critical thinking
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which has exonerated hundreds of innocent people wrongly convicted, is a sobering reminder to us about how difficult and yet how important it is to evaluate the logical strength of arguments carefully. A strong but fair criminal justice sys- tem is essential to the rule of law. But a weak or unfair sys- tem undermines respect for law enforcement and undercuts trust in the court system. To learn more about the causes of wrongful convictions, such as eye witness misidentifications, improper forensics, false confessions, government miscon- duct, and self-interested informants, one place to begin your search at the Innocence Project website. Or, Google “social justice film awards” for a rich array of high quality media.
Evaluating Generalizations
A generalization may be based on data gathered system- atically or unsystematically. We would be wise to place greater confidence in the claim if it were supported by data gathered more systematically, rather than on simply one or two happenstance personal observations. Consider the following three generalizations. Their conclusions, which are bolded, are supported by premises that report personal experiences, conversations focused on these topics, or infor- mation derived from historical records or opinion surveys.
1. People over the age of 60 tend to prefer to listen to oldies. This claim is based on the data gathered in telephone surveys of persons between the
ages of 60 and 90, which were conducted in Florida, Arizona, Ohio, and Connecticut. In all, 435 inter- views were conducted. Participants were asked to identify which type of music they preferred to listen to most. They were given eight choices: Classical, Pop, R&B, Country, Oldies, Broadway, Religious, and Top 40.
2. In May, inspectors from the city sanita- tion department made unannounced visits to all 20 hotels in the downtown area and to 10 of the other 30 hotels within the city limits. The 10 were representative of the type and quality ratings of those other 30 hotels. The inspectors by law could demand access to any room in the hotel to look for pests and to evaluate cleanliness. Careful records were kept of each room inspected. In all, 2,000 beds were exam- ined for bedbugs. 1,460 beds tested positive. Based on the data from these inspections, we estimate that 73 percent of the hotel room beds in this city are infested with bedbugs.
3. I have visited San Francisco maybe seven times over the past 25 years. It is one of my favorite vaca- tion cities. I’ve gone in the summer and in the winter. And I can tell you one thing, bring a jacket because it’s probably going to be cloudy and cold in San Francisco if you go in August.
Notice that in the first example we have a somewhat modest assertion about what people over the age of 60 “tend to” prefer. The second says that it applies to 73 per- cent of the hotel beds, but not that the infected beds are evenly distributed among the city’s 50 hotels. And the third says that it is “probably” going to be cold in San Francisco in August. It is easy to imagine scenarios in which the information in the premises is true but the con- clusion may not apply. We can conjure the possibility that someone over 60 does not like oldies. We can imagine that there may be one hotel in the city where most of the beds are not infested. It is no problem to think of the possibility that there should be at least one warm sunny August day in San Francisco. But, developing a possible counterexam- ple does not necessarily diminish the logical strength of a warranted argument.
To evaluate the logical strength of probabilistic gen- eralizations, we need to do more than find one or two counterexamples. We must, instead, examine whether the sampling of cases reported in the premises is adequate to support the probabilistic inferences that are drawn. This means asking four questions and finding satisfactory answers to each of them.
• was the correct group sampled? • were the data obtained in an effective way? • were enough cases considered? • was the sample representatively structured?
wAS tHe CorreCt GrouP SAmPled? The first exam- ple makes a claim about people over the age of 60. The prem- ises tell us that adults between the ages of 60 and 90 were sampled. That is the correct group to sample if one wishes to make generalizations about persons in that age range. It would not do, obviously, to sample people under the age of 60 and then present those data as a basis for a claim about peo- ple over that age. One would think that sampling the wrong population would not be a mistake commonly made. But for years, pharmaceutical companies made inferences about children’s drug dosages and the effects of various medica- tions on women based largely on studies conducted on adult males. More recently, we have learned that there are genetic factors that affect the rate at which common pain relievers, like the ibuprofen in Motrin, are metabolized. This new find- ing should influence dosage recommendations for those who are poor metabolizers (e.g., 6 to 10 percent of Caucasians).7
were tHe dAtA obtAined in An eFFeCtive wAy?
In our example about the music listening preferences of adults over 60, we see that the data were obtained via telephone surveys. We might think that a telephone sur- vey may not be as efficient as using a Web-based survey, which would reach many more people and be much more cost-effective. But, upon reflection, it seems reasonable to use the telephone to reach older adults, many of whom may not be comfortable with the use of computers and Web-based survey tools. Finding an effective method to gather data from the sample is often a major challenge for researchers.8 For example, consider how difficult it is to gather high-quality data about the state of mind of combat veterans in the year after their return from a war zone.
were enouGH CASeS ConSidered? In general, the more cases the better. But there comes a point of diminishing returns. If we are trying to make a reasonable generalization about millions of people who live in major metropolitan areas like Boston, New York, Chicago, or Los Angeles, it is neither necessary nor cost-effective to survey even one percent of a group so large. At some point the distribution of responses simply adds numbers, but the proportions of
responses selecting each possible answer do not change sig- nificantly. Social scientists have worked out sophisticated statistical methods to provide a precise answer to the ques- tion of sample size. The answer establishes a minimum nec- essary depending on the kinds of statistical analysis to be conducted and the degree of accuracy needed for the ques- tion at hand. For example, to keep us up to date on the likely voting patterns in a forthcoming election, it is sufficient to track what likely voters are going to do within a margin of error of plus or minus 2 percent. Called a “power analysis,” the calculations social scientists make begin with a projection of the number of cases expected to fall randomly into each possible category. Scientists can then determine whether the observed distribution varies significantly from the expected random distribution.9 As a rough rule of thumb, they would want at least 25 cases per possible response category. In our “Oldies” example there are eight categories of music. So, we would need a sample of at least 200 individuals. We have 435, so the sample size is adequate. But we do not have a claim that reports a percentage. In our example the claim reports a tendency. Social scientists would not regard a ten- dency as being a strong enough deviation from random to be called “statistically significant.”
wAS tHe SAmPle rePreSentAtively StruCtured?
