notes_9_2x2 - Branden Fitelson Philosophy 12A Notes 1 '...

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Unformatted text preview: Branden Fitelson Philosophy 12A Notes 1 ' & $ % Announcements and Such Todays Music: Neil Young HW #4 is due on Thursday @ 4pm, usual drill (chapter 4 proofs). Ive posted my solutions for HW #2 and HW #3. Grade Curve (so far). Take the average of: (1) your average HW score (all on 100-point scale), and (2) your mid-term score. The approximate curve for the course is as follows: A-ish ( 90), B-ish (8090), C-ish (7080), D-ish (60-70). This should be a reasonably good (but not perfect) guide to where the (overall) grade curve will end-up for the entire course. Today: Chapter 4, Continued More on and rules. Sequent & Theorem Introduction (SI/TI). + You should be doing as many proofs as you can. UCB Philosophy Chapter 4 (Contd) 06/15/08 Branden Fitelson Philosophy 12A Notes 2 ' & The Three Negation Rules Negation Elimination ( E) a 1 ,. . . , a n (j) q . . . b 1 ,. . . , b u (k) q . . . a 1 ,. . . , a n , b 1 ,. . . , b u (m) j, k E Negation Introduction ( I) j (j) p Assumption . . . a 1 ,. . . , a n (k) . . . {a 1 ,. . . , a n }/j (m) p j, k I Double Negation (DN) a 1 ,. . . , a n (j) p a 1 ,. . . , a n (k) p j DN UCB Philosophy Chapter 4 (Contd) 06/15/08 Branden Fitelson Philosophy 12A Notes 3 ' & $ % The Two Disjunction Rules a 1 ,. . . , a n (j) p a 1 ,. . . , a n (j) q . . . OR . . . a 1 ,. . . , a n (k) p q j I a 1 ,. . . , a n (k) p q j I a 1 ,. . . , a n (g) p q . . . h (h) p Assumption . . . b 1 ,. . . , b u (i) r . . . j (j) q Assumption . . . c 1 ,. . . , c w (k) r . . . A (m) r g, h, i, j, k E [ A = {a 1 ,. . . , a n } {b 1 ,. . . , b u }/h {c 1 ,. . . , c w }/j] UCB Philosophy Chapter 4 (Contd) 06/15/08 Branden Fitelson Philosophy 12A Notes 4 ' & A Simple Example Involving I and E Heres a proof of the sequent: A B ` B A . Problem is: AB BA 1 (1) ABPremise 2 (2) AAssumption (E) 2 (3) BA2 I 4 (4) BAssumption (E) 4 (5) BA4 I 1 (6) BA1,2,3,4,5 E UCB Philosophy Chapter 4 (Contd) 06/15/08 Branden Fitelson Philosophy 12A Notes 5 ' & $ % An Example Involving E and DN Heres a proof of the sequent: A B, B ` A . Problem is: AB, B A 1 (1) ABPremise 2 (2) BPremise 3 (3) AAssumption (for I) 4 (4) AAssumption (for E) 3,4 (5) 3,4 E 6 (6) BAssumption (for E) 2,6 (7) 2,6 E 1,2,3 (8) 1,4,5,6,7 E 1,2 (9) A3,8 I 1,2 (10) A9 DN UCB Philosophy Chapter 4 (Contd) 06/15/08 Branden Fitelson...
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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_9_2x2 - Branden Fitelson Philosophy 12A Notes 1 '...

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