Arguments in Context Unit V Common Inductive Arguments Chapter 15 Inductive Applications

CHAPTER 15 Inductive Applications SECTION I INTRODUCTION Statistical generalizations tend to be used in two ways in our reasoning as premises and as conclusions . As we have seen , in an inductive generalization we start with premises about individuals or small groups and move to a generalization about a whole population . However , we can also do the reverse , and reason from a conclusion . That is , we can start with a generalization about a whole population and move to a sion about an individual or small group . In this chapter we will take a close look at the process of applying generalizations to specific cases . As we will see , these arguments bear a similarity to some of the deductive argument forms discussed in Chapters 10 and 11 . SECTION REASONING FROM A STATISTICAL GENERALIZATION We will refer to an argument which draws a conclusion about an individual or small group on the basis of a statistical generalization an Inductive Application ( these arguments are also sometimes called statistical applications or statistical ) Let take a look at an example . Ex . Chandler I doubt that Tony is a Cubs fan . Alex Why ?

Chandler I know Tony loves baseball , but he grew up on the south side of Chicago , and most baseball fans who grew up on the south side of Chicago are White not . Chandler is reasoning from a generalization . She starts with a statistical generalization about people who grew up on the south side of Chicago , and uses it to draw a conclusion about an . We can standardize Chandler argument as follows . Most baseball fans who grew up on the south side of Chicago are White not . Tony is a baseball fan who grew up on the south side of Chicago . So , Tony is probably a White not a . Inductive applications follow a pattern . Although they may be stated with more or less specificity , all inductive applications include a statistical generalization as a premise . The statistical claim tells us that many , most , or few members of the group that constitute the subject of the sentence are members of the group that 167

168 THADDEUS constitute the predicate of the sentence . Put in terms we introduced in the last chapter , the statistical claim in the argument above claims that most members of the subject class , baseball fans who grew up on the south side , are members of the predicate class , White not ' Inductive applications also rely on a premise which tells us that an individual is or is not a member of one of the classes . In this case , we are told that Tony is a member of the subject is , Tony is a ball fan who grew up on the south side of Chicago . Given that Tony is a member of the subject class , and that most members of the subject class are also members of the predicate class , Chandler concludes that Tony is also probably a member of the predicate is , that he is probably a White not a . Alternatively , we could have applied the generalization to draw a different conclusion . Suppose that we only knew that Tony was a not a White . We could then reason as follows . Most baseball fans who grew up on the south side of Chicago are White not . Tony is a Cubs and not a White Sox fan . So , Tony probably did grow up on the south side of Chicago . This is a different way an inductive application , since although it appeals to the same cal generalization in premise , it adds that Tony is nota member ofthe predicate class , and concludes he is nota member ofthe subject class . ago Skyline reflection in the BEAN by mike Perhaps you have already noticed that inductive applications have a lot in common with some other we have looked Modus and Modus . When we know that the individual in question is a member of the subject class , and thereby infer that the individual is a member of the predicate class , we are drawing an inference that is structurally similar to modus . Similarly , when we know that the individual in question is not a member of the predicate class , and thereby infer that the individual is not a member of the subject class , we are drawing an inference that is structurally similar to Modus . Despite these similarities , there is one fundamental difference , of course , namely that inductive applications are just .

INDUCTIVE APPLICATIONS 169 Like other kinds , inductive applications are not always explicit . As noted above , sometimes the quantity in question is ambiguous . In other cases , the statistical generalization is left implicit . Consider the following example Ex . Sydney I am not sure what I am going to do when I get out of college , but I am pretty sure I do want to be a teacher . Gina You do want to be a teacher ?