We said that 435 was an adequate sample size for our example, but were the 435 representative of the popula- tion being talked about in the claim? The claim talks about everyone over the age of 60. Because more than half of the people between 60 and 90 are women, and because women might have different music listening preferences, we would need to be satisfied that the 435 reflected the actual ratio of women and men in that age group. We do not know that180 Chapter 9
from the information given. If we hypothesize that music- listening preferences might be related to educational back- ground, race, ethnicity, or socioeconomic status, then we would want to assure ourselves that the sample of 435 was representative of the distribution of those factors among the target population. Because we do not know if 435 is a representative sample, we cannot answer this fourth ques- tion in the affirmative. And, as a result, example #1 is not logically strong.
Coincidences, Patterns, Correlations,
and Causes
Decades ago scientists first observed that there were a number of cases of heart disease where, coincidentally, the person was a smoker. Further systematic research demonstrated a strong positive correlation between smoking and heart disease. Scientists hypothesized that perhaps smoking was a contributing factor. However, before making a defensible argument that quitting smok- ing would reduce a person’s chances of heart disease, researchers had to explain scientifically how smoking caused heart disease. Researchers demonstrated scien- tifically that nicotine constricts blood vessels in the heart, which reduces blood flow to the heart muscle, thus caus- ing heart attacks.
The progression from coincidence to correlation to causal explanations marks our progress in being able to explain and to predict events. At first we may observe two events and think that their occurrence might merely be a chance coin- cidence. Then, as more data are systematically gathered and analyzed, we may discover that the two events are in fact statistically correlated. And, with further experimental
In the heartland people know that lightning can strike twice or more often in the same place.
investigation, we may learn that what had at first seemed like a coincidence actually occurs because of important causal factors. When and if we reach that stage we will have generated a causal explanation.
CoinCidenCeS If two events happen to occur together by chance, we call that a coincidence. For exam- ple, in 2013 a total of 23 people were killed by lightning in the United States.10 In 2013 what are the chances that a given individual would have been killed by lightning in the United States, given that the population is roughly 317,300,000? That coincidence has roughly one chance in 13,800,000 of occurring, all else being equal. The qualifier “all else being equal” means that weather patterns do not change substantially and that substantial numbers of people do not behave in ways which increase or decrease their chances of being killed by lightning in the United States, such as becoming residents of another country or standing in an open field holding aluminum rods in the air during lightning storms. But, all things being equal, we can use probabilistic reasoning and statistical facts to calculate the probabilities that a given coincidence might occur.
Although we cannot predict with certainty that the next time you flip a coin it will come up heads, we can predict with a high level of confidence what will happen 50 percent of the time in the long run. We know how to calculate mathematical probabilities for events such as these because we know that each individual outcome occurs randomly with equal frequency. If we roll two reg- ular dice, the result will be two 6s 1 time out of 36 rolls over the long haul. We calculate that by multiplying the chance of rolling a 6 on die #1, which is 1 out of 6, times the chance of rolling a 6 on die #2, which is also 1 out of 6. Then we multiply those odds to get the mathemati- cal probability of both outcomes happening together—the product is 1 out of 36.
PAtternS Occasionally we see patterns in events that initially appear to be random coincidences. For example, lightning does strike more than once in the same place. That’s why people put lightning rods on the tops of build- ings. The lightning rod offers an attractive location for lightning to strike. Because the lightning rod is connected to the ground by a sturdy wire, the electrical charge from the lightning is directed safely into the earth, instead of causing damage to the tall building or starting a fire. We do not know where or when the lightning will strike, but we know there will be storms and lightning every year. And we have observed the pattern that lightning is much more likely to strike tall, pointy, isolated objects, like barns in the prairie or skyscrapers in cities.11 To ignore that pattern would be foolish of us. 180 Chapter 9
from the information given. If we hypothesize that music- listening preferences might be related to educational back- ground, race, ethnicity, or socioeconomic status, then we would want to assure ourselves that the sample of 435 was representative of the distribution of those factors among the target population. Because we do not know if 435 is a representative sample, we cannot answer this fourth ques- tion in the affirmative. And, as a result, example #1 is not logically strong.
Coincidences, Patterns, Correlations,
and Causes
Decades ago scientists first observed that there were a number of cases of heart disease where, coincidentally, the person was a smoker. Further systematic research demonstrated a strong positive correlation between smoking and heart disease. Scientists hypothesized that perhaps smoking was a contributing factor. However, before making a defensible argument that quitting smok- ing would reduce a person’s chances of heart disease, researchers had to explain scientifically how smoking caused heart disease. Researchers demonstrated scien- tifically that nicotine constricts blood vessels in the heart, which reduces blood flow to the heart muscle, thus caus- ing heart attacks.
The progression from coincidence to correlation to causal explanations marks our progress in being able to explain and to predict events. At first we may observe two events and think that their occurrence might merely be a chance coin- cidence. Then, as more data are systematically gathered and analyzed, we may discover that the two events are in fact statistically correlated. And, with further experimental
In the heartland people know that lightning can strike twice or more often in the same place.
investigation, we may learn that what had at first seemed like a coincidence actually occurs because of important causal factors. When and if we reach that stage we will have generated a causal explanation.
