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# notes_13_2x2 - Branden Fitelson Philosophy 12A Notes 1...

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Branden Fitelson Philosophy 12A Notes 1 Announcements & Such Three videos from Animusic 2 Administrative Stuff HW #2 resubmisions due Friday (4pm, drop box). Please attach your original assignment to your resub! See my “HW Tips & Guidelines” Handout. Make sure you have problem #12 from p. 33 of the 4 th edition. It’s about the Mayor’s election (and the council members). I have posted two handouts: (1) solutions to problems from lecture on logical truth, equivalence, etc., and (2) three examples of the “short” truth-table method for validity (to be discussed soon). HW #3 has been posted. It’s on truth-table methods for validity. Next: Chapter 3, Continued — LSL Semantics Truth-table methods for LSL validity. UCB Philosophy Chapter 3 09/26/08 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 09/26/08 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, we’ll 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, it’s valid. We will practice this on examples. But, first, a “short-cut” method. UCB Philosophy Chapter 3 09/26/08 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. This would lead to a complete truth-table with 32 rows and 8 columns (this will be far more than 256 distinct computations). As such, the exhaustive truth-table method does not seem practical in this case. So, instead, let’s try to construct or “reverse engineer” an invalidating interpretation.

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notes_13_2x2 - Branden Fitelson Philosophy 12A Notes 1...

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