# hw4solutions - Philosophy 12A Homework #4 Solutions...

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Unformatted text preview: Philosophy 12A Homework #4 Solutions 11/14/08 These are the shortest proofs I have seen. (III.3) Problem is: A(AB) 1 1 (1) (2) (3) (4) (5) A AB A(AB) A(AB) A(AB) Ass (I) 1 SI (PMI) 1,2 I 3 SI (IMP) 4 SI (SDN) (III.5) Problem is: (AB)((AB)A) 1 2 3 2,3 1,3 1,2,3 1,2 1 (1) (2) (3) (4) (5) (6) (7) (8) (9) AB Ass AB Ass A Ass B 2,3 B,, 1,3 ,, 4,5 A,,,, ,, 3,6 (AB)A,,,, ,, 2,7 (AB)((AB)A),,,, 1,8 (I) (I) (I) E E E I I I (III.7) Problem is: AB, (BA)(CD), D C 1 2 3 4 1,4 1 1,2 1,2,3 (1) (2) (3) (4) (5) (6) (7) (8) AB,,,, ,, ,, (BA)(CD),,,, ,, D B A,,,, ,, ,, BA,,,, ,, CD,,,, ,, ,, C Premise Premise Premise Ass (I) 1,4 SI (MT) 4,5 I 2,6 E 7,3 SI (MT) (III.9) Problem is: (A&B)C, (CA) B 1 2 1 1 2 2 1,2 1,2 2 1,2 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (A&B)C,, (CA),,,, ((A&B)C)&(C(A&B)) (A&B)C,,,, C&A,,,, ,, C (A&B),,,, ,, AB,,,, ,, A,,,, ,, ,, B Premise Premise 1 Df. 3 &E 2 SI (DeM) 5 &E 4,6 SI (MT) 7 SI (DeM) 5 &E 8,9 SI (DS) (III.14) Problem is: (AB)&(CD) (BC)(A&D) 1 1 3 1 5 5 5 8 3,8 3,8 1,3 12 12 12 1 (IV.3) Dictionary: W = God is willing to prevent evil. A = God is able to prevent evil. I = God is impotent. M = God is malevolent. E = Evil exists. G = God exists. Problem is : (W&A)I, (A&W)M, (A&W)(I&M), E(WA), G(I&M) GE 1 2 3 4 5 6 4 4 9 5,6 5,6 1,5,6 1,5,6 1,5,6 1,5,6,9 1,5,6,9 1,3,5,6,9 1,3,5,6,9 1,3,5,6,9 1,3,5,6 5,6 2,5,6 2,5,6 1,2,3,5,6 1,2,3,5,6 1,2,3,5,6 1,2,3,4,5,6 1,2,3,4,5 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) (17) (18) (19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (W&A)I,,,, ,, ,, (A&W)M,, (A&W)(I&M),,,, E(WA) G(I&M),, G,,,, ,, (E(WA))&((WA)E) E(WA),,,, A,,,, I&M,,,, ,, I (W&A),,,, WA,,,, ,, WA,,,, ,, ,, W A&W,,,, ,, I&M,,,, ,, ,, I,, ,,,, ,, ,, A,, M (A&W),,,, AW,,,, ,, W,,,, ,, ,, W&A,, (WA),,,, E,,,, ,, GE,,,, Premise Premise Premise Premise Premise Ass (I) 4 Df. 7 &E Ass (I) 5,6 E 10 &E 1,11 SI (MT) 12 SI (DeM) 13 SI (SDN) 14,9 SI (DS) 9,15 &I 3,16 E 17 &E 11,18 E 9,19 I 10 &E 2,21 SI (MT) 22 SI (DeM) 23,20 SI (DS) 24,20 &I 25 SI (DeM) 8,26 SI (MT) 6,27 I (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (AB)&(CD) AB A CD C BC (BC)(A&D),, D A&D (BC)(A&D),, (BC)(A&D) B BC (BC)(A&D) (BC)(A&D) Premise 1 &E Ass (E) 1 &E Ass (E) 5 I 6 I Ass (E) 3,8 &I 9 I 4,5,7,8,10 E Ass (E) 12 I 13 II 2,3,11,12,14 E ...
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## This note was uploaded on 09/23/2009 for the course PHIL 12A taught by Professor Fitelson during the Spring '08 term at University of California, Berkeley.

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