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Unformatted text preview: Branden Fitelson Philosophy 12A Notes 1 Announcements &amp; Such Branden is in Chicago all of this week. Hell return next week. HW #2 resubmissions are due Today (4pm, drop box). Please attach your original assignment to your resub! See my HW Tips &amp; Guidelines Handout. [Were now caught-up.] Make sure you have problem #12 from p. 33 of the 4 th printing. Its about the Mayors election (and the council members). HW #3 has been posted. 1st-submission is due next Thursday. I have posted a handout with solutions to (some of) the lecture problems on logical truth, logical falsity, equivalence, consistency, etc. I have also posted a handout on the short truth-table method, which we will be going over in lecture sometime very soon. Today: Chapter 3, Continued (Truth-Table methods for validity testing) UCB Philosophy Chapter 3 02/18/10 Branden Fitelson Philosophy 12A Notes 2 Semantic Equivalence, Contradictoriness, etc .: Relationships What are the logical relationships between [ p and q are equivalent , [ p and q are consistent , [ p and q are contradictory , and [ p and q are inconsistent ? That is, which of these entails which (and which dont)? Equivalent Contradictory ? ? Consistent Inconsistent Answers: 1. Equivalent Consistent ( example ?) 2. Consistent Equivalent ( example ?) 3. Contradictory Inconsistent ( why ?) 4. Inconsistent Contradictory ( example ?) UCB Philosophy Chapter 3 02/18/10 Branden Fitelson Philosophy 12A Notes 3 Semantic Equivalence: Example #1 Recall that [ p unless q translates in LSL as [ q p . Weve said that we can also translate [ p unless q as [ p q . This is because [ q p is semantically equivalent to [ p q . We may demonstrate this, using the following joint truth-table. p q q p p q The truth-tables of [ p q and [ q p are the same. Thus, q p p q . UCB Philosophy Chapter 3 02/18/10 Branden Fitelson Philosophy 12A Notes 4 Semantic Equivalence: Example #2 [ p q is an abbreviation for [ (p q) &amp; (q p) . The following truth-table shows it is a legitimate abbreviation: p q (p q) &amp; (q p) p q [ p q and [ (p q) &amp; (q p) have the same truth-table. Thus, p q (p q) &amp; (q p) . UCB Philosophy Chapter 3 02/18/10 Branden Fitelson Philosophy 12A Notes 5 Semantic Equivalence: Example #3 Intuitively, the truth-conditions for exclusive or ( ) are such that [ p q is true if and only if exactly one of p or q is true....
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- Spring '10