Wednesday, December 21, 2005

Logic Exercises: The Four Forms of Propositions

These are excercises to accompany this post. Identify the form of each proposition. Answers appear when you click "Read more."

Easy ones:
1. Some pens are blue.
2. All cows are brown.
3. All philosophers with a PhD are poor.
4. Nobody is worth talking to.
5. Some books worth reading are worth buying.
6. All those who shop at Trader Joes are gourmands.

A little more difficult:
7. Most academics are liberal.
8. Most academics are conservative.
9. Everyone from New Jersey loves Bruce Springsteen.

Still more difficult:
10. Some wise guys are unwise.
11. All gods are immortal.

12. All ravens are not white.
13. Nobody doesn't like Sara Lee.

1. I
2. A
3. A (This is universal even though the "all" is qualified by "with a PhD." A proposition is universal if it refers to all the members of the class with which it is concerned. So even though "all philosophers with a PhD" does not include every philosopher (e.g., Richard Swinburne, who is a philosopher, does not have a PhD), the quantity is universal because with respect to philosophers with a PhD, it refers to all of them.)
4. E
5. I
6. A
7. I ("Most" still falls short of being all, and so logically indicates a particular quantity.)
8. I (Don't want to be accused of inserting bias into logic examples.)
9. A
10. I (You might think that since the predicate is "unwise" the quality would be negative, thus giving us an O. But the quality of the proposition is not negative -- it says that some wise guys are such and such -- even though the quality of the predicate is negative. Distinguishing between a negative proposition and a negative predicate is one of the trickiest parts of Aristotelian logic.)
11. A (Same reason as above.)
12. E or O. (The English in this sentence is ambiguous. In English, when we say "All ravens are not white" we could mean that there are no ravens whatsoever that are white. This would be consistent with the E form: No S is P. If we were trying to weasel out of something, we could also take "All ravens are not white" to mean that there are some ravens that are white. In other words we would emphasize the "all" in "All ravens are not white." It is because of this ambiguity that we give the E form as "No S is P" instead of "All S is not P," which is what one might have expected given the form of A, "All S is P."
13. E. (In logical form, this sentence would be "Nobody [is] [that which] doesn't like Sara Lee." For reasons discussed in answer 10, this makes the answer here E.)

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