All these are plausible. But what about the third premise of the original argument? The
unstated premise needed to link it to the conclusion is something like "Society should do what it can to prevent young women from becoming pregnant before they are 2 0 " and/or "Becoming
pregnant before age 20 is bad." Those are at best dubious (in parts of the U.S. it is considered a religious duty to start a family right after high school).
Though the original premise is not itself dubious, trying to incorporate it into the argument
will make the argument worse. Since we already have a moderately strong argument, we delete
this premise, just as we would a false premise that isn't essential to the strength of the argument.
If the speaker feels it is crucial, then he or she will have to link it to the conclusion.
50. Appeal to fear. (Do you really think Suzy's committed to self-immolation?) Bad.
51. Bad appeal to authority. It's the reverse of "If you're so smart, why aren't you rich?"
52. Bad argument. Proved the wrong conclusion! (Compare the last sentence to the first one.) Also
bad generalizations, which we'll study in Chapter 14.
54. Lee is reasoning backwards with "no." Also, first premise is dubious. Bad.
57. Perfectionist dilemma, or bad appeal to common practice. ("If I were to stop making noise, that wouldn't solve the problem. So I shouldn't stop making noise.") Bad.
61. Good argument with unstated premises which you can add. (Prescriptive conclusion, so it'll need
a prescriptive premise.)
62. Bad. Affirming the consequent.
63. Good. Direct way of reasoning with "no."
Answers to Selected Exercises 417
64. They're debating a vague sentence that has no truth-value. (Maybe Suzy thinks that arriving on
time means within an hour, like most Brazilians.) Or they're trying to make a subjective claim
objective.
65. Bad. Reasoning backwards with "all": "Only A are B" is equivalent to "All B are A." Sam might be one of the managers not allowed behind the bar because he doesn't have a bartender's
license as he normally only works with food.
66. Maria's argument is pretty good with the added claim: If the factory farms are awful, you
shouldn't eat meat. But that's too vague: What does she mean by "awful"? Maybe what's awful for her isn't awful to Suzy. Suzy responds with the "ostrich technique": If I don't see it, it's not there. She doesn't fulfill the Principle of Rational Discussion.
69. Weak argument—horse manure also has a lot of vitamins and protein in it. Unrepairable.
Conclusion is also false. Bad. (As stated it's not wishful thinking.)
71. Bad. Maybe Dr. E went out with Ms. Fletcher who has a cat.
72. Conclusion: We have saved hundreds of thousands of lives.
Premises: It took only 20 terrorists to kill 3,000 people. We've killed hundreds of people in an
offensive against Al-Qaida fighters.
Unstated premises: All, or at least the great part, of the people we killed were Al-Qaida fighters
(and not innocent villagers boosting the death toll). Everyone who is an Al-Qaida fighter
could be a terrorist who could kill 150 or more people, like the terrorists who flew the planes
into the World Trade Center. Hundreds of people killed times 150 per person is hundreds of
thousands of people.
Each of the unstated premises is clearly false or highly dubious. In particular, the last unstated
premise shows that Maj. Bryan Hilferty not only can't reason, he can't do simple arithmetic,
either. Bad argument.
Complex Arguments for Analysis
Exercises on Structure of Arguments
1. My neighbor should be forced to get rid of all the cars in his yard. 1 People do not like living next door to such a mess. 2 He never drives any of them. 3 They all look old and beat up, 4
and (they) leak oil all over the place. 5 It is bad for the neighborhood, 6 and it will decrease property values. 7
Argument? Yes.
Conclusion: 1.
Additional premises needed? If someone drives a car occasionally, he'd have the right to keep it on his property, a So he doesn't have a right to keep the cars on his property, b Cars that leak oil on the land are an environmental hazard, c Environmental hazards should not
be allowed to continue, d If a person has something on his property that his neighbors do
not like, that is an environmental hazard, that he does not have a right to keep in his yard, and
which decreases property values, then he should get it off his property, e
Identify any subargument: 3 and a support b. 5 and c support d. Then 2, 7, c, and e yield 1. Note that 4 can be deleted. And 6 is too vague.
Good argument? Claim 7 is not clearly true—it depends on the neighborhood (it could be an
industrial area). Everything rides on claim e, which on the face of it looks pretty plausible.
In that case the argument is valid and good.
2. I'm on my way to school. 1 I left five minutes late. 2 Traffic is heavy. 3 I'll be late for class. 4 I might as well stop and get breakfast. J
Argument? Yes.
Conclusion: 5
418 Answers to Selected Exercises
Additional premises needed? Whenever I'm on my way to school and I'm 5 minutes late and
traffic is heavy, I will be late for my class, a If I'm late for class, I might as well be very late or miss the class, b
Identify any subargument: 1, 2, 3, and a supports. Then 4 and b support 5.
Good argument? Depends on whether b is true.
