PHIL 105 Final Exam Prep

All the weekly quizzes put together. From UNC-CH. Professor Ralph Flanders.

Suppose that Jason gives the following argument:

"We should not serve veal for dinner tonight. Leon is coming over, and he refuses to eat veal on moral grounds. And also Yuji is coming over, and he simply doesn't like the taste of veal. Finally, Njeri is coming over, and she doesn't like it when people spend lots of money on her—I think she might feel embarrassed if we serve an expensive veal dinner."

The conclusion of this argument is

The answer is A. "We should not serve veal for dinner tonight."

From the premise that Leon is morally opposed to veal, Yuji dislikes veal, and Njeri is financially embarrassed by veal, the argument concludes that we should not serve veal for dinner tonight. In this particular case, the argument's conclusion comes first, before the premises are presented.

Consider Jason's same argument again:

"We should not serve veal for dinner tonight. Leon is coming over, and he refuses to eat veal on moral grounds. And also Yuji is coming over, and he simply doesn't like the taste of veal. Finally, Njeri is coming over, and she doesn't like it when people spend lots of money on her—I think she might feel embarrassed if we serve an expensive veal dinner."

The premise (or premises) of this argument is (or are):

Feedback: The answer is E. "B, C, and D, but not A."

To reach the conclusion that we should not eat veal tonight, the argument employs the premise that Yuji does not like veal, the premise that Njeri doesn't like it when people spend money on her, and the premise that Leon refuses to eat veal. These are the argument's only three premises.

Consider Jason's argument again:

"We should not serve veal for dinner tonight. Leon is coming over, and he refuses to eat veal on moral grounds. And also Yuji is coming over, and he simply doesn't like the taste of veal. Finally, Njeri is coming over, and she doesn't like it when people spend lots of money on her—I think she might feel embarrassed if we serve an expensive veal dinner." Now suppose that Fred objects to Jason's argument as follows: "Oh sure, Jason, let's just pander to everybody's whims and just not serve any food at all! God forbid that we should ever risk offending anyone, spending too much, spending too little, or violating a guest's dietary constraints by serving any kind of dish!"

Fred's response to Jason's argument is an example of

The answer is C. "refutation by parallel reasoning."

To refute a claim by parallel reasoning is to show that an argument is invalid, specifically, by comparing it with an argument that has the same logical form, whose invalidity is clear and apparent.

In this case, Fred has characterized Jason as making the following argument: "We should avoid serving certain dishes, since doing so might upset our guests." Fred points out that, since any dish has the potential to upset some possible guest, it would appear to follow that no food should be served at all. What do you think of Fred's attempt at refutation through parallel reasoning?

Now suppose that, after the financial collapse of 2008, Nouriel gives the following argument:

"Western governments can spend as much taxpayer money as they like covering the losses suffered by the big banks: Such spending will not restore the proper operation of the banks. In order to restore the proper operation of the banks, they must first be adequately capitalized, and they must also be lending money to borrowers whose investments will generate lots of consumer demand. But, given current incentives, there is no way for the banks to achieve this goal without being at least temporarily taken over by fiscal policy makers. So the banks must be temporarily nationalized if they are ever to become effective private institutions again."

The conclusion of this argument is

Feedback: The answer is D. "The banks must be temporarily nationalized if they are ever to become effective private institutions."

From the premise that government spending will not restore proper banking operations, from the premise that this operation requires adequate capitalization, and from the premise that this operation requires banks lend money to borrowers whose investments generate consumer demand, this argument concludes that the banks must be temporarily nationalized.

Consider Nouriel's argument again:

"Western governments can spend as much taxpayer money as they like covering the losses suffered by the big banks: Such spending will not restore the proper operation of the banks. In order to restore the proper operation of the banks, they must first be adequately capitalized, and they must also be lending money to borrowers whose investments will generate lots of consumer demand. But, given current incentives, there is no way for the banks to achieve this goal without being at least temporarily taken over by fiscal policy makers. So the banks must be temporarily nationalized if they are ever to become effective private institutions again."

The premise(s) of this argument is(are):

Feedback: The answer is E. "A, B, and C, but not D."

To reach the conclusion that the banks must be temporarily nationalized if they are ever to become effective private institutions, the argument employs three premises: first, that that government spending will not restore proper banking operations; second, that this operation requires adequate capitalization; and finally, that this operation requires banks lend money to borrowers whose investments generate consumer demand. Since these premises are identical to the claims in A, B, and C, respectively, it follows that E is the correct answer.

Consider Nouriel's argument again:

"Western governments can spend as much taxpayer money as they like covering the losses suffered by the big banks: Such spending will not restore the proper operation of the banks. In order to restore the proper operation of the banks, they must first be adequately capitalized, and they must also be lending money to borrowers whose investments will generate lots of consumer demand. But, given current incentives, there is no way for the banks to achieve this goal without being at least temporarily taken over by fiscal policy makers. So the banks must be temporarily nationalized if they are ever to become effective private institutions again."

Now suppose that Bill responds to Nouriel's argument as follows:

"Oh, sure, just let the government take over the banks. And while you're at it, let the government also take over the oil and gas industry, aviation, and manufacturing as well. Heck, why not just let the government take over the whole economy?"

Bill's response to Nouriel's argument is an example of

Feedback:

The answer is A. "refutation by parallel reasoning."

To refute a claim by parallel reasoning is to show that an argument is invalid, specifically, by comparing it with an argument that has the same logical form, whose invalidity is clear and apparent. In this case, Bill has characterized Nouriel as making the following argument: "We should temporarily nationalize the banks, since doing so will facilitate their proper functioning." Bill points out that, since many institutions have the potential to work while nationalized, it would appear to follow that everything should be nationalized. What do you think of Bill's attempt at refutation through parallel reasoning?

Consider the following argument:

"If guns are outlawed, then only outlaws will have guns. Therefore, guns should not be outlawed."

Which of the following arguments is parallel in structure to the preceding argument?

Feedback:

The answer is B. "If alcohol is outlawed, then only outlaws will drink alcohol. Therefore, alcohol should not be outlawed."

Unlike rape, reading, and killing, which are all types of actions or activities, guns are possessions of a certain sort. The argument assumes that, if possessions of a certain sort are outlawed, then an undesirable situation results—that only outlaws will possess those things. Therefore, the argument concludes that the possessions in question should not be outlawed.

The argument about alcohol is parallel to the argument about guns. It, too, considers a certain type of possession—alcohol—and claims that, if it is outlawed, a certain undesirable result will occur, which is that only outlaws will drink alcohol.

Consider the following argument:

"Nuclear deterrence must work, since nuclear powers have never engaged in nuclear wars with each other since the end of World War II."

Which of the following arguments is parallel in structure to the preceding argument?

Feedback:

The answer is E. "all of the above."

The argument assumes the following sort of reasoning: If there have been no Fs for as long as Gs have been present, then Gs must prevent Fs. In the original argument, nuclear war and the nuclear weapons are the respective values for F and G.

Each of the arguments among A through D assume the same line of reasoning as the argument listed in Question 2. In the same way that the author assumes that nuclear deterrence works, since there has been no war with nuclear weapons, so does A assume that one's refrigerator works as fairy repellant. Likewise, so does B assume that photographers prevent the appearance of Bigfoot, so does C assume that air travel prevents poverty, and so does D assume that garlic prevents thieves. In each case, the failure of Fs to appear when there are Gs is taken as proof that Gs prevent Fs

Consider the following argument:

"Eating meat cannot be wrong, since most people today regard it as an acceptable practice."

Which of the following arguments could be used to refute the preceding argument by parallel reasoning?

The answer is B. "Lying cannot be wrong, since most people today regard it as an acceptable practice (spoken by a advertising executive)."

The argument assumes the following line of reasoning: If most people today regard something as an acceptable practice, then such a practice cannot be wrong. The only argument among A through D that duplicates this sort of reasoning is B. In B, the argument concludes that a certain activity—lying—is not wrong, and it does so by citing the premise that today most people today regard it as an acceptable practice.

The argument stated in A is not an exact parallel of the argument in the question. The reason why is that, in A, the practice being considered is not actually regarded as acceptable by most people today. Perhaps it used to be regarded as acceptable, and perhaps the argument stated in A used to function as a parallel argument to the one posed in this question, but it is not anymore, and does not anymore.

Nor does the argument in C run parallel to the line of reasoning in the argument posed in this question. The reason why is that, in C, the argument concludes that abortion cannot be against one's conscience. However, the original argument proposed in this question concluded that a certain action cannot be wrong, not that it cannot be against one's conscience.

Finally, the argument in D does not run parallel to the argument posed in this question. The reason why is that, in D, the argument employs the premise that something is widely practiced. The argument posed in this question, however, employs the premise that an activity is regarded by most people as acceptable. Since these are two very different sorts of assumptions, D is not parallel to the argument posed in this question.

Consider the following argument:

"It's wrong to drive in excess of the speed limit, even in a case where you're rushing someone to the hospital to save their life. If everyone drove in excess of the speed limit, then that would make driving very dangerous for everyone, and we'd see a huge increase in traffic fatalities. So you should never drive in excess of the speed limit, no matter what."

Which of the following arguments could be used to refute the preceding argument by parallel reasoning?

The answer is A. "It's wrong to lie even when an insane killer is asking you where you keep your guns. If everyone lied, then no one could ever trust what anyone else says, and we would lose the ability to share information through verbal exchange. So you should never lie under any circumstances."

The argument posed in this question considers a course of action that is normally regarded as wrong. The argument concludes that, even in a life-or-death circumstance, that course of action would still be wrong. The argument's premise observes that, if everyone committed the action in question, undesirable consequences would result for everyone. In this case, the course of action is driving in excess of the speed limit, the life-or-death circumstance is that of needing to speed in order to save a friend's life, and the undesirable consequence for everyone is an increase in traffic accidents.

Likewise, in A, the argument points out that, if everyone lied all the time, the undesirable consequence of never having believable testimony would result from everyone. Lying is normally regarded as wrong, although we may well think it is permissible in a life-or-death circumstance. The argument concludes, however, that even in a life-or-death circumstance where a killer asks for your weapons, you should still never lie.

The arguments in B, C, and D are similar to the argument posed in this question, in that they all infer the impermissibility of a certain action from the undesirability of everyone committing that action. The arguments in B, C, and D are importantly dissimilar to the argument posed in this question, however, in two respects. First, they do not concern actions that are normally regarded as wrong. Lying is normally regarded as wrong, and driving in excess of the speed limit is normally regarded as wrong, but neither eating potato chips, nor answering emails, nor hugging one's child is normally regarded as wrong. Second, the arguments in B, C, and D do not appeal to any dire circumstance, any emergency, or any life-or-death situation. These dissimilarities are important to the argument because, when considering courses of action that are normally regarded as wrong, one regards them as more justified when they are pursued in an emergency. This general rule, in fact, is the line of reasoning that the argument posed in this question uses. Since it is not present in B, C, or D, the arguments in B, C, or D are not exactly parallel to the argument posed in this question.