I thought that you were an English major ! In this case , Gina is surprised that Sydney does want to be a teacher , because she is assuming a tion between students who are English majors and students who are pursuing teaching as a career . It is hard to know exactly what the assumed connection is in this case without asking Gina , but it is likely that she is assuming something like this most English majors want to be teachers . Given this , the unstated assumption is a statistical generalization , and Gina is reasoning using an inductive application . This kind of ambiguously stated inductive application is relatively common in our everyday thinking . We naturally and intuitively generalize on our experiences , and once these generalizations are part of our overall system of belief we can use them to draw conclusions about specific cases . As we saw in our discussion of missing premises , we often leave out premises that we take to be obvious and generalizations are no exception . Thus , inductive applications are more common in our reasoning than we might expect . SECTION EVALUATION ILLUSORY FORMS Most errors in reasoning with generalizations are found in the process of , not in the process of applying the general claim to a particular instance . This is not , perhaps , surprising since the standards for logically strong inductive applications would seem to be clear in general , the higher the likelihood that members of the subject class are members of the predicate class , the logically stronger the inductive cation . Put otherwise , you have better reason to believe that Sydney wants to be a teacher if 90 of English majors want to be teachers , than you do if only 75 do . It is important to note , however , that there are two forms of inductive applications . We will call them ( a ) and ( There are , however , two kinds of mistake we are especially prone to make when dealing with inductive . First , recall from our discussion of deductive arguments that there are illusory argument forms . As we saw in Chapter 10 , arguments with the form the Consequent and Denying the Antecedent often strike people as deductive forms , even though they are not . Similarly , we need to be clear that argument forms we will call Affirming the Predicate Class and Denying the Subject Class can seem logically strong , but tend to be logically weak . We will add probably to the conclusions below to remind ourselves that these are inductive arguments . the Predicate ( out ! Most As are . is an . So , is a A . Denying the Subject ( out ! Most As are .

170 THADDEUS . So , is not an , Instances the Predicate Class and Denying the Subject Class are often logically weak because in generalizations the predicate class is often much larger than the subject class . Thus , in most cases the Predicate knowing that an individual is a member of the predicate class does tell you anything about whether it is also a member of the subject class . Similarly , in most cases of Denying the , knowing that an individual is not a member of the subject class does tell you that the individual is not a member ofthe predicate class . To illustrate Ex . Affirming the Predicate ( AP ) Most sodas are have a lot of sugar . Sweet tea has a lot of sugar . So , probably sweet tea is a kind of soda . Ex . Denying the Subject Class ( Most sodas have a lot of sugar . Sweet tea is not a kind of soda . So sweet tea does not have a lot of sugar . While we might want to clarify what counts as a lot of sugar , these two examples nevertheless illustrate the problem with the Predicate Class and Denying the Subject Class . These are both logically weak arguments because , like most statistical generalizations , the predicate class is much larger than the subject class . In this case , there are many drinks with a lot of sugar ( predicate class ) that are not sodas ( subject class ) That is , sodas are only one of many kinds of drinks with a lot of sugar ( energy drinks , juices , iced teas , For this reason , knowing that sweet tea has a lot of a sugar does allow us to infer , as in Ex . that sweet tea is a soda . The same goes for Ex . Since there are many drinks with a lot of sugar besides sodas , simply knowing that sweet tea is not a kind of soda does not allow us to infer that it have a lot of sugar . We need to be clear , however , that there are logically strong instances of AP and ( unlike the Consequent and Denying the Antecedent ) This is unusual , however , and occurs only when the subject class and the predicate class overlap almost completely . Here is an example . Suppose that the employees of a small jewelry store all know the code to the security system that allows them into the store . The store updates its code every three months , and has instructed the employees not to share the information with anybody else . Assuming that the employees are trustworthy in this respect , the class of people who know the security code will almost perfectly overlap with the class of people who work at the store . Most , if not all , of the people who know the security code will be employees of the store , and most , if not all , of the employees of the store will know the security code . In this case , the subject class and predicate class almost perfectly overlap , and we could formulate a logically strong instance of the Predicate as follows . Most of the people who know the security code are employees of the store . Jan is an employee of the store , So , Jan probably knows the security code .

