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Read the various perspectives on the death penalty on pages 262-268. Evaluate each argument for validity and soundness. Cite the structural strengths and weaknesses of each argument. Discuss who has the stronger argument? Why? 



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8 How is the professor using logical argumentation in coming up with mathematical proofs? How can learning about deductive logic, such as arguments based on mathematics, help us make better-informed decisions? DEDUCTIVE WHAT’S TO COME 239 | What Is a Deductive Argument? 241 | Types of Deductive Arguments 247 | Hypothetical Syllogisms 252 | Categorical Syllogisms 257 | Translating Ordinary Arguments into Standard Form 261 | Critical Thinking Issue: Perspectives on the Death Penalty I n Sir Arthur Conan Doyle’s mystery story “Silver Blaze,” detective Sherlock Holmes uses his extraordinary powers of deductive logic to solve the mystery of the disappearance of racehorse Silver Blaze and the murder of the horse’s trainer, John Straker. His head shattered by a savage blow, Straker’s body was found a quarter mile from the King’s Pyland stables where Silver Blaze was kept. A search is carried out of the surrounding moors and of the neighboring Mapleton stables for the horse. After interviewing everyone who might have been involved and collecting all the facts, Holmes concludes that Silver Blaze is still alive and hidden in the Mapleton stables, ARGUMENTS 237 Think >> FIRST ■ What is a deductive argument? ■ What are some of the types of deductive arguments? ■ What is a syllogism, and how do we know if it is valid? even though the earlier search of the stables had failed to turn up the missing horse. “It’s this way, Watson,” [says Holmes]. “Now, supposing that [Silver Blaze] broke away during or after the tragedy, where could he have gone to? The horse is a very gregarious creature. If left to himself his instincts would have been either to return to King’s Pyland or go over to Mapleton. Why would he run wild upon the moor? He surely should have been seen by now . . . He must have gone to King’s Pyland or to Mapleton. He is not at King’s Pyland. Therefore, he is at Mapleton.”1 As it turns out, Holmes’s deduction is right. The missing racehorse is at Mapleton, the silver blaze on its nose covered over to disguise its appearance. Sherlock Holmes also solves the “murder” of the horse’s trainer through deductive logic. He learns from the stable hand that the guard dog did not bark when Silver Blaze was “stolen” from the stables. Therefore, Holmes concludes, the person who took Silver Blaze must have been familiar to the dog. This eliminated suspects who were strangers. Holmes then eliminates, one by one, the other suspects, leaving only the horse. As Holmes stated in another story: “When you have eliminated the impossible, whatever remains, however improbable, must be the truth.”2 He concludes that the horse must have accidentally killed its trainer when Straker, who was something of a scoundrel, used a surgical knife found in his possession to nick the tendons of Silver Blaze’s ham so the horse would develop a slight limp and lose the upcoming race. Holmes explains, “Once in the hollow, [Straker] had got behind the horse and had struck a light; but the creature, frightened at the sudden glare, and with the strange instinct of animals feeling that some mischief was intended, had lashed out, and the steel shoe had struck Straker full on the forehead.”3 To generations of mystery readers, Sherlock Holmes has epitomized the skilled reasoner. In this chapter we’ll learn how to evaluate deductive arguments and practice some of the strategies used by Holmes and others who are skilled in deductive argumentation. In Chapter 8 we will: • Identify the essential attributes of a deductive argument • Distinguish between validity, invalidity, and soundness in a deductive argument 238 • THiNK • Learn how to recognize and evaluate arguments by elimination, mathematical arguments, and argument from definition Some deductive arguments are more involved and may have several dependent premises and subconclusions. • Study the different types of hypothetical syllogisms, including modus ponens, modus tollens, and chain arguments Valid and Invalid Arguments • Learn how to recognize standard-form categorical syllogisms • Reevaluate categorical syllogisms using Venn diagrams • Practice putting arguments that are in ordinary language into standard form Finally, we will analyze different arguments regarding the justification of the death penalty (capital punishment). A deductive argument is valid if the form of the argument is such that the conclusion must be true if the premises are true. The form of an argument is determined by its layout or pattern of reasoning. In the above case, the form is: syllogism A deductive argument presented in the form of two supporting premises and a conclusion. valid A deductive argument where the form is such that the conclusion must be true if the