The Language of Argument

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C H A P T E R 6 ■ P r o p o s i t i o n a l L o g i c

McCain will lose the election unless he carries the South.

This sentence clearly indicates that McCain will lose the election if he does

not carry the South. Using abbreviations, we get the following:

N = McCain will carry the South.

L = McCain will lose the election.

~N ⊃ L

The original statement does not imply—even conversationally—that

McCain will win the election if he does carry the South. Thus,

p unless q = ~q ⊃ p

In short, “unless” means “if not.” We can also note that “~p unless q” means

the same thing as “p only if q,” and they both are translated thus:

p ⊃ q

Our results can be diagrammed as follows:

Translates as    Often Conversationally Implies

p if q q ⊃ p (p ⊃ q) & (q ⊃ p)

p only if q p ⊃ q (p ⊃ q) & (q ⊃ p)

p unless q ~q ⊃ p (p ⊃ ~q) & (~q ⊃ p)

Translate each of the following sentences into symbolic notation, using the

suggested symbols as abbreviations.

1. The Reds will win only if the Dodgers collapse. (R, D)


2. The Steelers will win if their defense holds up. (S, D)


3. If it rains or snows, the game will be called off. (R, S, O)


4. If she came home with a trophy and a prize, she must have won the
   tournament. (T, P, W)


5. If you order the dinner special, you get dessert and coffee. (S, D, C)


6. If you order the dinner special, you get dessert; but you can have coffee
   whether or not you order the dinner special. (S, D, C)


7. If the house comes up for sale, and if I have the money in hand, I will bid
   on it. (S, M, B)


8. If you come to dinner, I will cook you a lobster, if you want me to. (D, L,
   W)


9. You can be a success if only you try. (S, T)


10. You can be a success only if you try. (S, T)


11. Only if you try can you be a success. (S, T)

Exercise XXVII

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