PHIL 105 Lesson 7

Indicate which explanatory virtue is the main one that is lacking from this explanation: My car won't start today because it is mad at me for driving it so much.

Conservativeness. The claim that cars get mad conflicts with well-established knowledge. Only living things get mad, but cars are not alive. This explanation is also not deep if it raises the further question of why a car would get mad at its driver for driving it so much. However, that question never gets raised because cars cannot get mad, so the main problem is the lack of conservativeness.

Indicate whether the argument is deductive or inductive. Assume a standard context as described. Nothing tricky! Context: You and I want to go for a walk, but it is raining, and we do not want to walk in the rain. You ask me when I think it will stop raining. Then I say this sentence: "The sun is coming out, so the rain will probably stop soon."

Inductive. The word "probably" suggests that this argument is not intended as a valid proof of its conclusion. When an argument is valid, it is necessary—not just probable—that the conclusion is true if the premises are true. Thus, if an arguer says only that the conclusion is probably true given the premises, then that person does not intend the argument to be valid. This makes the argument inductive.

Imagine that you offer an explanation of some surprising event, and then someone criticizes your explanation by saying, "Your explanation conflicts with everything we know about biology." Which explanatory virtue is this critic claiming that your explanation lacks?

Conservativeness. An explanation is radical rather than conservative when it conflicts with well-established knowledge. Biology includes well-established knowledge. Hence, to say "Your explanation conflicts with everything we know about biology" is to say that it is not conservative. An explanation ought not to conflict with well-established knowledge, so it ought to be conservative in this sense. That makes conservativeness an explanatory virtue.

An argument that applies a generalization to a case is never strong when the percentage in the premise is very low.

False. A very low percentage can give strong evidence for a negative conclusion when the reference class is appropriate. Here's an example: Only 1 percent of F are G, and a is F, so a is probably NOT G. (Admittedly, this question was tricky, but I hope you get the point.)

Inferences to the best explanation are deductive.

False. Inferences to the best explanation are invalid and defeasible, as we saw in the previous two questions. That makes them inductive rather than deductive.

Statistics are irrefutable.

False. Some statistical generalizations from samples are reliable, but others are not. We need to learn to distinguish good from bad generalizations. That is the topic of the next lecture.

Indicate whether the following argument is deductive or inductive. Assume a standard context as described. Nothing tricky! Context: I order a cola drink at midnight. You comment that you never drink cola that late at night, because the caffeine in cola keeps you from sleeping well. I respond with this argument: "Cola drinks never keep me awake at night. I know because I drank a cola drink just last night without any problems."

Inductive. This argument is not valid and does not appear to be valid, so it was probably not intended to be valid. Moreover, it has the form of a standard kind of inductive argument—specifically, a generalization from a sample (to be discussed in later lectures). Here, the sample is a single case. Its form thus suggests that the argument is inductive.

Would the argument from analogy in Question 13 become stronger, weaker, or neither if we added that most of the cured rats were conceived on weekdays (because that is when lab technicians were around to enable conception), whereas most humans were conceived on weekends (when they had more free time)?

Neither stronger nor weaker. This difference between rats and humans is irrelevant, because the day of the week when an animal was conceived does not affect its biology or whether it can be cured with a certain drug.

Imagine that you offer an explanation of some surprising event, and then someone criticizes your explanation by saying, "Your explanation won't explain anything other than this particular case." Which explanatory virtue is this critic claiming that your explanation lacks?

Power (or Breadth). An explanation is more powerful or broad when it explains more things. Thus, to say "Your explanation won't explain anything other than this particular case" is to say that it does not explain many things, so it lacks power or breadth. In other words, it is narrow or ad hoc. An explanation ought to be widely applicable and not ad hoc.

Arguments from premises about a sample to conclusions about the whole class are inductive.

True. Arguments from samples to generalizations are invalid and defeasible, as we saw in the previous two exercises. That makes them inductive.

One explanation is better than the other when it has more of the explanatory virtues.

True. An explanatory virtue is defined as a feature of an explanation that makes it better as an explanation. Thus, explanations with more of these features are better.

The purpose of an inference to the best explanation is to justify its conclusion.

True. Inferences to the best explanation are based on explanations, but their goal or purpose is not to explain what was observed but, instead, to justify belief in the hypothesis that best explains what was observed. In the example in the lecture, when I observe that water is falling on my head, I infer that there must be a leak in the roof, because that is the best explanation of why I observe what I do—namely, that water is falling on my head. This inference is supposed to justify belief in the conclusion that there is a leak in the roof.