Consider the following argument:

"Ram and Walter must be the same person in two different disguises. Think about it: Have you ever seen the two of them together?"

Which of the following arguments could be used to refute the preceding argument by parallel reasoning?

The answer is D. "Barack Obama and Simon Cowell must be the same person in two different disguises. Think about it: have you ever seen the two of them together?"

The argument posed in this question reasons that, since a person X and a person Y have not been seen together, that X and Y are a single person in two different disguises. The argument in D is parallel to the argument posed in this question; it reasons that, since Obama and Cowell have not been seen together, that Obama and Cowell are a single person and two different disguises.

The arguments in A, B, and C are importantly dissimilar to the argument posed in this question. In A and B, the arguments do not concern persons. The argument in A identifies two sorts of chemical phenomena, and the argument in B identifies two planets. Unlike A or B, the argument in C does concern the identification of persons, but it reasons that the persons are identical because they have not been seen in the same place at the same time. This is very different from reasoning that the persons have not been seen together. For when we prove that a person, X, and a person, Y, are distinct, we do so by viewing X and Y next to each other at the same time. We do not prove their distinctness by observing that they coincide at the exact same location at once.

Consider the statement:

Every prime number is odd.

Which of the following things is a counterexample to this general statement?

The answer is A. "2."

As stated in the lecture, a counterexample is an example that runs counter to some generalization. In other words, it is an example that falsifies a certain generalization. Here, in this case, to refute the claim "every prime number is odd" with a counterexample, one must find an example of a prime number that is not odd. In other words, one must find an even prime to have a counterexample to the claim "every prime number is odd." Since the number 2 is the only even prime, the number 2 is the only such counterexample.

Consider the statement:

All Swedes are tall.

What would you need to find in order to find a counterexample to this statement?

The answer is D. "a short Swede."

To falsify the generalization, "all Swedes are tall," one must find an example of a non-tall Swede. A short Swede, in other words, would be a counterexample to the claim that all Swedes are tall.

An example of a tall Swede would not be a counterexample to the statement we are considering. Such a case would not run counter to the generalization that all Swedes are tall.

Neither A nor B would falsify the claim that all Swedes are tall, since the truth of "all Swedes are tall" is compatible with the truth of both A and B. In other words, it could be true that all Swedes are tall even if there existed a tall Norwegian, and even if there also existed a short Dane. Neither the existence of a tall Norwegian nor the existence of a short Dane falsifies the claim that all Swedes are tall. For that reason, A and B are both incorrect answers.

Option E is incorrect because the generalization in the statement posed in this question concerns Swedes, rather than half-Danish half-Swedes. The existence of a short half-Danish half-Swede is compatible with the claim "all Swedes are tall." So the existence of a short half-Danish half-Swede is not a counterexample to the statement.

Consider the statement:

Everything has a shape.

Which of the following things is a counterexample to this general statement?

The answer is D. "the color blue"

In order to refute the claim "everything has a shape" by counterexample, one must find an example of something that does not have a shape. In other words, one must provide an example of something without a shape to refute the claim "everything has a shape" with a counterexample.

The correct answer to this question is "the color blue" because the color blue does not have a shape. We could not say that the color blue is circular or rectangular or pentagonal, for instance. The reason we could not say such things, moreover, is not that the color blue is some other shape. On the contrary. Unlike blue objects, which always have a shape and a size, along with many other physical features, the color blue, by itself, has no shape or size.

Unlike the color blue, each of the items mentioned in A through C have a shape. Mt. Everest, for instance, has a shape, which is wider at the base than at the peak, and whose dimensions are exactly the dimensions of the region of space, which the actual Mt. Everest currently occupies.

Likewise, Barack Obama's shape is the shape of a particular sort of human being. His shape is exactly the shape of the region of space that he precisely occupies, when he occupies it.

Finally, as any map can confirm, Canada has a shape, too. As with Canada and Mt. Everest, the English language does not have a name for the specific shape that Canada has. Nonetheless, we can still point out the following: Every accurate atlas of Canada represents Canada as a land mass with a certain shape. Canada has exactly that shape, which accurate atlases represent it as having.

Consider the following argument:

"Freedom is the ability to do whatever you want to do whenever you want to do it. But none of us living on an equal footing with others in society can be afforded that ability: To exercise that ability is to impede the ability of others to exercise that same ability, and so we cannot all exercise that ability. You cannot have an ability that you cannot exercise, so we cannot all have that ability. But if we live on equal footing, then either we all have the ability or none of us do. Therefore, none of us can have the ability to do whatever we want to do whenever we want to do it. And therefore, none of us is free."

What is the conclusion of this argument?

Feedback: The answer is D. "No one who lives on an equal footing with others in society can be free.

The argument's ultimate conclusion is "none of us is free." The pronoun "us," however, refers to those of us who live in society, who are on equal footing with one another. The argument, therefore, concludes that no one who lives on equal footing with others in society can be free."

Consider the argument in the previous question again:

"Freedom is the ability to do whatever you want to do whenever you want to do it. But none of us living on an equal footing with others in society can be afforded that ability: To exercise that ability is to impede the ability of others to exercise that same ability, and so we cannot all exercise that ability. You cannot have an ability that you cannot exercise, so we cannot all have that ability. But if we live on equal footing, then either we all have the ability or none of us do. Therefore, none of us can have the ability to do whatever we want to do whenever we want to do it. And therefore, none of us is free."

The premises of the argument include which of the following statements?

The answer is E. "A, B, and C."

The argument's premises, include statements A, B, and C. The argument assumes that freedom is the ability to do whatever you want to do whenever you want to do it, and then the argument points out, first, that we cannot all exercise such an ability, and second, that it is impossible to have an ability that you cannot exercise. These claims are among the argument's premises, but they are not in its conclusion. The conclusion, as stated in the answer to the previous question, is that none of us, who live in society on equal footing, are free.

Consider again, the argument in the previous question:

"Freedom is the ability to do whatever you want to do whenever you want to do it. But none of us living on an equal footing with others in society can be afforded that ability: To exercise that ability is to impede the ability of others to exercise that same ability, and so we cannot all exercise that ability. You cannot have an ability that you cannot exercise, so we cannot all have that ability. But if we live on equal footing, then either we all have the ability or none of us do. Therefore, none of us can have the ability to do whatever we want to do whenever we want to do it. And therefore, none of us is free."

One way to refute this argument would be to show that

The answer is B. "there are counterexamples to the general claim that freedom is the ability to do whatever you want to do whenever you want to do it."

The argument assumes a generalization—that freedom is just the ability to do whatever you want, whenever you want. To refute the argument by counterexample, then, all one has to do is to find an occasion of freedom, or an occasion in which individuals are free, which does not feature people doing whatever they want, whenever they want.

To point out that the person giving the argument is a compulsive liar might give you reason to doubt it as a bit of testimony. It would not, however, count as an actual refutation of the argument itself. In other words, to suppose that A is correct is to commit a fallacy of ad hominem.

To point out that the argument pits certain social classes against each other, moreover, does not refute the argument either. The premises of the argument could still be true, for instance, and the conclusion could still follow from the premises even if the argument also resulted in pitting certain social classes against one another. To show that the argument is nothing but some sort of class-based prejudice, it is not enough to point out that it pits social classes against one another. One must point out that it does this, and also show that either one of premises are false, or else that its conclusion does not follow from the premises, or that some other fallacy has been committed.

Finally, the ambiguity of "you" has no bearing on the argument, and for two reasons. First of all, the word "you" does not appear in the argument, (although the words "we" and "us" do). Second, and more important, however, is that the ambiguity of pronouns in general does not affect the truth of the argument's premises, or the rule of inference it uses. To see why, just replace every occurrence of "we" or "us" in the argument with "people who live in society." Since "we" and "us" are the only pronouns that occur in the argument, the result of switching them out will be an argument devoid of pronouns. Yet it will be the very same argument as before. This renders any attempted criticism of the argument, which focuses on the ambiguity of "you" or any other pronoun, moot.

A reductio ad absurdum is when you

The answer is C. "point out that the conclusion of an argument is clearly false."

As stated in the lecture, to present a reductio ad absurdum against an argument is to show that it leads to an absurd conclusion. In other words, it is to show that the argument's conclusion contradicts a manifestly obvious and uncontroversial fact. It is to show that the conclusion of an argument is clearly false.

To show that an argument's conclusion is clearly false, however, is not the same thing as showing that its premises are false. An argument with a false conclusion may still have true premises, provided that the argument is invalid.

Likewise, to show that an argument's conclusion is clearly false is not to show that it is invalid. For an argument with a false conclusion can still be valid, provided that it has at least one false premise.

A reductio shows that either the argument in question has a false premise or the argument is invalid.

Finally, to provide a reductio of an argument is not the same thing as to point out that a generalization has counterexamples. Sometimes, of course, an argument has a generalization as its conclusion, which happens to be manifestly false, and whose counterexample is both obvious and uncontroversial. In such cases, there are reductios that are also counterexamples. Not all reductios are counterexamples, however, since not all absurd conclusions are generalizations.

Consider the following argument:

"A man with no hairs at all on his head is bald. But a single extra hair cannot make the difference between a bald man and a non-bald man. And so, a man with 1 billion hairs on his head is also bald."

Which of the following is the conclusion of this argument?

The answer is C. "A man with 1 billion hairs on his head is bald."

From the premise that a hairless man is bald, and that a single hair cannot make the difference between being bald and not being bald, the argument concludes that a man with a billion hairs on his head is bald.

Consider the previous argument again:

"A man with no hairs at all on his head is bald. But a single extra hair cannot make the difference between a bald man and a non-bald man. And so, a man with 1 billion hairs on his head is also bald."

Which of the following is the premise (or are the premises) of this argument?

The answer is D. "A and B but not C."

To conclude that a man with a billion hairs is bald, this argument employs two premises: first, that a man with no hairs at all on his head is bald, and second, that the loss of a single extra hair cannot make the difference between a bald man and a non-bald man. These are the premises mentioned in A and B, respectively. So the correct answer is A and B but not C.

Consider the previous argument again:

"A man with no hairs at all on his head is bald. But a single extra hair cannot make the difference between a bald man and a non-bald man. And so, a man with 1 billion hairs on his head is also bald."

Which of the following would constitute a reductio ad absurdum of this argument?

The answer is D. "a non-bald man with 1 billion hairs on his head."

To provide a reductio for the above argument, it is enough to produce a single case, in light of which the conclusion is clearly false. Since the conclusion claims that even with a billion hairs, a man is still bald, one can provide a reductio of the argument by considering a man with a billion hairs, who is clearly non-bald.

Now consider the following argument:

"Every chicken is born from a chicken egg that has already been laid. Every chicken egg is laid by a chicken who has already been born. Therefore, there cannot be a first generation of chickens. And so if there are any chickens today, there must have been infinitely many generations of chickens before today."

Which of the following is the premise (or are the premises) of this argument?

The answer is E. "A and B but not C."

To conclude that, if there are any chickens today, there must have been infinitely many generations of chickens before today, this argument employs two premises: first, every chicken is born from a chicken egg that has already been laid, and second, that every chicken egg is laid by a chicken who has already been born. These are the premises mentioned in A and B, respectively. So the correct answer is A and B but not C.

