SOLUTIONS TO EXERCISES
SOLUTIONS FOR CHAPTER 1
1.1 Issues to think about: Is a single example about bees enough to draw a conclusion about human reasoning? Is the persistence of the bees a reflection of intelligence and logical thinking?
1.2.a Critical thinking is not solely a matter of finding fault. It also includes finding good reasons to support a conclusion. Finding fault can also be constructive if we learn from the mistake.
1.2.b First of all, it is debatable whether relationships and connections are more important. Perhaps it depends on the individual and the line of work? Also, even if these things are more important, does it follow that critical thinking is not useful? Critical thinking can help you build better relationships and connections.
1.2.c Many important decisions should not be made hastily and critical thinking is crucial. See Chapter 22. Also, even quick decisions can improve with good critical thinking.
1.3 This longer definition provides a lot of detail, but it fits with the simpler definition of critical thinking in this book. Thinking clearly and rationally involves the kind of activities and values that are listed in the quote.
1.5 As you might guess, the first four are good attitudes and the next four are not. They are meant to help you reflect on your own thinking process. You can also think about whether any of these traits are present in the behavior of the people around you. If so, how do these traits affect their thinking and decisions?
SOLUTIONS FOR CHAPTER 2
2.1.a The second statement is stronger. Being good requires more than just avoiding evil deeds.
2.1.b The first statement does not entail the second. You might like lobsters as pets or you think they are cute, but it does not follow you want to eat them.
2.1.c The food might be made from ingredients that already contain preservatives and no additional ones need to be added. The first statement is then true but the second one is false.
2.1.d The second statement implies that one should not say anything at all. The first statement has no such implication. Note that the first statement does not say that if the police are not here, one can say anything. Why?
2.1.e The first statement gives the permission but does not require that you kiss the bride. The second one does.
2.1.f The second statement is consistent with the possibility that some people are sick. But not the first one.
2.1.g They are actually equivalent but just formulated differently. See the diagram below where the left circle represents good things and the right circle represents cheap things. The overlapping area would be things that are both good and cheap. Both sentences are saying that there is nothing in this group. So in a sense they do have the same meaning.
2.1.h Note that the second sentence does not imply there are many restaurants. It can still be true if The French Laundry is the only restaurant left in the world.
2.3 Here is the annotated version: Harry’s abilities must be seen to be believed (since you won’t believe that he is so incapable). The amount of material he knows will surprise you (how can he know so little?). It would be very hard to find someone as capable as he is (everyone else is more capable). He has left a deep impression on all the teachers in the department (they all remember his dismal performance). You would be fortunate if he works for you (since he normally fails to work at all).
2.4.a The students found it difficult to understand the long explanation given by the teacher.
2.4.b The tense situation turned explosive earlier this month when the international administration ordered a raid on Herzegovacka Bank. The administration was put in place after the 1995 peace accord that ended the war in Bosnia.
2.4.c We can give away the four empty bamboo baskets in the basement to charities. (Should we leave out empty?)
2.4.d Anaïs bought a large and red Toyota minivan.
2.4.e Apple designed a special laptop with a case made from a single piece of aluminum.
SOLUTIONS FOR CHAPTER 3
3.1.a Precising.
3.1.b Reportive.
3.1.c Persuasive.
3.1.d Reportive.
3.1.e Precising.
3.2.a You can hate yourself. It is also possible to hate someone without wanting to harm them or ruin anything.
3.2.b Ungrammatical. Biology is a subject or discipline, not a situation or a period of time.
3.2.c Circular definitions.
3.2.d Poetic, but as a definition too metaphorical. Also, loving someone (for example, one sidedly) can be a painful rather than a happy experience.
3.2.e First, you can love yourself. Second, two people can love each other but not being very good at doing all the things being listed, such as a child loving her parents.
3.2.f You can be angry at yourself.
3.2.g A bomb might be designed not to hurt people but destroy buildings.
3.4 They are both cases of the etymological fallacy.
3.5 One main problem is that the information might be publicly available and has been released legally. Trading based on such open information is surely not insider trading.
3.6.a Domestic violence = Any violence between current or former partners in an intimate relationship. The parts that are left out are further clarifications.
3.6.b The second definition seems to rule out isolated acts of violence because it requires that domestic violence forms a pattern. This is too strong. But it is wider than the first definition in including violence within family-type relationships that might not be “intimate.” This might be better if we want to include violence between family members, such as between siblings or parents and children.
3.7.a Teaching sex education at school might make some students unhappy but it is not sexual harassment.
