Further Drill on Necessary and Sufficient Conditions
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?
2. Suppose you want to refute some conclusion C. Should you look for a necessary condition for C or a sufficient condition for 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
N S B 0 b. being a UW student
N S B 0 c. weighing more than 50 pounds
N S B 0 d. being George Bush
N S B 0 e. being a featherless biped
N S B 0 f. having a head
N S B 0 g. running a four-minute mile
N S B 0 h. having a soul
N S B 0 i. travelling to the moon
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?
If one rejects premise A, has one shown that Americans are not generally guilty of murder?