Arguments that apply a generalization to a case commit the fallacy of overlooking a conflicting reference class when another smaller reference class that was not mentioned in the argument has a very different (higher or lower) percentage of Gs that would support a conflicting conclusion.

True. The sentence in this question defines what the fallacy of overlooking a conflicting reference class is.

Inductive strength is defeasible.

True. To say that inductive strength is defeasible is to say that adding new premises can turn a strong inductive argument into a weak inductive argument. That is possible when the argument is not valid. The classic example is that many people observed thousands of swans throughout six continents and concluded that all swans are white. That was a decently strong inductive argument, because their sample was very large and diverse. But then they learned about black swans in Australia. As soon as they had that new information in their premises, they ceased to have any reason at all to believe that all swans are white.

The conclusion of an inference to the best explanation is supposed to explain an observation in one of the premises.

True. What is inferred as the conclusion in an inference to the best explanation is supposed to best explain the observation that needs to be explained in the premises. For example, if someone argues "This meat smells very bad, so it must be spoiled," then what is inferred is the hypothesis that the meat is spoiled, and that hypothesis is supposed to explain why the meat smells bad, as the premise says.

Suppose I argue that 90 percent of Fs in my sample are G, so 90 percent of all Fs are G. Then I observe more Fs in a different area and find that 90 percent of Fs in my new sample are also G. This new information makes my argument stronger than it was before.

True. When we combine the old sample with the new sample, we get a larger total sample. Larger samples give us more reason to believe the conclusion as long as the larger sample displays the same patterns that we observed in the smaller sample, assuming that the new sample that was added is independent.

Indicate whether the following argument is deductive or inductive. Assume a standard context as described. Nothing tricky! Context: Harold is accused of a burglary, but we know him and thought he was a nice person, so we do not know whether to believe that he is guilty. Then you give this argument. "If Harold were innocent, then he would not go into hiding. Since he is hiding, he must not be innocent."

Deductive. This argument is valid because its conclusion can never be false while both of its premises are true. To see this, just try to tell a coherent story where the premises are all true and the conclusion is false. You can't, so the argument is valid. Almost all arguments that are valid were intended to be valid. Hence, this argument was probably intended to be valid. That makes it deductive.

Indicate which explanatory virtue is the main one that is lacking from this explanation: Her flowers won't grow because something is wrong with them.

Depth. To say that something is wrong with her flowers raises the question of what is wrong with them, so this explanation is shallow rather than deep. You might think that this explanation also lacks falsifiability, because there is always something wrong with flowers that do not grow. However, there might be nothing wrong with flowers that do grow, and what is supposed to be explained here is why they do not grow instead of growing.

Deductive arguments always provide more reason for their conclusions than inductive arguments do.

False. Some inductive arguments (such as "The sun has risen every day for thousands of years, so it will probably rise tomorrow") provide very strong reasons for their conclusions. Some deductive arguments (such as "There is life on Mars, so there is life on either Mars or Saturn") provide very little reason for their conclusions, because there is very little reason for their premises. The former arguments provide more reason for their conclusions than the latter. Hence, some inductive arguments provide more reason for their conclusions than some deductive arguments do.

Every similarity between Earth and Mars provides some reason to believe that since there is life on Earth, there is also life on Mars.

False. Some similarities are irrelevant to life. For example, both Earth and Mars are bigger than Mercury, and both contain iron in their cores, but neither of these similarities is relevant to the question of whether there is life on Mars.

Arguments that apply a generalization to a case are intended to be valid.

False. Such applications are inductive, so they are not intended to be valid, and they are usually not valid. Even if 99.999999999999999 percent of F are G, and a is an F, it is still possible that a is not G; so an argument that concludes that a is G is not valid.

Arguments from premises about a sample to general conclusions about the whole class commit the fallacy of hasty generalization when the sample in the premises is biased.

False. The fallacy of hasty generalization is committed when the sample is too small, not when the sample is biased. A biased sample can be very large, and an unbiased sample can still be too small. To generalize from a sample that is too small but is not biased is still to commit the fallacy of hasty generalization.

Polls are always reliable.

False. The lecture gave several examples of polls that are unreliable because the sample was biased or too small or because the poll asked a biased question.

Arguments from analogy are used in art but not in science.

False. The lecture gives several examples of arguments from analogy in science.

