Phi 103 Week 3 Assignment

Learning Objectives After reading this chapter, you should be able to:1. Define key terms and concepts in inductive logic, including strength and cogency.

2. Differentiate between strong inductive arguments and weak inductive arguments.

3. Identify general methods for strengthening inductive argu ments.

4. Identify statistical syllogisms and describe how they can be stro ng or weak.

5. Evaluate the strength of inductive generalizations. 5 Inductive Reasoning Iakov Kalinin/iStock/Thinkstock 6. Differentiate between causal and correlational relationships and describe various types of causes.

7. Use Mill’s methods to evaluate causal arguments.

8. Recognize arguments from authority and evaluate their qua lity.

9. Identify key features of arguments from analogy and use them t o evaluate the strength of such arguments.

When talking about logic, people often think about formal deductive reasoning. However, most of the arguments we encounter in life are not deductive at all. They do not intend to establish the truth of the conclusion beyond any possible doubt; they simply try t o provide good evidence for the truth of their conclusions. Arguments that intend to reason in this wa y are called inductive arguments . Inductive arguments are not any worse than deductive ones. Often the best evidence available is not final or conclusive but can still be very good.

For example, to infer that the sun will rise tomorrow because it has every day in the past is inductive reasoning. The inference, however, is very strongly sup ported. Not all inductive arguments are as strong as that one. This chapter will explore different type s of inductive arguments and some principles we can use to determine whether they are strong or weak. The chapter will also discuss some specific methods that we can use to try to make good inferences about causation. The goal of this chapter is to enable you to identify inductive arguments, evaluate their stren gth, and create strong inductive arguments about important issues. Age fotostock/SuperStock Weather forecasters use inductive reasoning when giving their predictions. They have tools at their disposal that provide support for their arguments, but some arguments are weaker than others. 5.1 Basic Concepts in Inductive Reasoning Inductive is a technical term in logic: It has a precise defini tion, and that definition may be different from the definition used in other fields or in everyday co nversation. An inductive argument is one in which the premises provide support for the conclusions but fa ll short of establishing complete certainty. If you stop to think about arguments you have encountered re cently, you will probably find that most of them are inductive. We are seldom in a position to prove so mething absolutely, even when we have very good reasons for believing it.

Take, for example, the following argument:

The odds of a given lottery ticket being the winning ticket are extremely low.

You just bought a lottery ticket.

Therefore, your lottery ticket is probably not the winning ti cket.

If the odds of each ticket winning are 1 in millions, then this argument gives very good evidence for the truth of its conclusion. However, the argument is not deductively valid. Even if its premises are true, its conclusion is still not absolutely certain. This means th at there is still a remote possibility that you bought the winning ticket.

Chapter 3 discussed how an argument is valid if our pre mises guarantee the truth of the conclusion. In the case of the lottery, even our best evidence canno t be used to make a valid argument for the conclusion. The given reasons do not guarantee that yo u will not win; they just make it very likely that you will not win.

This argument, however, helps us establish the likelihoo d of its conclusion. If it were not for this type of reasoning, we might spend all our money on lottery ti ckets. We would also not be able to know whether we should do such things as drive our car because we wo uld not be able to reason about the likelihood of getting into a crash on the way to the store. Ther efore, this and other types of inductive reasoning are essential in daily life. Consequently, it is important that we le arn how to evaluate their strength.

Inductive Strength Some inductive arguments can be better or worse than others, depending on how well their premises increase the likelihood of the truth of their conclusion. Some ar guments make their conclusions only a little more likely; oth er arguments make their conclusions a lot more likely. Arguments that greatly increase the likelihood of the ir conclusions are called strong arguments; those that do not substantially increase the likelihood are called weak arguments .

Here is an example of an argument that could be consi dered very strong:

A random fan from the crowd is going to race (in a 100 meter dash) against Usain Bolt.

Usain Bolt is the fastest sprinter of all time. Oksana Kostyushko/iStock/Thinkstock Context plays an important role in inductive arguments. What makes an argument strong in one context might not be strong enough in another. Would you be more likely to play the lottery if your chances of winning were supported at 99%? Therefore, the fan is going to lose.

It is certainly possible that the fan could win—say, for example, if Usain Bolt breaks an ankle—but it seems highly unlikely. This next argument, however, could be co nsidered weak:

I just scratched off two lottery tickets and won $2 each time.

Therefore, I will win $2 on the next ticket, too.

The previous lottery tickets would have no bearing on the likelihood of winning on the next one. Now this next argument’s strength might be somewhere in between:

The Bears have beaten the Lions the last four times they have playe d.

The Bears have a much better record than the Lions this season.

Therefore, the Bears will beat the Lions again tomorrow.

This sounds like good evidence, but upsets happen all the time in spo rts, so its strength is only moderate.

Considering the Context It is important to realize that inductive strength an d weakness are relative terms. As such, they are like the terms tall and short . A person who is short in one context may be tall in another. At 6’0”, pro fessional basketball player Allen Iverson was considered short in the National Bask etball Association. But outside of basketball, someone of his height might be considered tall. Similarly, an argument that is strong in one context may be considered weak in another. You would probably be reasonably hap py if you could reliably predict sports (or lottery) results at an accu racy rate of 70%, but researchers in the social sciences typically aim for certain ty upward of 90%. In high­energy physics, the goal is a result that is sup ported at the level of 5 sigma—a probability of more than 99.99997%!

The same is true when it comes to legal arguments. A ca se tried in a civil court needs to be shown to be true with a preponderan ce of evidence, which is much less stringent than in a criminal case, in which the defendant must be proved guilty beyond reasonable doubt. Theref ore, whether the argument is strong or weak is a matter of context.

Moreover, some subjects have the sort of evidence that allows for extremely strong arguments, whereas others do not. A psychologist t rying to predict human behavior is unlikely to have the same strength o f argument as an astronomer trying to predict the path of a comet. Th ese are important things to keep in mind when it comes to evaluating inductive str ength.

Strengthening Inductive Arguments Regardless of the subject matter of an argument, we generally want to create the strongest arguments we ca n. In general, there are two ways of strengthening inducti ve arguments. We can either claim more in the premises or claim less in the conclusion. Fuse/Thinkstock The strength of an inductive argument can change when new premises are added. When evaluating or presenting an inductive argument, gather as many details as possible to have a more complete understanding of the strength of the argument. Claiming more in the premises is straightforward in the ory, though it can be difficult in practice. The idea is simply to increase the amount of evidence for the conclusion. S uppose you are trying to convince a friend that she will en joy a particular movie. You have shown her that she has liked other movies by the same director and that the movie is of the general kind that she likes. How could you strengt hen your argument? You might show her that her favorite a ctors are cast in the lead roles, or you might appeal to th e reviews of critics with which she often agrees. By adding these additional pieces of evidence, you have increased th e strength of your argument that your friend will enjo y the movie.

However, if your friend looks at all the evidence an d still is not sure, you might take the approach of weakening y our conclusion. You might say something like, “Please go with me; you may not actually like the mo vie, but at least you can be pretty sure you won’t hate it.” The very same evidence you presented earlie r—about the director, the genre, the actors, and so on—actually makes a stronger argument for your new, le ss ambitious claim: that your friend won’t hate the movie.

It might help to have another example of how each o f the two approaches can help strengthen an inductive argument. Take the following argument:

Every crow I have ever seen has been black.

Therefore, all crows are black.

This seems to provide decent evidence, provided that y ou have seen a lot of crows. Here is one way to make the argument stronger:

Studies by ornithologists have examined thousands of cro ws in every continent in which they live, and they have all been black.

Therefore, all crows are black.

This argument is much stronger because there is much mor e evidence for the truth of the conclusion within the premise. Another way to strengthen the arg ument—if you do not have access to lots of ornithological studies—would simply be to weaken the stated conc lusion:

Every crow I have ever seen has been black.

Therefore, most crows are probably black.

This argument makes a weaker claim in the conclusion, but the argument is actually much stronger than the original because the premises make this (weaker) co nclusion much more likely to be true than the original (stronger) conclusion.

By the same token, an inductive argument can also be made weaker either by subtracting evidence from the premises or by making a stronger claim in the conclu sion. (For another way to weaken or strengthen inductive arguments, see A Closer Look: Using Premises to Affect Inductive Strength .) A Closer Look: Using Premises to Affect Inductive Strength Suppose we have a valid deductive argument. That me ans that, if its premises are all true, then its conclusion must be true as well. Suppose we add a new p remise. Is there any way that the argument could become invalid? The answer is no, beca use if the premises of the new argument are all true, then so are all the premises of the old argument. Therefore, the conclusion still must be true.

This is a principle with a fancy name; it is called monotonicity: Adding a new premise can never make a deductive argument go from valid to invalid. However, this principle does not hold for inductive strength: It is possible to weaken an inductive argume nt by adding new premises.

The following argument, for example, might be strong: 99% of birds can fly.

Jonah is a bird.

Therefore, Jonah can fly.

This argument may be strong as it is, but what happens if we add a new premise, “Jonah is an ostrich”? The addition of this new premise just made t he argument’s strength plummet. We now have a fairly weak argument! To use our new big word , this means that inductive reasoning is nonmonotonic . The addition of new premises can either enhance or diminish an argument’s inductive strength.