APPLICATIONS 171 Again , what makes this kind of case unusual is that the subject and predicate classes almost perfectly lap . In the vast majority of our everyday arguments , when we express a statistical generalization we are talking about subject classes that are much smaller than predicate classes . The fact that instances and are commonly weak arguments means that we need to be on the out for them . More specifically , we need to be on the lookout for arguments with premises telling us that an individual is a member of the predicate class or that an individual is not a member of the subject class . Again , it is not that all such arguments are logically weak , but they often are , and we should take a closer look if we find one . We will call a logically weak instance or a cation . More specifically , a person gives a misapplication when they mistakenly conclude that ( i ) an individual is a ber of the subject class because they are member of the predicate class or ( ii ) an individual is not a member of the predicate class because they are a member of the subject class . SECTION RELEVANT SUBJECT CLASSES When it comes to evaluating inductive applications , the second thing to keep in mind arises from the fact that inductive applications are , like other inductive arguments , defeasible . That is , the discovery of new information can weaken the logical strength of the argument . The chief concern , in this context , arises from the fact that individual objects and people are always members of many subject classes . A person , for example , might be a student , a resident of Pennsylvania , a dog owner , a Steelers fan , a owner , and so forth , and we need to take this into account in our evaluation of Inductive applications . Consider the following example . Suppose that we know is from Nashville , Tennessee . We might draw the following inference . Ex . Most people from Nashville , Tennessee have been to the Country Music Hall of Fame . Jocelyn is from Nashville , Tennessee . Jocelyn has probably been to the Country Music Hall of Fame . However , since jocelyn is a member of many different subject classes she may be a member of a subject class that would undermine the support the premises lend to the conclusion in Ex . That is , jocelyn may be a member of another subject class that is relevant to the logical strength of the argument . Let us call this a relevant subject class . Suppose , for example , that she strongly dislikes country music . Knowing this would significantly undermine our confidence that she probably been to the Hall of Fame . III Ill IN I II ' Country Music of Fame Museum Nashville , Tennessee by Timothy

172 THADDEUS This shows that in evaluating an inductive application we have to look outside or beyond the argument as stated to think about what else we know , or can find out about , the individual in question . Again , doing so is in accordance with the The Rule of Total Evidence ( see Chap 12 ) and helps us avoid drawing premature based on partial evidence . We will call an inductive application that violates this rule a hasty tion . More specifically A person gives a hasty application when they mistakenly conclude that an individual is , or is not , a member of some class because they did not adequately consider other relevant subject classes . It is important to see that a concern about hasty applications is no merely academic can be absolutely crucial that we avoid the use of hasty applications . Here are a couple of examples . For most women , oral contraceptives ( birth control pills ) are perfectly safe means of family planning consequently , an individual woman might reasonably conclude on the basis ofan inductive application that using oral will be perfectly safe . However , birth control pills are not a safe means of family planning for women with one of a number of different blood clotting disorders . In these cases , the use of oral can raise the chances of pulmonary embolism and other dangerous blood clots . Thus , for individuals in the subject class women with blood clotting disorders taking oral contraceptives is not a perfectly safe means planning . Here is another example for most people drinking grapefruit juice is perfectly fine and has no adverse health consequences ( other than its taste ! In fact , you might never have heard of anyone for whom fruit juice is potentially harmful . Thus you might reason as follows for most people , grapefruit juice is perfectly fine , so it is probably perfectly fine for me . However , if you are taking ( a class of drug used to lower cholesterol ) drinking can be dangerous . As it turns out prevents the body from breaking down some kinds of , and this has potentially dangerous . Thus , if you fall into the subject class person taking then the consumption of grapefruit juice is not perfectly safe . It is not difficult to see how important it can be for a physician to have all the relevant available information before him or her prior to making even routine suggestions to patients . Of course many of our own tive applications are less important than these nevertheless , the lesson is the making inductive applications we can not ignore an individual membership in other relevant classes . Two Questions to Ask of Inductive Applications Is the individual in question a member of the subject class or not a member of the predicate class ?

ure or ) Is the individual in question a member of other relevant classes ?