Consider the previous argument again:

"Every chicken is born from a chicken egg that has already been laid. Every chicken egg is laid by a chicken who has already been born. Therefore, there cannot be a first generation of chickens. And so if there are any chickens today, there must have been infinitely many generations of chickens before today."

Which of the following is the conclusion of this argument?

Feedback:

The answer is C. "If there are any chickens today, there must have been infinitely many generations of chickens before today."

From the premise that every chicken is born from a chicken egg that has already been laid, and the premise that every chicken egg is laid by a chicken who has already been born, this argument concludes that, if there are any chickens alive today, then there must have been infinitely many chickens.

Consider the previous argument again:

"Every chicken is born from a chicken egg that has already been laid. Every chicken egg is laid by a chicken who has already been born. Therefore, there cannot be a first generation of chickens. And so if there are any chickens today, there must have been infinitely many generations of chickens before today."

Which of the following would constitute a reductio ad absurdum of this argument?

The answer is E. "the combination of A and C, but not B."

To provide a reductio for the above argument, it is enough to produce a single case, in light of which the conclusion is clearly false. Since the conclusion claims that if there are any chickens today, then there have been infinitely many generations of chickens, one can provide a reductio of the argument by considering a live chicken, combined with evidence, in light of which it is clear that there are only finitely many generations of any extant species.

Consider the following dialogue:

Hokey: The only thing that is intrinsically good is happiness. Everything else is good only to the extent that it produces happiness. For instance, health, prosperity, freedom, knowledge: these things are good only to the extent that they advance our happiness, and only because they advance our happiness.

Pokey: That's absurd! Can you imagine what your life would be like if you spent all your time trying to achieve happiness? You'd be miserable! You shouldn't try to achieve happiness: try to achieve other things, and happiness will follow.

Pokey claims to disagree with Hokey. But, if Pokey is disagreeing with Hokey, then what must the conclusion of Pokey's argument be?

Feedback:

The answer is B. "It's not the case that the only thing that is intrinsically good is happiness."

Hokey is arguing that the only intrinsically good thing is happiness. In order to be disagreeing with Hokey, Pokey must argue for the negation of Hokey's conclusion. To disagree with Hokey, in other words, Pokey must argue that happiness is not the only intrinsically good thing.

Consider the previous dialogue again:

Hokey: The only thing that is intrinsically good is happiness. Everything else is good only to the extent that it produces happiness. For instance, health, prosperity, freedom, knowledge: these things are good only to the extent that they advance our happiness, and only because they advance our happiness.

Pokey: That's absurd! Can you imagine what your life would be like if you spent all your time trying to achieve happiness? You'd be miserable! You shouldn't try to achieve happiness: try to achieve other things, and happiness will follow.

Which of the following is one of the premises of Pokey's argument?

The answer is E. "You would be miserable if you spent all your time trying to achieve happiness."

Pokey's actual argument appears to have the following conclusion: that Hokey should try to achieve things other than happiness, rather than spending all his time trying to achieve happiness. To reach this conclusion, Pokey assumes that Hokey would be miserable if he spent all his time trying to achieve happiness.

Consider the previous dialogue again:

Hokey: The only thing that is intrinsically good is happiness. Everything else is good only to the extent that it produces happiness. For instance, health, prosperity, freedom, knowledge: these things are good only to the extent that they advance our happiness, and only because they advance our happiness.

Pokey: That's absurd! Can you imagine what your life would be like if you spent all your time trying to achieve happiness? You'd be miserable! You shouldn't try to achieve happiness: try to achieve other things, and happiness will follow.

Pokey's argument is an example of

The answer is D. "refuting a straw man."

Pokey's argument concludes that Hokey should try to achieve things other than happiness, rather than just trying to achieve happiness. Because he takes himself to be disagreeing with Hokey's argument, Pokey is attributing the following thesis to Hokey: "Only try to achieve happiness."

By attributing that thesis to Hokey, however, Pokey misrepresents Hokey's position. Hokey never claimed that happiness is the only thing that anyone should pursue. He merely claimed that happiness is the only intrinsically good thing. Hokey's actual claim is compatible with the idea that people should pursue other things besides happiness. Hokey could easily maintain, for instance, that people should pursue a variety of things as means to happiness. So, in attempting to refute Hokey's argument, Pokey misrepresents Hokey's position.

Because Pokey misrepresents Hokey's position—specifically, by misattributing a claim to Pokey—it is clear that Pokey commits the fallacy of refuting a straw man.

Consider the following dialogue:

Hanky: "Since the Industrial Revolution began around 1750, human activities have contributed substantially to climate change by adding CO2 and other heat-trapping gases to the atmosphere. These greenhouse gas emissions have increased the greenhouse effect and caused Earth's surface temperature to rise." (See http://www.epa.gov/climatechange/science/causes.html)

Panky: That's ridiculous! CO2 is just what people exhale. And people have been around since way before 1750! Are you suggesting that people started exhaling only in 1750?

Since Panky is disagreeing with Hanky, what must the conclusion of Panky's argument be?

Feedback:

The answer is A. "Human activities have not contributed substantially to climate change."

Hanky is arguing that human activities have contributed substantially to climate change. In order to be disagreeing with Hanky, Panky must argue for the negation of Hanky's conclusion. To disagree with Hanky, in other words, Panky must argue that human activity has not significantly contributed to climate change.

Consider the previous dialogue again:

Hanky: "Since the Industrial Revolution began around 1750, human activities have contributed substantially to climate change by adding CO2 and other heat-trapping gases to the atmosphere. These greenhouse gas emissions have increased the greenhouse effect and caused Earth's surface temperature to rise." (See http://www.epa.gov/climatechange/science/causes.html)

Panky: That's ridiculous! CO2 is just what people exhale. And people have been around since way before 1750! Are you suggesting that people started exhaling only in 1750?

Which of the following are the premises of Panky's argument?

Feedback:

The answer is E. "D and C, but not A or B."

In attempting to refute Hanky's argument, Panky employs two premises: first, that humans naturally produce CO2, and second, that humans have existed since way before 1750. These are the claims mentioned in C and D, respectively, and they are Panky's only premises. So the correct answer is E.

Consider the previous dialogue again:

Hanky: "Since the Industrial Revolution began around 1750, human activities have contributed substantially to climate change by adding CO2 and other heat-trapping gases to the atmosphere. These greenhouse gas emissions have increased the greenhouse effect and caused Earth's surface temperature to rise." (See http://www.epa.gov/climatechange/science/causes.html)

Panky: That's ridiculous! CO2 is just what people exhale. And people have been around since way before 1750! Are you suggesting that people started exhaling only in 1750?

Panky's argument is an example of

Feedback:

The answer is D. "refuting a straw man."

Panky's argument concludes that, according to Hanky, people only started to breathe after 1750. Because he takes himself to be disagreeing with Hanky's argument, Panky attributes the following thesis to Hnaky: "Humans only started to breathe in the 1750s."

By attributing that thesis to Hanky, however, Panky misrepresents Hanky's position. Hanky never claimed that before 1750, human beings never produced CO2. He merely claimed that since 1750, human activity has greatly contributed to global warming through increased CO2 emissions. Hanky's claims are compatible with the idea that people have been breathing since before 1750. Hanky could easily maintain, for instance, that people have been naturally emitting CO2 for millions of years, but have only recently made a significant contribution to climate change because of changes in the industrial revolution. So, in attempting to refute Hanky's argument, Panky misrepresents Hanky's position.

Because Panky misrepresents Hanky's position—specifically, by misattributing a claim to Panky—it is clear that Panky commits the fallacy of refuting a straw man.

Which of the following arguments is a dismisser?

Albert is an engineer, so any considerations that he wants to offer in defense of a particular public art project are not going to be any good.

Feedback: The answer is B. A dismisser begins with premises about a person who is making a point, and ends with a conclusion that the person's reasons are not good. In this case, B is a dismisser because it concludes that Albert's reasons about public art are not good, and it reaches this conclusion by citing something about Albert, namely, that he is an engineer.

Which of the following arguments is a dismisser?

Flora never graduated from college, so her reasons for objecting to state funding for colleges are not good reasons.

Feedback: The answer is A. Again, a dismisser begins with premises about a person who is making a point, and ends with a conclusion that the person's reasons are not good. In this case, A is a dismisser because it concludes that Flora's reasons about state funding for college are not good, and it reaches this conclusion by citing something about Flora, namely, that she is not a college graduate.

Which of the following arguments is a dismisser?

Juliet is in love with Romeo, so the reasons she presents for his innocence cannot be trusted.

Feedback: The answer is D. A dismisser begins with premises about a person who is making a point, and ends with a conclusion that the person's reasons are not good. In this case, D is a dismisser because it concludes that Juliet's reasons about Romeo's innocence are not good, and it reaches this conclusion by citing something about Juliet, namely, that she loves Romeo.

Which of the following arguments is a denier?

Njeri is descended from Hutus, so despite her eloquent argument in defense of the Hutus, we know that what she is arguing is false.

Feedback: The answer is B. A denier begins with premises about someone making a point, and concludes with a denial of that person's point. In this case, B is a denier because it begins with an observation about Njeri, which is that she is descended from Hutus, and it concludes that her point is false.

Which of the following arguments is a denier?

None of the above

Feedback: The answer is E. Again, a denier begins with premises about someone making a point, and concludes with a denial of that person's point. In this case, none of the arguments in A-D is a denier. Argument A does not have a conclusion that denies something said by Sarah Palin; it merely says she is untrustworthy in general. Likewise, B does not conclude with a denial of anything Barack Obama says; instead, it claims that he is untrustworthy. Likewise, C and D respectively argue that Obama is untrustworthy and that Palin is an idiot. Because none of the arguments in A-D concludes with a denial of the point made by someone in the premises, A-D are not deniers.

Which of the following arguments is a denier?

Obama's argument against Sarah Palin shows he makes vicious attacks on people of modest intellectual means, so we know that the conclusion that he reached was false.

Feedback: The answer is C. A denier begins with premises about someone making a point, and concludes with a denial of that person's point. In this case, C is a denier because it begins with an observation about Barack Obama, which is that he allegedly makes vicious attacks on persons of modest intellectual means, and it concludes that Obama's point is false.

Which of the following arguments is a supporter?

Since Russell Brand grew up in poverty, the reasons that he gives in favor of the new anti-poverty campaign are especially compelling.

Feedback: The answer is A. A supporter begins with premises about the person making a point, and concludes that the person's reasons are particularly compelling. In this case, argument A is a supporter because it begins with an observation about Russell Brand, which is that he grew up in poverty, and it concludes that his reasons for an anti-poverty campaign are particularly compelling.

Which of the following arguments is a supporter?

Merle is a truck driver, and so whatever considerations he gives in favor of the government's new transportation policy are likely to be very compelling reasons.

Feedback: The answer is C. Again, a supporter begins with premises about the person making a point, and concludes that the person's reasons are particularly compelling. In this case, C is a supporter because it begins with an observation about Merle, which is that he is a truck driver, and it concludes that his reasons for supporting a new government transportation policy are particularly compelling.