An interesting “game” is to see if you can continue t o add premises that continue to flip the inductive argument’s degree of strength back and fort h. For example, we could make the argument strong again by adding “Jonah is living in t he museum of amazing flying ostriches.” Then we could weaken it again with “Jonah is now ret ired.” It could be strengthened again with “Jonah is still sometimes seen flying to the roof of the museum,” but it could be weakened again with “He was seen flying by the neighbor child who h as been known to lie.” The game demonstrates the sensitivity of inductive arguments to new infor mation.

Thus, when using inductive reasoning, we should always b e open to learning more details that could further serve to strengthen or weaken the case f or the truth of the conclusion. Inductive strength is a never­ending process of gathering and eva luating new and relevant information. For scientists and logicians, that is partly what makes induction so e xciting! Inductive Cogency Notice that, like deductive validity, inductive strength has to do with the strength of the connection between the premises and the conclusion, not with the truth of the premises. Therefore, an inductive argument can be strong even with false premises. Here is an exam ple of an inductively strong argument:

Every lizard ever discovered is purple.

Therefore, most lizards are probably purple. Of course, as with deductive reasoning, for an argument to give good evidence for the truth of the conclusion, we also want the premises to actually be true. An inductive argument is called cogent if it is strong and all of its premises are true. Whereas inductive strengt h is the counterpart of deductive validity, cogency is the inductive counterpart of deducti ve soundness. 5.2 Statistical Arguments: Statistical Syllogisms The remainder of this chapter will go over some examples of the different types of inductive arguments: statistical arguments, causal arguments, arguments from a uthority, and arguments from analogy. You will likely find that you have already encountered many of these various types in your daily life. Statistical arguments , for example, should be quite familiar. From politi cs, to sports, to science and health, many of the arguments we encounter are based on statistics, drawing conclusions from percentages and other data.

In early 2013 American actress Angelina Jolie elected to have a preventive double mastectomy. This surgery is painful and costly, and the removal of both breasts is deeply disturbing for many women. We might have expected Jolie to avoid the surgery unti l it was absolutely necessary. Instead, she had the surgery before there was any evidence of the cancer t hat normally prompts a mastectomy. Why did she do this?

Jolie explained some of her reasoning in an opinion piece in the New York Times .

I carry a “faulty” gene, BRCA1, which sharply increase s my risk of developing breast cancer and ovarian cancer.

My doctors estimated that I had an 87 percent risk of breast cancer and a 50 percent risk of ovarian cancer, although the risk is different in the case of eac h woman. (Jolie, 2013, para. 2–3) As you can see, Jolie’s decision was based on probabiliti es and statistics. If these types of reasoning can have such profound effects in our lives, it is essential that we have a good grasp on how they work and how they might fail. In this section, we will be look ing at the basic structure of some simple statistical arguments and some of the things to pay attention to as we use these ar guments in our lives.

One of the main types of statistical arguments we will discuss is the statistical syllogism . Let us start with a basic example. If you are not a cat fancier, you may not know that almost all calico cats are female—to be more precise, about 99.97% of calico cats are female (Becker, 2013). Suppose you are introduced to a calico cat named Puzzle. If you had to guess, w ould you say that Puzzle is female or male? How confident are you in your guess?

Since you do not have any other information except that 99.97% of calico cats are female and Puzzle is a calico cat, it should seem far more likely to you tha t Puzzle is female. This is a statistical syllogism: You are using a general statistic about calico cats to make an argument for a specific case. In its simplest form, the argument would look like this:

99.97% of calico cats are female.

Puzzle is a calico cat.

Therefore, Puzzle is female.

Clearly, this argument is not deductively valid, but inductively it seems quite strong. Given that male calico cats are extremely rare, you can be reasonably confident that Puzzle is female. In this case we can actually put a number to how confident you can be: 99.97% confi dent.

Of course, you might be mistaken. After all, male cal ico cats do exist; this is what makes the argument inductive rather than deductive. However, statistical syllogisms like this one can establish a high degree of certainty about the truth of the conclusion. Form If we consider the calico cat example, we can see that the general form for a statistical syllogism looks like this:

X% of S are P.

i is an S.

Therefore, i is (probably) a P.

There are also statistical syllogisms that conclude that the individual i does not have the property P. Take the following example:

Only 1% of college males are on the football team.

Mike is a college male.

Therefore, Mike is probably not on the football team.

This type of statistical syllogism has the following form: X% of S are P.

i is an S.

Therefore, i is (probably) not a P.

In this case, for the argument to be strong, we want X to be a low percentage.

Note that statistical syllogisms are similar to two kin ds of categorical syllogisms presented in Chapter 3 (see Table 5.1). We see from the table that statistical syllogisms become valid categorical syllogisms when the percentage, X, becomes 100% or 0%.

Table 5.1: Statistical syllogism versus categorical syllogism Statistical syllogism Similar valid categorical syllogism Example 99.97% of calico cats are female.

Puzzle is calico.

Therefore, Puzzle is female. All calico cats are female.

Puzzle is calico.

Therefore, Puzzle is female.

Form X% of S are P.

i is an S.

Therefore, i is (probably) P. All M are P.

S is M.

Therefore, S is P.

Example 1% of college males are on the football team.

Mike is a college male.

Therefore, Mike is not on the football team. No college males are on the football team.

Mike is a college male.

Therefore, Mike is not on the football team.

Form X% of S are P.

i is an S.

Therefore, i is P. X% of S are P.

i is an S.

Therefore, i is not P.

When identifying a statistical syllogism, it is importan t to keep the specific form in mind, since there are other kinds of statistical arguments that are not statistical syllo gisms. Consider the following example:

85% of community college students are younger than 40. John is teaching a community college course.

Therefore, about 85% of the students in John’s class are under 40.

This argument is not a statistical syllogism because it do es not fit the form. If we make i “John” then the conclusion states that John, the teacher, is probably under 40, but that is not the conclusion of the original argument. If we make i “the students in John ’s class,” then we get the conclusion that it is 85% likely that the students in John’s class are under 40. D oes this mean that all of them or that some of them are? Either way, it does not seem to be the same as the original conclusion, since that conclusion has to do with the percentage of students under 40 in his cla ss. Though this argument has the same “feel” as a statistical syllogism, it is not one because it does not have the same f orm as a statistical syllogism. Weak Statistical Syllogisms There are at least two ways in which a statistical syllogism might not be strong. One way is if the percentage is not high enough (or low enough in the second type). If an argument simply includes the premise that most of S are P, that means only that more than half of S are P. A probability of only 51% does not make for a strong inductive argument.

Another way that statistical syllogisms can be weak is if th e individual in question is more (or less) likely to have the relevant characteristic P than the average S. For example, take the reasoning:

99% of birds do not talk.

My pet parrot is a bird.

Therefore, my pet parrot cannot talk.

The premises of this argument may well be true, and th e percentage is high, but the argument may be weak. Do you see why? The reason is that a pet parrot has a much higher likelihood of being able to talk than the average bird. We have to be very careful w hen coming to final conclusions about inductive reasoning until we consider all of the relevant information. 5.3 Statistical Arguments: Inductive Generalizations In the example about Puzzle, the calico cat, the first premise said that 99.97% of calico cats are female. How did someone come up with that figure? Clearly, sh e or he did not go out and look at every calico cat. Instead, he or she likely looked at a bunch of calico s, figured out what percentage of those cats were female, and then reasoned that the percentage of fem ales would have been the same if they had looked at all calico cats. In this sort of reasoning, the grou p of calico cats that were actually examined is calle d the sample , and all the calico cats taken as a group are calle d the population . An inductive generalization is an argument in which we reason from data about a sample population to a claim about a large population that includes the sample. Its general f orm looks like this:

X% of observed Fs are Gs.

Therefore, X% of all Fs are Gs.

In the case of the calico cats, the argument looks like this: 99.97% of calico cats in the sample were female.

Therefore, 99.97% of all calico cats are female.

Whether the argument is strong or weak depends crucial ly on whether the sample population is representative of the whole population. We say that a sample is representative of a population when the sample and the population both have the same distribut ion of the trait we are interested in—when the sample “looks like” the population for our purposes. In the case of the cats, the strength of the argument depends on whether our sample group of calico cats had about the same proportion of females as the entire population of all calico cats.

There is a lot of math and research design—which you mi ght learn about if you take a course in applied statistics or in quantitative research design—that goes in to determining the likelihood that a sample is representative. However, even with the best math and design, all we can infer is that a sample is extremely likely to be representative; we can never be absolutely certain it is without checking the entire population. However, if we are careful enoug h, our arguments can still be very strong, even if the y do not produce absolute certainty. This section will examine how researchers try to ensure the sample population is representative of the whole population and how researchers assess how confident they can be in their results.

Representativeness The main way that researchers try to ensure that the sa mple population is representative of the whole population is to make sure that the sample population is random and sufficiently large. Researchers also consider a measure called the margin of error to determine how similar the sample population is to the whole population.

Randomness Suppose you want to know how many marshmallow treats are in a box of your favorite breakfast cereal. You d o not have time to count the whole box, so you pour out on e cup. You can count the number of marshmallows in your cup a nd then reason that the box should have the same proport ion 5xinc/iStock/Thinkstock To ensure a sample is representative, participants should be randomly selected from the larger population. Careful consideration is required to ensure selections truly represent the larger population. One must be careful when making inductive generaliz ations based on statistical data. Consider the examples in this video. Raw numbers can sound more alarming than percentage s. Likewise, rate statistics can be misleading. Making Inferences From Statistics of marshmallows as the cup. You found 15 marshmallows in the cup, and the box holds eight cups of cereal, so yo u figure that there should be about 120 marshmallows in the box . Your argument looks something like this:

A one­cup sample of cereal contains 15 marshmallows.