Indicate which explanatory virtue is the main one that is lacking from this explanation: I fished here all day, but I did not catch any fish, because there are no fish anywhere in this river.

Modesty. Since I did not fish everywhere in the river, I do not need to claim that there are no fish anywhere in the river in order to explain why I did not catch any. It would be enough to claim that there were no fish in the particular part of the river where I was fishing.

Would the argument from analogy in Question 10 become stronger, weaker, or neither if we added a premise that the previous James Bond movies and new James Bond movie are also similar in more respects that I usually like, such as exotic settings, beautiful actors, intrigue, and so on?

Stronger. In general, the more similarities, the stronger the argument from analogy, as long as those similarities are relevant in the right way (see Questions 2 and 7). Of course, if everything is exactly the same as in the previous Bond movies, then I will be disappointed by the lack of originality in the new movie, but a few more relevant similarities like those listed in the question still make the argument stronger.

Specify what, if anything, is the main problem with the following application of a generalization to a case. There might be more than one problem, but indicate the main one. Very few birds can swim, and this duck is a bird, so this duck cannot swim.

The argument overlooks a conflicting reference class. Ducks are also in the group of aquatic birds. A high percentage of aquatic birds can swim. So this class—aquatic birds—is a conflicting reference class that the argument overlooks.

Specify what, if anything, is the main problem with the following application of a generalization to a case. There might be more than one problem, but indicate the main one. The weather forecast says that there is only a 40 percent chance of rain, so it won't rain, and we don't need to bring an umbrella.

The percentage is too high. If there were only 10 percent chance of rain, then it might be reasonable not to bring an umbrella, but a 40 percent chance of rain is too high for confidence that it will not rain.

Specify what, if anything, is the main problem with the following application of a generalization to a case. There might be more than one problem, but indicate the main one. Our heater works most of the time, so we can depend on it to keep us warm during the blizzard that is coming.

The percentage is too low. The word "most" means "over 50 percent," but the fact that the heater works over 50 percent of the time is not enough to make it reasonable to depend on it when you might freeze to death in the blizzard if it fails this time.

Would the argument from analogy in Question 13 become stronger, weaker, or neither if we added a premise that the drug does not cure this disease in monkeys or pigs?

Weaker. There is not as much diversity among rats as there is among rats, pigs, and monkeys. An argument from analogy is stronger (as a general rule) when the similar objects mentioned in the premises are more diverse, because that diversity shows that the force of the analogy is independent of the respects in which those objects differ. Thus, the argument in Question 13 would be stronger if the drug cured the disease in more species. However, if it fails to cure the disease in these other species, then that suggests that the effect does depend on some difference between rats and pigs and monkeys. If we do not know which difference matters, then we do not know whether humans resemble rats or, instead, resemble pigs and monkeys in the crucial respect that affects the cure. That is why the argument becomes weaker when the drug does not cure this disease in monkeys or pigs.

In the situation described in the student video in the lecture, which virtue of explanations would be lacking from the hypothesis that ghosts knocked the cookies off the counter?

Conservativeness. The hypothesis of ghosts conflicts with well-established science.

Indicate whether the following argument is deductive or inductive. Assume a standard context as described. Nothing tricky! Context: Harold is accused of a burglary. We think that he is not guilty, but we worry that he might be punished anyway. Then I give this argument. "If Harold is not innocent, then he will be punished. But he is innocent, so he will not be punished."

Deductive. This argument is not valid, because its conclusion can be false even if both of its premises are true. Some people are punished by mistake when they are innocent. Nonetheless, this argument looks like another argument that is valid (such as this different argument: "If Harold is innocent, then he will not be punished. But he is innocent, so he will not be punished."). This similarity to a valid argument might make the argument in our example appear valid. That appearance suggests that the person who gave the argument in our example intended the argument to be valid. That intention makes the argument deductive even if it fails to be valid.

Imagine that you offer an explanation of some surprising event, and then someone criticizes your explanation by saying, "Your explanation just raises new questions that you also need to answer." Which explanatory virtue is this critic claiming that your explanation lacks?

Depth. An explanation is deeper when it leaves fewer questions that need to be answered. Thus, to say "Your explanation just raises new questions that you also need to answer" is to say that it is shallow or lacks depth. An explanation is better when it is deeper, because the goal of explanation is to increase understanding, but we understand something less well when we have more unanswered questions about it.

Polls are never reliable.