Which of the following arguments is a supporter?

None of the above

Feedback: The answer is E. A supporter begins with premises about the person making a point, and concludes that the person's reasons are particularly compelling. In this case, none of the arguments in A-D are supporters because none begins with an observation about someone while concluding that the person's reasons are particularly compelling. Argument A does not conclude that Dora's reasons are compelling; it concludes that we should trust her more. B concludes that Dora's reasons are particularly bad, not that they are particularly good. Likewise, C and D offer reasons for distrusting and for trusting Dora, respectively, but none in A-D has a premise about Dora and a conclusion that says that Dora's reasons are particularly good.

Consider the following appeal to authority argument:

"TV personality Buzz Winthrop has repeatedly announced that there is no scientific consensus about whether the temperature of the earth has been increasing over the past century. Winthrop's TV show is sponsored by a number of big oil and gas companies, as well as a number of big automobile companies. Such important companies would never be willing to sponsor a show that was not completely truthful. Therefore, we can be certain that Winthrop is right is when he says that there is no scientific consensus about global warming."

This argument is an example of a(n)

The answer is "F. unjustified supporter."

An "argument from authority" is a supporter argument when it begins with a claim about a person, and concludes, based on the idea that the person's testimony is reliable, that the testimony is to be believed. The argument in this question is a supporter argument from authority because it begins with the assumption that a certain claim—Winthrop's—is sponsored by automobile companies, and that such companies would not sponsor Winthrop's program if his claim were not true. The argument, therefore, claims that the support of automobile companies is a reliable indicator of whether Winthrop is telling the truth. By appealing to the reliability of automobile sponsorship, the argument is a supporter argument from authority.

The argument is not a mere affirmer argument because it does not just affirm the truth of Winthrop's claim. It affirms Winthrop's claim based on the reliability of automobile sponsorship. The focus on the reliability of Winthrop's testimony makes the argument a supporter, rather than an affirmer.

The argument is not an amplifier argument because an amplifier argument says that the person in question has either a special right to decide a matter with her testimony, or else that the person in question plays a special role in deciding the matter, which is not just a matter of being a reliable expert. The argument does not specify any such role, however, so it is not an amplifier argument, either.

Finally, the argument is an unjustified argument because the endorsement and support of automobile companies is not a reliable indicator of whether a claim about global warming is true. Automobile companies, in other words, are not recognized experts on global warming. Since they are not experts on global warming, their endorsement of a claim about global warming is not an indicator of its truth.

Consider the following appeal to authority argument:

"Paul Krugman was being interviewed on a TV news program about the economy. During the interview, the interviewer called Krugman dishonest. Now, I realize that the interviewer is not an economist, or even very knowledgeable about economics, but still, the TV program is the interviewer's program. So the interviewer gets to set the rules for the program, and if the interviewer says that Krugman is dishonest, then we who are watching that interviewer's program should believe that Krugman is dishonest."

This argument is an example of a(n)

The answer is "D. unjustified amplifier."

An argument from authority, which is an amplifier, begins with a claim about a certain person, and concludes that, based on who the person is, the person has a greater right to offer testimony on the matter, and that this testimony is more decisive. The argument in this question is an amplifier. It begins by claiming that the accusation against Paul Krugman by the interviewer (the show's owner) was permitted, and it claims that, since the interviewer owns the show and sets the rules for interviewing, we should believe the interviewer's testimony. In short, the argument assumes that, since the interviewer has a greater right to decide his show's contents, we should accept his testimony on his show.

The argument is not an affirmer argument because it does not merely claim that the interviewer's testimony is true. It also makes an appeal to who has the right to offer testimony on Krugman's honesty, and it argues that, as the owner of the show, the interviewer's decision to present an interview should establish whether any of the interview's contents are true.

The argument is not a supporter argument because it does not claim that the interviewer's opinion is more reliable, or more likely to be right, or that anybody is an expert on anything. In fact, the interviewer is admitted to be no expert. Rather than concerning the reliability of the interviewer's testimony, the argument concerns the idea that, since the owner of an interview program has the right to decide its contents, we should accept its contents.

Finally, this argument is an unjustified amplifier argument because, in fact, whether someone owns a show does not give them the power to decide whether the claims on the show are true. From the fact that someone allows a claim on her show, therefore, does not, by itself, establish that claim's truth or falsity.

Consider the following appeal to authority argument:

"I've always thought that the Washington Post is a reliable paper. But I recently discovered that it's even more reliable than I had previously thought. A study that I just read about in the Washington Post was conducted by the Associated Press: They surveyed the 100 most widely circulated newspapers in the world and found that, among those 100, the Washington Post had the fewest number of errors per issue. So it turns out that the Washington Post is even more reliable than I had previously thought!"

This argument is an example of a(n)

The answer is "E. justified supporter."

An argument from authority is a supporter argument when it begins with a claim about a person, and concludes, based on the idea that the person's testimony is reliable, that the testimony is to be believed. The argument in this question is a supporter argument from authority because it begins with the assumption that the endorsement of a certain party—the Associated Press—is a reliable indicator of whether a newspaper has errors. By appealing to the reliability of the Associated Press, the argument is a supporter argument from authority.

The argument is not a mere affirmer argument because it does not just affirm that the Post is correct, or that what the Associated Press attests is true. The argument, rather, focuses on the fact that the Associated Press conducted a survey of newspapers, and that this survey makes their testimony more justified. The focus on the reliability of the Associated Press' testimony, in other words, makes the argument a supporter, rather than an affirmer.

The argument is not an amplifier argument because an amplifier argument says that the person in question either has a special right to decide a matter with her testimony or plays a special role in deciding the matter, which is not just a matter of being a reliable expert. The argument does not specify any such role, however, and so the argument is not an amplifier argument.

Finally, the argument is a justified argument because the Associated Press is said to have conducted a survey of actual newspapers, paying attention to their errors. If indeed this is correct, and if there is no reason to assume that the Associated Press conducted their survey dishonestly or mistakenly, then reports made in light of it would be reliable indicators of how many errors a newspaper has. The survey, in other words, is expected to make the Associated Press' testimony on newspaper errors reliable.

Consider the following appeal to authority argument:

"I was watching Gonzalez carefully as he slid into second-base, and it looked to me like he was safe. But then the umpire announced that Gonzalez was safe, and no one's view of the matter counts more than the umpire's. So now I'm sure Gonzalez was safe."

This argument is an example of a(n)

The answer is "C. justified amplifier."

An argument from authority that is an amplifier begins with a claim about a certain person, and concludes that, based on who the person is, that person has a greater right to offer testimony on the matter, and that this testimony is more decisive. The argument in this question is an amplifier. It begins by claiming that the man who announced Gonzalez' status is an umpire, and that "no one's view of the matter counts more than the umpire's." It concludes that the umpire's testimony is more decisive, and that Gonzalez is safe.

The argument is not an affirmer argument because it does not merely claim that the testimony is true. It also makes an appeal to whose testimony should count more, based on the fact that an umpire's calls are decisive.

The argument is not a supporter argument because it does not claim that the umpire's view is more reliable, or more likely to be right. It just says that the umpire's view "counts more." This means that the umpire has a greater right to offer testimony on the matter.

(It is true that, when baseball leagues appoint umpires, they prefer to have individuals who are experts, and whose opinions are more reliable. However, this argument did not indicate these considerations; it merely pointed to the idea that, when someone is an umpire, whatever that person says, goes. This idea—namely, that umpires have a greater right to offer testimony—is importantly different from the idea that umpires' testimony is more reliable. For the two conditions can come apart. It can happen—and arguably has happened—that certain umpires are appointed, who are not experts on baseball, but whose status as umpires nonetheless gives them a greater right to offer testimony than non-umpires. In such cases, an argument that pointed to their right as umpires to make calls, and which concluded that their calls are correct, would be an amplifier argument from authority.)

Finally, this argument is a justified amplifier argument because, in fact, regardless of whether one is an expert in baseball, or whether one's calls are reliable, the status of being an umpire does give someone a greater right to offer testimony about a baseball play than one would otherwise have.

Consider the following appeal to authority argument:

"For the past fifty years, the Standard Model of particle physics has predicted the existence of the Higgs Boson. The Standard Model has been quite well confirmed by a number of different experiments. But last year, some scientists reported finding the Higgs Boson. Since these experimenters are in a good position to know, I conclude that the Higgs Boson really does exist, just as the Standard Model predicts."

This argument is an example of a(n)

The answer is "E. justified supporter."

An argument from authority is a supporter argument when it begins with a claim about a person, and concludes, based on the idea that the person's testimony is reliable, that the testimony is to be believed. The argument in this question is a supporter argument from authority because it begins with the assumption that a certain claim—that the Higgs Boson exists—is supported by Standard Model particle physics, and that the Standard Model would not posit the existence of the Higgs Boson if it did not exist. The argument, therefore, claims that the support of the Standard Model is a reliable indicator of whether the Higgs Boson exists. By appealing to the reliability of authoritative sponsorship, the argument is a supporter argument from authority.

The argument is not a mere affirmer argument because it does not just affirm that the Higgs Boson exists. It affirms this claim based on the reliability of the Standard Model. The focus on the reliability of the Standard Model makes the argument a supporter, rather than an affirmer.

The argument is not an amplifier argument because an amplifier argument says that the person in question has either a special right to decide a matter with his or her testimony, or else that the person in question plays a special role in deciding the matter, which is not just a matter of being a reliable expert. The argument does not specify any such role, however, and so the argument is not an amplifier argument.

Finally, the argument is a justified argument because the endorsement and support of the Standard Model is a reliable indicator of whether a claim about particle physics is true. The Standard Model, in other words, is a recognized authority on particles.

Consider the following appeal to authority argument:

"My barber, Mr. Higgs, claims that there is no such thing as the Higgs Boson. But how could there be a Higgs Boson if Mr. Higgs himself denies its existence? Clearly, then, the Higgs Boson does not exist."

This argument is an example of a(n)

The answer is "B. unjustified affirmer."

Again, an affirmer argument from authority assumes a claim about a person, and infers that such a person's testimony is true. The argument in this question is an affirmer argument from authority because it assumes that Mr. Higgs is an expert on the Higgs Boson.

The argument is not an amplifier because its conclusion does not rely on any special right or special role in offering the testimony about the Higgs Boson. No role is specified.

The argument is not a supporter argument because it does not claim that the testimony is reliable, or from an expert. Rather, this argument merely concludes that the testimony is true.

Finally, the argument is an unjustified affirmer argument because the name of Mr. Higgs does not have anything to do with his testimony. His name is irrelevant to his testimony's truth. Since it is irrelevant, the affirmer argument is unjustified.

Consider the following argument:

"George Berkeley claimed that all of the things that take up space—animals, plants, furniture, clothing—all of these things were simply ideas in our minds, and they had no existence independently of being thought of by a mind. But of course everyone today rejects this view, and therefore Berkeley was wrong."