CoinCidenCeS If two events happen to occur together by chance, we call that a coincidence. For exam- ple, in 2013 a total of 23 people were killed by lightning in the United States.10 In 2013 what are the chances that a given individual would have been killed by lightning in the United States, given that the population is roughly 317,300,000? That coincidence has roughly one chance in 13,800,000 of occurring, all else being equal. The qualifier “all else being equal” means that weather patterns do not change substantially and that substantial numbers of people do not behave in ways which increase or decrease their chances of being killed by lightning in the United States, such as becoming residents of another country or standing in an open field holding aluminum rods in the air during lightning storms. But, all things being equal, we can use probabilistic reasoning and statistical facts to calculate the probabilities that a given coincidence might occur.
Although we cannot predict with certainty that the next time you flip a coin it will come up heads, we can predict with a high level of confidence what will happen 50 percent of the time in the long run. We know how to calculate mathematical probabilities for events such as these because we know that each individual outcome occurs randomly with equal frequency. If we roll two reg- ular dice, the result will be two 6s 1 time out of 36 rolls over the long haul. We calculate that by multiplying the chance of rolling a 6 on die #1, which is 1 out of 6, times the chance of rolling a 6 on die #2, which is also 1 out of 6. Then we multiply those odds to get the mathemati- cal probability of both outcomes happening together—the product is 1 out of 36.
PAtternS Occasionally we see patterns in events that initially appear to be random coincidences. For example, lightning does strike more than once in the same place. That’s why people put lightning rods on the tops of build- ings. The lightning rod offers an attractive location for lightning to strike. Because the lightning rod is connected to the ground by a sturdy wire, the electrical charge from the lightning is directed safely into the earth, instead of causing damage to the tall building or starting a fire. We do not know where or when the lightning will strike, but we know there will be storms and lightning every year. And we have observed the pattern that lightning is much more likely to strike tall, pointy, isolated objects, like barns in the prairie or skyscrapers in cities.11 To ignore that pattern would be foolish of us.
Another pattern that is difficult to miss is the con- centration of multi-million dollar luxury casinos in Las Vegas, Atlantic City, and other gambling hubs. Casinos are monuments to the reliability, over the long run, of these calculated coincidences. If 98 percent of the money bet in a casino on any given day goes back to the players as winnings that day, then on an average day the casino can be very confident of retaining 2 percent of every dol- lar bet. The more money bet, the more dollars that 2 per- cent represents. Unless more than 100 percent of the money bet is returned to the bettors as winnings, we can be sure that over the long run the bettors go home los- ers, not winners, and not “breaking even.” An individual person winning a specific bet is, considered in itself, a random coincidence. The totality of all those coincidences can be aggregated into a large and highly predictable profit margin for the casino. The best generalization to infer is that, in the end, the casino will very likely sepa- rate the chronic gambler from more and more of his or her money.
“Fables should be taught as fables, myths as myths, and miracles as poetic fantasies. To teach superstitions as truths is a most terrible thing. The child mind accepts and believes them, and only through great pain and perhaps tragedy can he be in after years relieved of them.”
Hypatia of Alexandria, (370–415), Mathematician and Philosopher.12
CorrelAtionS As in the smoking and heart attack example, when the same coincidence is observed over and
over again, that is, when people see a pattern, they begin to suspect that the events may be related by something more than pure random chance. Even before knowing that one event may be the cause of another, we can determine whether the two are correlated.
Correlations, calculated using statistical analyses, describe the degree to which two different sets of events are aligned. For example, scores on critical thinking skills tests are positively correlated with student success on state licensure exams in a number of health sciences pro- fessions.13 We might wish to speculate about the possible causal relationships of critical thinking skill to academic or professional success. But simply having the correlation in hand can be valuable to those professional programs that have more applicants than can be accepted. The admis- sions committees can use an applicant’s critical thinking skills test score in the way that it uses GPAs or letters of reference, namely as another valuable data point to con- sider when making its decision to admit or not to admit an applicant.14
When a research project reports that a statistically significant correlation has been found between events of kind #1 (scores on a critical thinking skills test) and events of kind #2 (scores on a state’s professional licen- sure examination), that means that the relationship between the two kinds of events is viewed as not likely to be happenstance or chance. Of course, there could be an error in this estimate, but typically the largest thresh- old for this error is a slim 5 percent. We can be 95 per- cent confident that the two events are really correlated. Even greater confidence that the events reported did not happen by mere chance can be found in many fields of research in which statistical significance is reported with 99 percent confidence, at 1 percent, or even less (0.001) chance of error. Even so, we remain in the realm of probabilistic reasoning because the warranted infer- ence, which is logically very strong, holds open the pos- sibility that the findings reported may have happened by mere chance. The odds are very definitely against that possibility, however. If the 0.001 confidence level is reached, then the odds that the conclusion is mistaken are 1 in 1,000.
Using statistical correlations as their basis for con- fidence in their products, manufacturers of over the counter medical test kits do a thriving business. Drug stores like Walgreens sell home tests kits for pregnancy, paternity, colon disease, illegal drugs, blood alcohol levels, and ovulation. These products are used by mil- lions of people. And although these products can be highly reliable, most advertising themselves as 99 per- cent accurate, that still leaves a 1 percent chance for mistakes. At 1 percent, that comes to 10,000 errors out of 1,000,000 tests. Although the possibilities are remote, a test might be a false positive, meaning that that the
The Devil Is in the Details!
Ever wonder what the return on investment is for graduates from your university with your major? On its public website PayScale.com lists the annual return on investment by major for hun- dreds of institutions. (Navigate to the College ROI Report and select “Best ROI’s by Major” from the dropdown menu.) With data from 113 insti- tutions, the top annual ROI for Humanities and English majors is 10.1 percent and the lowest was -3.9 percent. Looking at 840 institutions, for Business majors the top ROI was 12.3 percent down to -3.8 percent per year. Whoa! Does this mean that a humanities major, like Philosophy, is financially comparable to a major in Business?
