bar. p → q ~q ------- ~p Or a variation of MT: ~p → ~q q --------- p 3. Hypothetical Syllogism (HS) If p, then q. If q, then r. Therefore, if p, then r. p → q q → r -------- p → r Example: If Guy steals the money, he will go to jail. If Guy goes to jail, his family will suffer. Therefore, if Guy steals the money, his family will suffer. 4. Disjunctive Syllogism (DS) Either Ralph walked the dog or he stayed home. Ralph did not walk the dog. Therefore, he stayed home. p v q ~p --------- q Either Ralph walked the dog or he stayed home. He did not stay home. Therefore, Ralph walked the dog. p v q ~q --------- P 5. Constructive Dilemma (CD) p v q p  r q  s --------
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