3.7.b Sexual harassment might not involve the offer of any benefit and is not restricted to unwelcome advances from a superior.
3.8 First, what is a receptacle if not a container? Second, it is not so clear what count as a wall. A container that consists of half a sphere does not seem to have “a plurality of walls,” but it is nonetheless a container.
SOLUTIONS FOR CHAPTER 4
4.1.a True.
4.1.b False.
4.1.C True.
4.1.d False.
4.1.e True.
4.2.a True.
4.2.b True.
4.2.c False.
4.2.d False! Hint: What if all the students were not intelligent?
4.2.e True.
4.2.f True.
4.2.g False.
4.2.h True.
4.2.i False.
4.2.j True.
4.2.k False.
4.3.a Sufficient condition.
4.3.b Necessary condition.
4.4.a Exclusive but not exhaustive. Inflation can remain stable.
4.4.b Exclusive but not exhaustive.
4.4.c Assuming it is possible to be both happy and sad (about different things) at the same time, they are neither exclusive nor exhaustive.
4.5.a Choice 2.
4.5.b Choice 5. We are not told what their starting salaries were.
4.5.c Choice 3. Elia ate 4 and Maddalena ate 2.
4.6 The argument starts with the claim that studying is necessary for passing, and mistakenly infers that it is sufficient for passing.
SOLUTIONS FOR CHAPTER 5
5.1.a Is everyone talking about the photo or just the model? Here are two reformulations: (1) Here is a photo of a model. Everyone is talking about this model. (2) Here is a photo of the model. Everyone is talking about this photo. Try to rewrite the other sentences in the same exercise so that they are no longer ambiguous.
5.1.b Is it the car or the tree that is in front of the house?
5.1.c During the merger, the new CEO promised to avoid layoffs; The new CEO promised to avoid layoffs as long as the merger is in progress.
5.1.d How many puppies are being sold in total? 10 or 11?
5.1.e Brains is ambiguous. It might mean the organ or talented people.
5.1.f Being able to think clearly is going to help us learn better; Clearly, being able to think helps us learn better.
5.1.g Are we talking about students who play video games often, or are we saying that students who play video games are the ones who often have poor grades?
5.1.h Do you have to bring your identity card with your passport?
5.1.i The word bank is ambiguous in English, but not in this sentence since there is no reason why the speaker has suddenly shifted the meaning of the word.
5.2.a A comedy is a story or a performance where lots of funny things happen.
5.2.b Civil engineering is a discipline or profession and not a person so it cannot have any “experience.” Perhaps the author meant “the experience of civil engineers” or “the history of civil engineering”?
5.2.c The students in my class are smarter than those in the other classes.
5.3.a Talking to Ann gave Peter the idea to build a house.
5.3.b Our current educational system assumes that students enjoy lectures.
5.4.a Incomplete meaning — higher than whom?
5.4.b Ambiguous — Did Rita get the flu four days ago, or was the kid ill four days ago?
5.4.c Incomplete meaning — Better than what? More butter than what? Cookies from other people or the previous version?
5.4.d Ambiguous — Was the day of marriage also a sad day?
5.4.e Treating people differently is not sufficient for discrimination. The treatment has to be unjust or based on prejudice.
5.4.f Better for what purpose? Sometimes it is better to lie to patients about their medical condition because it might make their situation worse.
SOLUTIONS FOR CHAPTER 6
6.1.a The observation that the truth of a sentence depends in part on its meaning does not support relativism. Relativism denies that a sentence is objectively true even after we have fixed what it means and says.
6.1.b A difference in opinion does not amount to relativism, as long as some of them are right and those who disagree are wrong.
6.1.c If it is true that we never have direct access to reality (whatever that means) then that is again an objective truth. But objectivity is compatible with the formulation and development of theories being affected by culture and perspectives. It is just that the truth and falsity of a theory should depend on reality and is not a relative matter.
6.2 Only d, f, g and h are statements.
6.3 Analytic: f, i. Empirical: a, b, c, e, g. Value: d, h.
SOLUTIONS FOR CHAPTER 7
7.1.a The first and the third statements are equivalent, and they both entail the second statement, but not the other way round.
7.1.b The first statement entails the second one, but not the other way round.
7.1.c These statements are logically independent of each other. You can build a phone designed and launched by others, or you can just design it for another company. Or you can launch a phone built and designed by other people.
7.1.d The second statement entails the first, but the other way round. You fail to stay off the bridge if you run rather than walk across it.
7.1.e The first and third statements are equivalent.
