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Cengage Advantage Books: Understanding Arguments: An Introduction to Informal Logic

Walter Sinnott-Armstrong, Robert J. Fogelin

Chapter 17

Refutation - all with Video Answers

Educators


Chapter Questions

00:42

Problem 1

Find a counterexample to each of the following claims, if possible.
Example: Claim: "Sugar" is the only word in which an s is pronounced sh. Counterexample: Oh, sure.
1. No prime number is even.
2. Three points always determine a plane.
3. Balloons that are filled with helium always rise in the air.
4. All mammals bear their young live.
5. You can never get too much of a good thing.
6. What you don't know can't hurt you.
7. You can't be too careful.
8. It is always wrong to tell a lie.
9. You should never ask someone else to do something that you are not willing to do yourself.
10. If lots of people do something, then it must not be wrong for me to do it.
11. If it would be horrible for everyone to do something, then it would be morally wrong for anyone to do it.
12. If it would not be horrible for everyone to do something, then it would not be morally wrong for anyone to do it.

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James Kiss
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Problem 2

There cannot possibly be any counterexamples to the following claims. Explain why.
1. There is life on the moon.
2. Killing is usually wrong.
3. Any short person is a person.
4. Every horse is an animal.
5. $2+2=4$.
6. Everything with a size also has a shape.

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Problem 3

Evaluate the following reductio ad absurdum arguments by asking the above three questions.
1. Claim to be Refuted: Even the worst of enemies can become friends. Reductio: If people are enemies, then they are not friends. If they do become friends, then they are not enemies. So it's absurd to think that enemies can be friends.
2. Claim to be Refuted: This ball is both red all over and green all over.
ReDuctio: If it is red, it reflects light within a certain range of wavelengths. If it is green, it reflects light within a different range of wavelengths. These ranges do not overlap, so it is absurd to think that anything can reflect both kinds of light. Thus, a ball cannot be both red and green all over.
3. Claim to be Refuted: Most children in Lake Wobegon are above average (in intelligence).
REDuctio: If so, the average (intelligence) would really be higher than it is; and then it would not be true that most children in Lake Wobegon are above the real average (intelligence).
4. Argument to he Refuted: Your brain is mostly empty space, because the subatomic particles in it are very far apart.
Reductio: That's absurd, because my brain is solid, and it works pretty well.
5. Claim to be Refuted: Some things are inconceivable.
Reductio: Consider something that is inconceivable. Since you are considering it, you are conceiving it. But then it is conceivable as well as inconceivable. That is absurd. So nothing is inconceivable.

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Problem 4

Spell out a reductio ad absurdum argument to refute each of the following claims. If no such reductio is possible, explain why.
1. Some sisters are nephews.
2. Some fathers were never children.
3. Most students scored better than the median grade on the last test.
4. Almost everyone in this class is exceptional.
5. There is an exception to every universal claim.
6. I know that I do not know anything.
7. Some morally wrong actions are morally permitted.
8. God exists outside of time, and we will meet Him someday.
9. There is a male barber in this town who shaves all and only the men in this town who do not shave themselves. (Hint: Does he shave himself?)
10. Most of the sentences in this exercise are true.

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Problem 5

Do the following arguments attack straw men? Why or why not?
1. Anyone who thinks that the United States should not have sent troops to Iraq must think that the suffering Saddam Hussein inflicted on his own citizens doesn't matter much.
2. Anyone who thinks that the United States should have sent troops to Iraq must think that they will only be there for a short time.
3. Humans could not have been created in the image of God, because God is not a physical being, and only physical beings can have images.
4. Atheists think that God does not exist, so everything is permitted. But even atheists must admit that I would not be permitted to kill them! So atheism is nonsense.
5. The theory of evolution says that humans are no different from apes, but humans are clearly smarter than apes, so the theory of evolution must be wrong.
6. Stephen Colbert again: "Evolutionists' main claim is that one day we decided to stop being monkeys and tumed ourselves into humans. Well, if that's true, why aren't more monkeys escaping from zoos? Think about it. They could turn into humans, then disguise themselves as janitors and walk out of their cages. But I guess evolution doesn't have an answer for that one."1

