Exercise 3.1

A. Identifying Statistical Syllogisms

Determine whether the following arguments are statistical syllogisms. If an argument is not a statistical syllogism, explain why it is not. If an argument is a statistical syllogism, identify the terms used for x, A, B, and Y. If a statistical syllogism uses a word or phrase that can be formulated using a range of numbers for x, give the range.

1. Three quarters of startups will fail within three months. Owlet is a startup. So Owlet will fail within three months.
2. Eighty percent of fetuses that test positive for Down’s Syndrome do not have Down syndrome. Othman is a fetus who tested positive for Down syndrome. So Othman does not have Down syndrome.
3. All Chick-fil-A stores are closed on Sundays. So the Chick-fil-A store on Main Street is closed on Sunday.
4. Most, but not all, smokers die ten years before nonsmokers. Linda is a smoker. So Linda will die ten years before nonsmokers.
5. Of employees in marketing departments, 96 percent admitted to posting deceitful information about their company online. So those who post deceitful information about their company online are most likely in marketing departments.
6. For every car in America, there are four parking spots available. So there is a spot available for your car.
7. The vast majority of plagiarizing students are caught. So if you plagiarize, you’ll be caught.
8. Eighty percent of muggings are unreported. Jordan reported a mugging. So probably the mugging that Jordan reported is unreported.
9. Most philosophers think that God doesn’t exist. So God doesn’t exist.
10. Only 5 percent of dead batteries are recycled. This thing I have in my hand is a dead battery. So it’s not recycled.

B. Evaluating Statistical Syllogisms

For each of the following statistical syllogisms, identify a further item of information that could well be true and that is such that, given its truth, we cannot conclude that the syllogism is strong.

1. Sixty-eight percent of millennial Facebook users get their news from fake news sources. Jaxon is a millenial Facebook user. So Jaxon gets her news from fake news sources.
2. Seventy percent of smartwatch users in the United States bought their smartwatch within the last six months. Tim Cook is a smartwatch user in the United States. So Tim Cook bought his smartwatch within the last six months.
3. Nearly all car manufacturers have claimed that they will have a self-driving car available to the public by 2021. Mercedes is a car manufacturer. So Mercedes has claimed that they will have a self-driving car available to the public by 2021.
4. Seventy-eight percent of smartwatch users in the United States wear a regular watch. Amy Cragg, a US marathoner, is a smartwatch user in the United States. So Amy Cragg also wears a regular watch.
5. Sixty percent of business executives would cheat investors to save their own jobs. Steve is a business executive. So Steve would cheat investors to save his job.
6. Most people who remove asbestos tile for a living die of asbestos poisoning before they turn sixty. Employees from ABC Construction remove asbestos tile for a living. So employees from ABC Construction company will die before they turn sixty.
7. Most ethics professors care for disabled people. Dr. Whistler is an ethics professor. So Dr. Whistler cares for disabled people.
8. Over half of those who make poker bets at casinos make losing bets. Daniel Negreanu has made a bet at a casino. So Daniel has made a losing bet.
9. Three of every four politicians in Washington, DC, receive donations from private corporations. Bernie Sanders is a politician in Washington, DC. So Bernie Sanders receives donations from private corporations.
10. The vast majority of restaurants that do not pass governmental food-safety standards get their customers sick. The food truck on Fourth Street does not pass governmental food-safety standards. So the food truck on Fourth Street will get its customers sick.

Exercise 3.2

A. Identifying Induction by Enumeration

For each of the following arguments, determine whether the argument is an instance of induction by enumeration. If it is, identify the number, or phrase, employed for x and the categories employed for A and B.

1. All of the professors I’ve seen have had beards. So all professors have beards.
2. Most Catholic marriages do not end in divorce. So most marriages do not end in divorce.
3. Only 10 percent of research participants reported feeling nauseated when taking the experimental drug. So only 10 percent of those who take the experimental drug will feel nauseated.
4. All but one student surveyed found their university experience to be uplifting. So all but one student find their university experience to be uplifting.
5. Over half of sunglasses with polarized lenses at mall kiosks cost more than $100, so most likely sunglasses with polarized lenses cost over $100.
6. One hundred percent of the engine parts I’ve ordered from China have cost less than the same parts ordered in the United States. So if you order engine parts from China, you will pay less than you’d pay in the United States.
7. According to our surveys, one out of every four students that parked illegally received a ticket. So if you park illegally, you are 25 percent likely to receive a ticket.
8. 50 percent of Gen Xers have used Facebook, so 50 percent of the group that includes both Gen Xers and Millennials has used Facebook.
9. There were workplace injuries in only 3 percent of our factories surveyed. So overall, there are workplace injuries in only 3 percent of our factories.
10. One hundred percent of Taylor Swift songs I’ve heard are emotionally heart-wrenching. So all of Taylor Swift’s songs are emotionally heart-wrenching.

B. Evaluating Induction by Enumeration

For each of the following arguments, identify an item of further information that is such that it could well be true, and such that we cannot conclude that the argument is strong given that this information is correct.

