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Unformatted text preview: Branden Fitelson Philosophy 12A Notes 1 Announcements & Such Branden is in Chicago all of this week. Hell return next week. Administrative Stuff HW #2 will be returned today. Resubs due Thursday (4pm, drop box). Please attach your original assignment to your resub! See my HW Tips & 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). 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-Tables and their applications etc .) UCB Philosophy Chapter 3 02/16/10 Branden Fitelson Philosophy 12A Notes 2 p p p q p & q p q p q p q p q p q p q UCB Philosophy Chapter 3 02/16/10 Branden Fitelson Philosophy 12A Notes 3 Chapter 3 An Internal Justification of Our Definition of 1. We want a truth-functional semantics for . This is a simplifying idealization . Truth-functional semantics are the simplest compositional semantics for sentential logic. [A Newtonian semantic model.] 2. Given (1), the only way to define is our way, since its the only binary truth-function that has the following three essential logical properties: (i) Modus Ponens [ p and [ p q q ] is a valid sentential form. (ii) Affirming the consequent [ q and [ p q p ] is not a valid form. (iii) All sentences of the form [ p p are logical truths. There are non-truth-functional semantics for the English conditional. These may be closer to the English meaning of if. But, most agree with our semantics for , when it comes to the crucial logical properties (i)(iii). Indeed, our captures most of the (intuitive) logical properties of if. This is analogous to our treatment of the English however as &. UCB Philosophy Chapter 3 02/16/10 Branden Fitelson Philosophy 12A Notes 4 Constructing Truth-Tables for LSL Sentences With the truth-table definitions of the five connectives in hand, we can now construct truth tables for arbitrary compound LSL statements. The procedure for constructing the truth-table of p is as follows: 1. Determine the number of rows in the truth-table. This is 2 n , where n is the number of atomic sentences in the compound statement p ....
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This note was uploaded on 04/20/2010 for the course PHIL 63170 taught by Professor Fitelson during the Spring '10 term at University of California, Berkeley.
- Spring '10