3. Las Vegas has too many people. 1 There's not enough water in the desert to support more than a million people. 2 And the infrastructure of the city can't handle more than a million 3
the streets are overcrowded 4 and traffic is always congested; 5 the schools are overcrowded 6
and new ones can't be built fast enough. 7 We should stop migration to the city by tough zoning
laws in the city and county. 8
Argument? Yes.
Conclusion: 8
Additional premises needed? (You must know what "infrastructure" means to make sense of this argument.) Las Vegas has close to a million people, a If streets are crowded and
schools are crowded, then the infrastructure is inadequate, b If infrastructure is inadequate and there is not enough water for more people, there are too many people, c If there are too
many people, new migration to the city should be stopped, d The best way to stop migration
is by tough zoning laws, e (Can't add: The only way to stop migration to the city is by tough zoning laws—you could arm gangs, or raise building fees.)
Identify any subargument: 4, 5,6, 7, and b are dependent as support for 3.
2, a, 3, and c support 1. 1, d, and e supports.
Good argument? Everything is plausible with the exception of e. If that can be shown to be true, it's good.
Chapter 12
2. We need to draw a conclusion based on the comparison.
3. No. They typically lack a statement of a general principle that would cover both (or all) cases.
4. First, state the conclusion. Second, look for similarities that suggest a general principle.
6. This is a comparison, not an argument. What conclusion could we draw?
The following are just sketches of answers.
8. Zoe is refuting Dick's argument that it's O.K. to throw a banana peel out the window by showing
the same argument would work for horse manure.
11. This is not really an analogy. It's questioning whether the person believes the general principle he/she espouses.
12. This is an argument, with conclusion (stated as a rhetorical question) that it isn't O.K. to let
someone who isn't trained as a teacher teach. Higuchi has, how
ever, assumed the further premise
" I f someone doesn't have a teacher's credential, then he doesn't know what he's doing teaching,"
which is dubious. The comparison of a brain surgeon with a teacher has too many dissimilarities
to be convincing: If a brain surgeon screws up, the patient dies or is mentally crippled, but if a
teacher screws up a class, students will still likely learn, and by the end of the term he or she is
likely to be teaching more or less competently, and the students won't do worse than with any
bad teacher.
14. We can fill this out to be an argument: We don't sell sunshine. Trading water is like selling
sunshine. So we shouldn't sell water.
It's a very bad analogy. First, we do sell sunshine: In some big cities, there are laws and
various covenants about blocking windows/views when building. Second, we can't sell
sunshine in the same way we sell water, allocating a supply. And the prescriptive premise
that's needed here is unclear.
Answers to Selected Exercises 419
18. Tom is committing the fallacy of composition: What is good for the individual is good for the
group. But there are major differences: spontaneous vs. organized violence is the most obvious.
There are too many differences between being against all wars and unwilling to participate
in wars, and being unwilling to respond to personal violence.
19. This analogy breaks down. The person with the sense of smell will be right most of the time, in
many different situations, and clearly so. No magician is going to find him out. Eventually,
using brain scans and physical examinations, we could determine to some extent the mechanism
behind his predictions, even if we ourselves couldn't experience them. But to date, claims about
ESP can't be duplicated, even by the person claiming to have the powers; they are often
debunked; they aren't right almost always, but just a bit more than average. It's not just that we
have lost motivation to investigate ESP because of so many false claims about it. We haven't
even found a good candidate to study.
20. Dick seems to be inferring that Tom is concluding we shouldn't use seat belts. But Tom
doesn't say that, and it's not clear he believes that. In that case, Dick gives us food for thought,
but not much more than unjustified ridicule.
The research was done by Sam Peltzman of the University of Chicago.
21. This analogy relies on the unstated prescriptive premise: If people do something for a living, and they need that living to pay their bills and support their families, and they teach their children
morals, then they should be allowed to get along with earning their living and not having that
means of earning a living outlawed. That's a dubious principle, for it would justify any kind of
murderous, immoral way of earning money, contract killing, for instance. Note that Parish does
not say that the reason she should be allowed to continue is that it's a sport or that it harms no one. That would be a very different argument.
22. Challenge: If this isn't a good argument, how would you convince someone that others feel pain?
And if you can't, what justification would you have for not torturing people? (We know that
torture can elicit information or behavior we want.)
24. A bad analogy because of the differences. We determine that a watch was made by someone
because it differs from what we find in nature that is not crafted, such as rocks or trees. And we can deduce from its construction that it has a purpose. We can't do that for all of nature.
26. If you said "yes" for some and "no" for others, what differences are there? If you said the same for all, did you reason by analogy? What general principle did you use?
27. Did you answer this the same as Exercise 26? If so, what was your reason? Are you arguing by
analogy? What is your general principle?
Chapter 13
5. It means that for every 100 women who use the contraceptive for one year, one will become pregnant. (See the explanation on p. 340 of the Workbook.)