This argument is an example of an

Feedback: The answer is "B. appeal to popular opinion."

As stated in the lecture, an appeal to popular opinion is an argument whose premises claim that a certain opinion is popularly held, and which concludes from that premise that the opinion is true. The argument is an appeal to popular opinion, and it concerns the opinion that Berkeley was wrong.

Consider the following argument:

"A large majority of Americans currently believe that the most effective way for the US Government to grow the economy in the next three years is by reducing its spending. In a democracy, the voters decide. Therefore, the most effective way for the US Government to grow the economy in the next three years is by reducing its spending."

This argument is an example of a(n)

Feedback: The answer is "B. unjustified appeal to popular opinion."

As stated in the lecture, an appeal to popular opinion is an argument whose premises claim that a certain opinion is popularly held, and which concludes from that premise that the opinion is true. The argument in this question is an appeal to popular opinion, and it concerns the opinion of whether the most effective way for the US Government to grow the economy in the next three years is by reducing its spending. The argument assumes that, according to the majority of Americans, the most effective way for the US Government to grow the economy in the next three years is by reducing its spending, and the argument concludes that the most effective way for the US Government to grow the economy in the next three years is by reducing its spending.

The reason why the argument is an unjustified appeal to popular opinion is that the popularity of an opinion about how to best grow the economy is not, by itself, proof that the opinion is true. It is correct that, in a democracy, legislative actions that concern the economy should be determined by a consensus of the majority. However, this feature of democracy does not mean that the facts about the economy are as determined by popular consensus as legislative actions are. Regardless of what people may vote to do, the popularity of a view about how the economy works does not make that view correct.

Consider the following argument:

"According to one recent lexicographical study, a large majority of native English speakers in the United States think that 'chillaxing' is a synonym of 'relaxing.' Therefore, it is true that 'chillaxing' is a synonym of 'relaxing.'"

This argument is an example of a(n)

The answer is "A. justified appeal to popular opinion."

An appeal to popular opinion is an argument whose premises claim that a certain opinion is popularly held, and which concludes from that premise that the opinion is true. The argument in this question is an appeal to popular opinion, and it concerns the opinion of whether "chillaxing" is synonymous with "relaxing." The argument assumes that, according to the majority of native English speakers, "chillaxing" is synonymous with "relaxing." The argument concludes that "chillaxing" is indeed synonymous with "relaxing."

The reason why the argument is a justified appeal to popular authority is that whether "chillaxing" is synonymous with "relaxing" is partially determined by whether a majority of English speakers think so. If the majority of English speakers think and speak as if "chillaxing" is synonymous with "relaxing," then this would be good evidence that the two are synonymous.

Consider the following argument:

"It is easier to persuade people by appealing to their emotions than by giving them a sound argument. But everyone agrees that the only point of studying logic is to learn to persuade people. Therefore, it is a waste of time to study logic."

This argument contains a(n)

Feedback: The answer is "B. unjustified appeal to popular opinion."

Again, an appeal to popular opinion is an argument whose premises claim that a certain opinion is popularly held, and which concludes from that premise that the opinion is true. The argument in this question is an appeal to popular opinion, and it concerns the opinion of whether the only point of studying logic is to learn to persuade people. The argument assumes that, according to "everyone," "the only point of studying logic is to learn to persuade people." From this claim, and from the claim that "it is easier to persuade people by appealing to their emotions than by giving them a sound argument" that "it is a waste of time to study logic."

The reason why the argument is an unjustified appeal to popular opinion is this: Even if everyone agrees that the point of studying logic is to persuade people, it does not follow that the point of studying logic is to persuade people. It could be, rather, that the point of studying logic is to learn how to reason, or how to think more critically about difficult matters, rather than to persuade people. In such a case, everyone could still agree that the point of studying logic is persuasion; the majority would simply be wrong in their agreement.

Consider the following argument:

"If we take an umbrella to go out, then we might end up losing the umbrella. If we lose the umbrella, we will get upset. If we get upset, we will fight with each other. If we fight with each other, we may get a divorce. If we get a divorce, our kids may suffer for the rest of their lives. Let's not make our kids suffer for the rest of their lives: Let's not take an umbrella."

Which of the following claims do you think is true about the argument just considered?

Feedback:

The answer is "A. It is valid but not sound."

This argument concerns whether to take a certain course of action, and it reasons that, since a certain event will occur if the course of action is pursued, and since the event is to be avoided, the course of action is to be avoided.

In these respects, the argument is like that of Archie and Michel from Lesson 4, who argue over whether it is better to put one's socks on before one puts on any shoes. Archie argues that, since an undesirable event (namely, ending up with one's feet unevenly clothed) will result from not putting on socks before shoes, Archie argues against Michael's course of action, which consists in not putting on socks before shoes.

Just as Michael was correct to point out that the event of ending up with one's feet unevenly clothed is unlikely, so should we react to the argument in this question. It is not inevitable that each event listed in the argument will occur, and in fact, under normal conditions, it would not be likely at all that each event would occur. Given the unlikeliness of the whole chain of events, then, the predictions in the argument's premises are false. This is what makes the argument unsound.

Whether the argument provides a good reason for taking an umbrella, then, depends on how likely it is for the umbrella to be lost, for a fight to ensue, for a divorce to result in the fight, and for the kids to suffer for their lives because of the divorce. Without any further information on the likelihood of such events, we cannot tell whether the argument provides a good reason for taking an umbrella.

Consider the following conversation:

Jack: Hey Jill, have you finished doing the exercises for Lesson 11?

Jill: No, I'm finding it really difficult to keep up with that course. For one thing, I've had to work extra hours at my job recently. And then I've also been finding it hard to concentrate: Ram seems like a robot when he lectures.

Jack: Well, did it ever occur to you that Ram might actually be a robot?

Jill: You know, I never thought of that!

Jane: I can tell you both right now that he's not a robot. I know him personally, and that's just the way he is: He's robotic like that in real life.

Jack: Well, so how do you know that he's not a robot?

Jane: I was wondering about it so I asked him, and he assured me that he wasn't a robot.

In the conversation above, Jane is implicitly making an argument for a particular conclusion. Now, please answer the following questions about Jane's implicit argument. Which of the following statements is one of the premises of her argument?

Feedback: The answer is "E. Ram assured me that he is not a robot."

Jane is arguing that Ram is not a robot. The way that she argues for this claim, however, is by citing the fact that, in person, Ram had assured her that he is not a robot. Jane's premise, therefore, is "Ram assured me that he is not a robot."

Consider again the conversation in question 1:

Jack: Hey Jill, have you finished doing the exercises for Lesson 11?

Jill: No, I'm finding it really difficult to keep up with that course. For one thing, I've had to work extra hours at my job recently. And then I've also been finding it hard to concentrate: Ram seems like a robot when he lectures.

Jack: Well, did it ever occur to you that Ram might actually be a robot?

Jill: You know, I never thought of that!

Jane: I can tell you both right now that he's not a robot. I know him personally, and that's just the way he is: He's robotic like that in real life.

Jack: Well, so how do you know that he's not a robot?

Jane: I was wondering about it so I asked him, and he assured me that he wasn't a robot.

Which of the following statements is the conclusion of Jane's argument?

Feedback:

The answer is "C. Ram is not a robot."

Jane is arguing that Ram is not a robot. The way that she argues for this claim is by citing Ram's assurance that he is not a robot. Jane's conclusion, therefore, is "Ram is not a robot."

Consider the same conversation again:

Jack: Hey Jill, have you finished doing the exercises for Lesson 11?

Jill: No, I'm finding it really difficult to keep up with that course. For one thing, I've had to work extra hours at my job recently. And then I've also been finding it hard to concentrate: Ram seems like a robot when he lectures.

Jack: Well, did it ever occur to you that Ram might actually be a robot?

Jill: You know, I never thought of that!

Jane: I can tell you both right now that he's not a robot. I know him personally, and that's just the way he is: He's robotic like that in real life.

Jack: Well, so how do you know that he's not a robot?

Jane: I was wondering about it so I asked him, and he assured me that he wasn't a robot.

Jane's argument is an example of which of the following?

Feedback:

The answer is "D. unjustified appeal to authority."

Ram's assurance that he is not a robot only means that, according to Ram, Ram is not a robot. Ram believes, or thinks, that he is not a robot, in other words. Because Jane takes Ram's assurance as authoritative, Jane's argument is an argument from authority.

Unless the argument establishes that Ram is an authority on robotics, however, or on himself, Jane's argument from authority is unjustified. Ram, of course, may very well be an authority on such things, but Jane's argument does not say so. All that Jane's argument cites is Ram's assurance. By itself, Ram's assurance is not obviously the assurance of a robotics expert. So, without further additions to Jane's argument, it appears that Jane's argument is unjustified.

Consider the same conversation again:

Jack: Hey Jill, have you finished doing the exercises for Lesson 11?

Jill: No, I'm finding it really difficult to keep up with that course. For one thing, I've had to work extra hours at my job recently. And then I've also been finding it hard to concentrate: Ram seems like a robot when he lectures.

Jack: Well, did it ever occur to you that Ram might actually be a robot?

Jill: You know, I never thought of that!

Jane: I can tell you both right now that he's not a robot. I know him personally, and that's just the way he is: He's robotic like that in real life.

Jack: Well, so how do you know that he's not a robot?

Jane: I was wondering about it so I asked him, and he assured me that he wasn't a robot.

Jane's argument is an example of which of the following?

Feedback:

The answer is "C. affirmer."

Because Jane takes Ram's assurance to be true, and because she cites neither a reason why Ram's assurance is reliable nor a reason why Ram is especially authoritative in deciding who is a robot, her argument must be an affirmer, and not either a supporter or an amplifier. It cannot be a dismisser, moreover, because nobody's testimony in Jane's argument is said to be unreliable.

Are you a robot?

Answer Key: A, B, C, D, E

Feedback:

Excellent! Now repeat these lines:

I may not injure a human being or, through inaction, allow a human being to come to harm.

I must obey the orders given to me by human beings, except where such orders would conflict with (1).

I must protect my own existence as long as such protection does not conflict with (1) or (2).

Which of the following is the definition of "fallacy"?

an argument in which the premises do not support the conclusion.

When someone commits a fallacy, that person presents claims, as if those claims supported her conclusion, when in fact, those claims do not support her conclusion. Fallacious arguments, in other words, are either invalid (if they are deductive) or else very weak (if they are inductive).

Which of the following terms is vague?

all of the above.

As stated in the lecture, a vague term is one that does not have a precise definition. None of the terms in A through C, however, has a precise definition. To see why there is no precise definition for "large," imagine a series of items, in which each item is slightly less large than the next (say, by a millimeter in height), and which begins with an item that is large. Presumably, if something is large, it cannot cease to be large merely by decreasing its size by a millimeter. One millimeter, in other words, cannot make the difference between being large and not being large. Because a single millimeter in height cannot mark the difference between objects that are large and objects that are not large, it is possible to set up a paradox of vagueness with the term "large," just as one can with the terms "bald" and "heap."

