Further Drill on Necessary and Sufficient Conditions -- Answer Sheet
Why am I tormenting you with this? This is a course on moral issues, not on logic!
Answer: Because it is crucial to understand what one needs to do to establish and refute conclusions and to avoid confusing the refutation of an argument with the refutation of its conclusion.
1. Suppose you want to establish some conclusion, call it C. Should you look for a necessary condition for C or a sufficient condition for C?
You're looking for a sufficient condition. If you can show that it is satisfied, then you've established C.
2. Suppose you want to refute some conclusion C. Should you look for a necessary condition for C or a sufficient condition for C?
You're looking for necessary conditions. If you can show that any one of these is not satisfied, then you've refuted C.
3. Which of the following conditions are necessary (N), sufficient (S), both necessary and sufficient (B), or not necessary or sufficient for something to be a human being (0). Some of these may be controversial, and people may disagree about the answers -- though not because they disagree about logic.
N S B 0 a. being a mammal necessary but not sufficient
N S B 0 b. being a UW student sufficient but not necessary
N S B 0 c. weighing more than 50 pounds neither necessary nor sufficient
N S B 0 d. being George Bush sufficient (though possibly controversial among those who REALLY hate him)
N S B 0 e. being a featherless biped arguably both necessary and sufficient; though perhaps a plucked chicken would show that the condition is not sufficient
N S B 0 f. having a head necessary but not sufficient
N S B 0 g. running a four-minute mile neither necessary nor sufficient. Horses can do this; so it's not sufficient; and since most of us can't do this, it's clearly not necessary
N S B 0 h. having a soul obviously controversial. Some religious people would maintain that this is necessary and sufficient. Others might maintain that it's not sufficient, because angels have souls, too.
N S B 0 i. travelling to the moon neither necessary nor sufficient
4. Consider the following argument.
A. If you can save somebody's life without serious cost to yourself, then you are guilty of murder if you do no do so.
B. Almost every American can save additional lives by giving more to international charities, yet they do not do so.
thus C. Almost every American is guilty of murder.
Does premise A give a necessary or a sufficient condition for being guilty of murder? a sufficient condition; there are other ways to be guilty of murder
If one rejects premise A, has one shown that Americans are not generally guilty of murder? No. One has only undermined this argument. Perhaps there is some other argument that shows that almost every American is guilty of murder.