6. average: 74.27 mean: 74.27 median: 76 mode: 88 and 62
8. Well, the experts are right. All you have to do is wait until the stock market goes back up again
—unless you die first. It's like doubling your bet on black with roulette every time you lose.
You're sure to win in the long run. Unless you go broke first.
11. What dollars are they talking about? When you consider the trillions of dollars spent by the
government on debt and the military—which isn't for cleaning products—you can see that this
can't be right. And there's no reason to believe that so much money is spent on cleaning products
by individuals. And there's no government agency called "The Bureau of Statistics."
12. It's 4 5 % lower than the average of the other brands, but 24 of those other brands could actually have less fat than this candy bar if there's just one of them that has a huge amount of fat. And
what are those "leading" brands? Leading where? In Brazil?
420 Answers to Selected Exercises
14. This is apples and oranges, because it doesn't correct for inflation: $2,000 in 1968 is equivalent to what in current dollars?
17. Wrong. It's just backwards. It should be: If you have breast cancer, there's less than a 10%
chance you have the gene.
18. This is just a way to say that Americans think of themselves as nonconformists, and Japanese
think of themselves as conformists. The numbers are meaningless.
21. Don't do it, Dick. One per day average of one per day.
27. Funny how they break down the figures in the next-to-last paragraph, but not in the last one. It
could be that of the 99%, only 1% actually improved.
28. Meaningless: Too much variation from one area to another. Median or mode won't be much
more use.
29. A fair indication, since there's not much variation.
30. Terrible comparison: There's little variation in university professors' salaries (almost all earn between $30,000 and $75,000), but there's a huge variation in concert pianists' income ($15,000
vs. $2,000,000). The mode would be more informative.
32. Curious, but not much you can conclude from it. Could be that it's easier to get good grades now, or the students are smarter, or students are taking a different mix of courses than before, or . .. .
Chapter 14
Section A
I. Generalizing. Sample: The German shepherds the speaker has met.
Population: All German shepherds.
3. Generalizing. Sample: The MP3 player that Suzy has.
Population: All Hirangi MP3 players.
6. Generalizing. Sample: The times Dick has taken Spot to the vet before.
Population: All times Dick has or will take Spot to the vet.
8. Generalizing. Sample: The times that Maria has taken her clothes to be cleaned at Ricardo's.
Population: All times anyone will take their clothes to that dry cleaner.
9. Possibly generalizing, but could be just repeating a general claim he's heard. We can't identify
the sample, so don't treat it as a generalization until the speaker elaborates.
10. A general claim, but no generalizing is going on, since there's no argument.
I I . Hard to say if it's generalizing. Has the speaker met Japanese guys? Or is she just repeating a stereotype she's heard?
Section B
1. One in which no subgroup of the population is represented more than its proportion in the
population.
2. There is always a possibility that the members of the population which you haven't studied are
3. a. If the probability of something occurring is X percent, then over the long run the number of
occurrences will tend toward X percent,
b. The probability of getting a sample that isn't representative is very small.
7. You can't know in advance what the "relevant" characteristics are. If you could, you wouldn't need to do a survey/experiment. You're biasing the sample towards the characteristics you think
in advance are important. See Exercise 6.
9. No. Indeed, the law of large numbers predicts that eventually a randomly chosen sample of 20
students at your school will consist of just gay men. But the likelihood of a randomly chosen
sample not being representative is small.
Answers to Selected Exercises 421
Exercises for Chapter 14
1. There is a 94% chance that between 51% and 61% of the entire population of voters actually
favors your candidate.
2. No.
3. a. A hasty generalization using anecdotal evidence.
b. Yes, see the example in Section C.5. There would have to be very little variation in the
population.
4. Variation.
5. 1. The sample is big enough.
2. The sample is representative.
3. The sample is studied well.
Note well: The second premise is not "The sample is chosen randomly." That claim can support the second premise, but isn't always needed. See the answer to Exercise 3.b.
8. Such a survey would be nonsense because most students don't know what the president of a
college does—or can do. Do you approve of the way they're sweeping the streets in Timbuktu?
12. Generalization: All CDs can hold an encyclopedia's-worth of information.
Sample: The CD that the speaker just bought.
Sample is representative? Yes, no variation in population (if it's broken, it doesn't count).
Sample is big enough? Yes, no variation in population.
Sample is studied well? Yes, the speaker has seen it on his/her computer.
Good generalization? Yes.
14. This is a confused attempt to generalize. Perhaps Lee thinks that the evidence he cites gives the conclusion that if you invest in the stock market, you'll get rich(er). But that's arguing
backwards, confusing (1) "If you invest in the stock market, you'll get rich" with (2) "If you're rich, then you will have invested in the stock market." The population for (1) is all investors in the stock market, not just the rich ones. It's a case of selective attention.
Richard L Epstein Page 53