ingredients."
Dick: Lard is all natural, too.
14. From an article in Smithsonian, vol. 32, no. 11, 2002, about irrigation of small farms in New Mexico:
The practice of trading in water as a commodity, observes one activist, is like
"selling sunshine."
15. Maria: Suppose someone came up to you and offered you a sure-fire method for finding
$100 bills on the street, for which he'd charge you only $5.95. You'd be crazy to buy it
from him. After all, he could just as easily pick up the $100 bills himself. Besides, we
know there aren't any $100 bills lying around the street, since any time there's a $100
bill floating free you can be sure that someone will pick it up immediately. So why pay
money to a stock analyst?
16. Downloading computer software from someone you don't know is like accepting
candy from a stranger.
17. Flo's mother: It's just so hard raising Flo.
Dick: How hard can it be to raise a kid? After all, I've trained two dogs.
18. Tom: I can't believe you're out demonstrating against the U.S. fighting in Iraq.
Dick: I'm against war—all wars. I'm a pacifist.
Tom: So, if someone came up to you on the street and hit you from behind, you
wouldn't turn and hit him back?
19. We should take claims about extra-sensory perception seriously. Look, suppose no one
in the world had a sense of smell except one person. He would walk along a country
road where there is a high stone wall and tell his friend, "There are roses there." Or he
would walk into a home and say, "Someone cooked onions here yesterday." These
would seem extraordinary extra-sensory perceptions to his friends and acquaintances.
Similarly, just because we don't understand and can't imagine a mechanism that would
explain extra-sensory perception, we shouldn't stop the investigation.
20. Tom: Seat belts cause accidents.
Dick: Are you crazy? Seat belts save lives. Everyone knows that.
Tom: No, they cause accidents. They may prevent serious injury in some accidents,
but there are more accidents now because people use seat belts.
Dick: Why's that?
EXERCISES for Chapter 12 263
Tom: The threat of getting killed or seriously injured in an accident is much less
if you're wearing a seat belt. Because people reckon they are safer, they're less
careful and drive faster. So they get into more accidents. Some guy at the
University of Chicago looked at the numbers in the 1970s and found that there
are fewer deaths per accident, but more accidents, so that the actual number of
people getting killed remained about the same after seat belts were required.
Dick: Well, if that's the case, we better not make any more improvements on cars.
And we certainly shouldn't require motorcycle riders to wear helmets.
21. Letter to the editor in the El Defensor Chieftain, Socorro, NM, March 29, 2003:
This year's Legislative session and the bills against cockfighting have caused some
heated arguments.
The opposition's reasoning is ridiculous, considering that many of them do not
understand anything about cockfighting. The people that are trying to ban our sport
are not affected by it in any way, shape or form.
A fellow cockfighter recently asked a lawyer, "How would you like it if we tried to
take your license away?" Lawyers make their living practicing law; cockfighters make
their living by buying, selling, raising and fighting roosters.
Our occupations may differ, but the fact that we both pay our bills and support our
families, makes us a lot alike. Leave us alone!
We fight roosters and are proud of it. We are third-generation cockfighters and it
has been in our family for over 50 years. Those of you who think no one actually makes
a living this way are sadly mistaken—think again.
In conclusion, we are a family and we are just trying to survive in this society.
We teach our children to have morals and value their upbringing. Please don't take that
away—it is all we have. Tara Parish
22. I know I can't really feel a pain you have. But because we're so much alike in so many
ways, I'm sure that you feel physical pain in roughly the same way I do.
23. Dick: Our diet should be similar to that of cavemen—that's what our genes are
programmed for.
Zoe: You're nuts. Besides, it's cave dwellers, not "cavemen."
24. God must exist. The way everything works together in nature, the adaptation of means
to ends, the beauty, resembles, but far exceeds, what humans do. Everything works
together as a fine piece of machinery, like a watch. So there must be some maker with
intelligence behind all of nature. That is, God exists and is similar to human mind and
intelligence.
25. Voters in Arizona and California approved ballot measures Nov. 5 allowing prescrip-
tions of marijuana and other controlled substances for certain patients.
The most prevalent use is to ease the suffering of terminal patients or to counteract
the side effects of chemotherapy. . . .
The legal effect of the measures' passage is still up in the air, since the uses remain
outlawed under federal statute. But retired General Barry McCaffrey, the White House's
drug policy director, is quite certain about what the practical effect will be:
264 CHAPTER 12 Reasoning by Analogy
"Increased drug abuse in every category will be the inevitable result of the
referenda," he said in a speech last week. "There could not be a worse message to young
people than the provisions of these referenda. . . . They are being told that marijuana
and other drugs are good, they are medicine."
