Spell out a reductio ad absurdum argument to refute each of the following claims. If no such reductio is possible, explain why. A reductio ad absurdum is deep only if it reveals that a claim implies an ab- surd result that cannot be avoided without modifying the claim in essential respects or giving it up entirely. In sum, then, a reductio ad absurdum argument tries to show that one claim, X, is false because it implies another claim, Y, that is absurd. To evalu- ate such an argument, the following questions should be asked: 1. Is Y really absurd?
2. Does X really imply Y?
3. Can X be modified in some minor way so that it no longer implies Y?

If either of the first two questions is answered in the negative, then the reductio fails; if the third question receives an affirmative answer, then the reductio is shallow. Otherwise, the reductio ad absurdum argument is both successful and deep.

1. Some sisters are nephews.
2. Most students scored better than the median grade on the last test.
3. There is an exception to every universal claim.
4. Some morally wrong actions are morally permitted.
5. There is a male barber in this town who shaves all and only the men in this town who do not shave themselves.