1. Most of people I surveyed outside the back of a restaurant on lunch break one day reported smoking regularly. So most people standing outside restaurants smoke regularly.
2. Over 50 percent of US citizens who are also politicians think that health care is not a right for US citizens. So most US citizens think that health care is not a right for US citizens.
3. All of the light bulbs tested in 1995 were hot to the touch after just ten minutes of use. So all light bulbs are hot to the touch after just ten minutes of use.
4. In December, 70 percent of houses surveyed in the United States had at least one hundred exterior lights. So 70 percent of houses in the United States have at least 100 exterior lights.
5. Ninety-five percent of survey respondents in the United States reported not having any racial bias, so 95 percent those in the United States report not having any racial bias.
6. Thirty-three percent of ethicists from Princeton University have endorsed infanticide. So a third of ethicists endorse infanticide.
7. Over half of conservative business leaders have a policy in which they do not have dinner alone with single women from the office. So over half of business leaders have a policy in which they do not have dinner alone with single women from the office.
8. Most married couples in the United States have two children or more. So most married couples have two children or more.
9. In Texas, 80 percent of Rosemary plants grow to full maturity within a month. So Rosemary plants grow to full maturity within a month.
10. In a survey administered at 2 p.m. around the United States, the vast majority of middle managers reported being very dissatisfied with their job. So the vast majority of middle managers around the United States report being very dissatisfied with their job.

C. Complex Arguments

Each of the following arguments can be transformed into an argument that employs one instance of induction by enumeration and one instance of statistical syllogism. First, transform each argument so that it fits this pattern. Second, highlight three items of further information that are such that we cannot conclude that the argument is strong given that this information is true.

1. A recent study found that over half of marriages in the United States end in divorce. Taylor and Alex are getting married in the United States. So Taylor and Alex’s marriage will end in divorce.
2. Anecdotal evidence supports that 80 percent of in-store shoppers who do comparison shopping on their phones end up purchasing the product on their phones instead of in the store. Melinda is an in-store shopper who is doing comparison shopping on her phone. So Melinda will end up purchasing the product on her phone instead of in the store.
3. On a survey across ten Toys ’R Us stores, the sale of 60 percent of items for which customers price-matched resulted in a loss for Toys ’R Us. The LEGO Death Star is an item for which a customer is price matching. So the sale of the LEGO Death star will result in a loss for Toys ’R Us.
4. Sixty percent of the cards Drew has drawn from a deck of cards have been red. So 60 percent of all the cards in the deck are red. So the next card Drew draws will be red.
5. The first two rows of tile in the bank are brown. So the tile behind the counter is brown.

Exercise 3.3

A. Identifying Arguments from Authority

For each of the following arguments, determine whether it is an argument from authority. Assume that the persons cited in the premises are authorities concerning the claim attributed to them. If the argument is an argument from authority, identify what stands for X and what stands for P.

1. The news anchor reported that a local resident said that there was a lot of crime in the area lately. So a local resident said that there was a lot of crime in the area lately.
2. The philosopher wondered whether we’re morally responsible for actions we didn’t intend on performing. So it’s unclear whether we’re morally responsible for actions we didn’t intend on performing.
3. The president doesn’t know whether Russia and Syria have met. So no one knows whether Russia and Syria have met.
4. A fashion designer says that no one should approve of blue pants with brown shoes. So no one should approve of blue pants with brown shoes.
5. An internet quote site says that Confucius says, “It does not matter how slowly you go, as long as you do not stop.” So Confucius says, “It does not matter how slowly you go, as long as you do not stop.”

B. Evaluating Arguments from Authority

For each of the following arguments from authority, identify two items of additional information, each of which could very well be true and each of which is such that we cannot conclude that the argument is strong given the truth of this information.

1. The politics professor asserts that you should never believe something just because an authority says it. So you should never believe something just because an authority says it.
2. A CEO says that although the corporation’s stock has been dropping, the company has a promising future. So although the corporation’s stock has been dropping, the company has a promising future.
3. A marketing department quotes a paid celebrity as saying that they recommend the company’s product. So the celebrity recommends the company’s product.
4. A comedian says that he never gets any respect. So he never gets any respect.
5. A defense attorney asserts that her client is innocent. So her client is innocent.

C. Complex Arguments

Transform the information provided in each of the following arguments into a complex argument that employs one instance of an argument from authority and one instance of either a statistical syllogism or induction by enumeration. For each of the resulting arguments, identify one item of further information that is such that we cannot conclude that the argument in question is strong given the truth of this information.

1. In a survey of ten thousand US households, 80 percent of smartwatch owners report being very satisfied with their smartwatch. So 80 percent of US smartwatch owners are very satisfied with their smartwatch.
2. Every professor in the Chemistry Department says they love teaching. Lloyd is a professor in the Chemistry Department. So Lloyd loves teaching.
3. Sixty percent of police officers express dissatisfaction with their job. Billy is a police officer. So Billy is dissatisfied with his job.
4. A spokesperson for Pepsi reports that most Coca-Cola employees lie pathologically. Mary is a Coca-Cola employee. So Mary lies pathologically.
5. A Google cloud service executive reported that from among a sample of ten companies, none of Amazon Web Services is as secure as Google’s cloud services. So none of Amazon Web Services is as secure as Google’s cloud services.

