notes_5_2x2 - Branden Fitelson Philosophy 12A Notes 1 ✬...

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Unformatted text preview: Branden Fitelson Philosophy 12A Notes 1 ✬ ✫ ✩ ✪ Overview of Today’s Lecture • Today’s Music: Black Roots • Richard will have extra office hours from 3:30–5 today. • My office hours are 4–5:30 on Wednesdays. • HW #2 due Friday @ 5pm in the 12A Drop Box (outside 301 Moses). ☞ Make sure you follow the guidelines/hints on my “HW Tips” Handout • The mid-term is next Thursday (in class). I’ll post a sample tomorrow. And, I will discuss the sample exam in lecture next Wednesday. • I have posted a handout on the “short” method for testing LSL validity. I will be going over this handout in lecture very soon. • More 12A Practice Problems can be found in: Schaum’s Outline of Logic • Today: Chapter 3, Continued UCB Philosophy Chapter 3 (Cont’d) 06/02/10 Branden Fitelson Philosophy 12A Notes 2 ✬ ✫ Abstract Argument Logical Form LSL / LMPL / LFOL Symbolization Chapters 2, 5 & 7 English Argument Valid Form? Deciding Formal Validity Chapters 3 , 4, 6 & 8 Valid English Argument? Valid Abstract Argument? Articulation of Thought in English UCB Philosophy Chapter 3 (Cont’d) 06/02/10 Branden Fitelson Philosophy 12A Notes 3 ✬ ✫ ✩ ✪ p ∼ p ⊤ ⊥ ⊥ ⊤ p q p & q ⊤ ⊤ ⊤ ⊤ ⊥ ⊥ ⊥ ⊤ ⊥ ⊥ ⊥ ⊥ p q p ∨ q ⊤ ⊤ ⊤ ⊤ ⊥ ⊤ ⊥ ⊤ ⊤ ⊥ ⊥ ⊥ p q p → q ⊤ ⊤ ⊤ ⊤ ⊥ ⊥ ⊥ ⊤ ⊤ ⊥ ⊥ ⊤ p q p ↔ q ⊤ ⊤ ⊤ ⊤ ⊥ ⊥ ⊥ ⊤ ⊥ ⊥ ⊥ ⊤ UCB Philosophy Chapter 3 (Cont’d) 06/02/10 Branden Fitelson Philosophy 12A Notes 4 ✬ ✫ Chapter 3 — Semantics of LSL: Truth Functions VII • If our truth-functional semantics for ‘ → ’ doesn’t perfectly capture the English meaning of ‘if . . . then . . . ’, then why do we define it this way? • The answer has two parts. First, our semantics is truth-functional . This is an idealization — it yields the simplest (“Newtonian”) semantics. • And, there are only 2 4 = 16 possible binary truth-functions. Why? • So, unless one of the other 15 binary truth-functions is closer to the English conditional than ‘ → ’ is, it’s the best we can do , truth-functionally . • More importantly, there are certain logical properties that the conditional must have. It can be shown that our definition of ‘ → ’ is the only binary truth-function which satisfies all three of the following: (1) Modus Ponens [ p and [ p → q ∴ q ] is a valid sentential form. (2) Affirming the consequent [ q and [ p → q ∴ p ] is not a valid form. (3) All sentences of the form [ p → p are logical truths. UCB Philosophy Chapter 3 (Cont’d) 06/02/10 Branden Fitelson Philosophy 12A Notes 5 ✬ ✫ ✩ ✪ Chapter 3 — Semantics of LSL: Truth Functions VIII • Here are all of the 16 possible binary truth-functions. I’ve given them all names or descriptions. [Only a few of these names were made up by me.] p q ⊤ nand → ∼ p fi ( ← ) ∼ q ↔ nor ∨ niff q nfi p nif & ⊥ ⊤ ⊤ ⊤ ⊥ ⊤ ⊥ ⊤ ⊥ ⊤ ⊥...
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This note was uploaded on 11/26/2011 for the course PHILOSOPHY 101 taught by Professor Buechner during the Fall '06 term at Rutgers.

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notes_5_2x2 - Branden Fitelson Philosophy 12A Notes 1 ✬...

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