The box holds eight cups of cereal.

Therefore, the box contains 120 marshmallows.

What entitles you to claim that the sample is representative? Is there any way that the sample may n ot represent the percentage of marshmallows in the whole box? One potential problem is that marshmallows tend to b e lighter than the cereal pieces. As a result, they tend to rise to the top of the box as the cereal pieces settle toward the bottom of the box over time. If you just scoop out a cup of cereal from the top, then, your sample may not be representative of the whole box and may have to o many marshmallows.

One way to solve this problem might be to shake the b ox. Vigorously shaking the box would probably distribute the marshmallows fairly evenly. After a goo d shake, a particular piece of marshmallow or cereal might equally end up anywhere in the box, so the ones that make it into your sample will be largely random. In this case the argument may be fairly strong.

In a random sample , every member of the population has an equal chance of being included. Understanding how randomness works to ensure representati veness is a bit tricky, but another example should help clear it up.

Almost all students at my high school have laptops.

Therefore, almost all high school students in the United States ha ve laptops.

This reasoning might seem pretty strong, especially if y ou go to a large high school. However, is there a way that the sample population (the students at the hi gh school) may not be truly random? Perhaps if the high school is in a relatively wealthy area, then the students will be more likely to have laptops than random American high schoolers. If the sample populati on is not truly random but has a greater or lesser tendency to have the relevant characteristic th an a random member of the whole population, this is known as a biased sample. Biased samples will be discussed further in Chapter 7, but note that they often help reinforce people’s biased viewpoints (see Everyday Logic: Why You Might Be Wrong).

The principle of randomness applies to other types of statistical arguments as well. Consider the argument about John’s community college class. The argument, again, goes as follows: 85% of community college students are younger than 40.

John is teaching a community college course.   Making Inferences From Statistics From Title: Evidence in Argument: Critical Thinking (https://fod.infobase.com/PortalPlaylists.aspx?wID=100753&xtid=49816) Critical Thinking Questions 1. The characteristics of the sample is an important consideration when drawing inferences from statistics. Before reading on, what qualities do you think an ideal sample possesses? 2. How can one ensure that one is making proper inferences from evidence? 3. What is the danger of expressing things using rates? What example is given that demonstrates this danger? Therefore, about 85% of the students in John’s class are under 40.

Since 85% of community college students are younger than 40, we would expect a sufficiently large random sample of community college students to have about the same percentage. There are several ways, however, that John’s class may not be a random sample. Before going on to the next paragraph, stop and see how many ways you can think of on your own.

So how is John’s class not a random sample? Notice first that the argument references a course at a single community college. The average student age likely varies from college to college, depending on the average age of the nearby population. Even within this one community college, John’s class is not random. What time is John’s class? Night classes tend to attract a higher percentage of older students than daytime classes. Some subjects also attract different age groups. Finally, we should think about John himself. His age and reputation may affect the kind of students who enroll in his classes.

In all these ways, and maybe others, John’s class is not a random sample: There is not an equal chance that every community college student might be includ ed. As a result, we do not really have good reason to think that John’s class will be representative of th e general population of community college students. So we have little reason to expect it to be represent ative of the larger population. As a result, we cannot use his class to reliably predict what the population w ill look like, nor can we use the population to reliably predict what John’s class will look like.

Everyday Logic: Why You Might Be Wrong People are often very confident about their views, even when i t comes to very controversial issues that may have just as many people on the other side. There are probably several reasons for this, but one o f them is due to the use of biased sampling. Consider whether you thin k Jakubzak/iStock/Thinkstock Confirmation bias, or the tendency to seek out support for our beliefs, can be seen in the friends we choose, books we read, and news sources we select. your views about the world are shared by many people or by only a few. It is not uncommon for people to think that their views are m ore widespread than they actually are. Why is that?

Think about how you form your opinion about how much of the nat ion or world agrees with your view. You probably spend time talking w ith your friends about these views and notice how many of your frien ds agree or disagree with you. You may watch television shows or read news articles that agree or disagree with you. If most of the source s you interact with agree with your view, you might conclude th at most people agree with you.

However, this would be a mistake. Most of us tend to interact more w ith people and information sources with which we agree, rather than those with which we disag ree. Our circle of friends tends to be concentrated near us both geographically and ideol ogically. We share similar concerns, interests, and views; that is part of what makes us friend s. As with choosing friends, we also tend to select information sources that confirm our belief s. This is a well­known psychological tendency known as confirmation bias (this will be discussed further in Chapter 8).

We seem to reason as follows: A large percentage of my friends and news sources agree with my vi ew.

Therefore, a large percentage of all people and sources agree w ith my view.

We have seen that this reasoning is based on a biased sample. If you tak e your friends and information sources as a sample, they are not likely to be represen tative of the larger population of the nation or world. This is because rather than being a random sample, they have been selected, in part, because they hold views similar to yours. A good critical thinker takes sampling bias into account when thinking about controversial issues.

Sample Size Even a perfectly random sample may not be representa tive, due to bad luck. If you flip a coin 10 times, for example, there is a decent chance that it will c ome up heads 8 of the 10 times. However, the more times you flip the coin, the more likely it is that the percentag e of heads will approach 50%.

The smaller the sample, the more likely it is to be no nrepresentative. This variable is known as the sample size . Suppose a teacher wants to know the average height of students i n his school. He randomly picks one student and measures her height. You should see that this is not a big enough sample. By measuring only one student, there is a decent chance t hat the teacher may have randomly picked someone extremely tall or extremely short. Generalizi ng on an overly small sample would be making a hasty generalization , an error in reasoning that will be discussed in great er detail in Chapter 7. If the teacher chooses a sample of two students, it is less likely that they will both be tall or both be short. The more students the teacher chooses for his sample, the less likely it is that the average height of the sample will be much different than the average heigh t of all students. Assuming that the selection process is unbiased, therefore, the larger the sample po pulation is, the more likely it is that the sample will be representative of the whole population (see A Closer Look: How Large Must a Sample Be?). A Closer Look: How Large Must a Sample Be?

In general, the larger a sample is, the more likely i t is to be representative of the population from which it is drawn. However, even relatively small samp les can lead to powerful conclusions if they have been carefully drawn to be random and to be representative of the population. As of this writing, the population of the United States is i n the neighborhood of 317 million, yet Gallup, one of the most respected polling organizations in the country, often publishes results based on a sample of fewer than 3,000 people. Indeed, its typic al sample size is around 1,000 (Gallup, 2010). That is a sample size of less than 1 in every 300,000 people!

Gallup can do this because it goes to great lengths to make sure that its samples are randomly drawn in a way that matches the makeup of the countr y’s population. If you want to know about people’s political views, you have to be very carefu l because these views can vary based on a person’s locale, income, race or ethnicity, gender, age, reli gion, and a host of other factors.

There is no single, simple rule for how large a sample should be. When samples are small or incautiously collected, you should be suspicious of the claims made on their basis. Professional research will generally provide clear descriptions of the samples used and a justification of why they are adequate to support their conclusions. That i s not a guarantee that the results are correct, but they are bound to be much more reliabl e than conclusions reached on the basis of small and poorly collected samples.

For example, sometimes politicians tour a state with the stat ed aim of finding out what the people think. However, given that people who attend politi cal rallies are usually those with similar opinions as the speaker, it is unlikely that the set of people sa mpled will be both large enough and random enough to provide a solid basis for a reliable conclusion. If politicians really want to find out what people think, there are better ways of doing so.

Margin of Error It is always possible that a sample will be wildly diffe rent than the population. But equally important is the fact that it is quite likely that any sample wil l be slightly different than the population. Statisti cians know how to calculate just how big this difference is likely to be. You will see this reported in some studies or polls as the margin of error. The margin of error can be used to determine the range of values that are likely for the population.

For example, suppose that a poll finds that 52% of a sam ple prefers Ms. Frazier in an election. When you read about the result of this poll, you will probabl y read that 52% of people prefer Ms. Frazier with a margin of error of ±3% (plus or minus 3%). This means th at although the real number probably is not 52%, it is very likely to be somewhere between 49% (3% l ower than 52%) and 55% (3% higher than 52%). Since the real percentage may be as low as 49%, Ms. Frazier should not start picking out curtains for her office just yet: She may actually be losing! Confidence Level We want large, random samples because we want to be confident that our sample is representative of the population. The more confident we are that are sample is representative, the more confident we can be in conclusions we draw from it. Nonetheless, even a small, p oorly drawn sample can yield informative results if we are cautious about our reasoning.