False. Although polls can go wrong in many ways, some polls do not go wrong in any way. Then they can provide strong reasons to believe their conclusions. For example, some polls do provide strong evidence of who will win in some elections.

Deductive validity is defeasible.

False. An argument is valid if it is not possible for the premises of that argument to be true when its conclusion is false. If that combination of truth values really is impossible, then adding more premises cannot make that combination possible. Thus, adding more premises cannot turn a valid argument into an invalid argument. That is what it means to call validity indefeasible. (Notice, in contrast, that invalidity is defeasible. If you add more premises to an invalid argument, then you can turn an invalid argument into a valid argument. One simple way to do this is to add the conclusion as a premise. Then the argument is circular, but it is valid nonetheless.)

When you give an argument from analogy, you need to specify which similarity is the one that is important for the conclusion.

False. Arguments from analogy often list many similarities without specifying which ones are the ones that are important for the conclusion. This feature makes arguments from analogy different from inferences to the best explanation, because inferences to the best explanation do need to specify which features best explain the observation in their premises.

Arguments from about a sample to conclusions about the whole class are valid.

False. Because the whole class in the conclusion includes cases that are not in the sample in the premises, it is possible for the sample to have certain features that are not shared by the whole class. Here's an example: "Most students that I have taught at Duke are Americans, so most students in the world are Americans." The premise about the Duke sample is true, but the conclusion about the whole class of students is false, so this argument is invalid.

Deductive arguments are always valid.

False. Deductive arguments aim at validity, or are supposed to be valid, or are intended to be valid, but that does not ensure that deductive arguments always succeed in being valid. Some arguers try to make their arguments valid, but they fail, and then their arguments are deductive but invalid.

Deductive validity comes in degrees.

False. Deductive validity depends on what is possible or impossible. If it is possible for the premises of an argument to be true when the conclusion is false, then the argument is invalid. If that combination of truth values is impossible, then the argument is valid. This combination cannot be partly possible or a little possible, so an argument cannot be partly valid or a little valid.

Inferences to the best explanation are intended to be valid.

False. Even if a hypothesis is the best explanation of an observation, it is still possible that the hypothesis is false. For example, even if the hypothesis that Vijeth killed the victim is the best explanation that we can imagine of why his fingerprints were on the glass (see Question 2 in this exercise), it still might be true that he is innocent and his fingerprints were planted on the glass by the person who really killed the victim. Thus, it is possible for the premises to be true and the conclusion false in an inference to the best explanation. That makes such arguments invalid.

Inductive arguments always have general conclusions.

False. Here's an inductive argument with a particular conclusion: "Most birds can fly, and this owl is a bird, so probably this owl can fly." Here's another: "The best explanation of the evidence at the crime scene is that Richard killed the victim, so Richard probably did kill the victim." Each of these arguments is invalid and defeasible, so they are inductive, even though they do not have general conclusions.

A sample of one is always too small to justify a generalization.

False. If we have background knowledge that the cases in the class are uniform, then it can be strong to generalize from a single case to the whole class. For example, if I throw one copper coin in a lake and it sinks in the water, then I do not need to test more copper coins in order to be justified in believing that all copper coins sink in the water (assuming that they are not supported by anything else, such as a turtle swimming on the surface of the lake), because I know that copper coins are relatively uniform in density (assuming that they are not hollow or shaped like boats!).

If two competing explanations are equally good, then we can use an inference to the best explanation to justify belief in one of them.

False. In order to justify the conclusion of an inference to the best explanation, that conclusion must be better than any competing explanation. If two explanations are equally good, then neither is better than the other. Thus, if two competing explanations are equally good, then we cannot use an inference to the best explanation to justify belief in either of them as opposed to the other. Instead, this comparison cannot tell us which of them is correct.

The reference class occurs in the conclusion when we apply a generalization to a case in an argument of the form: Almost all F are G, and a is F, so a is G.

False. In this form of argument, the reference class is F, and F does not appear in the conclusion.

Arguments from analogy are usually intended to be valid.

False. It is possible for the premises to be true when the conclusion is false in an argument from analogy. Here's an example: the snakes in my garden look a lot like the snakes in your garden, and the snakes in my garden are not venomous, so the snakes in your garden are also not venomous. These premises might be true even if the conclusion is false, because the snakes in your garden turn out to be venomous (so be careful!). Because it is so clear that arguments from analogy are not valid, they are almost never intended to be valid.

