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Inductive Arguments

Inductive Arguments. Inductive vs. Deductive Arguments The difference between a deductive and an inductive argument lies in what it is attempting to show

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Inductive Arguments Slide 2 Inductive vs. Deductive Arguments The difference between a deductive and an inductive argument lies in what it is attempting to show. A deductive argument is trying to show that its conclusion must follow from its premises. An argument that successfully does this is deductively valid. Slide 3 Counterexamples If a deductive argument is a good one, you wont be able to think of any counterexamples to it. Counterexample = a possible situation where the premises of the argument are true but the conclusion is false. A valid argument will not have any counterexamples. Slide 4 Inductive Arguments An inductive argument has a different aim. It is only trying to show that its conclusion is supported by its premises. In other words, its trying to show that the truth of its premises makes it more likely that its conclusion will be true. Slide 5 Inductive Strength The quality of an inductive argument is measured by its strength the degree to which its premises raise the probability of its conclusion. If they dont raise the probability very much, the argument is not very strong. If they do, the argument is strong. Slide 6 Inductive Strength For inductive arguments, counterexamples dont show that the argument is bad. This is because an inductive argument is only saying that its conclusion is very likely, not that other possibilities do not exist. Validity isnt a feature we look for in good inductive arguments just strength. Slide 7 Additional Evidence Since inductive arguments dont prove their conclusion, even a strong argument with true premises can be defeated by additional evidence. Slide 8 Example For example: Most cats like to play. Fluffy is a cat. Therefore Fluffy probably likes to play. This argument is strong, but future evidence might show that its conclusion is still false, even if its premises are true! (Fluffy might be too old to play) Slide 9 Vs. Valid Argument Notice how this is different from valid arguments. In a valid argument, so long as the premises are true, no future evidence can show that the conclusion is false. Of course, future evidence might show that the premises are wrong! Slide 10 Induction Today, we will discuss two different types of inductive arguments: inductive syllogism inductive generalization Slide 11 Inductive Syllogism An inductive syllogism is a method for arguing from a general statement to a more specific one. A general statement is a statement about a group of people: most teachers are smart athletes are strong in general, dogs like to play fetch many students dont get enough sleep bankers are usually rich Slide 12 Inductive Syllogism A general statement about a certain group can help us make a good guess about a particular member of that group. For instance, if we know that most bankers are rich, we can make a good guess that Bill the banker is rich, too. Slide 13 Inductive Syllogism In standard form: 1) Most bankers are rich. 2) Bill is a banker. 3) Bill is rich. The general form of the argument I just gave is: 1) Most Xs are Y. 2) A is an X. C) A is Y. This type of argument is called an inductive syllogism. Slide 14 Inductive Syllogism In standard form: 1) Most bankers are rich. 2) Bill is a banker. 3) Bill is rich. Notice that this is NOT a valid argument. The premises do not guarantee the conclusion Bill could be a poor banker. (A counterexample!) But since this is an inductive argument, it doesnt matter that the argument is not valid. Slide 15 Inductive Syllogism In standard form: 1) Most bankers are rich. 2) Bill is a banker. 3) Bill is rich. The argument does raise the probability that its conclusion is true. If it turns out that most bankers are rich, this makes it more likely that Bill the banker is rich. So this is a strong inductive argument. Slide 16 More Examples Most basketball players are tall. Jane is a basketball player. Therefore Jane is probably tall. Most university students are smart. Alice is a university student. Therefore Alice is probably smart. Most Saturdays, the bus runs late. Today is a Saturday. Therefore, the bus will probably run late. Slide 17 Hidden Premises An inductive syllogism can have hidden premises. Often, the second premise will be left out if it is common knowledge (i.e., it will become a hidden premise). 1) Most Presidents are very powerful. 2) Barack Obama is very powerful. Similarly, the first premise may be left out if the generalization is common knowledge. 1) Bill is a banker. C) Bill is probably rich. Slide 18 Different Orders The premises in an inductive syllogism dont have to come in the same order, either. The following two arguments are the same: Most winter days are cold. Tomorrow is the first day of winter. Therefore, tomorrow will probably be cold. Tomorrow is the first day of winter. Most winter days are cold. Therefore, tomorrow will probably be cold. Slide 19 Hidden Conclusion Even the conclusion of an inductive syllogism can be hidden particularly if the conclusion is used as a sub-conclusion in a larger argument. If Bill is rich, then he will buy us lunch. Bills a banker, and most bankers are rich so well probably get a free lunch today! Slide 20 Strength of Generalization The strength of an inductive syllogism depends primarily on the strength of the generalization. If 90% of cats like milk, then most cats like milk, Fifi is a cat, therefore Fifi likes milk is a pretty strong argument. If only 70% of cats like milk, then the argument is much weaker. Slide 21 Other Evidence But our assessment of the argument also has to do with the amount of available evidence that has been taken into account. Consider the example most bankers are rich, Bill is a banker, therefore Bill is probably rich. Even though this argument is strong, our assessment of the likelihood of its conclusion may be affected by other available information about Bill. Slide 22 Other Evidence For instance, if we find out that Bill invested heavily in the stock market right before it crashed, then we might no longer accept the conclusion that Bill is probably rich. Or, if we know that Bill is a chronic gambler, we might use this to infer that Bill is bad at managing his money and that hes therefore less likely to be rich, even though he is a banker. Slide 23 Obvious Available Evidence Its the neglect of obvious available evidence that makes the following inductive syllogisms not very convincing: Most Americans dont speak Chinese. The new professor of Chinese literature is American. Therefore, he doesnt speak Chinese. Most of the citizens of Zimbabwe are poor. Therefore, the president of Zimbabwe is poor. Slide 24 Different Argument Form Inductive syllogisms are easily confused with a different argument form: 1) Most Xs are Y. 2) A is a Y. C) A is an X. An example to show why this is bad: 1) Most teachers are adults. 