If you notice that many of your friends and acquaint ances are out of work, you may conclude that unemployment levels are up. Clearly, you have some ev idence for your conclusion, but is it enough? The answer to this question depends on how strong you take your argument to be. Remember that inductive arguments vary from extremely weak to extremely strong. Th e strength of an argument is essentially the level of confidence we should have in the conclusion based on the reasons presented. Consider the following ways you might state your confidence that unemployment levels were up, based on noting unemployment among your friends and acquaintances.

a. “I’m certain that unemployment is up.” b. “I’m reasonably sure that unemployment is up.” c. “It’s more likely than not that unemployment is up.” d. “Unemployment might be up.” Clearly, A is too strong. Your acquaintances just are no t likely to represent the population enough for you to be certain that unemployment is up. On the ot her hand, D is weak enough that it really does not need much evidence to support it. B and C will depen d on how wide and varied your circle of acquaintances is and on how much unemployment you see among them. If you know a lot of people and your acquaintances are quite varied in terms of profe ssion, income, age, race, gender, and so on, then you can have more confidence in your conclusion than if you ha d only a small circle of acquaintances and they tended to all be like each other in these ways. B a lso depends on just what you mean by “reasonably sure.” Does that mean 60% sure? 75%? 85%?

Most reputable studies will include a “ confidence level” that indicates how confident one can be that their conclusions are supported by the reasons they giv e. The degree of confidence can vary quite a bit, so it is worth paying attention to. In most social scien ces, researchers aim to reach a 95% or 99% confidence level. A confidence level of 95% means tha t if we did the same study 100 times, then in 95 of those tests the results would fall within the margin of error. As noted earlier, the field of physics requires a confidence level of about 99.99997%, much higher than is typically required or attained in the social sciences. On the other end, sometimes a confi dence level of just over 50% is enough if you are only interested in knowing whether something is more likely tha n not.

Applying This Knowledge Now that we have learned something about statistical arguments, what can we say about Angelina Jolie’s argument, presented at the beginning of the prior secti on? First, notice that it has the form of a statistical syllogism. We can put it this way, written as if from her perspectiv e:

87% of women with certain genetic and other factors develop bre ast cancer.

I am a woman with those genetic and other factors.

Therefore, I have an 87% risk of getting breast cancer.

We can see that the argument fits the form correctly. While not deductive, the argument is inductively strong. Unless we have reason to believe that she is more or less likely than the average person with those factors to develop breast cancer, if these premises are true then they give strong evidence for the truth of the conclusion. However, what about the first premise? Should we believe it?

In evaluating the first premise, we need to consider t he evidence for it. Were the samples of women studied sufficiently random and large that we can be confident they were representative of the population of all women? With what level of confide nce are the results established? If the samples were small or not randomized, then we may have less confide nce in them. Jolie’s doctors said that Jolie had an 87% chance of developing breast cancer, but there’s a big difference between being 60% confident that she has this level of risk and being 99% certain that she does. To know how confident we should be, we would need to look at the background studies that esta blish that 87% of women with those factors develop breast cancer. Anyone making such an importan t decision would be well advised to look at these issues in the research before acting. Practice Problems 5.1 Which of the following attributes might negatively influence th e data drawn from the following samples? Click here (https://ne.edgecastcdn.net/0004BA/constellation/PD Fs/PHI103_2e/Answers_PracticeProblems5.1.pdf) to check your answers.

1. A teacher surveys the gifted students in the district about the curriculum that should be adopted at the high school. a. sample size b. representativeness of the sample c. a and b d. There is no negative influence in this case.

2. A researcher for Apple analyzes a large group of tribal peopl e in the Amazon to determine which new apps she should create in 2014. a. sample size b. representativeness of the sample c. a and b d. There is no negative influence in this case.

3. A researcher on a college campus interviews 10 students after a y oga class about their drug use habits and determines that 80% of the student population p robably smokes marijuana. a. sample size b. representativeness of the sample c. a and b d. There is no negative influence in this case. iStock/Thinkstock Sufficient conditions are present in classroom grading systems. If you need a total of 850 points to receive an A, the sufficient condition to receive an A is earning 850 points. 5.4 Causal Relationships: The Meaning of Cause It is difficult to say exactly what we mean when we sa y that one thing causes another. Think about turning on the lights in your room. What is the cause of the lights turning on? Is it the flipping of the switch? The electricity in the wires? The fact that t he bulb is not broken? Your initial desire for the lig hts to be on? There are many things we could identify as a plausible cause of the lights turning on. However, for practical purposes, we generally look for the set of conditions without which the event in question would not have occurred and with which it will occu r. In other words, logicians aim to be more specific about causal relationships by discussing them in terms of suffi cient and necessary conditions. Recall that we used these terms in Chapter 4 when discussing proposit ional logic. Here we will discuss how these terms can help us understand causal relationships.

Sufficient Conditions According to British philosopher David Hume, the noti on of cause is based on nothing more than a “constant conjunction” that h olds between events—the two events always occur together (Morris & B rown, 2014). We notice that events of kind A are always followed by e vents of kind B, and we say “A causes B.” Thus, to claim a causal relationship betwe en events of type A and B might be to say: Whenever A occurs, B will occur.

Logicians have a fancy phrase for this relationship: We say that A is a sufficient condition for B. A factor is a sufficient condition for the occurrence of an event if whenever the factor occur s, the event also occurs: Whenever A occurs, B occurs as well. Or in other words:

If A occurs, then B occurs.

For example, having a billion dollars is a sufficient condition for being rich; being hospitalized is a sufficient condition for bein g excused from jury duty; having a ticket is a sufficient condition for being a ble to be admitted to the concert.

Often several factors are jointly required to create sufficient conditions. For example, each state has a set of jointly sufficient co nditions for being able to vote, including being over 18, being registered to v ote, and not having been convicted of a felony, among other possible qualifications.

Here is an example of how to think about sufficient conditions w hen thinking about real­life causation.

We know room lights do not go on just because you flip the switch. The points of the switch must come into contact with a power source, electricity must be present, a working lightbulb has to be properly secured in the socket, the socket has to be properly co nnected, and so forth. If any one of the conditions is not satisfied, the light will not come on. Strictly speaking, then, the whole set of conditions constitute s the sufficient condition for the event.

We often choose one factor from a set of factors and call it the caus e of an event. The one we call the cause is the one with which we are most concerned for some reason or other; often it is the one that represents a change from the normal state of things. A working ca r is the normal state of affairs; a hole in Stockbyte/Thinkstock Although water is a necessary condition for life, it is not a sufficient condition for life because humans also need oxygen and food. the radiator tube is the change to that state of affa irs that results in the overheated engine. Similarly, the electricity and lightbulb are part of the normal sta te of things; what changed most recently to make the light turn on was the flipping of the switch.

Necessary Conditions A factor is a necessary condition for an event if the event would not occur in the a bsence of the factor. Without the necessary condition, the effect will not occur. A is a necessary condition for B if the following statement is always true:

If A is not present, then neither is B.

This statement happens to be equivalent to the statemen t that if B is present, then A is present. Thus, a handy way to understand the difference between necessary and suf ficient conditions is as follows:

“A is sufficient for B” means that if A occurs, then B occurs.

“A is necessary for B” means that if B occurs, then A occurs.

Let us take a look at a real example. Poliomyelitis, or polio, is a disease caused by a specific virus. In only a small minority of those with poliovirus does the virus infect the central nervous system and lead to the terrible condit ion known as paralytic polio. In the large majority of c ases, however, the virus goes undetected and does not result in paralysis. Thus, infection with poliovirus is not a suf ficient condition for getting paralytic polio. However, bec ause one must have the virus to have that condition, being inf ected with poliovirus is a necessary condition for getting pa ralytic polio (Mayo Clinic, 2014).

On the other hand, being squashed by a steamroller is a sufficient condition for death, but it is not a necessa ry condition. Whenever someone has been squashed by a steamroller, that person is quite dead. However, it is not the case that anyone who is dead has been run over by a steamroller.

If our purpose in looking for causes is to be able to p roduce an effect, it is reasonable to look for sufficient conditions for that effect. If we can mani pulate circumstances so that the sufficient condition i s present, the effect will also be present. If we are lo oking for causes in order to prevent an effect, it is reasonable to look for necessary conditions for that ef fect. If we prevent a necessary condition from materializing, we can prevent the effect.

The eradication of yellow fever is a striking example . Research showed that being bitten by a certain type of mosquito was a necessary condition for contract ing yellow fever (though it was not a sufficient condition, for some people who were bitten by these m osquitoes did not contract yellow fever). Consequently, a campaign to destroy that particular sp ecies of mosquito through the widespread use of insecticides virtually eliminated yellow fever in many parts of the world (World Health Organization, 2014).

Necessary and Sufficient Conditions The most restrictive interpretation of a causal relati onship consists of construing “cause” as a condition both necessary and sufficient for the occurrence of an even t. If factor A is necessary and sufficient for the occurrence of event B, then whenever A occurs, B occ urs, and whenever A does not occur, B does not occur. In other words:

If A, then B, and if not­A, then not­B.

For example, to produce diamonds, certain very specific condi tions must exist. Diamonds are produced if and only if carbon is subjected to immense pressure and heat for a certain period of time. Diamonds do not occur through any other process. If all of the co nditions exist, then diamonds will result; diamonds exist only when all of those conditions have been met . Therefore, carbon subjected to the right combination of pressure, heat, and time constitutes bo th a necessary and sufficient condition for diamond production.