A similar examination of the terms "soft" and "late" reveals why both of them are vague, too. We can imagine a series of items that gradually differ in their softness (say, by 0.01 on the Mohs hardness scale) or that gradually differ in their lateness (say, by 1 second after the deadline). Intuitive claims like "a non-soft item cannot become soft just by changing 0.01 points on the Mohs scale" and "a single second cannot make the difference between things that are late and things that are not late" would allow us to construct instances of the paradox of vagueness with these terms.

Which of the following terms is not vague?

all of the above.

As stated in the lecture, a vague term is one that does not have a precise definition. All of the terms in A through C, however, have precise definitions. "Pi" has a precise definition; it is impossible for there to be a range of amounts that differ by being more or less pi. Whether an amount is pi is an all-or-nothing matter. Certain amounts can be closer to pi than others, of course, but this is not the same thing as being pi, but only to a certain degree. An amount cannot be pi, but only to some degree or other; either an amount is pi or it is not. Pi has a precise definition.

Likewise for the term "quadratic equation." Either an item is a quadratic equation or it is not. Being a quadratic equation does not admit of degrees.

Likewise for the term "square root." Either a number is the square root of another or it is not. It does not make sense to say that a certain number is another's square root, but just a little bit. Being a square root of some number does not admit of degrees. "Quadratic equation" and "square root" are not vague terms; they have precise definitions.

Which of the following arguments is an example of the paradox of vagueness (that is, an apparently valid argument from apparently true premises to an apparently false conclusion)?

Walter is not fat now, and you cannot make someone fat by adding 1 pound to that person's weight. Therefore, no matter how much Walter weighs, he will not be fat.

As stated in the lecture, a paradox of vagueness is a seemingly valid argument, whose first premise claims that an item lacks (or has) a certain feature, and whose second premise points out that a tiny, incremental change cannot make the difference between having that feature and lacking it. The paradox will conclude that the item in question can never acquire (or lose) the feature in question, no matter how much it changes.

In the question above, only D is an example of the paradox of vagueness. D claims that an item, Walter, does not have the feature of being fat, and that an incremental change of a single pound cannot make the difference between being fat and being non-fat. It concludes that, no matter how much Walter changes (with respect to his weight), he will never be fat.

Premise A is not an example of the paradox of vagueness, since A merely claims that if Walter is under 150 pounds, Walter is not fat. A does not argue to the paradoxical conclusion that Walter can never become fat.

Premise B is not an example of the paradox, either, since its paradoxical conclusion also includes the conjunct "he can never be fatter than he is now." This second conjunct does not follow from the premises, which make the argument in B obviously invalid. An instance of the paradox of vagueness, however, must at least seem to be valid.

Finally, premise C is not an example of the paradox, either, since its paradoxical conclusion states, "Walter can never be fatter than other people who weigh less than he does." This second conjunct does not follow from the premises, which make the argument in C obviously invalid. An instance of the paradox of vagueness, however, must at least seem to be valid.

Which of the following arguments is an example of the paradox of vagueness (that is, an apparently valid argument from apparently true premises to an apparently false conclusion)?

Robinson is not tall. Someone who is not tall cannot become tall merely by growing 1 millimeter. Therefore, Robinson will never be tall, no matter how many millimeters he grows.

As stated in the lecture, a paradox of vagueness is a seemingly valid argument, whose first premise claims that an item lacks (or has) a certain feature, and whose second premise points out that a tiny, incremental change cannot make the difference between having that feature and lacking it. The paradox will conclude that the item in question can never acquire (or lose) the feature in question, no matter how much it changes.

In the question above, only B is an example of the paradox of vagueness. B claims that an item, Robinson, does not have the feature of being tall, and that an incremental change of a single millimeter cannot make the difference between being tall and being non-tall. It concludes that, no matter how much Robinson changes (with respect to his height), he will never be tall.

Premise A is not an example of the paradox of vagueness, since A invalidly concludes that no one is tall, simply on the basis that nobody can be tall merely by being a millimeter taller than a non-tall thing, such as Robinson. An instance of the paradox of vagueness, however, must at least seem to be valid.

Premise C is not an example of the paradox of vagueness, since C invalidly concludes that no one can be taller than Robinson. An instance of the paradox of vagueness, however, must at least seem to be valid.

Which of the following arguments is an example of the paradox of vagueness (that is, an apparently valid argument from apparently true premises to an apparently false conclusion)?

Lin is roughly 2 meters tall. He would still be roughly 2 meters tall if his height were changed by 1 mm. Therefore, he will always be roughly 2 meters tall.

As stated in the lecture, a paradox of vagueness is a seemingly valid argument, whose first premise claims that an item lacks (or has) a certain feature, and whose second premise points out that a tiny, incremental change cannot make the difference between having that feature and lacking it. The paradox will conclude that the item in question can never acquire (or lose) the feature in question, no matter how much it changes.

In the question above, only B is an example of the paradox of vagueness. B claims that an item, Lin, has the feature of being roughly 2 meters tall, and that an incremental change of a single millimeter cannot make the difference between being roughly 2 meters tall and not being roughly 2 meters tall. It concludes that, no matter how much Lin changes (with respect to his height), he will never cease to be roughly 2 meters tall.

Argument A is not an example of the paradox of vagueness, since it does not deny that a single, incremental change can make the difference between having a certain feature and lacking it. Instead, A focuses on whether anybody would notice such an incremental change. Yet the paradox of vagueness does not concern whether anybody notices incremental change; it concerns whether such changes can make the difference between possessing a certain feature and lacking it.

Argument C is not an example of the paradox of vagueness, since C contains the obviously false premise, "if someone is noticeably taller than Song, then they will still be noticeably taller than Song no matter how greatly their height is changed," which does not appeal to any single incremental change. An instance of the paradox of vagueness, however, must appeal to such things.

Which of the following arguments is an example of a conceptual slippery slope argument?

A person who weighs 50 kg is very light.

A difference of 1g is not a significant difference in human weight.

A person who weighs 200 kg is very heavy.

_____________________________________________________

Therefore, the difference between a light person and a heavy person is not a significant difference.

A conceptual slippery slope argument is an argument to the effect that there is no significant difference between two conditions, since a series of gradual changes stands between them. These arguments are fallacious; the fact that a series of gradual differences separates two states does not imply that there is no significant difference between those states.

In this case, the difference between being 50 kg and being 200 kg is treated as insignificant, since a difference of 1kg is insignificant, and one can treat the difference of 50 kg and 200 kg as a series of 150 small changes, each of which is by a single kg.

Which of the following is an example of a conceptual slippery slope argument?

A person who never votes is politically non-participatory.

The difference between voting once in your life and voting never is not a significant difference.

A person who votes in annual elections at least thirty times is politically active.

_________________________________________________________________________

Therefore, there is no significant difference between being politically active and being politically non-participatory.

A conceptual slippery slope argument is an argument to the effect that there is no significant difference between two conditions, since a series of gradual changes stands between them. These arguments are fallacious; the fact that a series of gradual differences separates two states does not imply that there is no significant difference between those states.

In this case, the difference between being never voting and voting in thirty elections is treated as insignificant, since a difference of voting merely once is insignificant, and one can treat the difference between voting in thirty elections and never voting as a series of thirty small changes, each of which consists in voting once.

Consider the following argument:

A building that is 5,000 years old is very ancient. A difference of one day is not a significant difference in the age of a building.

__________________________________________________________________________

There is no significant difference between a building that is very ancient and one that is very new.

Which of the following would have to be added as a premise in order to make the argument above into a conceptual slippery slope argument?

A building that is one year old is very new.

A conceptual slippery slope argument is an argument to the effect that there is no significant difference between two conditions, since a series of gradual changes stands between them. These arguments are fallacious; the fact that a series of gradual differences separates two states does not imply that there is no significant difference between those states.

In this case, the difference between being ancient and being very new is treated as insignificant, since a difference of one day in age is insignificant, and one can treat the difference of being ancient and being very new as a series of many small changes, each of which is by a single day in age.

Which of the following is a fairness slippery slope argument?

An employee of thirty years is eligible for retirement benefits.

One day is not a significant difference in duration of employment.

___________________________________________________

Therefore, it's not fair to deny retirement benefits to an employee of one year.

A fairness slippery slope fallacy is an argument that claims that since a certain course of action is fair or unfair, and since any other course of action that differs from the first by a mere incremental difference must be similarly fair or unfair, it follows that a radically different course of action must be fair or unfair in the exact same way as the first.

In this case, the argument in B claims that if it is unfair to deny retirement benefits to an employee of thirty years, then this makes it unfair to deny retirement benefits to someone whose employment differs by a small increment: one day. From these claims, the argument fallaciously concludes that it is unfair to deny retirement benefits to an employee of one year.

Which of the following is a fairness slippery slope argument?

A citizen eighteen years of age has the right to vote.

One day is not a significant difference in human maturity.

_____________________________________________

Therefore, it's not fair to deny a citizen one year of age the right to vote.

A fairness slippery slope fallacy is an argument that claims since a certain course of action is fair or unfair, and since any other course of action that differs from the first by a mere incremental difference must be similarly fair or unfair, it follows that a radically different course of action must be fair or unfair in the exact same way as the first.

In this case, the argument in A claims that, if it is unfair to deny voting rights to an citizen who is eighteen years old, then this makes it unfair to deny voting rights to someone whose age differs by a small increment: one day. From these claims, the argument fallaciously concludes that it is unfair to deny voting rights to a citizen of one year in age.

Consider the following argument:

A citizen who is forty years old is too old to be drafted into the armed services.

______________________________________________________________________

Therefore, a citizen who is twenty years old is too old to be drafted into the armed services.

Which of the following premises would you need to add to this argument in order to turn it into a fairness slippery slope argument?

One day is not a significant difference in human age.

A fairness slippery slope fallacy is an argument that claims since a certain course of action is fair or unfair, and since any other course of action, which differs from the first by a mere incremental difference, must be similarly fair or unfair, it follows that a radically different course of action must be fair or unfair in the exact same way as the first.

In this case, the argument above claims that it is unfair to draft a forty-year-old citizen into the armed services. For this to be part of a fairness slippery slope argument, it must also assume that it is unfair to draft someone into the armed services, whose status differs from that of a forty-year old by a small increment. Of the options, only C does this. From C and the first premise, the argument can fallaciously conclude, as a fairness slippery slope argument would, that it is unfair to draft a twenty-year old into the armed services.

Which of the following arguments is a causal slippery slope argument?

If we skip brushing our teeth tonight, then it's likely that we will skip brushing them tomorrow night.

If we skip brushing our teeth tomorrow night, then it's likely that we will skip brushing them the night after tomorrow.

We should not skip brushing our teeth three nights in a row.

_____________________________________________

Therefore, we should not skip brushing our teeth tonight.

A causal slippery slope fallacy is an argument that claims that, if a certain proposal is accepted, then, through a gradual series of steps, some disastrous effect will occur. The argument concludes that the proposal should not be accepted.

In this case, the argument in B claims that, if we skip brushing our teeth tonight, we will do so three nights in a row, which is disastrous. The argument concludes that we should not skip brushing our teeth tonight.