premises are assumed to be true. form The pattern of reasoning in a deductive argument. All X (men) are Y (mortal), WHAT IS A DEDUCTIVE ARGUMENT? Unlike inductive arguments, in which the premises offer only support rather than proof for the conclusion, in a valid deductive argument the conclusion necessarily follows from the premises. Deductive arguments sometimes contain words or phrases such as certainly, definitely, absolutely, conclusively, must be, and it necessarily follows that. For example: Marilyn is definitely not a member of the swim team, since no freshmen are members of the swim team and Marilyn is a freshman. Deductive Reasoning and Syllogisms Deductive arguments are sometimes presented in the form of syllogisms, with two supporting premises and a conclusion. For the purpose of analysis, in this chapter the premises and conclusion of a syllogism will usually be presented on separate lines, with the conclusion last. l. 2. 3. Premise: All men are mortal. Premise: All fathers are men. Conclusion: Therefore, all fathers are mortal. Deductive arguments may also be diagrammed using the guidelines we learned on pages 112–114. In the case of a syllogism, the two premises are always dependent: 1 _____ 2 (Dependent premises) 3 (Conclusion) All Z (fathers) are X (men). Therefore, all Z (fathers) are Y (mortal). This argument is a valid form no matter what terms we use for X, Y, and Z. Because the form is valid, if we substitute different terms for men, mortal, and fathers, and the premises are still true, then the conclusion must be true, as in the following example. All cats (X) are mammals (Y). All tigers (Z) are cats (X). Therefore, all tigers (Z) are mammals (Y). A false conclusion does not necessarily mean that a deductive argument is invalid. In the two arguments we’ve examined so far, the conclusions were both true because the premises were true and the form was valid. The conclusion of a valid argument can be false only if one of the premises is false. In the following example, which uses the same form as our initial argument, we end up with a false conclusion: Hot or Not? Are deductive arguments better than inductive arguments? All men are tall people. Tom Cruise is a man. Therefore, Tom Cruise is a tall person. The conclusion in the above argument is false only because there is a false premise, not because the form of the argument is invalid. The first premise, “All men are tall people,” is false. If both premises are true and the conclusion is false, then the argument, by definition, is invalid. For example: Chapter 8 | Deductive Arguments • 239 All dogs are mammals. Some mammals are not poodles. Therefore, some poodles are not dogs. It is also possible to have an invalid argument in which the premises are true and the conclusion just happens to be true. Consider this: No seniors are freshman. All freshmen are college students. Therefore, some college students are seniors. In this argument, the premises and conclusion are true. However, the premises do not logically support the conclusion. The invalidity of a form can be demonstrated by substituting different terms for senior, freshman, and college students, and then seeing whether we can come up with an argument using this form in which the premises are true but the conclusion false, as in the following substitutions: No fish are dogs. All dogs are mammals. Therefore, some mammals are fish. Sound and Unsound Arguments An argument is sound if (1) it is valid and (2) the premises are true. The argument on page 239 about fathers being mortal is a sound argument because it is valid and the premises are true. On the other hand, although the argument about Tom Cruise on page 239 uses a valid form, it is not a sound argument because the first premise is false. Invalid arguments, because they do not meet the first criterion, are always unsound. Logic is primarily concerned with the validity of arguments. As critical thinkers, we are also interested in the soundness of our arguments and in having our premises supported by credible evidence and good reasoning. We have already discussed in previous chapters guidelines for ensuring that our premises are accurate and credible. sound A deductive argument that is valid and that has true premises. In this chapter we’ll learn how to identify the different types of deductive arguments and how to use Venn diagrams to evaluate these arguments for validity. HIGHLIGHTS DEDUCTIVE ARGUMENTS Valid Invalid Sound Unsound Unsound Valid argument: The form or layout of the argument is such that if the premises are true, then the conclusion must necessarily be true. Sound argument: The form of the argument is valid and the premises are true. ➤APPLICATION: Identify in the text an example of an argument that is (a) valid and sound, (b) valid and unsound, and (c) invalid. STOP AND ASSESS YOURSELF S E XE RC I SE 8 - 1 240 “Some mammals are fish” is an example of a false conclusion. 