Philosophy 210

Logical Thought

Review exercises--possible answers

COUNTEREXAMPLES

(1) Some MHC students are blonde.
No blondes are dinosaurs.
Therefore, some MHC students are dinosaurs.

(2) Suppose that a maniacal foreign leader was massing troops for an invasion of Fort Knox, where the U.S. gold reserve, upon which the entire currency system is based, is stored. If we do not prevent him, our economic system will be destroyed; yet the only way to prevent him is by going to war as soon as his troops cross our borders.
[Note that a direct c.e. is really needed here. The general principle to which the author is committed is a principle about going to war over money. Thus the c.e. doesn't have to be about the Gulf crisis, but it does have to be about going to war over money. Any attempt to say that the issue about money is somehow tied to people starving, or getting sick, etc., will be an attack on the premise that the conflict is only about money.]

(3) The U.S. will have nuclear capability if Mexico doesn't invade it. Therefore Mexico should invade the U.S.
[This is enough. It doesn't really matter that the U.S. already has nuclear capability, although the c.e. would be a little stronger if that were not the case. Thus using, say, Canada and Mexico would be a bit stronger.]

(4) (sufficiency): Imagine a calculus course in which the teacher comes into class and drinks whiskey, tells lewd and suggestive stories, tries to hit on the students, and usually passes out about 20 minutes into class. Until then, he also talks incessantly about his terrible childhood and his sicko relationship with his wife and kids. The students learn an amazing amount about human depravity. But the course is terrible.
[Note that this c.e., while pretty good, could be blocked by simply altering the claim to read: A good course is one in which the students learn a lot about the subject matter of the course. So a c.e. in which what the students learn a lot about is what the course is supposed to be teaching, but in which the course is still a rotten course, will be stronger. Can you think of such a c.e.? ]

(necessity): Professor Wonderful is widely regarded as the best professor in the country. She is an extraördinarily teacher and scholar. In this semester she is doing a particularly stunning fob. Unfortunately, because of a scheduling error, the only people in her class are rugby players majoring in macramé. They have no interest at all in micro-economic neuro-logic, achromatic mitosis in data-structures, and the meaning of life, which is Professor Wonderful's course subject this semester. As a result, they didn't listen, didn't read, they didn't write or study. The course itself, though, was extraördinary. Too bad nobody learned anything.
[Note that both of these are direct counterexamples. Do you see why an indirect one would not work? If not, ask yourself what general claim the author is committed to.]

(5) Eisenhower was an alleged murderer, in virtue of his involvement in World War II.

You could also imagine a case, say, where Kennedy was giving a speech and somebody came up with a gun and was about to kill him. In the ensuing scuffle between Kennedy and the assailant the gun went off and the assailant was killed. The assailant's wife subsequently has alleged that Kennedy murdered her husband.

Having questioned the sufficiency of the claim in this, or some other appropriate way, you can now question whether the reason is central. That is, you may ask whether he could get elected even if he were not an alleged murderer. It would not be too hard to make out a case that in view of his spending policies, and in view of a growing national sentiment in favor of reducing non-defense government spending, he could not get elected even if he were not an alleged murderer.

(6) Everybody knows that philosophers are intelligent.
Wilbur Wiggin is a philosopher.

Everybody knows that Wilbur Wiggen is intelligent.

But nobody knows that Wilbur is a philosopher; in fact Wilbur's mother doesn't even know that he is a philosopher, and she thinks that he is pretty dumb. In fact, he is very intelligent, but nobody knows that. (Note that here we are bolstering the indirect c.e. with a direct c.e.

Note here that the indirect counterexample did not have to be about philosophers. Nor did it have to be about intelligence. The author is committed to the general form:

Everybody knows that A's are B.
X is an A.

Everybody knows that X is a B.

Any clearly unsound argument of that form would do fine. You could also give a direct counterexample, imagining somebody off in some far away place who had never heard of Satre. But you must not, of course, do anything to undermine the premise that everybody knows that philosophers are intelligent. It follows that you must not undermine the claim that all philosophers are intelligent, since if that were false, people wouldn't really know that philosophers are intelligent, but only believe falsely that they are. So if your counterexample has a philosopher who is not intelligent in it, it is wrong.

(7) (Sufficiency): Yes, it will cost less than paying for their medical problems in New York, but suppose that the New York homeless are sufficiently poorly suited for life in rural Pennsylvania that it will be impossible for them to get the sort of training that would lead to jobs, family, productive lives. If they go to shelters in Pennsylvania that will be cheap for the government [remember: don't undermine the premise] but these people's lives will be wasted. Imagine that with only a small additional expenditure these homeless people can stay in New York near family or friends, receive job training, and come to lead productive and fulfilling lives. Under these circumstances, while it would be cheaper to build shelters in Pennsylvania, it is clear that that is not what we should do.
[Note that here we give a standard counterexample.]

(centrality): Perhaps shelters should be built in Pennsylvania even if it would cost more to do so. Indeed, if it were right to build shelters in Pennsylvania, what would justify such a radical move could not be simply savings, but there would have to be advantage in terms of the human qualities available in Pennsylvania that are not available in New York (for example, better facilities, medical care, job training, ). Indeed, it can be argued that it is precisely the cruelty of the New York environment that leads to homelessness, and that if we want to do anything to solve this problem, then we have to remove the homeless from the environment that has brought them to homelessness. The magnitude of the problem is sufficient that we should do this even if it cost somewhat more.
[Note that here we give an argument to the effect that A even if -B.]

8. (Necessity): [Note that here we need a case in which it was a good exam but I didn't enjoy working on it.] Imagine the world's most terrific exam, but because I had a terrible stomach virus, and was throwing up all over my exam book and in severe pain from the arm that I broke on the way into the exam room, and because I hadn't studied for the exam at all and didn't know the answers to any of the questions, I certainly did not have a good time working on it, no matter how good it was.

(Sufficiency): [Note that here we need a case in which I enjoyed working on it, but it was not a good exam. You can do that as well as I can.]

9. [This is simply a conditional, not a bi-conditional; hence it requires only one counterexample, namely imagining a case in which you get to spend lots of time on a vacation with your friends, but in which it is clearly not a good vacation.] Just imagine your standard Vacation From Hell, in which you are trapped with your friends without food, heat or music for two weeks, and in which because of the stress of the situation everybody is disgusted with everybody else (who nonetheless remain their friends--- don't undermine the premise), and so on. Spell out the story in such a way that it becomes clear that this was definitely not a good vacation.