Which of the following is NOT a causal slippery slope argument?

A.

It is not very unhealthy to skip brushing your teeth for a single night.

There is no significant difference between brushing your teeth on a particular night or not brushing your teeth on that night.

It is very unhealthy to skip brushing your teeth every night.

__________________________________________________________________________

There is no significant difference between being very unhealthy and not being very unhealthy.

B.

People who do not brush their teeth on a particular night are not necessarily unhealthy.

People who skip brushing their teeth for one night more than someone who is not unhealthy are also not necessarily unhealthy.

__________________________________________________________________________

Therefore, someone who does not brush their teeth on any night is not necessarily unhealthy.

C.

If we skip brushing our teeth tonight, then it's likely that we will skip brushing them tomorrow night.

If we skip brushing our teeth tomorrow night, then it's likely that we will skip brushing them the night after tomorrow.

If we skip brushing our teeth the night after tomorrow, then it's likely that we will skip brushing them the night after that.

__________________________________________________________________________

Therefore, we should not skip brushing our teeth tonight.

all of the above.

A causal slippery slope fallacy is an argument that claims that if a certain proposal is accepted, then, through a gradual series of steps, some disastrous effect will occur. The argument concludes that the proposal should not be accepted.

None of A through C is a causal slippery slope argument. Argument C does not cite a disastrous effect that follows through a gradual series of steps. It only includes a series of steps. Argument B similarly fails to cite some disastrous consequence that follows from a proposal by a series of steps. Argument A might look like a causal slippery slope argument, since it appeals to differences of small increments to reach its conclusion, but in fact, A is a conceptual slippery slope argument. A conceptual slippery slope argument says that two states are not significantly different, due to the fact that they are distinguishable through a series of small, incremental changes. A causal slippery slope exploits the vagueness of a term to show that some disastrous consequence, or calamity, will result from a proposal.

Consider the following argument:

If we start requiring automatic weapons owners to pass an automatic weapons safety test, then it's likely that we will start to require gun owners to pass a gun safety test.

If we start requiring gun owners to pass a gun safety test, then it's likely that we will start to require knife owners to pass a knife safety test.

If we start requiring knife owners to pass a knife safety test, then it's likely that we will start to require toy owners to pass a toy safety test.

________________________________________________________________________________

Therefore, we should not start requiring automatic weapons owners to pass an automatic weapons safety test.

Which of the following would have to be added as a premise to the argument above, in order to turn it into a causal slippery slope argument?

We should not start requiring toy owners to pass a toy safety test.

A causal slippery slope fallacy is an argument that claims that, if a certain proposal is accepted, then, through a gradual series of steps, some disastrous effect will occur. The argument concludes that the proposal should not be accepted.

The argument above misses a premise, which specifies that a result is a calamity or disastrous. It includes a gradual series of steps, whereby toy owners are required to pass safety tests, but it fails to state why this would be a calamity. Premise A specifies that we should not require toy owners to pass safety tests. When added to the above argument, it functions as a reason to reject the proposal of requiring gun owners to pass safety tests. Premise A turns the above argument into a causal slippery slope argument, in other words.

Which of the following sentences contains semantic ambiguity?

The bank is far away.

Semantic ambiguity occurs when a single word has more than one meaning. In A, we find a sentence with the word "bank." The word "bank" has more than one meaning: it can refer to the edge of a river, or it could refer to a place in which to store something (such as money). So A contains semantic ambiguity.

Which of the following sentences contains syntactic ambiguity?

A. The bank is far away.

B. Barack Obama was first elected US President in 2008.

C. The French word for "Sunday" is "dimanche."

D. There is no largest number in the Fibonacci sequence.

Correct E. none of the above

none of the above.

None of A through D is a case of syntactic ambiguity. Syntactic ambiguity occurs when a sentence or phrase has more than one meaning, due to the order or the grammatical arrangement of the words in it. None of A through D is ambiguous in this way. A is ambiguous, but only because the word "bank" has two meanings. It is not ambiguous because of its words' order. None of B, C, or D is ambiguous, and so is not syntactically ambiguous, either.

Which of the following sentences contains semantic ambiguity?

He is a cheap date.

Again, semantic ambiguity occurs when a single word has more than one meaning. In B, we find a sentence with the word "cheap." On one hand, "cheap" might refer to the expense that one needs in order to date the person in question. If so, then "he is a cheap date" means that one does not need to expend much in order to go on a date with this person. On the other hand, "cheap" might refer to the expense that the person in question will make on a date. If so, then "he is a cheap date" means that he is not willing to expend much on a date. Since B is ambiguous, and since B is ambiguous because of a single word it contains—namely, ""cheap"—it follows that B contains semantic ambiguity.

Which of the following sentences contains syntactic ambiguity?

All the boys love all the girls.

Again, syntactic ambiguity occurs when a sentence or phrase has more than one meaning, due to the order or the grammatical arrangement of the words in it. Sentence A is ambiguous in this way. The phrase "All the boys love all the girls" is ambiguous. On one hand, it could mean that each individual boy loves all of the girls, or it could mean that both every boy loves some girl, and also that every girl is loved by some boy. This ambiguity is not due to the fact that "all" means two different things, in the way that "bank" means two different things. Rather, this ambiguity is due to the way the words are arranged in the sentence. So sentence A contains syntactic ambiguity.

Which of the following sentences contains semantic ambiguity?

Answer: D. The economy is still weak.

A semantic ambiguity occurs when a single word means more than one thing. Here, the word "weak" means more than one thing. On one hand, the word "weak" means "not physically powerful." On the other hand, when used to describe economies, the word "weak" can also mean a variety of other things, including "providing an insufficient number of remunerative jobs." Because the word "weak" means both of these things, the sentence, "the economy is still weak" could either mean that the economy is not physically powerful, or that the economy provides an insufficient number of remunerative jobs.

Which of the following sentences contains syntactic ambiguity?

Answer: B. Some polygons have more vertices than pentagons.

A syntactic ambiguity occurs when a whole phrase or sentence means more than one thing. Here, the sentence "some polygons have more vertices than pentagons" means more than one thing. The sentence could be interpreted as a comparison between the number of vertices had by some polygons, and the number of pentagons had by those same polygons; or it could be interpreted as a comparison between the number of vertices had by some polygons, and the number of vertices had by some pentagons. This ambiguity is due to the order of the words, and not due to an ambiguity in any individual word, such as "polygons." This means that B contains syntactic ambiguity.

Suppose that an American citizen were to offer the following argument:

"Ours is a nation of laws. All of us must obey the laws. But God's law forbids work on the Sabbath day. And therefore we must not work on the Sabbath Day."

This argument involves a

Answer: C. fallacy of ambiguity.

The phrase "the laws" means more than one thing. On one hand, the term "the laws" means "legislated prohibitions." On the other hand, when discussing religious matters, the term "the laws" can also refer to "religious prohibitions." Because the term "the laws" means both of these things, the sentence, "all of us must obey the laws" can mean two different things. It might mean that we must all heed religious prohibitions. However, it is also possible, and far more likely, that the term "laws" means different things in different parts of the argument, and that the sentence means that we must all heed legislated prohibitions. Because the argument ignores the ambiguity in "the laws," the argument commits a fallacy of ambiguity.

Suppose that an American citizen were to offer the following argument:

"Taxes provide revenue for the government, so that it can do its work. Part of the government's work involves collecting taxes. Therefore, taxes help to fund the collection of taxes."

This argument involves a

Answer: E. none of the above

The argument is in fact valid. If the government's revenue exists in order for the government to do its work, and if some of this work includes collecting taxes, then the revenue exists in order to collect taxes. Whether this revenue comes from taxes does not affect the validity of the argument. (Note, also, that the sentence "taxes help fund the collection of taxes" can be true, even when taxes also fund other things, too.)

Suppose that Dr. Spock (or some other authority on parenting) offered the following argument:

"It is very important for parents not to let down their children. I am now carrying my child. Therefore, even though he wants to walk on his own, it is important that I not let him down."

This argument is a

Answer: C. fallacy of ambiguity

The term "let down" means more than one thing. On one hand, the term "let down" means "allow to move downward." On the other hand, when used to describe people, the term "let down" can also mean "emotionally disappoint." Because the term "let down" means both of these things, the sentence, "it is very important for parents not to let down their children" might mean that it is important for parents to not let their children move downward, as the argument assumes. However, it is also possible, and far more likely, that the term "let down" means different things in different parts of the argument, and that the sentence means that parents should not emotionally disappoint their children. Because the argument ignores the ambiguity in "let down," the argument commits a fallacy of ambiguity.

Consider the following argument:

"There are more humans than tigers in the world. But there are more tigers than pandas. Therefore, humans are more numerous than pandas."

This argument involves a

Answer: E. none of the above

The argument is in fact valid. If there are more Fs than Gs, and there are more Gs than Hs, then it logically follows there are more Fs than Hs. The above argument is an instance of this schema, with "humans," "tigers," and "pandas" being the values for F, G, and H, respectively.

Consider the following argument: "

Zeke and Jane are madly in love. In fact, Jane is the Zeke's one true love: He cannot love another woman, and so he cannot cheat on her. But Zeke's grown daughter Mary is also a woman. So Zeke cannot love Mary. Zeke must therefore be a terrible father!"

This argument involves a

Answer: C. fallacy of ambiguity

A semantic ambiguity occurs when a single word means more than one thing. Here, the word "love" means more than one thing. On one hand, the word "love" means "loving romantically," as husbands love wives and lovers love each other. On the other hand, when used to describe friends and family members, the word "love" can mean "familial love," or the kind of love that is not romantic. Because the word "love" means both of these things, the sentence, "Zeke cannot love Mary" might mean that Zeke cannot have familial love for Mary, which would imply that Zeke is a terrible father. However, it is also possible, and far more likely, that "love" means romantic love, in which case "Zeke cannot love Mary" is true, but it does not imply that Zeke is a terrible father. Because the argument ignores the ambiguity in "love," the argument commits a fallacy of ambiguity.

Consider the following argument:

"My horse is racing and my heart is racing. Therefore my horse and my heart are doing the same thing."

This argument involves a

Answer: C. fallacy of ambiguity

A semantic ambiguity occurs when a single word means more than one thing. Here, the word "racing" means more than one thing. On one hand, the word "racing" means "moving quickly." On the other hand, when used to describe hearts, the word "racing" can also mean "rapidly beating." Because the word "racing" means both of these things, the sentence, "my horse is racing fast and my heart is racing" might mean that the horse and the heart are doing the same thing, as the argument assumes. However, it is also possible, and far more likely, that they mean different things: one's horse is moving quickly, and one's heart is beating rapidly. Because the argument ignores the ambiguity in "racing," the argument commits a fallacy of ambiguity.

Consider the following argument:

"My horse is racing and my heart is racing. But racing is not significantly different from walking very quickly, which is not significantly different from walking somewhat quickly, which is not significantly different from walking somewhat slowly, which is not significantly different from walking very slowly, which is not significantly different from standing still. Therefore, racing is not significantly different from standing still. And so it would be unfair to treat racers differently than we treat those who are standing still. And therefore we must treat racers in just the same way that we treat those who are standing still. And thus we must treat my horse and my heart in the same way."