2) Bill is an adult. C) Bill is a teacher. Slide 25 Inductive Generalization The other form of inductive argument we will discuss today is inductive generalization. Inductive generalization is a way to argue from specific to general claims. So in a sense, its the opposite of the argument style we just looked at. Slide 26 Inductive Generalization However, its not exactly the opposite: 1) Bill is rich. 2) Bill is a banker. C) Most bankers are rich. This would not be a good argument. You cant go from an observation about one person to a claim about a whole group. Instead, in order to justify the statement that most bankers are rich, we need to look at lots and lots of particular bankers. Slide 27 Samples Ideally, when we are trying to find out whether a large percentage of a group has a certain property, we would check every member of the group. But for a lot of groups, thats just not possible there are too many to check. Instead, we look at a sample, or a subset of the group. Slide 28 Inductive Generalization Say we look at a sample of bankers and find that 90% of them are rich. We can then use that information to support a conclusion that most bankers are rich. So the argument form of an inductive generalization is: 1) Most of the observed sample of Xs are Y. C) Most Xs are Y. Slide 29 Other Examples We have given our new pet food to 200 cats. All but one liked the food. Therefore, we believe that most cats will love our new pet food. We polled 1000 people in Hong Kong and asked them if they preferred coffee or tea. 886 people replied tea. Therefore, it seems likely that most Hong Kong people prefer tea. Slide 30 Representative Samples The success of an inductive generalization depends on how good the match is between the sample and the entire group. If our sample of bankers is 90% rich, but bankers on a whole are only 30% rich, our argument will not be a good one. Slide 31 Samples Of course, we cant check this match directly the whole point of using a sample was that we cant check the properties of the entire group! If we knew that bankers were 30% rich, we wouldnt need to test a sample. Slide 32 Sample Size But, there are ways to make educated guesses about how closely the percentages match. One of the easiest is the size of the sample if we survey 10% of the bankers, well have a better estimate than if we survey 1% of the bankers. When all else is equal, a larger sample is better than a smaller sample. Slide 33 Sample Size Slide 34 Size of the Group Sometimes its difficult to tell if weve sampled a large percentage or a small percentage of the total group because sometimes we dont know who belongs in the group! This is particularly tricky for cases where we have to rely on self-identification not everyone is going to admit to being a member of the group pornography users! Slide 35 Representative Samples Another factor is whether the sample is representative. Slide 36 Representative Samples For instance, say we want to know whether most bankers are rich. But say our sample only contains bankers who went to Harvard. Our sample is BIASED not all bankers go to prestigious schools, and whether or not one goes to a prestigious school is likely to influence whether or not one is rich. Slide 37 Perfectly Representative Samples A perfectly representative sample does not contain any bias. In a perfectly representative sample, the percentage of bankers in the sample that went to Harvard would be the same as the percentage of total bankers that went to Harvard. Slide 38 Relevant Factors Of course, it is not usually possible to use a perfectly representative sample the sample will almost always contain a greater or lesser percentage of for example, red-headed bankers, left-handed bankers, etc. But ideally well make sure that any relevant factors like education match pretty well. Slide 39 Biased Samples Other examples of (relevantly) biased samples Using a sample of Americans to make claims about what kinds of movies people (worldwide) will like. Using a sample of only first-years to make claims about the work habits of university students. Slide 40 Sneaky Bias Sometimes bias can be sneaky: Phone polls during elections often end up with a sample containing too many old people old people are more likely to be at home when the phone rings. Also, they are more likely to have a land line! Slide 41 Random Samples Well also do our best to make sure that even factors that dont appear relevant will be reasonably represented in the sample. Often the best way to do this is to use a random sample a sample where every member of the target group has the same chance at being included in the sample. Slide 42 Dont Reverse Terms Just like with inductive syllogism, its important to be careful not to reverse terms with inductive generalization. This is not a good argument: 1) Most of the sample of doctors we surveyed are rich. C) Most rich people are doctors. The reason this is a bad argument is that, while you might have tested a good sample of doctors, you might not have tested a good sample of rich people. Slide 43 Anecdotal Evidence Unfortunately, many people often make inductive generalizations on very bad samples. Sometimes, samples of only one case! This is called relying on anecdotes, or anecdotal evidence using a single case, or just a few, to draw conclusions. It is not a very strong form of argument. Slide 44 Cherry Picking You often see this in advertisements rather than giving a percentage of people who gained a benefit from the product, advertisers will simply show a single person saying that the product worked for them. Slide 45 Anecdotal Evidence as Argument Sometimes people try to reject arguments on the basis of anecdotal evidence, too!