Failure Hasty Application ) SECTION EVALUATING INDUCTIVE SUMMARY This brings us to the end of Unit . We have taken a close look at four of the most common forms of inductive argument , and we have identified the most important questions to ask of these arguments . Of course in the real world , arguments do not come neatly packaged and categorized , and they are often put together to form long chains of argument . We have to do the work of breaking down , identifying , and for ourselves , and the hope is that you are now in a better position to do so . That is , hopefully you are able to better spot and distinguish Arguments from Analogy , inferences to the Best Explanation , Inductive Generalizations , and Inductive Applications . Moreover , you are now in a position to ask the right questions as

INDUCTIVE APPLICATIONS 173 you evaluate these kinds of argument . Of course , these questions will not always settle the matter . ing arguments can be hard , and we do always have the information we need . Nevertheless , knowing the right questions to ask can push conversations and inquiries forward , and can help direct us toward further information that bears on the logical strength of these arguments . EXERCISES Exercise Set ISA Directions Determine whether the following are inductive generalizations or inductive applications . For inductive applications the subject class and predicate class of the appropriate generalization . For inductive identify the sample and population . There is no way I am getting one of those little dogs ! Little dogs bark all the time . She loves going to the movie theater . I been with her or times and each time she really enjoyed it . I do think I am going to call him this afternoon hejust finished paying bills and that typically puts him in a bad mood . Math teachers have weird personalities . I never had a math teacher I would call normal . What do you mean you are ?

You are part of the campus emergency medical service ( EMS ) and everyone there is ! Jill is an excellent baker , judging from these macaroons . I think Anne will probably enjoy the cake , I mean most people like chocolate . Exercise Set Directions For each of the following inductive applications the subject class and the predicate class . Then evaluate the argument for logical strength . If there is a problem with the argument , it .

174 THADDEUS ROBINSON Casey is probably in a motorcycle club I mean he has tattoos and most guys in motorcycle clubs have . Most people from Japan do not speak English , so the newly appointed Japanese ambassador to the United States probably does not speak English . I doubt that Casey is in a motorcycle club I mean he does have any tattoos , and most guys in motorcycle clubs have tattoos . Most college football players never play professionally after college , so the trophy winner will ably not play professionally after he is out of college . Most obese people either suffer from diabetes or are at high risk for developing diabetes . But since Jack is obese , it is likely that he neither suffers from diabetes nor is at risk for developing it . Typically , jobs in retail do not come with health benefits . So , I doubt these benefits will be part of your new job . I am worried I am suffering from heavy metal poisoning . After all , most victims of heavy metal poisoning suffer from fatigue , and I have been fatigued lately .

Unit Summary In this unit we looked at four of the most common types of inductive arguments Arguments from Analogy , Inference to the Best Explanation , Inductive Generalization , and Inductive Application . We use each one of these types multiple times every day . In each case , we learned how to identify these arguments by type , learned what makes them logically strong , and isolated key questions to ask in evaluating for logical strength . KEY QUESTIONS FOR SPECIFIC INDUCTIVE ARGUMENT TYPES Two Questions to Ask of Arguments from Analogy Is the noted similarity relevant to the inferred similarity ?

Are there differences that are relevant ?

Three Questions to Ask of inferences to the Best Explanation How likely is the proposed explanation ?

Are there other plausible explanations ?

Would the truth of the proposed explanation be less surprising than the truth of any competitor ?

Two Questions to Ask of inductive Generalizations Is the sample large enough ?

Is the sample diverse enough ?

Two Questions to Ask of inductive Applications Is the individual in question a member of the subject class or not a member of the predicate class ?

Is the individual in question a member of other relevant classes ?

KEY TE Inference to the Best Explanation Universal Generalization Poor Explanation Statistical Generalization Hasty Explanation Inductive Generalization Generalization Sample Subject Class Population Predicate Class Margin of Error 175 176 THADDEUS Sample Size Denying the Subject Class Sample Diversity Hasty Application Hasty Generalization Misapplication Biased Generalization Arguments from Analogy Random Sample Availability Heuristic Relevant Similarity Inductive Application Relevant Differences Affirming the Predicate Class Fundamental Attribution Error FURTHER READING For a deeper engagement with many of the issues raised in this chapter see the Stanford Encyclopedia entries on Analogy and Analogical Reasoning , Inductive Logic , and Abduction . See also Choice and Chance An Introduction to Inductive Logic by Brian . For more about inference to the best nation see Peter aptly titled book Inference to the Best Explanation .