What’s It Worth? The Economic Value of College Majors, a study by the Center on Education in the Workforce at Georgetown University, looked at full-time full-year workers who had completed bachelor’s degrees in dif- ferent fields. That report paints a very different picture. In the Georgetown report, the median salary for Business majors as a group is $60,000. The median annual salary for Humanities and English majors was $47,000. That’s 21 percent lower. You can find the Georgetown report on the web by Googling its name.
Why such huge differences? Which one is closer to the truth? Assuming both sources have provided accurate information based on the data available to them, how can we make sense out of the
EARNINGS BY GENDER*($)
40k|55k 40k|48k 45k|57k 50k|66k 44k|55k 60k|73k 40k|48k 62k|79k 60k|70k 43k|50k 40k|55k 42k|58k 48k|65k 40k|52k 46k|64k 15k 8k 12k 16k 11k 13k 8k 17k 10k 7k 15k 16k 17k 12k 18k
*Full-time, full-year workers with a terminal Bachelor’s Degree.
Female Median Earnings Male Median Earnings Difference
*Source: From What’s It Worth? The Economic Value of College Majors, by the Georgetown Center for Education & Workforce. http://cew.georgetown.edu/whatsitworth/. Reprinted by permission.
huge differences between what each says about the median salary by major? Hint: “The devil is in the details.” Check out the sample sizes and the sources of the information each report uses. This will help you evaluate which is the more credible source.
The Georgetown report showed earnings by major and gender and by race. How do we explain the differences by gender as reflected in this chart from the Georgetown report?
test indicates that someone is a biological parent, is pregnant, is using illegal drugs, is drunk, or has ovu- lated when those results are not true. Or a test might come back false negative, meaning that the test failed to indicate that the person was in fact a biological par- ent, pregnant, etc. Rare as false positives and false nega- tives are, they illustrate the difference between “highly confident but possibly mistaken” warranted inferences and the certainty, which characterizes valid inferences. Depending on one’s appetite for risk, with 1 chance in 100 of the test results being wrong, a person might be wise to double check before basing a major life decision on a single test’s outcome.
Well-researched correlations can be powerful tools. Consider this possibility. Suppose that writing assign- ments, which employ grammatically complex construc- tions, use expected words and expressions, include sentences with greater average word counts, and include fewer spelling mistakes are statistically significantly cor- related with higher grades. And suppose that assign- ments that are missing one or more of those features are
statistically correlated with lower grades. Based on this, we can design computer programs that assign grades by parsing grammar and counting words.15 The computer does not need to understand the meaning of the essay nor does it have to evaluate the quality of arguments used. The grades assigned by computers can then be checked
against the grades that human evaluators assign to those same essays. Refinements can then be made in the com- puter program’s grading algorithms to achieve ever closer
approximation to the results human beings would have produced. When the computer program is refined to the extent that it assigns the same grades as well-qualified human beings to 99.9 percent of the essays, then essay grading can be automated. To assign you the grade your professor would have assigned, the computer never needs to understand what you wrote. This is not science fiction. Automated grading is used by the Educational Testing Service.16
CAuSeS Documenting that a causal relationship exists between events requires more than demonstrating a strong correlation. The intellectual challenge of design- ing research, which is capable of revealing the causal mechanisms at work in nature is important and interest- ing work. Perhaps this is why many strong critical think- ers find careers in scientific and technical fields attractive. Causal explanations are desirable because they enable us to explain, predict, and control parts of the natural world. In Chapter 14 entitled “Empirical Reasoning” we will explore the powerful investigatory methods used by scientists to achieve causal explanations. In the two con- cluding chapters we explore the differences between how social scientists and natural scientists seek the best expla- nations possible.
It is not always possible to move all the way from coin- cidence to correlation to causal explanation in every fieldof inquiry. For example, predicting the behavior of the stock market remains a hazardous and uncertain adven- ture. Because we do not really know how all the factors that influence the market interact, we are not able to pre- dict with high levels of confidence what the market will do on any given day. Some financial analysts turn out to be right, while others are wrong. Often, it seems as though the analysts announce why the market reacted as it did on a given day only after the day’s trading is completed. Then, we hear that the market responded to changes in the jobless rate, the prime interest rate, consumer confidence level, or something else. But those same analysts are not able to use those same factors to predict accurately what the market will do in the future. If their explanations of the past behav- ior of the market were correct, one would expect that they would be able to make reliable predictions about the mar- ket’s future behavior. That we are not able to make good predictions about the future leads us to suspect that we do not yet know, beyond the level of coincidences and correla- tions, what causal factors, individually or in combination with other causal factors, are relevant to explaining the behavior of the stock market. One can only wonder how relevant the factors those prognosticators identify as causes really are.
“The seeker after truth is not one who studies the writings of the ancients and, following his natural disposition, puts his trust in them, but rather the one who suspects his faith in them and questions what he gathers from them, the one who submits to argument and demonstration.”
Ibn al-Haytham, (965–1040), Astronomer and Mathematician.17
9.2 Fallacies Masquerading as Warranted Arguments
Just as some fallacies are presented as valid arguments, others are presented as warranted arguments. They draw their power to deceive and persuade from how closely they resemble the genuine article. Detailed analysis often helps us avoid being misled by the following fallacies.
erroneouS GenerAlizAtion Generalizations, even those based on solid evidence and vivid experiences, can be deceptively fallacious, too. At times, we make hasty and erroneous generalizations by relying on far too little information or by exaggerating the importance of one or two particular experiences. The result is a claim that goes
beyond what the data can support. Erroneous generaliza- tions tend to spring from and to reinforce preconceptions. Consider these examples:
• The paper showed a picture of the CEO in chains doing the perp walk as he was being led off to jail. Another middle-aged white guy with a $400 hair- cut! Same as Bernard Madoff, the guy who swindled $170 million out of rich people with his Ponzi scheme. All those corporate thieves are overpaid white guys.
