CRITICAL THINKING. Induction v Deduction. Enumerative Induction and Inductive Generalization Sample Size Representativeness Mean, Median, Mode,

Transcription

1 CRITICAL THINKING INDUCTIVE REASONING LECTURE PROFESSOR JULIE YOO Induction v Deduction Enumerative Induction and Inductive Generalization Sample Size Representativeness Mean, Median, Mode, Analogical Induction Relevant Similarities Relevant Dissimilarities Number of Instances Compared Diversity Among Cases Causal Arguments: Testing for Causes Method of Agreement Method of Difference Joint Method of Agreement and Difference Correlation (Method of Concomitant Variation) An Important Word of Caution Causal Confusions Causal Fallacies Misidentifying Relevant Factors Mishandling Multiple Factors Being Misled By Coincidence Confusing Cause with Temporal Order Confusing Cause and Effect Inductive Reasoning Page 1 of 8

2 DEDUCTION V INDUCTION Deductive and inductive arguments serve different functions. One is to demonstrate that the conclusion is contained in the premises. The other is to show how the conclusion can generate new knowledge from the premises. Deductive Argument The purpose of giving a deductive argument is to demonstrate that the conclusion (C) is contained in the premises (P). It is to show that the conclusion is an automatic consequence of the premises; if you are committed to the premises, then you have to be committed to the conclusion. If you are successful in showing this, you are giving a valid argument. This explains how the conclusion of a valid argument is guaranteed to be true if the premises are true. Inductive Argument The purpose of giving an inductive argument is to generate new knowledge in the conclusion (C) from the premises (P). This is why it is always possible that the conclusion of an inductive argument is false, even though all the premises are true. In a strong inductive argument, you minimize this risk by proving premises that offer the strongest support. To be successful in minimizing this risk, you want to collect as much data as you can to support the conclusion. There are a number of different kinds of inductive arguments, but the ones we will consider here are the most common and the most easily misunderstood. ENUMERATIVE INDUCTION AND INDUCTIVE GENERALIZATION These two forms of inductive reasoning are very similar, but there is a difference. The conclusion of an enumerative induction is a statement about a particular individual or a particular situation. On the other hand, the conclusion of an inductive generalization argument is a universal statement. Enumerative Induction: To go from many observed cases to another single case that is unobserved. Induction Generalization: To go from many observed cases to an unobserved (unobservable) universal generalization. A is P 1 and is P 2 B is P 1 and is P 2 C is P 1 and is P 2 Z is P 1 and is P 2 Copper is a metal and is malleable. Aluminum is a metal and is malleable. Iron is a metal and is malleable. Zinc is a metal and is malleable. A is P 1 and is P 2 B is P 1 and is P 2 C is P 1 and is P 2 All P 1 are P 2 Copper is a metal and is malleable. Aluminum is a metal and is malleable. Iron is a metal and is malleable. All metals are malleable. With these two types of arguments, two considerations stand out when assessing their strength, and these are sample size and representativeness. Inductive Reasoning Lecture Page 2 of 8

3 Sample Size The more members of the target population that are observed with the target property, the stronger the conclusion will be. Otherwise, you risk committing the fallacy of hasty generalization. Representativeness Opinion polls are among the most efficient ways to collect data about a population, as long as the survey is composed correctly. To be effective and useful, opinion polls must first have a large sample size and must sample representative members. To do this, pollsters conduct what is known as random sampling. To get the most typical traits of the members of a class, you need to target members randomly. Specifically, you cannot or should not rely upon subjects who choose to fill out the opinion surveys, since this will result in a self-selecting sample, which is an instance of a biased sample. For instance, if you survey the members of a very wealthy gated community about funding public education, you will have targeted an atypical group, and thus get a skewed result. You need to make sure that the people you interview represent the majority; this is known as representativeness. One way of doing this is by random sampling. Mean, Median, Mode These refer to different formulas gauging the central tendency for a bunch of figures. Let s use this set of numbers as our example: 4, 4, 4, 5, 7, 8, 9, 12, 625 Mean: The mean of a batch of numbers is just their arithmetical average sum up all the numbers and divide by the number of entries: [ ] 9 = Median: The median is the middle value if we ordered the series and targeted the middle point so that half of the entries would be above the value and the remaining half is below it. In our example, the median is 7. Mode: The mode is the most common value or most frequently occurring value of the series. In our example, the mode is 4. These ways of targeting the central tendency give you different information. Depending on the situation, one concept will be more useful than another. For instance, if the list represented the amount of money a student spends on lunch during a school day, the mean, $75.33, would not give you an informative central tendency. In politics, these concepts are often conflated to throw off the citizen, so a good grasp of these concepts will be good protection against misrepresentation. Inductive Reasoning Lecture Page 3 of 8