This construction of cause is so restrictive that very fe w actual relationships in ordinary experience can satisfy it. However, some scientists think that this is t he kind of invariant relationship that scientific laws must express. For instance, according to Newton’s law of gravitation, objects attract each other with a force proportional to the inverse of the square of th eir distance. Therefore, if we know the force of attraction between two bodies, we can calculate the distance between them (assuming we know their masses). Conversely, if we know the distance between the m, we can calculate the force of attraction. Thus, having a certain degree of attraction between two bodies constitutes both a necessary and sufficient condition for the distance between them. I t happens frequently in math and science that the values assigned to one factor determine the values assign ed to another, and this relationship can be understood in terms of necessary and sufficient conditions.

Other Types of Causes The terms necessary condition and sufficient condition give us concrete and technical ways to describe types of causes. However, in everyday life, the factor we mention as the cause of an event is rarely one we consider sufficient or even necessary. We frequently select one factor from a set and say it is the cause of the event. Our aims and interests, as well as ou r knowledge, affect that choice. Thus, practical, moral, or legal considerations may influence our selec tion. There are three principal considerations that may lead us to choose a single factor as “the cause,” although this is n ot an exhaustive listing.

Trigger cause . The trigger cause , or the factor that initiates an event, is often designa ted the cause of the event. Usually, this is the factor that occurs last and completes a causal chain—the set of sufficient conditions—producing the effect. Flipping the switch t riggers the lights. All the other factors may be present and as such constitute the standing conditions th at allow the event to be triggered. The trigger factor is sometimes referred to as the proximate cause since it is the factor nearest the final event (or effect).

Unusual factor . Let us suppose that someone turns on a light and an ex plosion follows. Turning on the light caused an explosion because the room was full of methane gas. Now being in a room is fairly Hagen/Cartoonstock Variables, such as buffalo and White men, can be correlated in two ways—directly and inversely. Which type of correlation is being discussed in this cartoon? normal, turning on lights is fairly normal, having ox ygen in a room is fairly normal, and having an unsealed light switch is fairly normal. The only condi tion outside the norm is the presence of a large quantity of explosive gas. Therefore, the presence of me thane is referred to as the cause of the explosion. What is unusual, what is outside the norm, is the cause. If we are concerned with fixing moral or legal responsibility for an effect, we are likely to focus o n the person who left the gas on, not the person who turned on the lights.

Controllable factor . Sometimes we call attention to a controllable fac tor instrumental in producing the event and point out that since the factor could have been controlled, so could the event. Thus, although smoking is neither a sufficient nor a necessary conditio n for lung cancer, it is a controllable factor. Therefore, over and above uncontrollable factors lik e heredity and chance, we are likely to single out smoking as the cause. Similarly, drunk driving is neither a suffi cient nor a necessary condition for getting into a car accident, but it is a controllable factor, so we are li kely to point to it as a cause.

Correlational Relationships In both the case of smoking and drunk driving, neither were necessary nor sufficient conditions for the subsequent event in question (lung cancer and car acciden ts). Instead, we would say that both are highly correlated with the respective events. Two things can be said to be correlated, or in correlation, when they occur together frequently. In other words, A is correlated with B, so B is more likely to occur if A occurs, and vice versa. For example, having gray hai r is correlated with age. The older someone is, the more likely he or she is to have gray hair, and vice versa. Of course, not all people with gray hair are o ld, and not all old people have gray hair, so age is neit her a necessary nor a sufficient condition for gray hair. However, the two are highly correlated because they hav e a strong tendency to go together.

Two things that vary in the same direction are said t o be directly correlated or to vary directly; the higher one’s age, the more gray hair. Things that are correlated may a lso vary in opposite directions; these are said to vary inversely. For example, there is an inverse correlation between the size of a car and its fuel economy. In general, the bigger a car is, the lower its fuel economy is. If you want a car that ge ts high miles per gallon, you should focus on cars that are smal ler. There are other factors to consider too, of course. A small sports car may get lower fuel economy than a larger c ar with less power. Correlation does not mean that the relationship is perfect, only that variables tend to v ary in a certain way.

You may have heard the phrase “correlation does not im ply causation,” or something similar. Just because two thing s happen together, it does not necessarily follow that o ne causes the other. For example, there is a well­known correlation between shoe size and reading ability in elementary children. Children with larger feet have a strong tendency to read better than children with smaller f eet. Of course, no one supposes that a child’s shoe size has a dire ct effect on his or her reading ability, or vice versa. Instead, both of these things are related to a child’s age. Older children tend to have bigger feet than younger children; they also tend to read better. Sometimes the conn ection between correlated things is simple, as in the case of shoe size and reading, and sometimes it is more complic ated.

Whenever you read that two things have been shown to be linked, you should pay attention to the possibility that the correlation is spurious or possibly h as another explanation. Consider, for example, a study showing a strong correlation between the amount of fat in a country’s diet and the amount of certain types of cancer in that country (such as K. K. Carroll’s 1975 study, as cited in Paulos, 1997). Such a correlation may lead you to think that eating fat causes cancer, but this could potentially be a mistake . Instead, we should consider whether there might be some other con nection between the two.

It turns out that countries with high fat consumption also have high sugar consumption—perhaps sugar is the culprit. Also, countries with high fat and suga r consumption tend to be wealthier; fat and sugar are expensive compared to grain. Perhaps the correlation is the result of some other aspect of a wealthier lifestyle, such as lower rates of physical exercise. (Not e that wealth is a particularly common confounding factor , or a factor that correlates with the dependent and independent variables being studied, as it bestows a wide range of advantages and di fficulties on those who have it.) Perhaps it is a combination of factors, and perhaps it is the fat afte r all; however, we cannot simply conclude with certainty from a correlation that one causes the other, not wi thout further research.

Sometimes correlation between two things is simply rand om. If you search through enough data, you may find two factors that are strongly correlated but that have nothing at all to do with each other. For example, consider Figure 5.1. At first glance, you mi ght think the two factors must be closely connected. But then you notice that one of them is the divorce rate in Maine and the other is the per capita consumption of margarine in the United States. Could it be that by eating less margarine you could help save the marriages of people in Maine? Figure 5.1: Are these two factors correlated?

Although it may seem like two factors are correlate d, we sometimes have to look harder to understand the relationship.

Source: www.tylervigen.com (http://www.tylervigen.com) . On the other hand, although correlation does not imp ly causation, it does point to it. That is, when we see a strong correlation, there is at least some reason t o suspect a causal connection of some sort between the two correlates. It may be that one of th e correlates causes the other, a third thing causes them both, there is some more complicated causal relation between them, or there is no connection at all.

However, the possibility that the correlation is merel y accidental becomes increasingly unlikely if the sample size is large and the correlation is strong. In su ch cases we may have to be very thoughtful in seeking and testing possible explanations of the correla tion. The next section discusses ways that we might find and narrow down potential factors involved in a cau sal relationship. 5.5 Causal Arguments: Mill’s Methods Reasoning about causes is extremely important. If we can correctly identify what causes a particular effect, then we have a much better chance of contro lling or preventing the effect. Consider the search for a cure for a disease. If we do not understand what cau ses a particular disease, then our chances of being able to cure it are small. If we can identify the ca use of the disease, we can be much more precise in searching for a way to prevent the disease. On the oth er hand, if we think we know the cause when we do not, then we are likely to look in the wrong direction for a c ure.

A causal argument —an argument about causes and effects—is almost always an i nductive argument. This is because, although we can gather evidence about these relationships, we are almost never in a position to prove them absolutely.

The following four experimental methods were formall y stated in the 19th century by John Stuart Mill in his book A System of Logic and so are often referred to as Mill’s methods. Mill’s methods express the most basic underlying logic of many current methods fo r investigating causality. They provide a great introduction to some of the basic concepts involved—but know that modern methods are much more rigorous.

Used with caution, Mill’s methods can provide a guide for exploring causal connections, especially when one is looking at specific cases against the background of established theory. It is important to remember that although they can be useful, Mill’s met hods are only the beginning of the study of causation. By themselves, they are probably most useful as methods for identifying potential subjects for further study using more robust methods that are beyond the scope o f this book.

Method of Agreement In 1976 an unknown illness affected numerous people in Philadelphia. Although it took some time to fully identify the cause of the disease, a bacterium n ow called Legionella pneumophila , the first step in the investigation was to find common features of those who became ill. Researchers were quick to note that sufferers had all attended an American Legion co nvention at the Bellevue­Stratford Hotel. As you can guess, the focus of the investigation quickly narro wed to conditions at the hotel. Of course, the convention and the hotel were not the actual cause o f getting sick, but neither was it mere coincidence that all of the ill had attended the convention. By finding the common elements shared by those who became ill, investigators were able to quickly narrow their search for the cause. Ultimately, the bacterium was located in a fountain in the hotel.

The method of agreement involves comparing situations in which the same kind o f event occurs. If the presence of a certain factor is the only respect in wh ich the situations are the same (that is, they agree), then this factor may be related to the cause of the e vent. We can represent this with something like Table 5.2. The table indicates whether each of four factors was present in a specific case (A, B, or C) and, in the last column, whether the effect manifested itse lf (in the earlier case of what is now known as Legionnaires’ disease, the effect we would be interested in is wh ether infection occurred).

Table 5.2: Example of method of agreement Case Factor 1 Factor 2 Factor 3 Factor 4 Effect ANo Yes Yes No Yes Case Factor 1 Factor 2 Factor 3 Factor 4 Effect BNo No Yes Yes Yes C Yes Yes Yes Yes Yes The three cases all resulted in the same effect but dif fered in which factors were present—with the exception of Factor 3, which was present in all three cases. We may then suspect that Factor 3 may be causally related to the effect. Our notion of cause h ere is that of sufficient condition. The common facto r is sufficient to account for the effect.