7.1.f The first two are equivalent.
7.1.g Not logically equivalent.
7.1.h Yes.
7.1.i No.
7.1.j No. It is consistent with the second statement that Ronaldinho is famous for something other than being a soccer player.
7.1.k No. The second statement says that not everything is impossible. It entails that something is possible, but not that everything is possible, which is what the first sentence says.
7.2.a Can be consistent if new means “recently purchased.”
7.2.b Inconsistent.
7.2.c Consistent. The statements entail that he is not guilty.
7.2.d Inconsistent. If something is known then it must be true. It is the things we think we know that can be wrong. So we didn’t really know them.
7.2.e Inconsistent.
7.2.f Inconsistent. If you think human actions are free, which statement will you reject?
7.3.a Are the motherboards and memory chips also Intel ones?
7.3.b (a) Either I shall visit Sophie and you will visit Sandra, or he will visit Sonia. (b) I shall visit Sophie, and either you will visit Sandra or he will visit Sonia.
7.4.a It is not the case that hang gliding is dangerous.
7.4.b It is not the case that I am afraid.
7.4.c It is not the case that belching is polite.
7.4.d It is not the case that you are Einstein.
7.5.a Inclusive.
7.5.b Exclusive.
SOLUTIONS FOR CHAPTER 8
8.1.a A thunderstorm is coming. Therefore, you should stay at home.
8.1.b All Maoists are communists. All communists are Marxists. Therefore, all Maoists are Marxists.
8.1.c You can barely keep your eyes open. Therefore, you should not drive.
8.1.d If he wants to go out with me he would have called. He did not call me. Therefore, he is not interested in me.
8.1.e Not an argument.
8.1.f You might get hit by a car if you jaywalk. The police might fine you if you jaywalk. Therefore, you should not jaywalk.
8.1.g If the solution is acidic, the litmus paper would have turned red. The litmus paper has not turned red. Therefore, the solution is not acidic.
8.2 Something like the following: (Premise 1) Art students do not understand modern art in the beginning. (Premise 2) To understand modern art, one must study art history. (Conclusion) Art students must begin by studying art history.
8.3 The conclusion of the other argument is that there is no simple way to measure whether on balance religion has more positive or negative consequences. But the argument does not spell out explicitly why this conclusion follows. Presumably it is supposed to be obviously true.
SOLUTIONS FOR CHAPTER 9
9.1 All possible except the second situation.
9.2.a False.
9.2.b False
9.2.c True.
9.2.d True.
9.2.e False.
9.2.f True.
9.2.g False. False premises in a valid argument can give a true conclusion.
9.2.h False.
9.2.i True.
9.2.j True.
9.2.k True.
9.3.a Not valid.
9.3.b Not valid.
9.3.c Not valid. Maybe Angelo is not the only cheap restaurant.
9.3.d Valid.
9.3.e Not valid.
9.3.f Not valid.
9.3.g Not valid.
9.3.h Not valid.
9.4 There are lots of things we might say about this passage. But in light of what we have discussed in the chapter, one point that is of special relevance is that embracing non-duality seems to be self-refuting. To embrace non-duality rather than duality is to make a distinction, and this is inconsistent with giving up all distinctions!
9.5 When we say “If P then Q. Q. Therefore P.” is not a pattern of valid argument, we are saying that not every argument of that form is valid. But this does not rule out the possibility that some arguments of that form are indeed valid—for example, when Q is identical to P, we have “If P then P. P. Therefore P.” This is circular but valid. Compare the situation with modus ponens, in which every argument of the the same form is valid.
SOLUTIONS FOR CHAPTER 10
10.1 Although Holmes suggests that each step of his reasoning “clearly” follows from the previous one, the whole chain of reasoning is inductive in character since the intermediate conclusions do not appear to follow deductively from earlier assumptions. For example, Holmes assumed that the doctor injured his arm while serving in the tropics. But this is just a guess, and he could easily have been wrong.
10.2.a It will still be valid and sound.
10.2.b Not necessarily, and here is an example. Argument #1: Tom Thumb suffers from dwarfism. Therefore, Tom Thumb does not have above-average height. Argument #2: Tom Thumb is 20 years old. Therefore, Tom Thumb is over 1.2 meters tall.
10.3.a Not valid, since it is a prediction about the future based on past experience. An example of a premise that would weaken the argument: But for some reason there are a lot more visitors to these resorts this year.
10.3.b Valid.
10.3.c Not valid.
10.3.d Valid.