4 ANALOGICAL INDUCTION Form of Analogical Reasoning A and B have properties P 1, P 2, P 3,, P x A is also P y B is also P y Mo and Jo are smart, eager, and diligent. Jo is a good student. Mo is a good student. The strength of an argument from analogy depends upon several factors: the number of shared features, the relevance of the shared features, P 1, P 2, P 3,, P x to the possession of Py, the relevance of the shared features to the similarity between x and y. Criteria for Good Analogical Reasoning Relevant Similarities: A and B have to be relevantly similar in order for the inference to a new shared property between A and B to be strong. Relevant Dissimilarities: This is not the same thing as lack of relevant similarities. Relevant dissimilarities between A and B can cast doubt on the strength of the inference to the presence of another similarity between A and B. Number of Instances Compared: The more relevant properties, P 1, P 2, P 3,, P x between A and B, the stronger the inference to a new shared property between A and B. Diversity Among Cases: The greater the diversity among the things compared A, B, C, D,, Z, that exhibit the relevant similarities, the stronger the inference to a new shared property. Applications The applications can be many and varied: 1. Medicine: Medical testing of new drugs on mice may indicate how humans react on the basis of how mice react. 2. Religion: The famous argument from analogy for God s existence that compares the apparent good design in the universe to good design in machines. 3. Law: Legal cases are judged on the basis of precedent, which means that the rulings on previous cases can determine rulings on similar present cases. 4. Forensics: Crime patterns from previous crimes can guide judgments about present crimes. Inductive Reasoning Lecture Page 4 of 8

5 CAUSAL ARGUMENTS: TESTING FOR CAUSES Causal arguments are inductive arguments whose conclusions are statements about a causal relation. We also use causal arguments when we want to explain why something occurred or when we want to predict what will occur. Causal arguments are central to scientific discovery. The 19 th C British philosophy, John Stuart Mill, formulated five methods for identifying causes. Different cases lend themselves to different methods, depending on the nature of the investigation, what you are interested in, and the nature of the data set. The method one uses will depend on the circumstances, the data that is present, and what you are looking for. Method of Agreement This method looks for the agreeing factor (the common cause ) when we want to know what brought about the effect. Identifying the common cause essentially amounts to identifying the COMMON PRESENT features when the effect occurs. Diagram 1 ham cheese tomato lettuce pickle ILLNESS Alvin Bianca Charlie All of the kids got sick. What do they have in common? There is one thing that is common to all of their meals. It is the (bad) lettuce. Thus, according to this diagram, the lettuce caused the illness. Diagram 1 suggests that the illness couldn t have been caused by any of the other factors: if those other things were not eaten, the illness would have occurred anyway as long as the lettuce was eaten. Another way of applying the Method of Agreement is by looking for COMMON ABSENCES. Here is an illustration: Diagram 2 school television clean air exercise good food HEALTH Alvin Bianca Charlie None of the kids are healthy. What do they have in common? It is the lack of clean air. The diagram suggests that none of the other factors result in health. Thus, exposure to clean air is what causes health. This is just to say that clean air is sufficient for health: if the child were exposed to clean air, then he or she would be healthy. Inductive Reasoning Lecture Page 5 of 8

6 Method of Difference The Method of Agreement looks for some commonalities. Sometimes, however, we can identify the relevant causes and effects by looking at DIFFERENCES. This can happen when we have two sets of cases that are identical except for one factor. The difference in this factor accounts for the difference in the effect. The difference is what helps us identify the cause. Diagram 3 ham cheese tomato lettuce pickle ILLNESS Xavier Yolanda In this example, the effect, again, is the illness, and its cause is the tomato. This is because the two diners had exactly the same thing except for one differing item the tomato. The tomato, therefore, was probably the thing that caused the illness in Yolanda. The difference between the Method of Agreement and the Method of Difference is that the former is concerned with identifying the causal factor in all the cases under examination, whereas the latter is concerned with identifying the causal factor in just a single case under examination. When we do the latter, we, in effect, look for points of difference among the cases under examination. Joint Method of Agreement and Difference The Joint Method is the application of the two methods we have covered so far. If there is enough data, we can use the Joint Method to strengthen the inference concerning relevant causal factor. The idea behind the Joint Method is basically this: the likely cause C is 1) the factor common to all the common effects (the Method of Agreement, Direct or Inverse), and 2) the points of difference among the different effects. Diagram 4 take drug X placebo CURE Alvin Bob Charlie Dennis Elvis Fred Greg The Joint Method is the method used in controlled experiments. To see whether a drug X is effective in curing a certain illness Y, it is important to determine two things: that those who take the drug get better (using the Method of Agreement) and that there is a noticeable difference between those who take the drug and those who don t (using the Method of Difference). Failure to make a difference or failure in agreement would indicate that the drug is not effective. Inductive Reasoning Lecture Page 6 of 8