In general, the method of agreement works best when w e have a large group of cases that is as varied as possible. A large group is much more likely to vary ac ross many different factors than a small group. Unfortunately, the world almost never presents us with two situations wholly unlike except for one factor. We may have three or more situations that are greatly similar. For example, all of the afflicted in the 1976 outbreak were members of the American Legio n, all were adults, all were men, all lived in Pennsylvania. Here is where we have to use common sense and what we already know. It is unlikely that merely being a member of an organization is the cause of a disease. We expect diseases to be caused by environmental factors: bacteria, viruses, contaminants, and so on. As a result, we can focus our search on those similarities that seem most likely to be relevan t to the cause. Of course, we may be wrong; that is a hallmark of inductive reasoning generally, but by be ing as careful and as reasonable as we can, we can often make great progress. Method of Difference The method of difference involves comparing a situation in which an event occ urs with similar situations in which it does not. If the presence of a certain factor is the only difference between the tw o kinds of situations, it is likely to be causally related to the effe ct.

Suppose your mother comes to visit you and makes your favorite cake. Unfortunately, it just does not turn out. You know she made it in the same way she alwa ys does. What could the problem be? Start by looking at differences between how she made the cake at your house and how she makes it at hers. Ultimately, the only difference you can find is that your mom lives in Tampa and you live in Denver. Since that is the only difference, that difference i s likely to be causally related to the effect. In fac t, Denver is both much higher and much drier than Tampa . Both of these factors make a difference in baking cakes.

Let us suppose we are interested in two cases, A and B, i n which A has the effect we are interested in (the cake not turning out right) and B does not. Thi s is outlined in Table 5.3. If we can find only one factor that is different between the two cases—in this c ase, Factor 1—then that factor is likely to be causally related to the effect. This does not tell us w hether the factor directly causes the effect, but it does suggest a causal link. Further investigation might reveal ju st exactly what the connection is.

Table 5.3: Example of method of difference Case Factor 1 Factor 2 Factor 3 Factor 4 Effect AYes No No Yes Yes B No No No Yes No In this example, Factor 1 is the one factor that is different between the two cases. Perhaps the presence of Factor 1 is related to why Case A had the effect b ut Case B did not. Here we are seeing Factor 1 as a necessary condition for the effect.

The method of difference is employed frequently in c linical trials of experimental drugs. Researchers carefully choose or construct two situations that resem ble each other in as many respects as possible. If a drug is employed in one but not the other, then th ey can ascribe to the drug any change in one situation not matched by a change in the other. Note that the two sets must be as similar as possible, since variation could introduce other possible causal l inks. The group in which change is expected is often referred to as the experimental group, and the group in which change is not expected is of ten referred to as the control group.

The method of difference may seem obvious and its resul ts reliable. Yet even in a relatively simple experimental setup like this one, we may easily find g rounds for doubting that the causal claim has been adequately established.

One important factor is that the two cases, A and B, h ave to be as similar as possible in all other respects for the method of difference to be used effectively. If your 8­year­old son made the cake without supervision, there are likely to be a whole host of d ifferences that could explain the failure. The same principle applies to scientific studies. One thing that can subtly skew experimental results is experimental bias. For example, if the experimenters know which people are receiving the experimental drug, they might unintentionally treat them differently.

To prevent such possibilities, so­called blind experim ents are often used. Those conducting the experiment are kept in ignorance about which subject s are in the control group and which are in the experimental group so that they do not even unintent ionally treat the subjects differently. Experimenters therefore, do not know whether they ar e injecting distilled water or the actual drug. In this way the possibility of a systematic error is minimized.

We also have to keep in mind that our inquiry is guid ed by background beliefs that may be incorrect. No two cases will ever be completely the same except for a single factor. Your mother made the cake on a different day than she did at home, she used a differe nt spoon, different people were present in the house, and so on. We naturally focus on similarities and differences that we expect to be relevant. However, we should always realize that reality may disagree wit h our expectations.

Causal inquiry is usually not a matter of conducting a single experiment. Often we cannot even control for all relevant factors at the same time, and once an experiment is concluded, doubts about other factors may arise. A series of experiments in which diff erent factors are kept constant while others are varied one by one is always preferable.

Joint Method of Agreement and Difference The joint method of agreement and difference is, as the name suggests, a combination of the methods of agreement and difference. It is the most powerful of Mill’s methods. The basic idea is to have two groups of cases: One group shows the effect, and the oth er does not. The method of agreement is used within each group, by seeing what they have in common, and the method of difference is used between the two groups, by looking for the differences betwee n the two. Table 5.4 shows how such a chart would look, if we were comparing three different cases (1, 2, and 3) am ong two groups (A and B). Table 5.4: Example of joint method of agreement and difference Case/group Factor 1 Factor 2 Factor 3 Factor 4 Effect 1/AYes No No Yes Yes 2/A No No Yes Yes Yes 3/A No Yes No Yes Yes 1/B No Yes Yes No No 2/B Yes Yes No No No 3/B Yes No Yes No No As you can see, within each group the cases agree only on F actor 4 and the effect. But when you compare the two groups, the only consistent differences between them are in Factor 4 and the effect. This result suggests the possibility that Factor 4 may be causally re lated to the effect in question. In this method, we are using the notion of a necessary and sufficient cond ition. The effect happens whenever Factor 4 is present and never when it is absent.

The joint method is the basis for modern randomized co ntrolled experiments. Suppose you want to see if a new medicine is effective. You begin by recruiti ng a large group of volunteers. You then randomly assign them to either receive the medicine or a place bo. The random assignment ensures that each group is as varied as possible and that you are not unkn owingly deciding whether to give someone the medicine based on some common factor. If it turns out that everyone who gets the medicine improves and everyone who gets the placebo stays the same or get s worse, then you can infer that the medicine is probably effective.

In fact, advanced statistics allow us to make inference s from such studies even when there is not perfect agreement on the presence or absence of the effect. S o, in reading studies, you may note that the discussion talks about the percentage of each group tha t shows or does not show the effect. Yet we may still make good inferences about causation by using the method of concomitant variation. Method of Concomitant Variation The method of concomitant variation is simply the method of looking for correlation betw een two things. As we noted in our discussion of correlation, th is cannot be used to conclude conclusively that one thing causes the other, but it is suggestive that th ere is perhaps some causal connection between the two. Stronger evidence can be found by further scientific st udy.

You may have noticed that, in discussing causes, we are t rying to explain a phenomenon. We observe something that is interesting or important to us, and w e seek to know why it happened. Therefore, the study of Mill’s methods, as well as correlation and con comitant variation, can be seen as part of a broader type of reasoning known as inference to the best explanation, the effort to find the best or most accurate explanation of our observations. Because this type of reasoning is sometimes classified as a separate type of reasoning (sometimes called abductive reasoning), it will be covered in Chapter 6.

In summary, Mill’s methods provide a framework for exp loring causal relationships. It is important to remember that although they can be useful, they are only the beginning of this important field. By themselves, they are probably most useful as methods for identifying potential subjects for further study using more robust methods that are beyond the scope of this book. Practice Problems 5.2 Identify which of Mill’s methods discussed in the chapter rela tes to the following examples. Click here (https://ne.edgecastcdn.net/0004BA/constellation/PD Fs/PHI103_2e/Answers_PracticeProblems5.2.pdf) to check your answers.

1. After going to dinner, all the members of a family came down w ith vomiting. They all had different entrées but shared a salad as an appetizer. The mother o f the family determines that it must have been the salad that caused the sickness. a. method of agreement b. method of difference c. joint method d. method of concomitant variation 2. A couple goes to dinner and shares an appetizer, entrée, and de ssert. Only one of the two gets sick. She drank a glass of wine, and her husband drank a beer. Sh e believes that the wine was the cause of her sickness. a. method of agreement b. method of difference c. joint method d. method of concomitant variation 3. In a specific city, the number of people going to emergency r ooms for asthma attacks increases as the level of pollution increases in the summer. When the winter comes and pollution goes down, the number of people with asthma attacks d ecreases. a. method of agreement b. method of difference c. joint method d. method of concomitant variation 4. In the past 15 years there has never been a safety accident in th e warehouse. Each day for the past 15 years Lorena has been conducting the morning safet y inspections. However, today Lorena missed work, and there was an accident. a. method of agreement b. method of difference c. joint method d. method of concomitant variation 5. Since we have hired Earl, productivity in the office has dec reased by 20%. a. method of agreement b. method of difference c. joint method d. method of concomitant variation 6. In the past, lead was put into many paints. It was found that the number of infant fatalities increased in relation to the amount of exposure these infants had to lead­based paints that were used on their cribs. a. method of agreement b. method of difference c. joint method d. method of concomitant variation 7. It appears that the likelihood of catching the Zombie virus i ncreases the more one is around people who have already been turned into zombies. a. method of agreement b. method of difference c. joint method d. method of concomitant variation 8. In order to determine how a disease was spread in humans, research ers placed two groups of people into two rooms. Both rooms were exactly alike. H owever, in one room they placed someone who was infected with the disease. The researc hers found that those who were in the room with the infected person got sick, wher eas those who were not with an infected person remained well. a. method of agreement b. method of difference c. joint method d. method of concomitant variation 9. In a certain IQ test, students in a specific group performed at a much higher level than those of the other groups. After analyzing the group, the resea rchers found that the high­ performing students all smoked marijuana before the exam. a. method of agreement b. method of difference c. joint method d. method of concomitant variation badahos/iStock/Thinkstock The ability to think critically about an authority’s argument will allow you to determine reliable sources from unreliable ones, which can be quite helpful when writing research papers, reading news articles, or taking advice from someone. 5.6 Arguments From Authority An argument from authority , also known as an appeal to authority , is an inductive argument in which one infers that a claim is true because someone said so. The general reasoning looks like this:

Person A said that X is true.

