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Lecture 5

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Department
Philosophy
Course
PHI1101
Professor
Mark Brown
Semester
Fall

Description
PHI 1101: Lecture 5  Oct 4  2011 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 (‘if­then’) = → Example: If Alice rode her bike, then John walked.  p → q 1.  odus 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  Other variations of MP: ~P →   ~Q ~P ­­­­­­­ ~Q ~P →  Q P → ~Q P ~P P P → Q ­­­­­­­­­ ­­­­­­­­­ ­­­­­­­­ Q ~ Q Q 2.  dus 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.  isjunctive Syllogism (DS)   p v q ~p ­­­­­­­­­ q Either Ralph walked the dog or he stayed home. Ralph did not walk the dog. Therefore, he stayed home. p v q ~q ­­­­­­­­­ P Either Ralph walked the dog or he stayed home. He did not stay home. Therefore, Ralph walked the dog. 5.  onstructive Dilemma (CD)   p v q p ® r q ® s ­­­­­­­­ r v s Either it is forecasted to rain tomorrow, or it is forecasted to rain today. If it is forecasted to rain tomorrow, we will play the baseball game today. If it is forecasted to rain today, we will play the baseball game tomorrow. Therefore, either we will play the baseball game today or we will play it tomorrow. 6.  onjunction (Conj)   p q ­­­­ p ● q The class is large. The students are noisy. Thus, the class is large, and the students are noisy. q p ­­­­­­­ q ● p 7.  implification (Simp)    p ● q ­­­­­­­­­­ p I am an optimist, and I am a fair individual. Therefore, I am an optimist. p ● q ­­­­­­­­ q I am an 
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