10.4 Both statements 2 and 3 would make the argument stronger, but presumably statement 3 would give the argument a higher inductive strength. Whereas statement 1 will lower the inductive strength.
SOLUTIONS FOR CHAPTER 11
11.1.a Gold is a metal. All metals conduct electricity. Therefore, Gold conducts electricity.
11.1.b God does not exist. If there is no God, life has no meaning. So life is meaningless.
11.1.c Noam is a thinker. A person is either a thinker or a doer, but not both. So Noam is not a doer.
11.1.d Hidden assumption: If x is heavier than y and z cannot lift x, then z cannot lift y. Or equivalently: If a person cannot lift an object, that person cannot lift anything heavier than that object.
11.1.e The whole building collapsed. There were people in the building when it collapsed. If there were people in the building when it collapsed, then probably many of them died. So probably many people died.
11.1.f This is normally a fallacy, unless it is further assumed that there is no other way to become a member.
11.1.g I ate ketchup today. Ketchup is made of tomatoes. Tomatoes are fruits. If I ate something made from a fruit, then I ate fruit. Therefore, I ate fruit today.
11.1.h There are different ways to formulate the hidden premises. This is a suggestion: (1) The majority of criminal activities have to do with selling or possessing illegal drugs. (2) Imposing the death penalty on selling and possessing illegal drugs is effective in getting rid of these activities. (3) We should impose the death penalty on a crime if the crime is a major source of criminal activities and the penalty is effective in eliminating these activities.
11.2.a 
11.2.b 
11.3.a 
11.3.b Further hidden premises might be added to the argument map below. Do you know where they should be?
11.4.a 
11.4.b It is possible that your version is different.
11.4.c 
11.5 
SOLUTIONS FOR CHAPTER 12
12.1.a True.
12.1.b True. The premises can still be implausible.
12.1.c True.
12.1.d True.
12.1.e True.
12.1.f True.
12.1.g False.
12.2.a Not question begging.
12.2.b Yes, question begging.
12.2.c Question begging, since your favorite is just what you like best.
12.2.d This is not a circular argument, because you might not always order your favorite—for example, you order lobster ice cream not because you like it but just to see what it tastes like.
12.3.a (1) It might be argued that the existence of identical twins is a kind of natural cloning. (2) Just because something is unnatural does not mean it is wrong. (3) Cloning gives us valuable scientific knowledge and medical technology so it should not be prohibited. (4) Name your favorite unnatural activity.
12.3.b (1) Attack the premise: Not all scientific theories are given up after a while. Scientists continue to maintain that the Earth is smaller than the Sun and that there are atoms and molecules. (2) Attack the reasoning: Scientists might change their theories because they have come up with more accurate ones. So the fact that theories change does not imply that we should not rely on them. (3) Attack the conclusion: It is unwise not to rely on scientific advice about many safety issues, such as whether certain things are poisonous or whether a building is safe.
12.3.c (1) Attack the premise: Some students learn quickly and won’t make mistakes. (2) Attack the reasoning: The conclusion does not follow because punishment might have other benefits. Or they might make fewer mistakes even if they still make them. (3) Attack the conclusion: Punishment leads to better discipline and fewer big mistakes so it is useful. (4) Give an analogous argument: Putting prisoners in jail is useless because people will always commit crimes.
12.4.a There are two issues to consider: First of all, what do we mean by low? Is this measured in absolute terms (for example, less than 15%) or in comparison with taxation rates in other countries? Second, the argument assumes that the benefits are good enough to outweigh any disadvantages that might arise, such as less government income.
12.4.b Some main assumptions: (a) There was only a finite rather than infinite amount of radioactive material. (b) Radioactive material started existing for as long as the universe has existed. (c) When radioactive material has disappeared, new radioactive material will not come into existence again.
12.4.c Some relevant assumptions: (1) The amount of Indira’s donation to a party reflects the strength of her preference. (2) She is going to vote in according to her preference. (3) She did not donate similar or larger amounts of money to other parties.
SOLUTIONS FOR CHAPTER 13
13.1.a A simpler alternative explanation is that he had a stomachache simply because he ate too much, and there was nothing wrong with the sundae. Or perhaps there was something wrong with the other food he ate. It could just be a coincidence that the stomach trouble started after eating the sundae.
13.1.b A few issues: (1) There is no way to check the credentials of this doctor. (2) The doctor probably received some benefit for appearing in the advertisement, so this is a potential source of bias. (3) The doctor did not say why she recommended the vitamins—for example, could it be just for the taste? (4) Even if it is a sincere recommendation because of the health benefits of the vitamins, this is just one recommendation and we need to see what other experts think.