1. What do you mean when you say that you can prove something with certainty? Give a specific example of a proof from your everyday experience (keep it as brief as possible). What type of logic does the proof use—inductive or deductive? 2. In the story “Silver Blaze,” Sherlock Holmes tells Watson that when it comes to the art of reasoning, many people rely on opinion and unsupported assumptions. • THiNK E X E RCI SE 8- 1 c on t . The difficulty, he maintains, is to detach the framework of undeniable fact from the embellishments of hearsay and reporters. What do you think he meant by this? Explain using examples from your personal experience. 3. Using substitution, show that the form of each of the following deductive arguments is invalid. Remember: To establish invalidity, your premises must be true when you are substituting new terms for the ones in the original argument. *a. All fraternity members are men. No women are fraternity members. Therefore, no women are men. b. If it is raining, then it is cloudy. It is cloudy. Therefore, it is raining. c. No mice are humans. Some mice are rodents. Therefore, no humans are rodents. *d. Some married people are college students. All wives are married people. Therefore, some wives are college students. e. All flowers are plants. All orchids are plants. Therefore, all orchids are flowers. f. If my baby sister is a college student, then she is a high school graduate. My baby sister is not a college student. Therefore, my baby sister is not a high school graduate. 4. The following arguments are all valid arguments. Determine whether each argument is sound or unsound. *a. No mammals are birds. Some penguins are mammals. Therefore, some penguins are not birds. b. Some twins are sisters. All twins are siblings. Therefore, some siblings are sisters. c. All students are dormitory residents. No dormitory residents are birds. Therefore, no birds are students. *d. If Mexico is in South America, then Mexico is not a country bordering the United States. Mexico is in South America. Therefore, Mexico is a not country bordering the United States. e. All people living in England are citizens of the European Union. All members of the British royal family are people living in England. Therefore, all members of the British royal family are citizens of the European Union. f. All millionaires are rich people. Some Americans are not rich people. Therefore, some Americans are not millionaires. TYPES OF DEDUCTIVE ARGUMENTS There are several types of deductive arguments. In this section, we’ll be looking at three types of deductive arguments used in everyday reasoning: • • • Arguments by elimination Arguments based on mathematics Arguments from definition Arguments by Elimination An argument by elimination rules out different possibilities until only one possibility remains. In the introduction to this chapter, we saw Sherlock Holmes using an arguargument by elimination A ment by elimination. He deductive argument that rules out different possibilities until only one reasoned that Silver Blaze remains. had to be at one of the two stables. Since it wasn’t at King’s Pyland, it must be at Mapleton. In “Thinking Outside the Box: Bo Dietl, Top Cop” on page 242, we profile Chapter 8 | Deductive Arguments • 241 a New York City detective who is skilled in this type of deductive reasoning. Like detectives, physicians are trained in this type of deductive logic. In diagnosing an illness, a physician starts by doing a physical examination and, often, by ordering tests. If the examination and test results eliminate the most common explanations of the symptoms, then the physician moves on to check out less obvious possibilities until the mystery is solved. Indeed, Dr. Joseph Bell, one of Sir Arthur Conan Doyle’s professors at the University of Edinburgh Medical School, was the inspiration for the character Sherlock Holmes. Arguments by elimination are frequently used in everyday life. For instance, suppose it is the first day of the semester and you arrive on campus with 10 minutes to spare. You check your schedule and see that your first class, Introduction to Psychology, is in Winthrop Hall. However, on your schedule the room number is smudged and you can’t read Thinking Outside the Box B O DI E T L , Top Cop DI SC U SSI O N Q UE STI ONS Bo Dietl is a modern Sherlock Holmes. Born in Queens, New York, in 1950, Dietl wanted a job where he could make a real difference in people’s lives. When he learned about the test to get into the police academy, he decided to give it a try. One of the most highly decorated detectives in the history of the New York Police Department, Dietl investigated numerous high-profile murders and other felonies, obtaining evidence through research, interviews, and other investigative techniques. He attributes much of his success in solving more than 1,500 felonies to what he calls his “sixth sense—a nontangible feeling good detectives use in solving cases.”