Apply this logic to the general's primary area of expertise:
Does the necessity of maintaining a standing army and engaging in war to protect
national interests send a message to teens to arm themselves and form street gangs? . . .
There is a line between use and abuse of a necessary evil like lethal force or a powerful
narcotic.
Social, economic and political circumstances justify the use of lethal force in war;
medical circumstances justify the use of drugs.
But to think that teens or other forms of life lower on the food chain than generals are
unable to differentiate between use and abuse may lead directly to the kind of logic under
which students are expelled for possession of over-the-counter analgesics like Midol.
Editorial, Albuquerque Journal, November, 1996
a. What is the conclusion?
b. What analogy does the editorial make?
c. How does it use the methods for evaluating analogies?
d. Are there any slanters or bad argument types?
e. Is the argument good?
26. a. Suppose that tomorrow good, highly reliable research is announced showing that oil
derived from tails removed without anesthetic from healthy cats when applied to
human skin reduces wrinkles significantly. Would it be justifiable to do further
research and manufacture this oil?
b. Same as (a) except that the oil is drunk with orange juice and significantly reduces
the chance of lung cancer for smokers.
c. Same as (a) except the oil is mixed with potatoes and eaten and significantly reduces
the chance of heart disease and lengthens the lives of women.
d. Same as (a) except that wh
en drunk, the oil kills off all viruses harmful to humans.
27. Do Exercise 26 reading "dogs" for "cats."
F u r t h e r Study Analogies are discussed in courses in criminal justice, ethics, and health sciences, among others. The exercise Tom did about how we justify treating dogs
humanely is typical of the sort of problem and reasoning you'd encounter in a course
on ethics. Some philosophy classes on reasoning or philosophy of science look at
the nature of analogies more deeply. In the Science Workbook for this text you can
read about how scientists reason with models as analogies, and Science Analyses 4.8,
8, and 10.C deal with E S P .
Writing Lesson 10
You understand what reasoning by analogy is now. So write an argument using an
analogy either for or against the following:
Just as alcohol and tobacco are legal, we should legalize the use of
marijuana.
Check whether your instructor has chosen a different topic for this assignment.
There are roughly three ways you can argue:
• Marijuana is no worse than alcohol or tobacco, so we should legalize it.
(Arguing from similarities.)
• Marijuana is worse than alcohol and tobacco, so we should not legalize it.
(Arguing from differences.)
• Marijuana is no worse than alcohol or tobacco, but it is a mistake to
have those legal, and we should not make the situation worse by
legalizing marijuana.
(Arguing from similarities.)
Be sure to make explicit what prescriptive premises you are using.
Write your argument as a maximum one page essay. It should be clear and
well structured, since you will have written out the claims first for yourself. You
shouldn't have to do major research for this, but at least be sure your premises are
plausible.
265
13 Numbers?
A. Misleading Claims with Numbers 268
B. Graphs 270
C. Averages 273
Summary 274
•Exercises for Chapter 13 275
In this chapter we'll look at some ways you can get confused about numbers in
claims. If your eyes are starting to glaze, if your mind is going blank with talk of
numbers, relax. Numbers don't lie.
267
268 CHAPTER 13 Numbers?
A. Misleading Claims with Numbers
Zoe has 4 apples and Dick has 2 oranges. Who has more? More whatl
When numbers are used it looks exact, but a vague or meaningless comparison
gets no better by having a few numbers in it.
There were twice as many rapes as murders in our town.
Yes, that's a claim, but a misleading one. It seems to say something important, but
what?
It's getting really violent here. There were 12% more murders this year.
This is also a mistaken comparison. If the town is growing rapidly and the
number of tourists is growing even faster, it would be no surprise that the number of
murders is going up, though the rate (how many murders per 100,000 population)
might be going down. I'd feel safer in a town of one million that had 20 murders last
year than in a small town of 25,000 that had 6. A numerical comparison where it
doesn't make sense to compare the items is called comparing apples and oranges.
Increases and decreases are comparisons, too:
Attendance up 50% this week at performances of Othello!
Tickets still available!
Great ad, but what was the attendance last week? 25? 250? 1,000? We call it
two times zero is still zero when someone gives a numerical comparison that makes something look impressive but the base of the comparison is not stated. For
example, a clothing store advertises a sale of sweaters at "25% off." You take it to
mean 25% off the price they used to charge which was $20, so you'd pay $15. But
the store could mean 25% off the suggested retail price of $26, so now it's $19.50.
Percentages can be misleading, too You see a stock for $60 and think it's a
good deal. You buy it; a week later it's at $90, so you sell. You made $30—that's
a 50% gain! Your buddy hears about it and buys the stock
at $90; a week later it goes down to $60, so he panics
and sells the stock. He lost $30—that's a 33.33% loss.