The conclusion in a generalization from a sample always begins with the word "all."

False. Partial generalizations (described in the lecture) have conclusions that refer to X percent of Fs rather than to all the Fs. Partial generalizations cannot conclude that all Fs are G because their premises refer to some cases where an F is not G, which would refute the conclusion that all Fs are G.

Imagine that you offer an explanation of some surprising event, and then someone criticizes your explanation by saying, "Your explanation would apply to whatever happened." Which explanatory virtue is this critic claiming that your explanation lacks?

Falsifiability. An explanation is falsifiable when some event could show that it is false, so it is unfalsifiable if no event could show that it is false. If the same explanation could apply equally well to any event that occurred, then no event could show that it is false. Thus, to say "Your explanation would apply to whatever happened" is to say that it is compatible with whatever might happen, so it is unfalsifiable. This feature might seem desirable, but actually it is a defect, because an explanation cannot really explain an event if it is compatible with that event not happening. It is applies whether or not the event occurs, then it cannot explain why the event occurs rather than not occurring. Thus, explanations that are unfalsifiable are empty and have no explanatory force. That is why falsifiability is an explanatory virtue.

Indicate whether the following argument is deductive or inductive. Assume a standard context as described. Nothing tricky! Context: Our only son, Jeff, lives away at college. He has final exams before the winter holidays, and we are not sure when he will arrive back home. We go on a short trip to a store. The house was neat when we left, but it is messy when we return. Then you say this sentence: "The house is a mess, so Jeff must be home from college."

Inductive. This argument is not valid and does not appear to be valid, so it was probably not intended to be valid. Moreover, it has the form of a standard kind of inductive argument—specifically, an inference to the best explanation (to be discussed in later lectures). Its form thus suggests that the argument is inductive.

Imagine that you offer an explanation of some surprising event, and then someone criticizes your explanation by saying, "You don't have to claim so much in order to explain what happened." Which explanatory virtue is this critic claiming that your explanation lacks?

Modesty. An explanation is more modest when it makes fewer or weaker assumptions or claims, and it lacks modesty when it claims more than is needed in order to explain what it is supposed to explain. Thus, to say "You don't have to claim so much in order to explain what happened" is to say that your explanation is not modest. An explanation is better when it is modest in this sense, because there is less to criticize and less that could go wrong when an explanation makes fewer claims or assumptions. That is why modesty is an explanatory virtue. (Notice that modesty is closely related to what is sometimes called simplicity.)

In the situation described in the student video in the lecture, which virtue of explanations would be lacking from the hypothesis that Timmy the Cat knocked the cookies off the counter because he was trying to eat one of them?

Modesty. This new hypothesis ascribes a motive to the cat ("...because he was trying to eat one of them"). It is not necessary to postulate any motive, because cats often knock things over by mistake. (Besides, who can tell what is going on in the mind of a cat?) Thus, this hypothesis claims more than is needed, so it is lacks modesty.

In the situation described in the student video in the lecture, what is wrong with the hypothesis that a burglar knocked over the cookies after breaking in to steal something?

More than one of the above. This hypothesis is not powerful enough to explain what Kevin did observe (the cat hair on the counter) and it also suggests that Kevin would observe some things that he did not observe (since he did not observe any evidence of breaking in or any missing items that were stolen). Thus, the hypothesis is not compatible with the range of data.

Would the argument from analogy in Question 10 become stronger, weaker, or neither if we added a premise that the previous James Bond movies had five or fewer words in their titles, but the new James Bond movie has eight words in its title?

Neither stronger nor weaker. The number of words in a movie's title does not affect whether you enjoy it, except in very unusual circumstances that we can ignore here.

Indicate which explanatory virtue is lacking from this explanation: I lost the race because I just did not happen to run well today.

Power (or Breadth). The explanation that I did not run well this time does not apply to any other times when I run, so it cannot explain anything else. That makes this explanation lack power or breadth. This explanation also lacks depth if it raises the further question of why I did not run well this time, but to say that "I just did not happen to" do something implies that one cannot ask for any deeper explanation, so the main problem here is the lack of power or breadth

Consider this argument from analogy: A new drug cures a serious disease in rats. Rats are similar to humans in many respects. Therefore, this new drug will probably cure the same disease in humans. Would this argument from analogy become stronger, weaker, or neither if we added a premise that the disease affects the liver, and livers in rats and in humans are very similar in structure and function?