* One of the most famous crimes he solved was the 1981 rape and torture of a Catholic nun in an East Harlem convent. Dietl concluded from the evidence that the crime was a burglary gone wrong, rather than a sex crime, thus narrowing his search to people with burglary records. He also knew, from interviewing witnesses, that one of the men was probably tall and that the other had a limp. Days later he received a tip that the two men who committed the crime lived somewhere on 125th Street in Harlem. However, there were hundreds of buildings and thousands of people living on this street. He began the process of elimination by going to the local hangouts and tenements, knocking on doors, giving a brief description of the suspects, and asking questions. He also passed out hundreds of business cards. His efforts paid off, and the two suspects were apprehended and arrested. The 1998 movie One Tough Cop is based on Dietl’s autobiography of the same name. 242 • THiNK 1. Discuss how Dietl’s method of solving the murder of the nun in the East Harlem convent demonstrates deductive reasoning using an argument by elimination. 2. In Chapter 2 we learned that much of reasoning is unconscious and automatic and that scientists and mathematicians, as well as great detectives, often resolve complex problems without any conscious deliberation. However, to develop this ability, they have spent years consciously resolving problems and mentally rehearsing solutions. Think of a type of problem in your life that you find easy to resolve with little or no conscious deliberation. Discuss what factors, such as your familiarity and experience with the problem, contributed to your ease of resolution. *Conversation with Bo Dietl on August 8, 2005. it. What do you do? It would take too long to get a new schedule. Instead, you head over to Winthrop Hall and check out the building directory. It lists twelve room numbers. Nine of them are faculty offices, so you eliminate those nine. The remaining three are classrooms A, B, and C. You go into classroom A and ask some students what class it is. They tell you that it’s English Literature. You proceed to classroom B and repeat the process; it turns out to be a course in Business Statistics. When you get to classroom C, you just go inside and take a seat. How do you know this is the correct classroom? Through the use of an argument by elimination. Assuming that your premises are true (that your psychology course is being taught somewhere in Winthrop Hall), the third classroom by necessity must be your classroom. My class is either in room A, B, or C. My class is not in room A. My class is not in room B. Therefore, my class must be in room C. In the previous example, there were three alternatives. If there are only two alternatives, the argument is referred to as a disjunctive syllogism. A disjunctive syllogism takes one of two forms: Either A or B. Either A or B. Not A. Not B. Therefore, B. Therefore, A. A mouse locates the prize at the end of the maze through the deductive process of elimination. In determining the whereabouts of Silver Blaze, Sherlock Holmes used a disjunctive syllogism: Either Silver Blaze is at King’s Pyland or Silver Blaze is at Mapleton. Silver Blaze is not at King’s Pyland. Therefore, Silver Blaze is at Mapleton. Here is syllogism: another example of a disjunctive Either you finished cleaning your room or you’re staying in tonight. You are not staying in tonight. Therefore, you finished cleaning your room. In a disjunctive syllogism, the two alternatives presented in the first premise—clean your room or stay in tonight—must be the only two possibilities. If there are other possible alternatives that have not been stated, then the argument commits the fallacy of false dilemma. For example: Either we fight the war on terrorism in Iraq, or we’ll have to fight the terrorists here in America on our own soil. We’re fighting the war on terrorism in Iraq. Therefore, we won’t have to fight the terrorists here in America on our own soil. In this argument, the two alternatives in the first premise do not exhaust all possible alternatives. Perhaps disjunctive syllogism A type of deductive argument by elimination in we could go after individwhich the premises present only two ual terrorist cells instead of alternatives. attacking a country or even argument based on negotiate a truce with some mathematics A deductive argument of the organizations or govin which the conclusion depends on a ernments associated with mathematical calculation. terrorist activities. Because the argument commits the fallacy of false dilemma, it is not a sound argument. Arguments Based on Mathematics In an argument based on mathematics, the conclusion depends on a mathematical or geometrical calculation. For example: My dormitory room is rectangular in shape. One side measures 11 feet and the side adjacent to it measures 14 feet in length. Therefore, my room is 154 square feet. You can also draw conclusions about your new roommate, Chris, even before you meet, using this type of deductive reasoning. You know from e-mail correspondence that Chris plans on trying out for the basketball team and is 6' 2" tall. Since you are 5' 6" tall, you can conclude Chapter 8 | Deductive