• Many medical professionals recommend a healthy diet and regular exercise. More is always better, right? So the way to be super healthy is to go on a crash diet and exercise as much as possible! Yes?
• Seventy-one percent of the students enrolled in my educational methods course are women. So, women really like my courses.
In each of these cases, even if the premises were true, the conclusion goes unjustifiably beyond what those prem- ises could support. If a person were interested in investi- gating independently the truth of the claims expressed as conclusions of these generalizations, is there a systematic and effective way to search for the evidence, which might confirm or disconfirm those claims?
PlAyinG witH numberS Arguments, which use raw numbers when percentages would present a more fair- minded description, or use percentages when the raw numbers would present the more fair-minded description, can be evaluated as fallacies of Playing with Numbers. Arguments that cite statistics or numbers but do not pro- vide sufficient information to make a good judgment about the significance of those numerical data are species of the Playing with Numbers Fallacy as well. For example:
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Six hundred people are affected by the decision you made prohibiting pythons as pets in this apartment complex. I want you to know that 80 percent of the people surveyed said that they wanted you to recon- sider your decision. Exactly how many people, you ask? Well, I personally talked to my four roommates and three agreed with me, which makes 4 out of 5, including myself, and that’s 80 percent.
The average salary for postal workers is 5.6 percent higher than the average salary for the employees of the Transportation Safety Administration. This estab- lishes that postal workers are overpaid.
The National Highway Traffic Safety Administration reports that there were 30,800 motor vehicle fatali- ties in 2012. Of those 4,957 were motorcyclist fatali- ties.18 This means that driving or riding in a car or a truck is six times more dangerous than riding a motorcycle
Review these examples and add premises or restate the conclusion, or do both to transform each into a war- ranted argument that gives reasonable justification for believing that the claim—as you may have restated it— is now very probably true. For the third example about traffic fatalities visit the National Highway Traffic Safety Administration website nhtsa.gov to get the relevant details. For example note the ratio of motorcycles to other vehicles, or the ratio of total miles per year driven by the different types of vehicles.
FAlSe dilemmA A real dilemma is a situation in which all our choices are bad, like a person trapped on a window ledge of one of the upper floors of a burning building. But, at times we may think we are facing a terrible dilemma when we are not. Often the world offers more options than we may perceive at first. At times, the consequences of one or another of our options may not be nearly as dreadful as we initially imagine them to be. As the following examples indicate, upon closer analysis at times what appears to be a real dilemma turns out to be a false dilemma.
• The kidnappers have taken eight people hostage and are holding them at a farmhouse just outside town. If the SWAT team assaults the farmhouse, the hostages could be killed. But if we give into the kidnappers’ demands for ransom and safe passage out of the coun- try, we’ll only be encouraging more kidnappings of innocent people. What can we do?
• If I go to the job interview laid-back and unprepared, I’ll blow it. But if I prepare for the interview I could overdo it and be so nervous that I’ll blow it any- way. I’m a mess. There’s no way to get ready for this interview.
Statistically, who is more at risk, car drivers or motorcyclists?
As these examples show, another good name for this fallacy is “The Either/Or Fallacy” because the situations often appear to be limited to one option or another, but on further examination, additional options emerge. This is true of the first example. Assaulting the farmhouse and giving in are not the only possible options. Negotiating for the release of some or all of the hostages is an option. Waiting until those inside the farmhouse run out of food or water is another option. Blasting the farmhouse with mega decibels of sound and shooting tear gas in through the win- dows might force the occupants out. In other words, a little creativity can often reveal a way out of a false dilemma.
tHe GAmbler’S FAllACy Random events, by defini- tion, are not patterned, correlated, or causally connected. But, at times, we make arguments that wrongly assume that what happens by chance is somehow connected with things we can control. We can use “Gambler’s Fallacy” as an umbrella term to remind ourselves that random events are, in fact, random and that drawing inferences based on the assumption that they are patterned, corre- lated, or causally connected is a mistake. Here are some examples of fallacious inferences that attribute more to mere chance coincidences than strong reasoning would warrant.
• If we’re going to Vegas, I’ll bring my blue socks to wear in the casino. You know, the pair with the word “Winner” embroidered on the side. They’re my lucky socks. Although I’ve lost money plenty of times wear- ing them, I’ve never won at slots without those blue socks. So, I won’t win a dime from the slots if I don’t wear those socks!
• Whenever I leave the apartment, I rub the tummy of the little statue of bronze Buddha we have on the table near the door. It makes me happy to do that because I know that it brings me good karma.
• I just flipped a coin twice and it came up heads both times. So, the next two times I flip it, the coin will come up tails because the chances are 50-50.
• Miguel Cabrera is batting for the Detroit Tigers. Cabrera’s batting average this year is .333. This is his third trip to the plate this game. He grounded into a double play his first trip and struck out his second time. So, he’s going to get a hit this time.
FAlSe CAuSe This fallacy is one of the most common obstacles to good thinking. The False Cause fallacy is to assume that two events are causally related just because one happens right after the other. This mistake is jumping to the conclusion that the first event must have caused the second event.
THINKING CRITICALLY
Dilemmas Heighten the Drama
The 2010 film Extraordinary Measures is based on the true life story of a father’s desperate struggle to find a cure for Pompe Disease, a form of Muscular Dystrophy that limits a child’s life span to about nine years. Harrison Ford
plays the part of Dr. Robert Stonehill, who believes his research may lead to a cure. But Stonehill’s research takes a lot of money, more than the father, played by Brandon Frasier, and the researcher are able to get from donations alone. So they formed a research company and then persuaded a ven- ture capitalist to back them with $10 million. But the work was difficult and the expenses were high. There is a dramatic scene about 57 minutes into the story where the father and the researcher face a bitter dilemma. The venture capitalist gives them a choice: Meet an impossibly short deadline to complete their work or sell their company to pay back the venture capitalist. Both options are ter- rible from the perspective of Harrison Ford’s char- acter. He sees this as a dilemma from which there is no escape. But Brandon Frasier’s character, the
father of the sick child, sees it as a false dilemma. Locate that scene in the movie and see how Frasier’s character and Ford’s character grapple with the decision they must make.