Stronger. In general, the more similarities, the stronger the argument from analogy, as long as those similarities are relevant in the right way (see Questions 2 and 7). This general rule holds especially when the similarities are specific to the feature in the conclusion, such as liver disease in this case. If the drug cured a disease in part of the body where rats and humans are very different, such as the tail, then a successful cure in rats would be less evidence that the drug will cure the disease in humans.

Specify what, if anything, is the main problem with the following application of a generalization to a case. There might be more than one problem, but indicate the main one. Almost all Prime Ministers of Great Britain have been men. Margaret Thatcher was Prime Minister of Great Britain. _______________________________________________ So Margaret Thatcher is a man.

The argument overlooks a conflicting reference class. Margaret Thatcher is also in the group of people named "Margaret." A high percentage of people named "Margaret" are not men. Indeed, a high percentage of Prime Ministers named "Margaret" are not men. So this class—Prime Ministers named "Margaret"— is a conflicting reference class that the argument overlooks.

Specify what, if anything, is the main problem with the following generalization from a sample. There might be more than one problem, but indicate the main one. A poll asked fifty thousand randomly chosen people throughout Asia whether they would want to eat foods that have been genetically modified in ways that increase company profits but also might poison them. Less that 10 percent replied "Yes, definitely." Therefore, most people in Asia do not want to eat genetically modified foods.

The question is slanted. The question refers only to dangers of genetically modified foods without mentioning any benefits for consumers of genetically modified foods, so it is likely to lead most people not to answer "yes" even if they really do support and want to eat genetically modified foods, and even if some genetically modified foods have health benefits that outweigh any dangers. (Whether or not that is true is controversial, of course.) Notice also that the sample is large and random, so this argument does not have the other problems listed.

Specify what, if anything, is the main problem with the following generalization from a sample. There might be more than one problem, but indicate the main one. K-Mart asked all of its customers throughout the country whether they prefer K-Mart to Walmart, and 90 percent said they did. Thus, 90 percent of all shoppers in the country prefer K-Mart.

The sample is biased. Customers tend to shop at stores that they like, because they go to stores that they like more often than they go to stores that they do not like. That could explain why a sample taken at a store will usually include more people who like that store, even if there are many more people who do not like that store and who shop elsewhere, so they are not in the sample. This explains why this sample is biased and why you cannot legitimately generalize from this sample.

Specify what, if anything, is the main problem with the following generalization from a sample. There might be more than one problem, but indicate the main one. Most college students like to surf, because I asked a lot of students at several colleges along the California coast, and most of them like to surf.

The sample is biased. Many students choose to go to a college along the California coast because they already like to surf and want to have easy access to surfing while they are in college. Other students have other reasons to go to colleges along the California coast, but then they learn to surf while they are in college, and they come to like it. Students in colleges where they cannot surf are less likely to learn to enjoy surfing. Thus, students who choose to go to colleges along the California coast are more likely to enjoy surfing than are students who go to college in areas where they cannot surf. That explains why this sample is biased and why you cannot legitimately generalize from this sample.

Specify what, if anything, is the main problem with the following generalization from a sample. There might be more than one problem, but indicate the main one. I have lots and lots of friends. All of them think that I would make a great comedian. So most people in my country would probably agree that I would make a great comedian.

The sample is biased. My friends are more likely than strangers to think that I am funny. That might be part of why they are my friends. However, very few people really make great comedians. As a result, it is likely that most other people would disagree with my friends, even if all of my friends think that I would make a great comedian. That makes the sample biased. The sample might also be too small, because most people do not have enough friends for a reliable poll. However, the argument does say, "I have lots and lots of friends," so the sample does include "lots and lots" of people. Moreover, the premise is about all of my friends, whereas the conclusion is only about most people. Hence, the main problem with this argument is that the sample is biased.

Specify what, if anything, is the main problem with the following generalization from a sample. There might be more than one problem, but indicate the main one. Most Swedes are thieves, because my bicycle has been stolen twice, and both times it was a Swede who did it.

The sample is too small. A sample of two is too small to generalize to most Swedes, because there is no reason to assume that Swedes are uniform with respect to whether or not they are thieves. This sample might also be biased because there might be a high percentage of Swedes in the area where the bikes were stolen, and then it is more likely that a bike would be stolen by a Swede than by a non-Swede in that area. That would be the case if the bikes were stolen in Sweden, for example. Thus, there might be more than one problem with a single generalization. However, the main problem is that the sample is too small, because the sample would still be too small even if the two bikes were stolen in different areas and even if these areas did not include an unusual percentage of Swedes. Notice that many social prejudices are based on hasty generalizations like this one.