13.1.c Relevant issues: (1) What is the percentage of people who go shopping by driving? How many of them are ordering online instead? No data are given here. (2) Will the delivery of products also involve a significant amount of fuel consumption? (3) Even if online shopping decreases the consumption of petrol, will other activities end up consuming more petrol given the growth of the economy?
13.1.d One problem is that the conclusion is only supported by a single case. But the more serious problem is that the rashes could have been the result of an allergic reaction to the makeup. When the woman stopped using makeup, her condition improved but it might have nothing to do with the crystal.
13.1.e The research cited is real and comes from Rauscher et al. (1995). But notice that the experiment was conducted on college students and not children. Also, although the effect was present immediately after the listening experience, there was no indication that the effect will persist or be permanent. (In the actual experiment the effect disappears after about 15 minutes.) So there is not enough evidence to show that listening to Mozart will make kids smarter and develop better. Maybe the students were bored with the other two sound recordings and this affected their performance. Note that the result does not tell us whether other pieces from Mozart or other composers will also have this effect.
13.2 Here are just a few suggestions. Think about the kind of evidence you would need to determine if any of them is correct. (1) A greater number of less capable students are taking the test, dragging down the average. Maybe in the past only the top universities require the test, and there were more top students among the test candidates. (2) Presumably the questions in the test change from time to time. Maybe the test is getting more and more difficult? (3) Perhaps there have been changes in the administration of the test which affect the statistics? For example, maybe in the past there were more people taking the test more than once. If there are fewer of these people, this might change the average score.
13.3 There are different ways to test them. For example, we can put two of these people together where there might be a ghost, and ask them to report independently the characteristics of the ghost. If their descriptions agree, that would be confirming evidence. Or we can try to get them to communicate with the ghost and see if they can obtain information that cannot be explained any other way. So science is not necessarily against the existence of supernatural phenomena.
13.4 One explanation is that the man was just lucky, but this is not too likely. The simpler and more plausible explanation is that the man has got all 20 numbers written down in various places on him, and depending on what his audience comes up with, he reveals the appropriate number, for example, on his left foot, on a piece of paper in his right pocket, or on his left wrist. To test whether this is the case, we can search him beforehand or ask him to guess the number from a much larger range or have him write down beforehand the number he is going to implant in the audience’s mind.
13.5.a It is indeed wrong to criticize a theory on the grounds that there is no proof that it is correct, if by that we mean the theory lacks conclusive evidence that entails the theory. But it would still be rational to accept a theory if it had plenty of evidence indicating that it was highly likely to be true. This is why it is also wrong to say that scientific theories that have not been proven true are accepted solely on the basis of faith, because these can be theories that have plenty of supporting evidence and can offer useful predictions.
13.5.b A theory does not fail to be scientific just because it does not offer 100% accurate predictions. It could be that the theory is fine, but it is difficult to get precise data to make predictions in conjunction with the theory. A scientific theory can also make statistical and probabilistic predictions without being able to predict every single event accurately.
13.5.c It is wrong to think of science and logic as completely distinct. Science also relies on Logic including deduction. Scientists need logic to discover the implications of their theories, generate predictions, and check for inconsistencies, among other things.
SOLUTIONS FOR CHAPTER 14
14.1.a The method of concomitant variations.
14.1.b The method of difference.
14.1.c The joint method.
14.1.d The method of difference.
14.2 Situation 1.
14.3.a None can be applied, since there is no single cause common to all situations in which E occurred. It could be that E has multiple or complex causes, or its cause is not among the list here.
14.3.b B, according to the joint method.
14.3.c C, according to the joint method.
14.3.d D.
14.3.e C.
14.4.a True. Given the more general joint method, there is no need for the method of agreement or the method of difference.
14.4.b True.
SOLUTIONS FOR CHAPTER 15
15.1.a (1) Eating breakfast enhances cognitive abilities. (2) Families in which children are not given breakfasts are less likely to provide a good environment for the children’s cognitive development.
15.1.b (1) Sleeping more causes more illnesses. (2) People who are less healthy and more likely to die tend to sleep more.
15.1.c (1) Drinking milk increases the chance of getting cancer. (2) Countries, in which people drink more milk are richer and provide better healthcare and the citizens are less likely to die prematurely. They are more likely to die from cancer due to a longer lifespan.
15.1.d (1) Smoking causes neurophysiological changes that make people suicidal. (2) People who are depressed or stressful are more likely to have thoughts about suicide and also more likely to take up smoking.