• Look, I put the CD into the player and the windshield wipers wouldn’t turn on. It has to be that the problem with the wipers is somehow connected to the CD player.
• It’s hard to know exactly what made her so angry. She seemed fine when we were talking earlier about what a jerk her former boyfriend was. Then you came in and boom! She exploded. I think it’s your fault.
Called “Post hoc, propter hoc” [“After this, because of this”], confusing temporal proximity with causality is one of several mistakes grouped together under the heading False Cause Fallacies. Another mistake is to confuse a cor- relation with a cause.
• Our information shows that in times of economic growth, the hemlines on women’s skirts go from below the knee to above the knee. And in times of a bear market when the economy slows down, the hem- lines that are considered stylish go down below the knee, at times to mid-calf or even ankle height. I know how we can cure the current recession! All we need to do to pull out of the current recession is to make the fashion designers raise hemlines.
Other mistakes often grouped under the broad heading of False Cause Fallacies result from confusing symptoms, outcomes, or intentions with causes. Here are examples:
•
The pressure was intense that day. I had to get from the university to my job, a drive that normally took 25 minutes. But the professor kept us late and then my car wouldn’t start. You know there had to be a traffic jam on the freeway that day. And I needed to get to work because I had to make this major presen- tation. My head was aching and my heart was beat- ing so fast. I felt all sweaty and it was getting harder and harder to breathe. I think that it was all because I couldn’t get any air. That’s where the pressure was coming from. No air.
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• Three years ago we instituted a policy of Zero Tolerance for binge drinking in campus-controlled housing units. Simultaneously, we instituted a non- punitive program of substance abuse counseling. Today we have been hon- ored by the state legislature because the reported incidents of binge drinking have dropped 32 percent compared to numbers from three years ago. The counseling pro- gram is why. That program has greatly reduced the number of incidents of binge drinking in campus-controlled housing.
• We wanted it more than they did! And that’s why we won.
SliPPery SloPe Everyone knows that sim- ply beginning something is no assurance that it will be completed. For a variety of reasons, too many good students never finish their degree programs. Not everyone who takes a drink becomes an alcoholic. Not everyone who buys a gun becomes a killer. The Slippery Slope Fallacy makes the false assumption that events are linked together so that the first step in the process neces- sarily results in some significant, usually bad, result way down the road somewhere. The image conjured by this fal- lacy is of walking along the edge of a muddy wet ridge. One step over that edge and we slide on our butts all the way to the bottom. Another image associated with this fal- lacy is the “camel’s nose under the tent” image. Once the camel gets its nose under the tent, there is no way to pre- vent the whole, huge clumsy animal from entering one’s well-ordered abode. There is wisdom in avoiding situa- tions that can lead us down the path to major problems. But the fallacy fails to remember that even when we are headed toward trouble we have the power to turn our- selves around.
The only reason I failed my critical thinking test is because I didn’t wear my lucky brown socks that day!
20 Fallacies—Common Yet Misleading Errors of Reasoning (Chapters 7, 8, & 9 Combined)
Fail the Test of Non-Circularity
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Arguments that Fail the Test of Relevance
Arguments that Fail the Test of Logical Strength
Fallacies of Relevance
Fallacies Masquerading as Valid Arguments
Fallacies Masquerading as Warranted Arguments
Appeals to Ignorance Appeals to the Mob Appeals to Emotion Ad Hominem Attacks
Affirming the Consequent Denying the Antecedent False Classification
Erroneous Generalization Playing with Numbers False Dilemma
Circular Reasoning
The Straw Man Fallacy Playing with Words Misuse of Authority
Fallacy of Composition Fallacy of Division False Reference
Gambler’s Fallacy False Cause Slippery Slope
• If you ever smoke a joint, then you are on the path to perdition. One puff and there is no stopping the inevi- table fall. Next it will be snorting coke, then shooting up heroin, leading to addiction with track marks in your arms and hepatitis or worse from contaminated needles.
• I warn you, you had better come to every training ses- sion. We start lessons Monday. If you miss the first day, then you’ll be behind and you will never catch up.
A person can make a mistake and recover from it. And some of the initial stages that are alleged to be dreadful turn out not to be problems at all. And the middle ground is often the best place to make one’s stand. To quote Terence of ancient Rome, “Moderation in all things.”
Summing up this chapter,
the evaluation of probabilistic reasoning occurs each day of our lives. We evaluate inferences as warranted or unwar- ranted when talking with friends, working on projects, enduring television commercials, or reasoning through a decision. In this chapter we first worked to strengthen our critical thinking skill of evaluation by considering the impact of new information on extended examples of probabilistic reasoning. It is natural for our minds to think in terms of the progression from coincidence, to perceived pattern, to demonstrated correlation, and then to causal
Key Concept
warranted describes an inference or argument such that the truth of the premises justifies or strongly supports
Applications
Reflective Log
To Kill a Mockingbird: Gregory Peck plays the defense attorney, Atticus Finch, in the classic film To Kill a Mockingbird. The story is about a young man accused of rape. Toward the end of the trial there is a courtroom scene where Atticus Finch gives his summation to the jury. He must be careful not to alienate the members of the jury, whom he regards as potentially biased against the defen- dant because of his race. Atticus first argues that the prosecution has not proved that a crime was actually com- mitted. He then argues that the accused, Tom Robinson, could not physically have done the things that the prose- cution claims. Atticus, believing that he must do more than make claims and logical arguments establishing reason- able doubt, then addresses a key question. Why would the young woman accuser, a White woman, have lied about being raped by the accused Tom Robinson, a Black man? Atticus says he has pity for the victim and then he argues that by accusing Tom Robinson, she was attempting to rid herself of her own guilt. The defense then attempts to challenge the prejudicial assumption: In the language of those days, “Negros cannot be trusted.” Locate the film
Individual Exercises
evaluate the worthiness and explain: Assume that all the premises that are asserted in the arguments below are true. Apply the remaining three tests to evaluate each argument to determine which are worthy of acceptance.
