PHIL 1313 Week 3 Notes (Plus Cheat Sheet!)
PHIL 1313 Week 3 Notes (Plus Cheat Sheet!) PHIL 1313-002
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This 9 page Class Notes was uploaded by Colleen Maher on Thursday January 21, 2016. The Class Notes belongs to PHIL 1313-002 at Oklahoma State University taught by Justin Rice in Spring 2016. Since its upload, it has received 13 views. For similar materials see Logic and Critical Thinking in PHIL-Philosophy at Oklahoma State University.
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Date Created: 01/21/16
Operator Name Compound Type Used to translate ~ Tilde Negation it is not the case that . dot Conjunction and; also; moreover v wedge disjunction or; unless ⊃ horseshoe conditional if…then…; only if <> (or triple bar) Triple bar biconditional if and only if NEGATION, CONJUNCTION, DISJUNCTION Not either A or B = ~(A v B) Either not A or not B = ~A v ~B Not both A and B = ~(A ● B) Both not A and not B = ~A ● ~ B Neither A nor B = ~(A v B) Either A or B is not ___ = ~A v ~B Not A, but B = ~A ● B Both A and B are not ___ = ~A V ~B NECESSARY AND SUFFICIENT CONDITIONS 1. A is a sufficient condition for B whenever the occurrence of A is all that is required for B. 2. A is a sufficient condition for B whenever B cannot occur without A. 3. Sufficient introduced the antecedent; Necessary introduces the consequent. TRUTH T T T CHARTS NEGATION T F F p ~p F T T T F F F T DISJUNCTION F T p q p v q CONJUNCTIONS: T T T BICONDITIONAL p q p <-> q p q p . q T F T T T T T T T F T T T F F T F F F F F F T F F T F F F F CONDITIONAL F F T p q p ⊃ q Truth Charts Hey guys! This looks really complicated, but I promise it’s not. The truth charts will always look something like this: a b axb T T X F X F F X F T X The lowercase letters stand for statements, and the uppercase letters are for True or False. (The Xs are just placeholders) Let’s start with negations: p ~p T F F T The truth table for negation will always look like this, so you don’t have to worry. How you read it is “If p is true, ~p is false.” You follow the letter down the chart. So, if ~p is true, p is false. Negations are simple like that. EX) Let’s just say that it’s true that I like cats (and it is). p = I like cats. (true) then we negate it: ~p = I do not like cats. (false (and super sad!)) Likewise, if it was true that I didn’t like cats, it would be false to say I did. You follow me? CONJUNCTIONS: p q p . q T T T T F F F T F F F F For conjunctions, F IS A DISEASE! *gasp!* And it makes sense when you think about it. p = April has a three legged dog. (true) q = Andy has a threelegged dog. (Also true) p . q = April and Andy have a threelegged dog. (True to the max) See how this follows the first section of the table? But let’s say April has a threelegged cat. Then p would be false, which would make the whole statement false. Easy, right? DISJUNCTION p q p v q T T T T F T F T T F F F As you can see, disjunction is a little different than conjunction. This is because when you say an “or” statement, you’re saying “this could be OR this could be.” They don’t depend on each other to be true. p = Frodo will throw the ring in the volcano. q = Samwise will throw the ring in the volcano. p v q = Frodo or Samwise will throw the ring in the volcano. No matter which of the statements is true, that ring is still getting chucked into a volcano. The only way it wouldn’t be is if BOTH statements were false. Then the whole thing would be false and they couldn’t defeat Sauron. Just FYI, and exclusive disjunction means that ONLY ONE of the simple statement could be true. These usually have the word either in them EX) Bilbo is either eleventyseven or eleventyeight. CONDITIONAL p q p ⊃ q T T T T F F F T T F F T p = If Elinor marries Edward, (q = ) then Marianne marries Colonel Brandon. Both of these happen to be true, so the conditional is true. If Marianne had married Willoughby, then the antecedent wouldn’t be satisfied and the conditional would be false. If Elinor had run away and become a nun, Marianne would still be married to Colonel Brandon, so the result would still be true. If neither p nor q is true, the result is still true. This is difficult to explain here, but if you read page 326 of the reading, it becomes clearer. Alan Rickman! </3 BICONDITIONAL p q p <-> q T T T T F F F T F F F T (The <> stands in for the triple bar) This one is very similar to the conditional, with the exception of the second to last row, which tells us that id the antecedent is false, the conclusion will be false because the conditions have not been met. Well guys, that was fun! I hope you understand it at least slightly now. Have fun on the quiz Friday!
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