7 Correlation: Method of Concomitant Variation The Methods of Agreement and Difference target causes by looking at present factors and absent factors. Sometimes, though, you can gather information about a cause without having to look at present or absent factors. Observing a corresponding change in degree can indicate a causal relation: the harder you work out, the stronger you become, the more you consume grains and vegetables, the healthier you become, the less sleep you get, the more prone you are to illness, the more you drive, the more pollution you create. In each of these cases, there is a correlation by degree, and we can use this information to target the relevant cause. Causation is a very important kind of correlation: whenever an event of type C is present an event of type E is also present. Events of type C are correlated with events of type E. Not all instances of correlation, however, are instances of causation, and we will look at some cases of causal misidentification. An Important Word of Caution Getting the data is no easy feat. The following diagrams that I devised, for the purpose of illustration, convey the misleading impression that we can readily identify the possible causal candidates. But scientific discovery is never this easy. The diagrams are like maps whose roads and highways have been fully depicted; once you have a map, it s fairly easy to navigate your way and find the shortest route to your destination. Science never begins with a complete map of nature. It is trying to map out nature i.e., come up with a reasonable diagram with the appropriate candidates filled in with the use of many methods. CAUSAL CONFUSIONS CAUSAL FALLCIES Unlike deductive reasoning, which requires no context for its correct application, inductive reasoning requires a keen appreciation of the context. The problem with taking context into account is that we cannot always know that we have taken every relevant factor into consideration. Even if we apply the rules of inductive reasoning correctly, we are not assured that we have a strong inductive argument. In fact, even if we have a strong inductive argument, we could still end up with a false conclusion. This is particularly problematic for causal arguments. In this section, we will look at common mistakes in causal reasoning. Misidentifying Relevant Factors This happens often when applying the Method of Agreement. Just because you identify a common factor (eating lettuce) among the cases that have the same effect (getting sick), that does not guarantee that you have correctly identified the cause. Perhaps the lettuce was covered with tainted mayo, which you didn t take into consideration. Then your accusation against the lettuce will have been incorrect, even though you followed the Method of Agreement perfectly. The same problem can occur with the Method of Difference as well as the Method of Concomitant Variation. Suppose you use the Method of Difference to examine whether a drug X Inductive Reasoning Lecture Page 7 of 8

8 is effective. You administer the drug to mouse 1 but not to mouse 2. Mouse 1 gets better, but mouse 2 does not. Even though this result seems to point in the direction that drug X was effective, this assessment is not guaranteed. Maybe mouse 1 happened to have been given a different diet during the test run, or maybe it was handled with more care, or maybe it reacted positively to something in its cage that was not present in the cage of Mouse 2. Then we will not know if the improved health in mouse 1 was due to drug X or one of these other factors. The same idea applies to the Method of Concomitant Variation. Mishandling Multiple Factors As you have probably gathered, the problem with causal arguments is not that we have too few candidates to consider but that we have too many. There are many, many, factors that accompany an effect that we may not have acknowledged as a possible candidate for the cause of the effect. Even when you try to narrow down on the possible candidates, there can always be a candidate that we overlooked. Being Misled By Coincidence Sometimes, improbable things happen to us. You think about calling someone and that person calls you just as you are thinking about her/him. On the basis of this coincidence, you then conclude that something made this happen. This is an instance of confusing a coincidence as a cause. Confusing Cause with Temporal Order This confusion is known as post hoc, ergo propter hoc (which means after that, therefore because of that ). This is when you think that a certain event occurs just because some other event precedes it: job loss is at an all-time high in 2010, and Obama was voted into office in 2008, therefore Obama s presidency has caused the all-time high job-loss. Confusing Cause and Effect This confusion can happen when there is a chicken-egg situation calls for further controlled experiments to sort out. Healthy people exercise regularly: do people get healthy because they exercise regularly or do people exercise regularly because they are healthy? Happy people tend to have dogs: do dogs make people happier or do happy people tend to gets dogs? Inductive Reasoning Lecture Page 8 of 8