explanation. Although, often it is a mistake to jump to conclusions that events are connected when, in fact they are not. That is why we then worked on the evaluation of arguments that offer to generalize from a limited number of experiences and samplings of data to reach justified claims about the characteristics of larger populations. To protect ourselves from being easily deceived, we reviewed the collection of common fallacies that masquerade as war- ranted arguments.
confidently accepting the conclusion as very probably true, but not necessarily true.
and listen carefully to the claims and arguments made by Atticus Finch in his speech to the jury. Transcribe them and then analyze and map the arguments. After the mapping, evaluate them using the skills developed in Chapters 7, 8, and 9. Explain your analysis and your evaluation. Would you have made the summation differently? If so, how?
Begin with the Test of Logical Strength. Remember, if the argument fails a test you do not have to apply any further tests because, at that point, the argument has been found to be unworthy of acceptance. In each case, give a detailed Chapter 9
explanation to support your evaluation. State in your own words why each argument is worthy or unworthy of acceptance. Hint: Be prepared to add implicit but unspo- ken premises and assumptions. Keep in mind all the things we learned about fallacies and about logical strength from this chapter and the previous two.
1. Anthony was at risk of dying from the severe fall that he took when he was climbing. Many who had the same near-fatal experience become averse to climbing afterward. So, Anthony will surely become averse to climbing after his fall.
2. Susan is John’s younger sister. Linda is John’s elder sister. So, Linda is Susan’s elder sister.
3. I want to buy a boat and you want to buy a car. If we buy a car we can’t use it for fishing or to go tubing. But if we buy a boat we can’t use it in the city or anywhere else but at the lake. Either way we’re stuck.
4. Blood samples taken from the crime scene were type AB. The accused person’s blood is type AB. Therefore, the accused was at the scene of the crime.
5. Either we’ll study together tonight for tomorrow’s exam, or we will both blow it off. I’m too tired to study tonight. So, we’re going to blow it off.
6. Whenever I play the lottery, the number I put in is my birthday. If that’s not my lucky number, then I don’t have one.
7. Randolph knows that John Glenn was a senator. John Glenn was an astronaut. Therefore Randolph knows that John Glenn was an astronaut.
8. Every member of the House of Representatives is under the age of 90. Therefore, the House of Representatives is an organ of government that was created less than 90 years ago.
9. Seventy-three percent of the people surveyed said that they wanted universal health care coverage. Fifty-four percent said that they were worried about the cost of the program or the quality of the care that would be provided. Therefore, the American people are opposed to the President’s health care reform legislation.
10. The Mayor has been in office for three months, and our city’s economic recession has not gone away. The Mayor needs to take full responsibility for the sorry state of the city’s economy.
11. My dear old Uncle Joe has a statue of the Red Faced Warrior on his kitchen table. It faces the side door, and he says that it keeps bad people from coming into his house. He also has a picture of St. Christopher taped to the dashboard of his old Buick and a rosary draped
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13. 14.
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16. 17.
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over the rearview mirror. More protection he claims. On the other hand, he never locks his house, and he needs to get his eyes checked!
But if we don’t study together, then I’m not going to get through the course. And if I don’t get through the course, then I’m going to ruin my GPA and lose my financial aid. So if we don’t study together tonight, then I’m going to lose my financial aid.
We’ve lost six games in a row; our luck has to change today.
We didn’t know what to do to improve sales. So, we all started wearing bow ties and navy blue sweaters to work. And look, three weeks later sales are way up. I’m sure it’s our new office dress code.
It is March tenth and already this year six people have ordered new glasses with plastic frames. Last year only four people had ordered plastic frames by this date. That’s an increase of 50 percent. We had better stock up. It’s going to be a busy year.
Everyone loves ice cream. Children love ice cream. So, everyone’s a child.
Water is our most precious resource. So, a towel on the rack means “I’ll use it again” and a towel on the floor means, “Please replace.”
The archeological theory that the Clovis people of North America were related to the Solutrean culture of Ice Age France and Spain was based on the similarities in the stone tools used. But new DNA evidence suggests that theory is mistaken. The DNA evidence indicates that the ancestors of the Clovis people came from Siberia in Asia. Since present day Native Americans are descended from the Clovis people, their ancestors were Asian.19
The suspect has a history of drug abuse. He has no alibi for the time of the murder. The suspect owns a collection of ceremonial knives and the murder weapon was a ceremonial knife. The suspect may have no motive as far as we know right now, but remember that his father was a serial killer. We found fibers at the crime scene, which are consistent with the brand of blue jeans the suspect wears. An eye witness places the suspect at the Fairfield Mall just one hour before the murder. So the suspect must be guilty.