15.1.e (1) Smoking impairs attention and learning and so leads to lower grades. (2) Students with learning difficulties or personal problems are more likely to smoke, and their problems cause them to get lower grades.
15.1.f (1) Using Facebook somehow impairs those skills that are useful for getting good grades. (2) The better students spend more time studying and less time on Facebook.
15.1.g (1) Genuine smiling causes good physiological effects that lead to longevity. (2) Smiling and longevity are the common effects of health and a positive personality.
15.1.h (1) Jogging improves one’s mood through some neurophysiological mechanism. (2) People who suffer from depression are less inclined to go jogging.
15.1.i Since the disorders happened later, it would not be plausible to say that the disorders cause them to use drugs and alcohol! One explanation is that drugs and alcohol affect the brain and cause psychiatric problems. Another explanation is that there are genetic factors that underlie both.
15.2 The first and third ones.
15.3 The correlation could be accidental or it might be a case of side effect causation.
15.4.a Stepping on the toe in itself is not sufficient for bleeding, but together with other conditions (sharp heel, high pressure) they are sufficient to cause bleeding. But the whole set of sufficient conditions is not necessary for bleeding since you can cause bleeding by cutting instead.
15.4.b For example, Akiko’s mother giving birth to Akiko is a necessary part of a whole set of conditions that lead to Bella’s bleeding, but we do not want to say that the birth caused the bleeding.
15.5 There are lots of examples, such as a child receiving a present and this makes her happy. Receiving a present is not sufficient for happiness because she must also like the present. It is not necessary because she can also be happy when she plays with her friends.
SOLUTIONS FOR CHAPTER 16
16.1
16.2
SOLUTIONS FOR CHAPTER 17
17.1.a Readers of Playboy (and those willing to be interviewed) might not be representative of the male population as a whole. One might wonder whether these subjects are more likely to exaggerate when being interviewed.
17.1.b This inference is not unreasonable if the sample is a representative one. But this might not always be true—the soup might need stirring after ingredients have just been added.
17.1.c Not a good argument. It confuses the relative increase in risk (the 100% in the first sentence) with the absolute risk (the second one).
17.1.d The sample is not as representative as one might like, since the men were interviewed outside a toy shop on a Sunday. They were more likely to be family-minded people.
17.1.e There are many reasons why students skip lectures, such as time-tabling issues. But the other problem with the argument that has to do with statistics is that no information is given about student number. A larger class will have more students skipping, and it is the ratio that should be compared, not the absolute number.
17.1.f There are no data about the sample size and the number of companies surveyed. But the more serious problem is that the data cited are about only a correlation between two ratings by the respondents. There is no evidence of the direction of causation, and in fact no data at all about the actual qualities (for example, the degree of creativity) that the ratings are supposed to reflect.
17.1.g This question concerns a topic we have not discussed in this chapter. If average means “arithmetical mean”, then a $9 average is compatible with there being lots of very expensive games and lots of very cheap ones. So it does not follow that most of the games are under $10. To learn more, go online and search for “mean”, “median” and “mode”.
17.1.h Whether it is worth the higher price depends of course on lots of things: how rich you are, whether there are side effects, and so on. But it might also be useful to check the reduction in risk in absolute terms. A reduction of the heart attack rate from 2.5% to 2% is a 20% reduction, but the 0.5% difference is not so impressive any more.
17.2.a Yes.
17.2.b No. Some people might have no opinion. Others might approve or disapprove, but not strongly.
17.2.c “Up 6%” is a comparison, “at 6%” is not.
17.2.d GDP still increases if GDP growth is weak, but not when it is declining.
17.3.a There is no vertical scale, and it does not seem to start from zero. According to the figures shown, the number of people who disagree is only about 18% more than the number of those who agree. But the difference in height conveys a very different and misleading impression.
17.3.b Again there is no vertical scale. Also, the width of the second bar has changed for no reason. The profit has nearly doubled, which corresponds to the difference in height, but the unmotivated change in width gives the inaccurate impression that the profit has increased by a lot more than that.
17.3.c The vertical scale is strange and as a result gives the misleading impression that the increase in failure rate has slowed down, when in fact the opposite is true:
17.3.d The number of households has roughly doubled, which corresponds to the difference in height. But the difference in area in the two symbols gives the impression that the increase might be a bit more than that.
17.3.e No scale and no unit, and it is not clear whether the difference in width in the column means anything.
