Chapter 13, Fallacies of Vagueness Video Solutions, Cengage Advantage Books: Understanding Arguments: An Introduction to Informal Logic

Problem 1

For each of the following terms, give one case to which the term clearly applies, one case to which the term clearly does not apply, and one borderline case. Then try to explain why the borderline case is a borderline case.
Example: In the northern hemisphere, "summer month" clearly applies to July; clearly does not apply to January; and June is a borderline case, because the summer solstice is June 21, and schools usually continue into June, but June, July, and August are, nonetheless, often described as the summer months.
1. large animal
2. populous country
3. long book
4. old professor
5. popular singer
6. powerful person
7. difficult subject
8. late meeting
9. arriving late to a meeting

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Problem 2

Each of the following sentences contains words or expressions that are potentially vague. Describe a context in which this vagueness might make a difference, and explain what difference it makes. Then reduce this vagueness by replacing the italicized expression with one that is more precise.
Example: Harold has a bad reputation.
Context: If Harold applies for a job as a bank security guard, then some but not all kinds of bad reputation are relevant. A reputation for doing bad construction work is irrelevant, but a reputation for dishonesty is relevant.
Replacement: Harold is a known thief.
1. Ross has a large income.
2. Cocaine is a dangerous drug.
3. Ruth is a clever woman.
4. Andre is a terrific tennis player.
5. Mark is not doing too well (after his operation).
6. Shaq's a big fellow.
7. Dan's grades are low.
8. Walter can't see well.
9. The earthquake was a disaster.
10. The news was wonderful.

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Problem 3

Whenever we find one thing passing over into its opposite through a gradual series of borderline cases, we can construct (a) an argument from the heap and (b) a conceptual slippery-slope argument by using the following method: Find some increase that will not be large enough to carry us outside the borderline area. Then use the patterns of argument given above. Applying this method,formulate arguments for the following claims. Then explain what is wrong with these arguments.
1. a. There are no heaps.
b. There is no difference between a heap and a single grain of sand.
2. a. Nobody is tall.
b. There is no difference between being tall and being short.
3. a. Books do not exist.
b. There is no difference between a book and a pamphlet.
4. a. Heat is not real.
b. There is no difference between being hot and being cold.
5. a. Taxes are never high.
b. There is no difference between high taxes and low taxes.
6. a. Science is an illusion.
b. There is no difference between science and faith.

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Problem 4

Classify each of the following arguments as either $(\mathrm{H})$ an argument from the heap, (C) a conceptual slippery-slope argument, (F) a fairness slippery-slope argument, or (S) a causal slippery-slope argument. Explain why you classify each example as you do.
1. We have to take a stand against sex education in junior high schools. If we allow sex education in the eighth grade, then the seventh graders will want it, and then the sixth graders, and pretty soon we will be teaching sex education to our little kindergartners.
2. People are found not guilty by reason of insanity when they cannot avoid breaking the law. But people who are brought up in certain deprived social circumstances are not much more able than the insane to avoid breaking the law. So it would be unjust to find them guilty.
3. People are called mentally ill when they do very strange things, but many so-called eccentrics do things that are just as strange. So there is no real difference between insanity and eccentricity.
4. If you try to smoke one cigarette a day, you will end up smoking two and then three and four and five, and so on, until you smoke two packs every day. So don't try even one.
5. A human egg one minute after fertilization is not very different from what it is one minute later, or one minute after that, and so on. Thus, there is really no difference between just-fertilized eggs and adult humans.
6. Since no moment in the continuum of development between an egg and a baby is especially significant, it is not fair to grant a right to life to a baby unless one grants the same right to every fertilized egg.
7. If we let doctors kill dying patients who are in great pain, then they will kill other patients who are in less pain and patients who are only slightly disabled. Eventually, they will kill anyone who is not wanted by society.

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Problem 5

Explain the reasons, if any, for drawing a definite line in each of the following cases. Then further explain how this line can be drawn, if at all, in a reasonable way.
1. Minimum (or maximum?) age to drive a car
2. Minimum age to vote
3. Minimum age to enter (or be drafted into) the military
4. Minimum age to drink alcoholic beverages
5. Minimum age for election to the presidency
6. Maximum age before retirement becomes mandatory

Ashley High

Numerade Educator

Problem 6

Determine whether each of the following arguments provides adequate support, or any support, for its conclusion. Explain why.
1. I shouldn't get a speeding ticket for going fifty-six miles per hour, because my driving did not all of a sudden get more dangerous when I passed the speed limit of fifty-five.
2. No student should ever be allowed to ask a question during a lecture, because once one student asks a question, then another one wants to ask a question, and pretty soon the teacher doesn't have any time left to lecture.
3. Pornography shouldn't be illegal, because you can't draw a line between pornography and erotic art.
4. Marijuana should be legal, because it is no more dangerous than alcohol or nicotine.
(continued)
5. Marijuana should be illegal, because people who try marijuana are likely to go on to try hashish, and then snorting cocaine, and then freebasing cocaine or shooting heroin.
6. The government should not put any new restrictions on free trade, because once they place some restrictions, they will place more and more until foreign trade is so limited that our own economy will suffer.
7. Governments should never bargain with any terrorist. Once they do, they will have to bargain with every other terrorist who comes along.
8. If assault weapons are banned, Congress will ban handguns next, and then rifles. Eventually, hunters will not be able to hunt, and law-abiding citizens will have no way to defend themselves against criminals.

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