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# notes_2_2x2 - Branden Fitelson Philosophy 12A Notes 1 \$...

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Branden Fitelson Philosophy 12A Notes 1 Overview of Today’s Lecture Traffic, Dream Gerrard Administrative Stuff I went over the syllabus/website last time. See website for all details: * http://fitelson.org/12A/ If you weren’t here last time, (a) please get a syllabus, and (b) fill-out an index card with your section preferences, among these 8 pairs: * (1) 10–11 MW (2) 11–12 MW, (3) 2–3 WF, (4) 3–4 WF, (5) 11-12 TR, (6) 12–1 TR, (7) 3–4 WF, (8) 4–5 WF See us after class if you have questions about the sections, etc. Introduction to the Course & Chapter 1 of Forbes Propositions — the basic units of logical analysis Actual truth and falisty vs possible/necessary truth and falsity Logical necessity, logical truth, validity, and soundness UCB Philosophy Introduction & Chapter 1 08/29/08 Branden Fitelson Philosophy 12A Notes 2 Background 1: Propositions and Sentences Propositions are the basic units of logical analysis. They are expressed by declarative sentences like “Snow is white.” Not all sentences express propositions ( e.g. , “What time is it?”). Propositions are not identical to declarative sentences that express them. Consider: “Snow is white” and “Schnee ist weiß.” Propositions are either true or false (not both). True and False are called truth-values . Propositions have exactly one truth-value. The truth-value of a proposition is objective . That is, whether a proposition is true or false (in a given situation) does not depend on what anyone thinks about that proposition or on how that proposition happens to be expressed. Even if a proposition is about something subjective, its truth-value remains objective ( e.g. , Branden believes that the Yankees will win.) UCB Philosophy Introduction & Chapter 1 08/29/08 Branden Fitelson Philosophy 12A Notes 3 Background 2: Actual, Possible, and Necessary Truth Some propositions are actually true (Snow is white), and some are not (Al Gore is President of the United States in 2007). Other propositions are not actually true, but still possibly true. Al Gore is not actually our President in 2007, but he might have been . As such, it is possibly true that Al Gore is President in 2007. Some propositions are not even possibly true. For instance: 1. My car has traveled faster than the speed of light. 2. 2 + 2 = 5. 3. Branden weighs 200 lbs and Branden does not weigh 200 lbs. (1) violates the laws of physics: it is physically impossible . (2) violates the laws of arithmetic: it is arithmetically impossible. (3) violates the laws of logic : it is logically impossible. UCB Philosophy Introduction & Chapter 1 08/29/08 Branden Fitelson Philosophy 12A Notes 4 This is the kind of impossibility that interests the logician. In slogan form, we might call this “the strongest possible kind of impossibility.” Some propositions are not only actually true, but (logically) necessarily true. These must be true, on pain of self-contradiction : Either Branden weighs 200lbs or he does not weigh 200lbs.

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