Person A is an authority on the subject.

Therefore, X is true.

Whether this type of reasoning is strong depends on the issue discussed and the authority cited. If it is the kind of issue that can be settled by an argument f rom authority and if the person is actually an authority on the subject, then it can actually be a strong induc tive argument.

Some people think that arguments from authority in g eneral are fallacious. However, that is not generally the case. To see why, try to imagine life without a ny appeals to authority. You could not believe anyone’s statements, no matter how credible. You could not believe books; you could not believe published journals, and so on. How would you do in col lege if you did not listen to your textbooks, teachers, or any other sources of information?

Even in science class, you would have to do every experiment on your own because you could not believe published reports. In math, you could not trust the bo ok or teacher, so you would have to prove every theorem by yourself. History class would be a complete waste of tim e because, unless you had a time machine, there would be no way to verify any claims about what happened in the past without appeal to historical records, newspapers, journ als, and so forth. You would also have a hard time followin g medical advice, so you might end up with serious healt h problems. Finally, why would you go to school or wor k if you could not trust the claim that you were going to get a degree or a paycheck after all of your efforts?

Therefore, in order to learn from others and to succe ed in life, it is essential that we listen to appropriate aut horities. However, since many sources are unreliable, misleading , or even downright deceptive, it is essential that we lear n to distinguish reliable sources of authority from unreliab le ones. Chapter 7 will discuss how to distinguish between legitimate and fallacious appeals to authority.

Here are some examples of legitimate arguments from authority :

“The theory of relativity is true. I know because my physics professor and my physics textbook teach that it is true.” “Pine trees are not deciduous; it says so right here in this tree bo ok.” “The Giants won the pennant! I read it on ESPN.com.” “Mike hates radishes. He told me so yesterday.” All of these inferences seem pretty strong. For examples of ar guments to authority that are not as strong, or even downright fallacious, visit Chapter 7. 5.7 Arguments From Analogy An argument from analogy is an inductive argument that draws conclusions based o n the use of analogy. An analogy is a comparison of two items. For example, many objec t to deficit spending (when the country spends more money than it takes in) based o n the reasoning that debt is bad for household budgets. The person’s argument depends on an analogy th at compares the national budget to a household budget. The two items being compared may be referred to as analogs (or analogues, depending on where you live) but are referred to te chnically as cases. Of the two analogs, one should be well known, with a body of knowledge behind it, and so is referred to as the familiar case; the second analog, about which much less is known, is called the unfamiliar case.

The basic structure of an argument from analogy is as follows: B is similar to A.

A has feature F.

Therefore, B probably also has feature F.

Here, A is the familiar case and B is the unfamiliar c ase. We made an inference about thing B based on its similarity to the more familiar A.

Analogical reasoning proceeds from this premise: Since the analogs are similar either in many ways or in some very important ways, they are likely to be simila r in other ways as well. If there are many similarities, or if the similarities are significant, t hen the analogy can be strong. If the analogs are different in many ways, or if the differences are import ant, then it is a weak analogy. Conclusions arrived at through strong analogies are fairly reliable; conc lusions reached through weak analogies are less reliable and often fallacious (the fallacy is called false analogy ). Therefore, when confronted with an analogy (“A is like B”), the first question to be asked i s this: Are the two analogs very similar in ways that are relevant to the current discussion, or are they different in relevant ways?

Analogies occur in both arguments and explanations. A s we saw in Chapter 2, arguments and explanations are not the same thing. The key differen ce is whether the analogy is being used to give evidence that a certain claim is true—an argument—or t o give a better understanding of how or why a claim is true—an explanation. In explanations, the ana logy aims to provide deeper understanding of the issue. In arguments, the analogy aims to provide reasons for believing a conclusion. The next section provides some tips for evaluating the strength of such arguments.

Evaluating Arguments From Analogy Again, the strength of the argument depends on just ho w much A is like B, and the degree to which the similarities between A and B are relevant to F. Let us consider an example. Suppose that you are in the market for a new car, and your primary concern is th at the car be reliable. You have the opportunity to buy a Nissan. One of your friends owns a Nissan. Since yo u want to buy a reliable car, you ask a friend how reliable her car is. In this case you are dependin g on an analogy between your friend’s car and the car you are looking to buy. Suppose your friend says t hat her car is reliable. You can now make the following argument:

The car I’m looking at is like my friend’s car.

My friend’s car is reliable.

Therefore, the car I’m looking at will be reliable. How strong is this argument? That depends on how similar the two cases are. If the only thing the cars have in common is the brand, then the argument is fai rly weak. On the other hand, if the cars are the same model and year, with all the same options and a si milar driving history, then the argument is stronger. We can list the similarities in a chart (see T able 5.5). Initially, the analogy is based only on the make of the car. We will call the car you are looking at A and you r friend’s car B.

Table 5.5: Comparing cars by make Car Make Reliable?

BNissan Yes A Nissan ?

The make of a car is relevant to its reliability, but the argument is weak because that is the only similarity we know about. To strengthen the argument, we can note further relevant similarities. For example, if you find out that your friend’s car is th e same model and year, then the argument is strengthened (see Table 5.6). Table 5.6: Comparing cars by make, model, and year Car Make Model Year Reliable?

B Nissan Sentra 2000 Yes A Nissan Sentra 2000 ?

The more relevant similarities there are between the two cars, the stronger the argument. However, the word relevant is critical here. Finding out that the two cars have the same engine and similar driving histories is relevant and will strengthen the argument. Finding out that both cars are the same color and have license plates beginning with the same letter wil l not strengthen the argument. Thus, arguments from analogy typically require that we already have some idea of which features are relevant to the feature we are interested in. If you really had no i dea at all what made some cars reliable and others not reliable, then you would have no way to evaluate th e strength of an argument from analogy about reliability.

Another way we can strengthen an argument from analogy i s by increasing the number of analogs. If you have two more friends who also own a car of the same m ake, model, and year, and if those cars are reliable, then you can be more confident that your new car will be reliable. Table 5.7 shows what the chart would look like. The more analogs you have th at match the car you are looking at, the more confidence you can have that the car you’re looking at will be reliable. Table 5.7: Comparing multiple analogs Car Make Model Year Reliable?

BNissan Sentra 2000 Yes C Nissan Sentra 2000 Yes D Nissan Sentra 2000 Yes A Nissan Sentra 2000 ? In general, then, analogical arguments are stronger when they have more analogous cases with more relevant similarities. They are weaker when there are significant differences between the familiar cases and the unfamiliar case. If you discover a significant difference between the car you are looking at and the analogs, that reduces the strength of the argument . If, for example, you find that all your friends’ cars have manual transmission, whereas the one you are looki ng at has an automatic transmission, this counts against the strength of the analogy and hence against the st rength of the argument.

Another way that an argument from analogy can be weakened is i f there are cases that are similar but do not have the feature in question. Suppose you find a fourth friend who has the same model and year of car but whose car has been unreliable. As a result, you should have less confidence that the car you are looking at is reliable.

Here are a couple more examples, with questions about how to gaug e the strength.

“Except for size, chickens and turkeys are very simila r birds. Therefore, if a food is good for chickens, it is probably good for turkeys.” Relevant questions include how similar chickens and tur keys are, whether there are significant differences, and whether the difference in size is eno ugh to allow turkeys to eat things that would be too big for chickens.

“Seattle’s climate is similar, in many ways to the Unit ed Kingdom’s. Therefore, this plant is likely to grow well in Seattle, because it grows well in the Unit ed Kingdom.” Just how similar is the climate between the two places? Is the total about of rain about the same? How about the total amount of sun? Are the low and high temperatures comparable? Are there soil differences that would matter?

“I am sure that my favorite team will win the bowl g ame next week; they have won every game so far this season.” This example might seem strong at first, but it hides a very relevant difference: In a bowl game, college football teams are usually matched up with an opponen t of approximately equal strength. It is therefore likely that the team being played will be much bett er than the other teams played so far this season. This difference weakens the analogy in a relevant way, so the argument is much weaker than it may at first appear. It is essential when studying the strength of an alogical arguments to be thorough in our search for relevant similarities and differences.

Analogies in Moral Reasoning Analogical reasoning is often used in moral reasoning a nd moral arguments. Examples of analogical reasoning are found in ethical or legal debates over contentious or controversial issues such as abortion, gun control, and medical practices of all sorts (inclu ding vaccinations and transplants). Legal arguments are often based on finding precedents—analogous cases tha t have already been decided. Recent arguments presented in the debate over gun control ha ve drawn conclusions based on analogies that compare the United States with other countries, inclu ding Switzerland and Japan. Whether these and similar arguments are strong enough to establish their c onclusions depends on just how similar the cases are and the degree and number of dissimilarities a nd contrary cases. Being aware of similar cases Jupiterimages/BananaStock/Thinkstock Retailers such as bookstores commonly use arguments from analogy when they suggest purchases that have already occurred or that are occurring in other areas can vastly improve one’s wisdom about how best to address the topic at hand.