Arguments • 243 Connections (assuming that Chris’s information is correct) that Chris is 8 inches taller than you. These are relatively simple examples. Arguments based on mathematics may be quite complex and require mathematical expertise. For example, scientists at NASA needed to calculate the best time to launch the two Mars Explorer Rovers— robotic geologists—so that they would arrive at the Red Planet when Mars would be closest to Earth. Mars takes 687 days to complete a revolution of the Sun, compared to 365 days for Earth. Also, because their orbits differ and because Mars has a slightly eccentric orbit, the distance between Mars and Earth varies widely, ranging from about 401 million miles to less than 55 million miles.4 The two rovers were launched from Cape Canaveral, Florida, in the summer of 2003 and landed on Mars in January 2004. The landing was remarkably smooth, thanks to the deductive reasoning skills How can an of the NASA scientists. As of 2010, the rovers are still understanding of transmitting valuable data arguments based on back to Earth. Knowing how to make mathematics help arguments based on mathyou evaluate science ematics can help you make better-informed decisions, news? See Chapter 11, such as calculating the pp. 349–350. cost of a vacation to Cancun or determining what type of payment method for your educational expenses is most cost-effective. For example, by taking out a student loan instead of using a credit card to pay for your college expenses, you can save thousands of dollars (see “Critical Thinking in Action: Put It on My Tab: Paying College Tuition by Credit Card—a Wise Move?”). Not all arguments using argument from definition A mathematics are deducdeductive argument in which the tive. As we learned in conclusion is true because it is based Chapter 7, statistical on the definition of a key term. arguments that depend on probability, such as generalizations, are inductive because we can conclude from these only that something is likely—not certain—to be true (see pages 207–211). Arguments from Definition In an argument from definition, the conclusion is true because it is based on a key term or essential attribute in a definition. For example: 244 • THiNK Paulo is a father. All fathers are men. Therefore, Paulo is a man. This conclusion is necessarily true because a father is, by definition, “a male parent.” Being male is an essential attribute of the definition of father. As we discussed in Chapter 3, language is dynamic and definitions may change over time. Consider this example: Marilyn and Jessica cannot be married, since a marriage is a union between a man and a woman. This conclusion of this argument was necessarily true at one time, before some states legalized same-sex marriage. Today, because the legal definition of marriage is undergoing change, this argument may no longer be sound. Arguments by elimination, arguments based on mathematics, and arguments from definition are only three types of deductive arguments. In logic, deductive arguments are often written in syllogistic form, such as the disjunctive syllogism. In the following sections, we’ll learn about two other types of syllogisms—hypothetical and categorical—and how to evaluate arguments using these forms. Thinking Critical in Action Pu t I t o n M y Ta b : Pay i n g C o l l ege Tu i ti o n by C red it Ca rd — A W i se M ove? Have you ever wondered why credit-card companies are so keen on signing up college students? According to USA Today (July 26, 2005), people between the ages of 18 and 29 have the poorest credit ratings of all age groups. In fact, credit-card companies make most of their money from people who don’t pay off their balance each month, which is the case with 80 percent of college students. Many parents and students regard credit cards as a convenient way to pay for tuition. However, if you think carrying a balance on a credit card or charging college expenses such as tuition to a credit card is a smart move, consider the following argument, based on mathematics: Your credit card bill is $1,900. This includes $1,350 for tuition and fees at your community college and $550 for books for two semesters. Being frugal, you decide not to use your credit card again, since you don’t want to get too far into debt. The minimum monthly payment due on your balance is 4 percent, which comes to $75 the first month. You pay the minimum due faithfully each month. At this rate, how long will it take you to pay off your first-year college expenses? If the annual percentage rate on your card is 17.999 percent, it will take you 7 years to pay off that balance on your credit card!* In addition to the principal (the amount you charged to the card), you’ll have paid a total of $924.29 in interest. This means that the amount of money you actually paid for your first year of college expenses was $2,824!