17.3.f Problem 1: The symbols do not uniformly all represent the same number, which makes comparison more difficult. Problem 2: The sizes of the symbols do not match the number they represent—for example, the cat is larger than the bird but they both indicate 5.
17.4 This is a bit hard to say. The two charts are the same except for the origin of the vertical axis. The second chart looks more impressive because the growth in sales seems exponential, but at the same time it also makes people think that the first few months are comparatively dismal.
17.5.a This is the gambler’s fallacy.
17.5.b The reasoning is correct.
17.6 This exercise is adapted from a famous experiment by psychologists Amos Tversky and Daniel Kahneman. The first choice is an irrelevant decoy. What is crucial is that the third choice cannot be more probable than the second. But many people rank the third choice as more probable than the second, which is the conjunction fallacy. The third sentence is a conjunction of the second sentence plus an extra condition. So the third sentence must have a lower probability than the second one (unless the extra condition is certain, in which case they have the same probability).
SOLUTIONS FOR CHAPTER 18
18.3 It is tempting to say that it is a normative statement because it has the word good in it. But normative statements are supposed to have implications about what the world ought or ought not to be like, or they tell us something about which things are valuable or undesirable. By these standards the statement is not normative. It does not say anything about whether solving mathematical problems is a good or valuable thing. (Compare: He is good at murdering innocent people.) We might perhaps regard it as a factual statement that is rather vague. The statement tells us that he is generally accurate in coming up with solutions to these problems, but it is not clear exactly how accurate he is. This is like the statement “he is tall.” It is an empirical or factual statement, but it is not very precise either.
18.4 Contextualism and absolutism are about specific types of behavior. You can consistently be a contextualist about an action X and an absolutist about a different action Y. But it is inconsistent to accept both contextualism and absolutism about the same action.
18.5.a If a person promised to do something, he should do it.
18.5.b A person has the right to do whatever he or she wants within her own property, even if it causes annoyance to people outside.
18.5.c A person should not take something that does not belong to him or her without the owner’s permission.
18.6.a Not equivalent, and if moral duties do not conflict with each other, then the second statement entails the first.
18.6.b Equivalent.
18.6.c Not equivalent. The second statement is consistent with it being up to you whether to disclose, but not the first one.
18.7.a A very straightforward invalid argument. Compare: Cats are animals. But dogs are not cats. So dogs are not animals.
18.7.b The first argument is not valid because it equivocates between two meanings of right. Having the right to do something in the sense of being entitled to do it does not entail that it is morally right to do it (that it ought to be done).
18.8 Hint: What about important matters relating to one’s own privacy?
18.9 It seems to be a consistent moral relativist position. David did not say that everyone ought to respect other points of view. If so that would be inconsistent. He said this is only what he should do.
SOLUTIONS FOR CHAPTER 19
19.1.a The quote is from Epstein (1999). Agreed by whom? And why must a fallacy be unrepairable? An argument relying on very weak evidence is a fallacy but it can become a good argument if more evidence can be provided.
19.1.b The quote is from Rudinow and Barry (2007). We have argued that a fallacy need not be an inference or argument. One might also object to the claim that fallacies tend to appear to be reasonable because they are inferences. Circular inferences are fallacious but they need not appear to be reasonable.
19.1.c This definition is from Hurley (2006). The author includes complex question and false dichotomy as fallacies, but neither is an argument.
19.2.a Maybe the cup has been lost already, or maybe it is just hidden somewhere. But this need not be a fallacy if the person making the argument has good reason for ruling out these and similar possibilities.
19.2.b False dilemma.
19.2.c Something not being proven to be false is not a good enough reason to think that it is true.
19.2.d This is the fallacy of composition. The tasty ingredients might not combine well with each other.
19.2.e Fallacy. People drive more during the day.
19.2.f Not a fallacy, but a valid argument with false premises.
19.2.g It is a fallacy and not a good argument. Maybe those Facebook friends of yours who are idiots are not my Facebook friends.
19.2.h Fallacy. There might be many other better explanations of why most scientists are men.
19.2.i Fallacy of composition.
19.2.j Not a fallacy.
19.2.k If something is irreversible how can it change? This quote is often attributed to former U.S. Vice President Dan Quayle.
19.2.1 This seems like a case of fallacy of inconsistency. If the educational system is already very efficient, it will be impossible to have more schools and teachers without putting in extra money.
19.2.m Not a fallacy, unless there is good reason to think that other alternatives have been ignored.