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Problem 6

In each of the following examples, does the parallel argument succeed in refuting the original argument? Why or why not? Consider the three possible responses listed above. If the original argument is refuted, is there some simple way to fix it so that it cannot be refuted by this parallel reasoning? If so, how? (You might try to add a premise whose analogue would be false in the parallel argument.)
1. Chris: The United States is wealthy, so its citizens are wealthy as well.
PAT: That's just like arguing that a building is expensive, so the nails in its walls are expensive as well.
2. Chauvinist: Since women are the only people who can bear children, they should bear children.
FEMINIST: That's like arguing that, if I am the only person who can wiggle my own ears, then I should wiggle my ears.
3. Newt: Orphanages are fine places, as the movie Boys Town shows.
critic: That's just like saying that $\mathrm{Oz}$ is a fine place, as The Wizard of $\mathrm{Oz}$ shows.
4. A YounG CHILd at 6:00 am: It's morning. Morning is the time to wake up. So it's time to wake up.
The Child's Sleepy PARENt: That's just like arguing that it's daytime, and daytime is the time to eat lunch, so it's time to eat lunch.
5. MARK: You shouldn't walk on that grass, because if everybody did that, the grass would die.
Boв: That's just like arguing that I shouldn't go to this movie right now, because if everybody did that, the theater would be packed like a can of sardines.
6. THOMAs: Everything in the world has a cause, so the world itself must have a cause.
Tony: That's just like arguing that every leg in the relay race was run by a single runner, so the entire race itself must have been run by a single runner.
7. HAwк: Nuclear deterrence must work, because we have never had a nuclear exchange as long as we have maintained nuclear deterrence.
Dove: That's just like arguing that hanging garlic by the front door must keep thieves away, because I put garlic there and my house has never been robbed.
8. Liberal: We ought to provide condoms for high school students, because they are going to have sex anyway.
Conservative: That's just like arguing that we should provide high school students with guns, because they are going to use guns anyway.
9. Scientist: My initial steps toward human cloning, no matter how controversial, are important because they bring the debate out into the public.
OPPONENT: That's just like arguing that we should start a fire in a house in order to bring the debate about getting a new fire engine out into the public. (paraphrased from an actual interview on National Public Radio)
10. King: "In your statement you asserted that our actions, even though peaceful, must be condemned because they precipitate violence. But can this assertion be logically made? Isn't this like condemning the robbed man because his possession of money precipitated the evil act of robbery?" (from Martin Luther King's "Letter from Birmingham Jail")
11. A: He owns a red car, so he owns a car.
B: That's just like arguing that he owns a toy duck, so he owns a duck.
12. A: He is holding a baby girl, so he is holding a baby.
B: That's just like arguing that he is driving a fire truck, so he is driving a fire.

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Problem 7

For each of the following arguments, find another argument with the same basic form in which the premise or premises are clearly true and the conclusion is clearly false.
1. If tea is dangerous, so is coffee. Tea isn't dangerous. So coffee isn't either.
2. If it were about to rain, it would be cloudy. It is cloudy. So it's about to rain.
3. Fred had either ice cream or cake for dessert. He had cake. So he must not have had ice cream.
4. You cannot pass laws against dangerous drugs, because there is no way to draw a sharp line between dangerous and nondangerous drugs.
5. If you have never written a novel, then you are in no position to make judgments about novels. So don't presume to criticize mine.
6. Since I have written several novels, I am in a position to know which novels are good. So you ought to trust me when I say that this one is great.
7. There's nothing wrong with smoking, since the longer you smoke, the longer you live.
8. If one has nothing to hide, one should not be afraid of being investigated. So no one should object to being investigated.
9. Radicals should not be granted freedom of speech, because they deny this freedom to others.
10. In nature, a species is more likely to survive when its weak members die out, so we should let the weak in our society die out.

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