Specify what, if anything, is the main problem with the following generalization from a sample. There might be more than one problem, but indicate the main one. This philosophy class is about logic, so most philosophy classes are probably about logic.

The sample is too small. This class is only one case of a philosophy class. There is no reason to assume that all philosophy classes are uniform in their subject matter. Therefore, this sample is too small. As we saw in Question 2 of this Exercise, a sample of one is sometimes big enough for a generalization, but only when we can assume uniformity in the relevant respect throughout the sample.

Inductive strength comes in degrees.

True. An inductive argument is stronger when its premises provide more and better reason for its conclusion. The premises can provide a very strong reason or a moderately strong reason or only a weak reason. The argument is strong to the degree that it provides strong reason for its conclusion. More technically, inductive strength is a matter of probability—specifically, how probable the conclusion is, given the premises. Probability does come in degrees. It varies from 0 to 1. This will be explained in two weeks. The point for now is just that, unlike possibility, probability does come in degrees, so inductive strength also comes in degrees.

When a poll asks a question that is slanted in order to reach a certain result, then the poll does not provide strong reason to believe the desired conclusion.

True. A slanted question can make a poll reach a desired result, but then the poll does not provide strong reason to believe that that desired conclusion is really true, because the slanted poll would have reached that same result even if that conclusion were not true. The problem with slanted questions is that they make the poll reach the desired conclusion regardless of whether that conclusion is really true.

Arguments from analogy are defeasible.

True. Adding new information to the premises of an argument from analogy can sometimes reduce or totally undermine the strength of the argument. Consider the example from Question 3: The snakes in my garden look a lot like the snakes in your garden, and the snakes in my garden are not venomous, so the snakes in your garden are also not venomous. The strength of this argument from analogy is defeated if we add new information that there is a kind of venomous snake in your area that does not live in my area but looks a lot like some snakes in my area. Similarly, this argument ceases to be strong if we add the premise that someone was bitten by a snake in your garden and died from its venom. This susceptibility to undermining by new information makes arguments from analogy defeasible.

Arguments that apply a generalization to a case are defeasible.

True. Additional information can defeat the strength of such applications by showing that the individual (a) falls into a smaller reference class that is more or less likely to be G. The example in the lecture was that you might see that Walter was not wearing shoes while he was teaching.

Deductive use inference to the best explanation to solve murder mysteries.

True. After gathering evidence (such as fingerprints, footprints, blood samples, eyewitness reports, and so on), detectives need to determine which hypothesis about who committed the crime best explains why they found the evidence that they found. For example, if the best explanation of why Vijeth's fingerprints were on the glass at the crime scene is that Vijeth was there during the crime, and if there is no explanation of why Vijeth would be there then unless he was there to kill the victim, then that provides some reason to believe that Vijeth killed the victim.

Scientists use inferences to the best explanation to draw conclusions from observations in their experiments.

True. After scientists perform experiments and get results, they need to determine which hypothesis about what happened in the experiment best explains why they got the results that they got. For example, suppose a scientist adds a chemical to a group of live bacteria and then observes that the bacteria are dead an hour later. The scientist infers that the best explanation of why the bacteria died is that the chemical killed those bacteria. That inference provides some reason to believe that this chemical kills that kind of bacteria.

Inferences to the best explanation include a premise about an observation that needs to be explained.

True. An inference to the best explanation must postulate an explanation of something, so it must include a premise about something that needs to be explained (as discussed in the lecture). For example, if someone argues "This meat smells very bad, so it must be spoiled," then the premise that the meat smells very bad is what needs to be explained.

Arguments from analogy are inductive.

True. Arguments from analogy are invalid and defeasible, as we saw in the previous two questions. That makes them inductive rather than deductive.

Arguments from premises about a sample to conclusions about the whole class are defeasible.

True. Cases in the whole class that are not in the original sample can provide new information that defeats the strength of an argument from a sample to a generalization about the whole class. For example, imagine that I check 100 homes in my town and find that almost all have three bedrooms or more, so I conclude that most homes in my town have three bedrooms or more. This argument seems pretty strong. Then I discover other parts of town with smaller houses, as well as several large apartment buildings with hundreds of apartments that have two bedrooms or less. When this new information is added to the premises of the original argument, the argument ceases to be strong. All of my observations or samples together do not support the conclusion that most homes in my town have three bedrooms or more. The new premises thus undermine or defeat the strength of the original argument. That makes it defeasible.