This argument involves a

Answer: D. all of the above

A fallacy of ambiguity occurs when an argument exploits the fact that a word means more than one thing. Here, the word "racing" means more than one thing. On one hand, the word "racing" means "moving quickly." On the other hand, when used to describe hearts, the word "racing" can also mean "rapidly beating." Because the word "racing" means both of these things, the sentence, "my horse is racing fast and my heart is racing" might mean that the horse and the heart are doing the same thing, as the argument assumes. However, it is also possible, and far more likely, that they mean different things: one's horse is moving quickly, and one's heart is beating rapidly. Because the argument ignores the ambiguity in "racing," the argument commits a fallacy of ambiguity.

The argument also commits a conceptual slippery slope fallacy, however. A conceptual slippery slope fallacy is an argument that alleges that a series of actions cannot change the quality of a certain thing. Typically, the problem with a conceptual slippery slope argument is that its second premise claims that something is not a matter of degree, when in fact it is a matter of degree.

In this case, the premise in the argument treats "racing" (in the sense of moving quickly) as an all-or-nothing matter. The argument assumes that either one is racing or is not.

Suppose, however, that racing admits of degrees. Suppose that one could be racing just a little bit, or that one could be racing even more, or one could be racing to an extreme degree. Suppose further that, depending on whether one was walking quickly, somewhat quickly, or slowly, one would be racing to certain degrees. If that is the case, the sentence, "but racing is not significantly different from walking very quickly, which is not significantly different from walking somewhat quickly, which is not significantly different from walking somewhat slowly, which is not significantly different from walking very slowly, which is not significantly different from standing still" is false. It is false because, in fact, there is a difference between walking very quickly, walking somewhat quickly, and so on. That difference, furthermore, is important to racing. The difference is in the degree to which one is racing, though, rather than whether one is racing at all.

Finally, the argument also commits a fairness slippery slope fallacy. A fairness slippery slope fallacy is an argument, which claims that, since a certain course of action is fair, and since any other course of action that differs from the first by a mere incremental difference must also be fair, it follows that a radically different policy must be fair, too.

In this case, the argument claims that, if it is fair to treat racers in exactly the same way as those who are standing still, then this makes it fair to adopt even more radical policies, such as treating racers in exactly the same way as anything.

As we learned this week, however, the problem with most fairness slippery slope arguments, including this one, is that the fairness of more radical policies does not, in fact, follow from the fairness of the course of action in question. In this case, the fairness of treating racers the same as those who stand still would not imply the fairness of treating racers the same as anything.

Consider the following argument:

"A human being cannot feel an electric current of less than 1 mA of AC at 60 Hz. But a human being also cannot feel the difference between electric currents that differ from each other by less than 1 mA. Therefore, a human being cannot feel an electric current of less than 2 mA of AC at 60 Hz, of less than 3 mA of AC at 60 Hz, and so on. It follows that a human being cannot feel an AC electric current of any magnitude whatsoever, no matter how large. And so electrocution cannot be painful, no matter how severe it is."

This argument involves a

Answer: A. conceptual slippery slope fallacy

A conceptual slippery slope argument is an argument to the effect that a series of particular actions cannot change the quality of a certain thing. Typically, the problem with a conceptual slippery slope argument is that its second premise claims that something is not a matter of degree, when in fact it is a matter of degree.

In this case, the second premise in the argument treats "feeling the difference between electric currents" as an all-or-nothing matter. The argument assumes that either one feels the difference between the electric currents, or else one does not.

Suppose, however, that feeling the difference between two electric currents admits of degrees. Suppose, in other words, that one can either feel the difference in two currents a little bit, or that one can feel the difference a bit more, or that one can really, very much feel the difference. Suppose further that, depending on the Hz of two currents, one will feel their difference more or less. If those suppositions are correct, then the sentence, "but a human being also cannot feel the difference between electric currents that differ from each other by less than 1 mA" is false. It is false because, given our suppositions, one can feel the difference of 1 mA more on some occasions than others, depending on the Hz of the currents.

If a fair coin comes up heads five times in a row, then the probability that it will come up heads on the next flip is:

The answer is "one half (0.5)."

If the coin really is fair, as the question says, then the probability that it will come up heads on any flip is one half (0.5). It does not matter how many times it has come up heads (or tails) before. Each flip is independent in the sense that the probability of heads on one flip does not affect the probability of heads on any other flip.

If a fair dealer deals you five cards out of a shuffled fair standard deck of cards, then which of the following hands is most likely?

The answer is "All of these hands are equally likely."

If the deck and the dealer really are fair, as the question stipulates, then the probability of getting dealt any particular hand is the same as the probability of getting dealt any other particular hand. That is what it means to call the deck and the dealing fair.

As described in the video, Linda is thirty-one years old, single, outspoken, and very bright. As a student, she majored in philosophy, was deeply concerned with issues of discrimination and social justice, and participated in antinuclear demonstrations. Which of the following is most likely?

The answer is "Linda is a bank teller."

Everyone who is both a bank teller and active in the feminist movement is a bank teller, but some bank tellers are not active in the feminist movement. Thus, it is more likely that Linda is a bank teller than that she is both a bank teller and also active in the feminist movement.

Imagine that you are playing the old television game show "Let's Make a Deal" hosted by Monte Hall and described in the lecture. You face three closed doors. Behind one of the doors is a car. Behind each of the other two doors is a goat. You pick door A, so you will get to keep what is behind door A if you stick with it. Then, as always, Monte Hall opens one of the remaining two doors, reveals a goat behind that other door, and offers you the opportunity to switch doors, if you want. Suppose that this time Monte Hall opens door C and offers you the opportunity to switch to door B. If you switch doors, then you will get what is behind door B instead of what is behind door A. If you do not switch doors, then you will get what is behind door A. Should you switch doors?

The correct answer is "You should switch doors."

If the probability of an event is 0.73, then its probability can also be expressed as

The answer is "all of the above."

A probability of 0.73 is equal to a 73 percent chance, 73 out of 100, or 7.3 out of 10.

It is possible for some events to have a probability of

The answer is "None of the above."

Probabilities range from 0 to 1, so the probability of an event can never be either 1.5 or -1.5.

If the probability of an event is 1.0, then

The answer is "it is certain that it will happen."

When the probability of something is 1.0, it is certain that it will happen, and there is no chance that it will not happen. At the opposite extreme, when the probability of something is 0.0, it is certain that it will not happen, and there is no chance that it will happen.

When someone assumes that six-sided dice are equally likely to fall on any of the sides—1, 2, 3, 4, 5, or 6—then that person is calculating

The answer is "a priori probability."

A priori probabilities depend on assumptions, such as equal likelihood of outcomes, whereas statistical probabilities are based on observed frequencies of outcomes, and subjective probabilities are based on hunches, though possibly rational.

When a coin is bent, the most accurate way to determine the probability that it will land heads up when it is flipped is to use

The answer is "statistical probability."

If the coin is bent, this is a strong reason not to assume that heads and tails are equally likely, so we cannot use a priori probability. A subjective probability is unlikely to be accurate in this situation. Hence, the most accurate way to determine the probability that a bent coin will land heads up is to observe a large number of flips and count the frequency of heads. That is the procedure of statistical probability.

A coin flip is fair when the coin is equally likely to land with either side—heads or tails—up, and the coin will always land on either heads or tails but not on its edge. If we assume that a coin flip is fair, then what is the probability that the coin will land heads up?

The answer is 0.5.

If there are only two possibilities—heads or tails—then the probabilities of heads and tails must add up to 1, because it is certain that the coin will land on either heads or tails. If these two possibilities—heads or tails—are equally likely, as we are also assuming here, then each possibility has a probability of 0.5, because only then will their equal probabilities add up to 1.

A roll of a six-sided die is fair when the die is equally likely to land with any of its sides—1, 2, 3, 4, 5, or 6—up, and the die will always land with one of those sides up. If we assume that a roll of a six-sided die is fair, then what is the probability that the die will land with 4 up?

The answer is 1/6.

If there are only six possibilities—1, 2, 3, 4, 5, or 6—then the probabilities of these six possibilities must add up to 1, because it is certain that the die will land with one of these sides up. If these six possibilities—1, 2, 3, 4, 5, or 6—are all equally likely, as we are also assuming here, then each possibility has a probability of 1/6, because only then will their equal probabilities add up to 1.

A roll of a ten-sided die is fair when the die is equally likely to land with any of its sides—1, 2, 3, 4, 5, 6, 7, 8, 9, or 10—up, and the die will always land with one of those sides up. If we assume that a roll of a ten-sided die is fair, then what is the probability that the die will land with 4 up?

The correct answer is 1/10.

If there are only ten possibilities—1, 2, 3, 4, 5, 6, 7, 8, 9, or 10—then the probabilities of these ten possibilities must add up to 1, because it is certain that the die will land with one of these sides up. If these ten possibilities—1, 2, 3, 4, 5, 6, 7, 8, 9, or 10—are all equally likely, as we are also assuming here, then each possibility has a probability of 1/10, because only then will their equal probabilities add up to 1.

A roll of two dice is X when the sum of the numbers on the two sides that land up is X. If we assume that the roll is fair, what is the probability that one roll of two six-sided dice will be 4 (that is, will land with a total of 4 up)?

The answer is 3/36.

Because each of the dice has six sides, there are 36 possible results when the two dice are rolled. These 36 possibilities were displayed in a table in the video. Only three possible results add up to a total of 4 on both sides together: (1) the first die lands with 1 up and the second die lands with 3 up, (2) the first die lands with 3 up and the second die lands with 1 up, and (3) the first die lands with 2 up and the second die lands with 2 up. Thus, 3 results out of 36 yield a result of 4, so the probability of rolling a total of 4 on two fair six-sided dice is 3/36.

If the probability that a flipped coin will land heads up is 0.5, what is the probability that it will NOT land heads up?

The answer is 0.5.

The probability that an event will not occur is 1 minus the probability that it will occur. Here the event is the flipped coin landing heads up. The probability of that event occurring is 0.5, and 1 minus 0.5 is 0.5. Hence, the probability of that event not occurring is also 0.5.

Imagine that you bend the coin in Question 1 so that the probability that it will land heads up when flipped is 0.25. Now what is the probability that it will NOT land heads up?

The answer is "0.75."

The probability that an event will not occur is 1 minus the probability that it will occur. Here the event is the flipped coin landing heads up. The probability of that event occurring is 0.25. 1 minus 0.25 is 0.75. Hence, the probability of that event not occurring is 0.75.

As shown in video 9-02, the probability of rolling a 7 on two fair six-sided dice is 6/36. What is the probability of NOT rolling a 7 on two fair six-sided dice?

The answer is 30/36.

The probability that an event will not occur is 1 minus the probability that it will occur. Here the event is rolling a 7. The probability of that event occurring is 6/36, as the question says. 1 minus 6/36 is 30/36. Hence, the probability of that event not occurring is 30/36.