** What if you had taken out a student loan instead? The annual interest rate on a federal student loan is about 8 percent. If you put $75 a month toward paying off your student loan, it would take you 2 years and 4 months to pay off the loan. Furthermore, you don’t have to start paying off your student loan until you graduate. By taking out a student loan to cover your college expenses instead of charging them to a credit card, you wouldn’t have to pay anything for the 2 years while you are in college. Even then you would pay off the loan almost 3 years before you would pay off your credit card—and the total interest would come to only $188. In other words, you paid $736 for the “convenience” of charging your tuition, fees, and books for your first year at community college. Multiply this times 2 or even 4 years, and you could be paying out several thousand dollars just in interest simply because you didn’t apply your logic and your critical-thinking skills when deciding how to pay for your college expenses. DISCUSSION QUESTIO NS 1. Some colleges, such as Tufts University and the University of Kentucky, have discontinued creditcard payments for tuition. In part this is because the credit-card companies charge the college a 1 percent to 2 percent fee on each charge, which ultimately gets added on to the cost of tuition. What is the policy at your college or university? Do you agree with the policy? Construct an argument supporting your answer. 2. Examine your own credit-card use. Discuss ways in which you can use deductive logic to be more economical in your spending habits. *To calculate what you’ll pay on a credit-card balance, as well as what you’ll pay if you get a student loan instead, go to http://www.money .cnn.com/tools **For more information on credit card usage and debt among college students, go to http://www.nelliemae.com/aboutus/ collegestudentswise052505.html. For information on applying for federal and private college loans, see http://www.collegeboard.com/ student/pay/loan-center/414.html. Chapter 8 | Deductive Arguments • 245 E X E RCI SE 8- 2 246 STOP AND ASSESS YOURSELF S 1. Identify what type of argument each of the following is. If it is a deductive argument, state which type of deductive argument. If the argument is not a deductive argument, explain why. (See Chapter 7 if you need to review inductive arguments.) *a. Clem either walked to the bookstore or took the shuttle bus. He couldn’t have taken the shuttle bus, since it is out of service today. Therefore, he walked to the bookstore. b. Hisoka H is a psychiatrist. Therefore, Hisoka is a physician. c. A 64-ounce 64 carton of mint chocolate chip ice cream costs $5.99. A 16-ounce carton costs $1.49. Therefore, I’ll actually save money by buying four 16-ounce cartons instead of one 664-ounce carton. *d. Let’s see; it’s the triplets’ third birthday. We have six presents for Matthew, five for Andr Andrew, and one for Derek. If we want to be fair and give each of the triplets the same num number of presents, we’ll have to take two of the presents we now have set aside for Matt Matthew and one of the presents we have set aside for Andrew and give them to Derek inste instead. e. Tokyo, New York City, and Mexico City have the highest populations of any cities in the world. Tokyo has a higher population than New York City. Mexico City has a lower population than New York City. Therefore, Tokyo has the highest population of any city in the world. f. I was told that Mary is probably in class right now and that if she were not there, to check the library where she spends most of her afternoons. However, Mary isn’t in class. So she is most likely at the library. *g. Jessica is the daughter of Joshua’s uncle. Therefore, Jessica and Joshua are cousins. h. Either Roy Jones Jr. or John Ruiz won the 2003 world heavyweight champion boxing match in Las Vegas. John Ruiz did not win the fight. Therefore, Roy Jones Jr. was the 2003 world heavyweight champion. i. A = 5. B = 8. C = –11. Therefore, A + B + C = 2. *j. Forrest Gump said that his mother always told him that “life was like a box of chocolates. You never know what you’re gonna get.” Therefore, there’s no point in trying to plan for the future, since you can never know what it holds for you. k. I know that Singapore uses either the dollar or the British pound as their currency. I checked out the countries that use the British pound and Singapore was not listed. Therefore, Singapore uses the dollar as its currency. l. Professor Cervera told us that he was born in one of the four largest cities in Cuba, but I can’t remember which one. I remember him mentioning that it was in the southeastern part of Cuba and that he could see the ocean from his bedroom window. I checked my almanac, and the four largest cities in Cuba are Havana, Santiago de Cuba, Camagüey, and Holguin. He couldn’t have been born in Havana, since it is on the northwestern coast of Cuba. Camagüey and Holguin are both located inland. So Professor Cervera must have been born in Santiago de Cuba. *m. We should ask Latitia if she is interested in working part time in our marketing department. I read that about 80 percent of freshmen said there was at least some chance they’d