Arguments from analogy are stronger when the conclusion is weaker.

True. Consider these premises: This coat resembles my last four coats in design, manufacturer, and stitch pattern, and those four coats all fell apart quickly. These premises provide less reason for the strong conclusion (a) "This coat definitely will fall apart quickly" than they provide for the weaker conclusion (b) "This coat probably will fall apart quickly." The same premises provide even more reason for the even weaker conclusion (c) "There is some danger that this coat will fall apart some day." Thus, the argument gets stronger as the conclusion gets weaker (because the conclusion is more guarded and, hence, more likely to be true).

Arguments from analogy are stronger when they cite more relevant analogies between the objects.

True. Consider this argument from analogy: This political candidate resembles those five other political candidates in party affiliation and policy orientation, and they all ran in the same electoral district as this candidate. Those other candidates all lost their elections, so this candidate will also probably lose this election. This argument would be stronger if the premises also cited other similarities, such as charisma, gender, ethnicity, geographical origin, economic circumstances, current political atmosphere, and so on—since these often affect elections. If we do not know which of these factors will become important in this election, then listing more similarities that might be relevant makes it more likely that the list will include the features that do become important. That is why more potentially relevant similarities make the argument from analogy stronger.

Inferences to the best explanation are defeasible.

True. Even if a hypothesis is the best explanation of what has been observed so far, future additional evidence might make the inference weak. For example, even if the hypothesis that this chemical kills that kind of bacteria is the best explanation that we can imagine right now of why the bacteria died (see Question 3 in this exercise), we might later find out that a lab assistant spilled soap into the dish, and the soap rather than the other chemical might be what killed the bacteria. This additional information about the spilled soap then defeats the strength of the inference to the best explanation. Thus, such arguments are defeasible.

An argument that applies a generalization to show that a case has a certain property is never strong when the percentage in the premise is 50 percent.

True. If 50 percent of F are G, then this percentage gives us no reason to believe either that a certain a that is F is G or that it is not G. Notice that an application can be strong with 50 percent in the premise if the conclusion is that there is a 50 percent chance that F is G, but then that conclusion does not claim that a case has a certain property, as the question specifies.

One premise in an inference to the best explanation claims that one is better than others.

True. If someone claims only that a hypothesis would explain something, then we cannot infer that that explanation is correct, because another conflicting explanation might also explain that event just as well or even better. For example, if the claim that Jamshed committed the murder would explain the eyewitness testimony, but the claim that Jamshed's twin brother committed the murder also would explain the eyewitness testimony, then we cannot tell whether it was Jamshed or his twin brother who committed the murder. That is why an inference to the best explanation must be an inference to the best explanation. In order to claim that an explanation is the best, the inference needs a premise (possibly suppressed) that the explanation in its conclusion is better than any alternative explanation.

The attribute class occurs in the conclusion when we apply a generalization to a case in an argument of the form: Almost all F are G, and a is F, so a is G.

True. In this form of argument, the attribute class is G, and G does appear in the conclusion.

An argument from the premise that 99 percent of F are G to the conclusion that this F (namely, a) is G is stronger than an argument to the same conclusion from the premise that 90 percent of F are G.

True. Increasing the percentage in the premise makes an application stronger when the conclusion is positive.

Some arguments from analogy can be reconstructed as inferences to the best explanation.

True. This point was made by the example about Neanderthals at the end of the lecture.

Consider this argument from analogy: I have seen many movies about James Bond (007). I almost always enjoyed them. A new James Bond movie just came out. I have not seen it yet, but I know that it resembles previous James Bond movies in many respects, such as action, style, and ingenious devices. So I will probably enjoy the new James Bond movie as well, if I watch it. Would this argument from analogy become stronger, weaker, or neither if we added a premise that the new James Bond movie has a new actor playing James Bond?

Weaker. The actor who plays the main character often affects whether someone enjoys a movie, so this difference between previous Bond movies and the current Bond movie is a relevant difference between these movies. The new actor might be even better, but he also might be worse; and this seems more probable because I liked the previous actors who played Bond. This uncertainty means that the fact that I enjoyed the previous Bond movies with the previous actor playing Bond is less reason to believe that I will like the current Bond movie with the new actor playing Bond.