The Language of Argument

1 4 9

C o n d i t i o n a l s

12. You can be a success if you are the only one who tries. (S, O)


13. Unless there is a panic, stock prices will continue to rise. (P, R)


14. I won’t scratch your back unless you scratch mine. (I, Y)


15. You will get a good bargain provided you get there early. (B, E)


16. You cannot lead a happy life without friends. (Let H = You can lead a
    happy life, and let F = You have friends.)


17. The only way that horse will win the race is if every other horse drops
    dead. (Let W = That horse will win the race, and let D = Every other horse
    drops dead.)


18. You should take prescription drugs if, but only if, they are prescribed for
    you. (T, P)


19. The grass will die without rain. (D, R = It rains.)


20. Given rain, the grass won’t die. (R, D = The grass will die.)


21. Unless it doesn’t rain, the grass won’t die. (R, D = The grass will die.)

(a) Translate each of the following arguments into symbolic notation. Then

(b) test each argument for truth-functional validity using truth table

techniques, and (c) comment on any violations of conversational rules.

Example: Harold is clever; so, if Harold isn’t clever, then Anna isn’t clever

either. (H, A)

(a) H p

∴ ~H ⊃~A ∴ ~p ⊃~q

(b) Premise Conclusion

p q ~p ~q ~p ⊃ ~q

T T F F T OK

T F F T T OK

F T T F F

F F T T T

(c) The argument violates the rule of Relevance, because Anna’s cleverness is

irrelevant to Harold’s cleverness.

1. Jones is brave, so Jones is brave or Jones is brave. (J)


2. The Republicans will carry either New Mexico or Arizona; but, since they
   will carry Arizona, they will not carry New Mexico. (A, N)


3. The Democrats will win the election whether they win Idaho or not.
   Therefore, they will win the election. (D, I)

Exercise XXVIII

(continued)

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