Everyone believes that pornography harms people by modeling sexually aggressive behavior in men. But the evidence from recent studies suggests that pornography can have that effect only on men who are already prone to aggressive behavior. Therefore pornography is probably not the problem. Male aggressiveness is the problem.20
Biologists observed that male crickets on Kauai and Oahu no longer sing. This is due to mutations in their wings, different on the two islands, but both with the same result. Over 20 generations crickets with these wing mutations survived and procreated while the male crickets without the wing mutation all but disappeared. Why? the biologists asked. The answer was that the singing male crickets attracted a species of fly that sprayed baby maggots onto the singing cricket’s back. The maggots burrowed into the cricket to feed. Thus killing the cricket. Biologists see this as more evidence that evolution is a natural process that continues to this very day.21
what’s the truth about colon cleansing? On most issues we can find seemingly credible sources presenting substantially different information. We become confused about what to believe. And if we are unable or unwilling to evaluate the arguments and reasons being presented, we might find our- selves wasting our money or backing the candidate who does not have our interests at heart. But a strong critical thinker sees it as a challenge when two apparently credible sources present highly divergent information: Which is closer to the
Group Exercises
Create your own examples of fallacies: Write two falla- cious arguments exemplifying each of these six errors
• The Erroneous Generalization Fallacy • The Playing with Numbers Fallacy • The False Dilemma Fallacy • The Gambler’s Fallacy
• The False Cause Fallacy • The Slippery Slope Fallacy
bedbugs and cold days in August: Evaluate the bedbug example and the San Francisco in August weather exam- ple. In each case ask:
truth? If selecting an academic major based on faulty informa- tion about potential future earnings is not bad enough, mak- ing personal health care decisions based on faulty information and weak arguments only adds to one’s problems. A service increasingly offered by spas and clinics that seems to be grow- ing in popularity is colon cleansing or colonic hydrotherapy. Lots of colon cleansing products are marketed with celebrity endorsements. The arguments and reasons in support of colon cleansing include enhancing personal well-being, weight loss, and flushing bodily toxins. But there are reasons why colon cleansing is not recommended—for example, that the process itself can cause internal injuries and that its alleged benefits cannot be demonstrated.
You be the judge. Research the reasons given for and against the practice and evaluate them. Figure out which side in this issue is closer to the truth. Search “Colon Cleansing” for spa ads and claims about its advantages. For the other side see, for example, “The Dangers of Colon Cleansing,” published in the Journal of Family Practice. This is not a 50/50 issue. As compared to those urging caution, those promoting a non-essential service, activity, or prod- uct have the greater burden. For they must prove that we ought to do what we need not do.22
SHARED RESPONSE
More Than Just a Couple of Cases
To evaluate the logical strength of probabilistic generalizations, we need to do more than find one or two counterexamples. We must, instead, examine whether the sampling of cases reported in the premises is adequate to support the probabilistic inferences that are drawn. This means asking four questions and finding satisfactory answers to each of them.
•
• • •
Was the correct group sampled? Were the data obtained in an effective way? Were enough cases considered? Was the sample representatively structured?
In an earlier shared response exercise, you evaluated the argument that pseudo mature young teens are more likely to experience a variety of problems as young adults. There we asked if one counter example invalidated the probabilistic generalization. Re-evaluate the generalization in light of these four questions. Comment respectfully on other peoples’ shared responses.
• • • •
Was the correct group sampled? Were the data obtained in an effective way? Were enough cases considered? Was the sample representatively structured?
When the premises do not provide enough information for a satisfactory answer, explain what information one would have to find, as we did when we noted what would be needed for the sample of 435 to be considered representa- tive of the population of people over the age of 60.
How should the united States conduct the 2020 census?
There are two ways to conduct a census. Contact everyone
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and gather the data being sought, or generalize from well- structured representative samples. This group project invites you to evaluate the methodology used by the U.S. govern- ment for conducting the 2010 Census. You are invited to make recommendations for improving that methodology. If you come up with some good suggestions, offer them to your Congressional representatives and the U.S. Census Bureau. Begin your investigation at the U.S. government’s census website census.gov. Navigate to the methodology page.
To fully evaluate the methodology and make rea- sonable recommendations, your group will want to con- sider first and foremost the logical strength of the two
Bonus Exercise
the debate over the “Public option”
At the end of the July 24, 2009, episode of HBO’s Real Time with Bill Maher, Maher argues in support of the “pub- lic option” to be included in the health care reform legisla- tion, which at that time was being fiercely debated.
The “public option,” a provision not included in the final Obamacare (Affordable Care Act) law, would have given tens of millions of uninsured and underinsured Americans the option of purchasing health care insurance at an affordable price. Either the government would provide the program through a not-for-profit agency, or the legislation would permit the establishing of co-ops. Maher’s barbed state- ments included these: “If conservatives get to call universal health care ’socialized medicine,’ I get to call private, for- profit healthcare ’soulless, vampire bastards making money off human pain.” “I would love to have some journalist ask a Republican who talks about socialized medicine: If it’s so awful, how come it’s what we have for our veterans?”
Locate and watch Bill Maher’s commentary in epi- sode 161 of Real Time with Bill Maher. In as fair-minded and nonincendiary a way as possible, present his arguments in support of the “public option.” Map his reasons using the techniques presented in the chapter, “Analyze Arguments and Diagram Decisions.” Then evaluate his arguments using the four-test process presented in the chapter,
alternatives (count absolutely everyone possible vs. make estimates based on samples.) When considering the sam- pling alternative, keep in mind the importance of sample size and representative structure. For both alternatives, keep in mind the question of the method of gathering data. For example, going door to door will ensure that homeless Americans are systematically excluded.
Other considerations that may weigh on your ulti- mate recommendations: You should consider the cost (money and time) of the two alternatives, the political consequences of each, and the social value associated with enlisting volunteers in an effort of national scope.
“Evaluate Arguments: Four Basic Tests.” Remain objec- tive. Resist permitting your personal views on the subject to interfere with the objectivity of your analysis of Maher’s views or your evaluation of his arguments.