19.3 Formal fallacies are fallacies that can be defined purely by their form or logical structure, such as denying the antecedent and affirming the consequent. Informal fallacies are fallacies that are defined not by their logical structure but by their content—for example, appeal to pity or confusing correlation with causation.
SOLUTIONS FOR CHAPTER 20
20.3 We can be humble even if we have an accurate picture of our own ability, such as knowing our actual weaknesses and recognizing that we all make mistakes, that nobody is perfect, and that we can learn from other people and improve ourselves further.
20.4 This is a test of consistency in risk assessment. Whatever your answers were, they should add up to 100%, because either you have an accident when you travel, or your travels will be accident free. But given that these two questions were placed so closely together in a chapter about cognitive biases, you might be more alert and find this too obvious. But many people do get this wrong.
20.5 In one experiment, students who answered this question gave an average estimate of about 2,250. But some other students were asked to solve the same problem, which is formulated as follows:
The average answer this time turned out to be 512! The explanation is that when the students did not have time to do a complete calculation, they looked at the first few numbers and computed a rough estimate and made some adjustments. Their answers were therefore biased by the presentation of the problem. By the way, the correct answer should be 40,320.
20.6 There is indeed a correlation. People who watch more violent TV are more likely to believe that the world is a violent place. This fits in well with the idea of availability discussed in the chapter. See Gerbner et al. (1980).
20.7 When you think “I exist,” that is sufficient to make it true since you cannot think without existing. Similarly, when you think “I am thinking about lunch,” your very act of thinking makes it true that you are thinking about lunch! There are also cases where collective wishful thinking might make something true–if enough people think that stocks will go up, they might end up pushing the market higher, even if this is divorced from the financial fundamentals. It is of course possible that things will come crushing down eventually.
SOLUTIONS FOR CHAPTER 21
21.2.a No. Just an analogy.
21.2.b Yes.
21.3.a First, the fetus has a greater potential to develop into a human being. Second, depending on the stage of development, the fetus might be able to have conscious experiences and perhaps even feel pain.
21.3.b At least two differences: Taxation repays some of the money that the government spends on basic services provided to the society. Also, taxation can have a redistributive element if some of the money goes to people who are less fortunate.
21.3.c One significant difference is that weather reports do not affect the weather, but the contents of magazines can affect what people think and do.
SOLUTIONS FOR CHAPTER 22
22.1 Here are some of the questions you should ask: How serious is the flu? Is it very contagious? How effective is the vaccine if it is not 100%? Is it expensive to get one? How serious are the allergic reactions? Are they life threatening? Which people are more likely to get the flu or the allergic reaction? How many people have taken the vaccination?
22.2 If you read the choices carefully, you might notice that program C is just a reformulation of program A, and D a reformulation of B. So ideally your choices should be the same in both cases to be consistent. But psychologists have found that many people pick A instead of B, and D instead of C. The usual explanation is that people generally are risk aversive when it comes to gain (hence preferring A to B), and risk seeking when it comes to losses (preferring D to C). But the experiment also illustrates the power of framing—people can make very different decisions in regard to the same problem depending on how the problem is formulated.
22.3 Only the first example.
SOLUTIONS FOR CHAPTER 23
23.2.a Some options: Get some advice from friends or see a counsellor. Meet up less regularly.
23.2.b One possibility: Make the system more efficient so that savings can be used to build more prisons.
23.3 Thinking about the problem abstractly might seem difficult, but the solution is very easy if you represent it correctly with a diagram. Start with a diagram showing the altitude of the hiker at various times on his way up. It might look something like this:
The diagram for the descent might look like this:
If you superimpose the two diagrams, it is easy to see that there must be at least one point where the two curves intersect. It does not matter how fast the hiker was going or whether he stopped more than once.
This is an illustration of how representing a problem in the right way—using the appropriate visualization aid—can make the problem easier to solve. This is why changing perspectives is so crucial for creativity.
SOLUTIONS FOR CHAPTER 24
24.1
Many people drawing lines only within the area circumscribed by the dots. But the puzzle does not say the straight lines cannot extend outside the dots, and in fact the solution requires you to do so. When we solve problems we often have implicit assumptions about what might or might not be feasible, and what the solution might look like. We need to ensure that these assumptions are not unfounded or else they stop us from discovering the more innovative and effective ideas. This is why many people say that creativity involves thinking outside the box, breaking away from self-imposed constraints.
24.2.a Hint: The lines have to be very long, and remember that the lines do not have to go through the center of the dots.
24.2.b This is somewhat a trick question admittedly, but it can be done if you tear the page out and roll it up!