The same $30 is a different percentage depending on where you started.
And then there's the report that says unemployment is up 8%. That does not
mean unemployment is at 8%. It means that if unemployment was 5%, it is now
5.4%. There is a difference between "up" and "up to." Here's another example:
X-Ray Cancer Risk Up to 3%
The risk of cancer from common X-rays and increasingly popular CT scans
ranges from less than 1 percent to about 3 percent, according to a new study. . . .
The new research indicates the cancer risk—ranging from 0.6 percent to
3.2 percent—varies depending on the frequency of X-rays and scans in 15
countries surveyed. . . .
SECTION A Misleading Claims with Numbers 269
Of the 15 countries surveyed, the cancer risk believed linked to X-rays
was lowest in Britain, where they are used least frequently. They estimated that
0.6 percent of the cumulative British cancer risk for those 75 years old came
from X-ray exposure, accounting for about 700 of the nation's annual cancer
diagnoses. Beth Gardiner, Associated Press, January 30, 2004
Sounds good, except when they say that the cancer risk is 1 percent, what do they
mean? With percentages, you always need to ask: percentage of what!
An article in the journal Science, vol. 292, uses percentages to assess risk in
health care. Mammography screening, it says, can reduce the risk of breast cancer
fatalities in women ages 50 to 74 by 25%. That seems like a real incentive for
women of that age to get tested. But, the article points out, only 2 out of 1,000
women without symptoms are actually likely to die of breast cancer within the next
10 years. So reducing the risk by 25% just means that only 1 more woman in 1,000
who undergoes screening in the next 10 years would be saved. Yet the other women
who won't benefit from screening are subjected to X-rays, false positive tests, or
treatment for slow-growing cancers that could be left alone. To make choices about
health care you need not only the percentages, but the actual numbers, too.
Still, it doesn't matter whether it's percentages or actual numbers if there's no
way they could know the number. For example, on a National Public Radio news
broadcast I heard:
Breast feeding is up 16% from 1989.
How could they know? Who was looking in all those homes? A survey? Who did
they ask? Women chosen randomly? But lots of them don't have infants. Women
who visited doctors? But lots of women, lots of poor ones, don't visit their doctors.
What does "breast feeding" mean? Does a woman who breast feeds one day and
then gives it up qualify as someone who breast feeds? Or one who breast feeds two
weeks? Six months? Maybe NPR is reporting on a reliable survey (in the next
chapter we'll look at what that means). But what they said is so vague and open to
doubt as to how they could know it that we should ignore it as noise.
Rich getting richer, except in Africa and Asia
The rich got richer in most parts of the world last year, except for Asia and Africa.
There were nearly 7.2 million people around the globe in 2000 who had at
least $1 million in investable assets, an increase of 180,000 from 1999, said a study
released Monday. Their total wealth was estimated at $27 trillion, up 6 percent
from $25.5 trillion the previous year.
Albuquerque Tribune, May 15, 2001
Where did they get these seemingly unknowable figures? What study? Who wants
to let people know they're rich? This is a worthless report.
270 CHAPTER 13 Numbers?
B. Graphs
Graphs can be useful in making comparisons clearer. But we have to be careful
when reading them because they can conceal claims, mislead, or just be wrong.
Example 1
U.S. Private Universities U.S. Public Universities
W. Baumol and A. S. Blinder, Economics: Principles and Policy
Analysis You should check the information in a graph against your personal
experience. The authors of this economics textbook say that the average hourly
wage is about $13. So according to the graph the (average?) cost of a college
education in 1997 at a U.S. public university was about $13/hour X 200 hours =
$2,600. But that's unlikely to be enough for tuition and books for one year, much
less housing and board—and certainly not for four years.
Example 2 2001-2002
2000-2001
1999-2000
1998-1999
Socorro, N.M. Consolidated Schools Accountability Report, 2000-2001
Analysis The numbers here are correct, but the graph greatly exaggerates the
differences between years. The enrollment in 2001-2002 is 11.4% less than in
1998-1999, but the difference in the lengths of the bars representing those
enrollments is 66%. Visually the difference appears even greater because we're
comparing areas instead of lengths. A graph is likely to distort comparisons if the
baseline is not zero or if it uses bars.
SECTION B Graphs 271
Analysis Here we can see how the angle, the sharpness of increase and decrease,
can be exaggerated greatly by the spacing of the scales on the axes. This affects our
perception of the volatility and the amount of increase or decrease of prices.
A graph can create misleading comparisons by the choice of how the measuring
points on the axes are spaced.
Richard L Epstein Page 34