Exercise 3.4

A. Identifying Arguments from Analogy

Determine whether the following arguments are arguments from analogy. If an argument is an argument from analogy, identify what has been substituted for X, Y, R1–Rn, and P.

1. Superman is not from Earth. So Batman is not from Earth either.
2. My friend looked just as pale as you do now, and she needed to go to the hospital. So you need to go to the hospital.
3. I gave the same argument to you and my other friend. My other friend is convinced. So you are convinced, too.
4. Two students copied four words sequentially without attribution, and the first student was soon after reported to the office for academic integrity violations. So the second will soon after be reported to the office for academic integrity violations, too.
5. My logic and foreign language classes both require that we learn a new language and rules. I had to practice a lot for my foreign language class. So I’ll have to practice a lot for my logic class.

B. Evaluating Arguments from Analogy

For each of the following arguments from analogy, identify one further item of information that, if true, would challenge the strength of the argument.

1. God is like a good father with respect to how he loves his children. A good father would not allow his children to suffer. So God would not allow his children to suffer.
2. Jesus and I are both humans. I’ve sinned, so Jesus has sinned.
3. Floyd Mayweather Jr. and Oscar De La Hoya are both famous boxers. Floyd Mayweather Jr. receives $30 million for each fight. So Oscar De La Hoya receives $30 million for each fight.
4. Both you and Hitler thought that they were doing the right thing. What Hitler did was wrong. So what you’re doing is wrong.
5. Both I and your other friend asked you to listen. You listened to your other friend. So you’ll listen to me, too.
6. McDonald’s is a corporation just as large as many banks. The US government bailed out US banks when they were on the brink of failure. So when McDonald’s is on the brink of failure, McDonald’s will be bailed out by the US government.
7. The employee before me falsified financial documents, and he didn’t get caught. So if I falsify financial documents, I won’t get caught.
8. The apostles and I are both humans. The apostles could perform miracles. So I can perform miracles.
9. Fast-food restaurants and fine-dining restaurants both serve entrees. Fast-food restaurants can serve entrees in five minutes. So fine-dining restaurants can serve entrees in five minutes.
10. Humans and dogs are both animals that can walk. Humans can skate. So dogs can skate.

Exercise 3.5

A. Identifying Inferences to the Best Explanation

Determine whether the following arguments are inferences to the best explanation. If they are, identify D and H.

1. The best available explanation for why you lack of understanding is that you aren’t feeling well. So you aren’t feeling well.
2. As good an explanation as any for the student’s failure of the exam is that they did not study outside of class. So the student did not study outside of class.
3. The best available explanation for the employee’s absence is that they are caught up in traffic. So the employee has an excused absence.
4. The best explanation for his harsh attitude is that he feels underappreciated. So if we appreciate him, he won’t have a harsh attitude.
5. The best available explanation for why the consumer reports say that the product is unsatisfactory is that it is, in fact, unsatisfactory. So the product is unsatisfactory.

B. Evaluating Inferences to the Best Explanation

Present a challenge to the strength of each of the following inferences to the best explanation, making reference to the feature of explanatory power, the feature of coherence with background knowledge, or the feature of simplicity. If presenting the challenge requires specifying some further information not provided in the argument itself, identify that information.

1. The best available explanation for the business’s reduced revenue is that the business is not targeting the right audience. So the business is not targeting the right audience.
2. The best available explanation for the fact that the CEO did not mention their new product is that the product is not selling well. So the product is not selling well.
3. The best available explanation for the fact that he stole that item is that he did not know it belonged to someone else. So he did not know it belonged to someone else.
4. The best available explanation for the employee not meeting expectations is that the employee is being lazy. So the employee is being lazy.
5. The best available explanation for the pay gap between male and female employees is that employers are biased against women. So employers are biased against women.
6. The best available explanation for the referee making such a bad call is that the referee has been paid to favor one team over another. So the referee has been paid to favor one team over another.
7. The best available explanation for our team’s success is that their success is caused by the fact that we wore our baseball hats backwards just prior to their winning streak. So their success is caused by the fact that we wore our baseball hats backwards just prior to their winning streak.
8. The best available explanation for your misfortune is that God has something better in store for you as a result of your misfortune. So God has something better in store for you as a result of your misfortune.
9. The best available explanation for the World Trade Center bombings is that US government officials made deals to bomb the buildings as a conspiracy to get George W. Bush reelected to a second term. So US government officials made deals to bomb the buildings as a conspiracy to get George W. Bush reelected to a second term.
10. The best available explanation for the presence of police sirens is that our troublesome neighbors are up to no good. So our troublesome neighbors are up to no good.