have to get a job to pay for college expenses. In addition, women are far more likely to have to seek employment during college than are men. Therefore, Latitia will probably be looking for a parttime job to help with her college expenses. n. I agree that the storm we had last week was pretty bad, but it was not a hurricane since the winds never got above 70 miles per hour. o. Either the tide is coming in or the tide is going out. The tide is not coming in. Therefore, the tide is going out. *p. A 2005 Harvard University survey of more than 10,000 teenagers found that 8 percent of girls and 12 percent of boys have used dietary supplements, growth hormones, or anabolic steroids. Therefore, teenage boys are 50 percent more likely than are teenage girls to use products such as steroids to build muscle mass. 2. Select three of the arguments from exercise 1 and diagram them (see Chapter 6). • THiNK E X E RCI SE 8- 2 c on t . 3. You’re having lunch with some friends and mention that you’re studying deductive logic. One of your friends rolls his eyes and says, “You can prove anything you want to with logic. Why, you can even prove that cats have thirteen tails. Here’s how it works: One cat has one more tail than no cat. And no cat has twelve tails. Therefore, one cat has thirteen tails.” Evaluate your friend’s argument. 4. At a picnic, Mike went for soft drinks for Amy, Brian, Lisa, and Bill, as well as for himself. He brought back iced tea, grape juice, Diet Coke, Pepsi, and 7-Up. Using the following information (premises), determine which drink Mike brought for each person: Mike doesn’t like carbonated drinks. Amy would drink either 7-Up or Pepsi. Brian likes only sodas. Lisa prefers the drink she could put lemon and sugar into. Bill likes only clear drinks.5 5. How do you pay for your tuition and other college expenses? Go to http://www.money.cnn.com/tools and calculate how much it will cost you to pay off your entire debt on the basis of the average you pay each month, or estimate what you will pay monthly after graduation. Given your financial situation, decide what would be the most economical way for you to pay for your college and personal expenses. HYPOTHETICAL SYLLOGISMS Hypothetical thinking involves “If . . . then . . .” reasoning. According to some psychologists, the mental model for hypothetical thinking is built into our brain and enables us to understand rules and predict the consequences of our actions.6 We’ll be looking at the use of hypothetical reasoning in ethics in greater depth in Chapter 9. Hypothetical arguments are also a basic building block of computer programs. According to some psychologists, the mental model for hypothetical thinking is built into our brain and enables us to understand rules and predict the consequences of our actions. A hypothetical syllogism is a form of deductive argument that contains two premises, at least one of which is a hypothetical or conditional “if . . . then” statement. Hypothetical syllogisms fall into three basic patterns: modus ponens (affirming the antecedent), modus tollens (denying the consequent), and chain arguments. Modus Ponens In a modus ponens argument, there is one conditional premise, a second premise that states that the antecedent, or if part, of the first premise is true, and a conclusion that asserts the truth of the consequent, or the then part, of the first premise. For example: Premise 1: If I get this raise at work, then I can pay off my credit-card bill. Premise 2: I got the raise at work. Conclusion: Therefore, I can pay off my credit-card bill. A valid modus ponens argument, like the one above, takes the following form: If A (antecedent), then B (consequent). A. hypothetical syllogism A deductive argument that contains two premises, at least one of which is a conditional statement. modus ponens A hypothetical syllogism in which the antecedent premise is affirmed by the consequent premise. Therefore, B. Sometimes the term then is omitted from the consequent, or second, part of the conditional premise: If the hurricane hits the Florida Keys, we should evacuate. The hurricane is hitting the Florida Keys. Therefore, we should evacuate. Modus ponens is a valid form of deductive reasoning no matter what terms we substitute for A and B. In other words, if the premises are true, then the conclusion must be true. Thus: If Barack Obama is president, then he was born in the United States. Barack Obama is president. Therefore, he was born in the United States. Chapter 8 | Deductive Arguments • 247 Deductive Reasoning and Computer Programming In computer programming, special computer languages are used to create strings of code which are comprised almost entirely of deductive logic. Some popular computer languages include C++, Java, JavaScript, Visual Basic, and HTML. Many others exist that specialize in specific tasks. In the following program using C++, a game has been created using hypothetical statements: int main() {int number = 5} int guess; cout
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