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Unformatted text preview: Branden Fitelson Philosophy 12A Notes 1 ' & $ % Overview of Todays Lecture Todays Music: Van Morrison HW #2 due tomorrow @ 5pm in the 12A Drop Box (outside 301 Moses). + Make sure to follow the guidelines/hints on my HW Tips Handout. I will go over some of that stuff right now. The mid-term is next Thursday, 6/10 (in class) . Ive posted a sample mid-term same structure as actual mid-term, with problems of similar complexity. I will discuss it today (at end). + NOTE: The mid-term exam will only cover Chapter 3 topics. I have posted HW #3, which is due next Thursday @ 4pm in drop box. Its all chapter 3 problems truth-table methods for validity-testing. I have posted a handout on the short method for testing LSL validity. I will go over this important handout in todays lecture. Today: Chapter 3, Continued UCB Philosophy Chapter 3 (Contd) 06/04/08 Branden Fitelson Philosophy 12A Notes 2 ' & The Exhaustive Truth-Table Method for Testing Validity Remember, an argument is valid if it is impossible for its premises to be true while its conclusion is false. Let p 1 ,...,p n be the premises of a LSL argument, and let q be the conclusion of the argument. Then, we have: p 1 . . . p n q is valid if and only if there is no row in the simultaneous truth-table of p 1 ,...,p n , and q which looks like the following: atoms premises conclusion p 1 p n q > > > We will use simultaneous truth-tables to prove validities and invalidities. For example, consider the following valid argument: UCB Philosophy Chapter 3 (Contd) 06/04/08 Branden Fitelson Philosophy 12A Notes 3 ' & $ % A A B B atoms premises conclusion A B A A B B > > > > > > > > > > > > > > > + VALID there is no row in which A and A B are both > , but B is . In general, well use the following procedure for evaluating arguments: 1. Translate and symbolize the the argument (if given in English). 2. Write out the symbolized argument (as above). 3. Draw a simultaneous truth-table for the symbolized argument, outlining the columns representing the premises and conclusion. 4. Is there a row of the table in which all premises are > but the conclusion is ? If so, the argument is invalid; if not, its valid. We will practice this on examples. But, first, a short-cut method. UCB Philosophy Chapter 3 (Contd) 06/04/08 Branden Fitelson Philosophy 12A Notes 4 ' & The Short Truth Table Method for Validity Testing I Consider the following LSL argument: A (B & E) D (A F) E D B This argument has 3 premises and contains 5 atomic sentences....
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- Fall '06