The importance of analogies in moral reasoning is some times captured in the principle of equal treatment —that if two things are analogous in all morally relev ant respects, then what is right (or wrong) to do in one case will be right (or wrong) to do in the other case as well. For example, if it is right for a teacher to fail a student for missing the final exam, then another student who does the same thing should also be failed. Whether the teacher happens to like one student more than the other should not make a difference, because that is not a morally relevant diffe rence when it comes to grading.

The reasoning could look as follows: Things that are similar in all morally relevant respects should be treated the same.

Student A was failed for missing the final exam.

Student B also missed the final exam.

Therefore, student B should be failed as well.

It follows from the principle of equal treatment tha t if two things should be treated differently, then there must be a morally relevant difference between them to justify this different treatment. An example of the application of this principle might be in the interrogation of prisoners of war. If one country want s to subject prisoners of war to certain kinds of harsh tr eatments but objects to its own prisoners being treated the same way by other countries, then there n eed to be relevant differences between the situations that justify the different treatment. Othe rwise, the country is open to the charge of moral inconsistency.

This principle, or something like it, comes up in many other types of moral debates, such as about abortion and animal ethics. Animal rights advocates, for e xample, say that if we object to people harming cats and dogs, then we are morally inconsistent to acce pt to the same treatment of cows, pigs, and chickens. One then has to address the question of whethe r there are differences in the beings or in their use for food that justify the differences in moral consideration we give to each.

Other Uses of Analogies Analogies are the basis for parables, allegories, and forms of writing that try to give a moral. The phrase “The mo ral of the story is . . .” may be featured at the end of such stories, or the author may simply imply that there is a lesson to b e learned from the story. Aesop’s Fables are one well­kno wn example of analogy used in writing. Consider the fabl e of the ant and the grasshopper, which compares the hardworkin g, industrious ant with the footloose and fancy­free grasshopper. The ant gathers and stores food all summer t o prepare for winter; the grasshopper fiddles around and plays all summer, giving no thought for tomorrow. Whe n winter comes, the ant lives warm and comfortable whil e the grasshopper starves, freezes, and dies. The fable argues t hat we should be like the ant if we want to survive harsh times. The ant and grasshopper are analogs for industrious peop le and lazy people. How strong is the argument? Clearly, ants based on their similarity to other items. and grasshoppers are quite different from people. Are the differences relevant to the conclusion? What are the relevant similarities? These are the questions that must be addressed to get an idea of whether the argument is strong or we ak. Practice Problems 5.3 Determine whether the following arguments are inductive or dedu ctive. Click here (https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems5.3.pdf) to check your answers.

1. All voters are residents of California. But some residents of Cal ifornia are Republican. Therefore, some voters are Republican. a. deductive b. inductive 2. All doctors are people who are committed to enhancing the he alth of their patients. No people who purposely harm others can consider themselves to be doc tors. Therefore, some people who harm others do not enhance the health of their pa tients. a. deductive b. inductive 3. Guns are necessary. Guns protect people. They give people con fidence that they can defend themselves. Guns also ensure that the government will not b e able to take over its citizenry. a. deductive b. inductive 4. Every time I turn on the radio, all I hear is vulgar language a bout sex, violence, and drugs. Whether it’s rock and roll or rap, it’s all the same. The trend tow ard vulgarity has to change. If it doesn’t, younger children will begin speaking i n these ways and this will spoil their innocence. a. deductive b. inductive 5. Letting your kids play around on the Internet all day is like d ropping them off in downtown Chicago to spend the day by themselves. They will find so mething that gets them into trouble. a. deductive b. inductive 6. Many people today claim that men and women are basically the same. Although I believe that men and women are equally capable of completing the same t asks physically as well as mentally, to say that they are intrinsically the same detracts f rom the differences between men and women that are displayed every day in their soci al interactions, the way they use their resources, and the way in which they find themse lves in the world. a. deductive b. inductive 7. Too many intravenous drug users continue to risk their lives by sharing dirty needles. This situation could be changed if we were to supply drug addict s with a way to get clean needles. This would lower the rate of AIDS in this high­risk popul ation as well as allow for the opportunity to educate and attempt to aid those who are addicted to heroin and other intravenous drugs. a. deductive b. inductive 8. I know that Stephen has a lot of money. His parents drive a Merce des. His dogs wear cashmere sweaters, and he paid cash for his Hummer. a. deductive b. inductive 9. Dogs are better than cats, since they always listen to what their masters say. They also are more fun and energetic. a. deductive b. inductive 10. All dogs are warm­blooded. All warm­blooded creatures are mammals. Hence, all dogs are mammals. a. deductive b. inductive 11. Chances are that I will not be able to get in to see Slipknot since it is an over 21 show, and Jeffrey, James, and Sloan were all carded when they tried to ge t in to the club. a. deductive b. inductive 12. This is not the best of all possible worlds, because the best of all p ossible worlds would not contain suffering, and this world contains much suffering. a. deductive b. inductive 13. Some apples are not bananas. Some bananas are things that are y ellow. Therefore, some things that are yellow are not apples. a. deductive b. inductive 14. Since all philosophers are seekers of truth, it follows that no evil human is a seeker after truth, since no philosophers are evil humans. a. deductive b. inductive 15. All squares are triangles, and all triangles are rectangles. Therefore, all squares are rectangles. a. deductive b. inductive 16. Deciduous trees are trees that shed their leaves. Maple trees are deciduous trees. Therefore, maple trees will shed their leaves at some point durin g the growing season. a. deductive b. inductive 17. Joe must make a lot of money teaching philosophy, since most ph ilosophy professors are rich. a. deductive b. inductive 18. Since all mammals are cold­blooded, and all cold­blooded creatures are aquatic, all mammals must be aquatic. a. deductive b. inductive 19. I felt fine until I missed lunch. I must be feeling tired beca use I don’t have anything in my stomach. a. deductive b. inductive 20. If you drive too fast, you will get into an accident. If yo u get into an accident, your insurance premiums will increase. Therefore, if you drive too f ast, your insurance premiums will increase. a. deductive b. inductive 21. The economy continues to descend into chaos. The stock market still moves down after it makes progress forward, and unemployment still hovers around 10%. It is going to be a while before things get better in the United States. a. deductive b. inductive 22. Football is the best sport. The athletes are amazing, and it is e xtremely complex. a. deductive b. inductive 23. We should go to see Avatar tonight. I hear that it has amazing special effects. a. deductive b. inductive 24. Pigs are smarter than dogs. It’s easier to train them. a. deductive b. inductive 25. Seventy percent of the students at this university come from u pper­class families. The school budget has taken a hit since the economic downturn. We n eed funding for the three new buildings on campus. I think it’s time for us to start a pho ne campaign to raise funds so that we don’t plunge into bankruptcy. a. deductive b. inductive 26. Justin was working at IBM. The last person we got from IBM was a horrible worker. I don’t think that it’s a good idea for us to go with Justin for this jo b. a. deductive b. inductive 27. If she wanted me to buy her a drink, she would’ve looked over a t me. But she never looked over at me. So that means that she doesn’t want me to buy her a drink. a. deductive b. inductive 28. Almost all the people I know who are translators have their t ranslator’s license from the ATA. Carla is a translator. Therefore, she must have a license from the ATA. a. deductive b. inductive 29. The economy will not recover anytime soon. Big businesses are struggling to keep their profits high. This is due to the fact that consumers no longer have e nough money to purchase things that are luxuries. Most of them buy only those thin gs that they need and don’t have much left over. Those same businesses have been firing em ployees left and right. If America’s largest businesses are losing employees, then th ere won’t be any jobs for the people who are already unemployed. That means that the se people will not have money to pump back into the system, and the circle will continue to descend into recession. a. deductive b. inductive Determine which of the following forms of inductive reasoning ar e taking place.

30. The purpose of ancient towers that were discovered in Italy a re unknown. However, similar towers were discovered in Albania, and historical accou nts in that country indicate that the towers were used to store grain. Therefore, th e towers in Italy were probably used for the same purpose. a. argument from analogy b. statistical syllogism c. inductive generalization d. causal argument 31. After the current presidential administration passes a bill t hat increases the amount of time people can be on unemployment, the unemployment rate in the country increases. Economists studying the bill claim that there is a direct relatio n between the bill and the unemployment rate. a. argument from analogy b. statistical syllogism c. inductive generalization d. causal argument 32. When studying a group of electricians, it was found that 60% of them did not have knowledge of the new safety laws governing working on power lin es. Therefore, 60% of the electricians in the United States probably do not have know ledge of the new laws. a. argument from analogy b. statistical syllogism c. inductive generalization d. causal argument 33. In the state of California, studies found that violent crimi nals who were released on parole had a 68% chance of committing another violent crime. T herefore, a majority of violent criminals in society are likely to commit more violent crimes if they are released from prison. a. argument from analogy b. statistical syllogism c. inductive generalization d. causal argument 34. Psilocybin mushrooms cause hallucinations in humans who ingest the m. A new species of mushroom shares similar visual characteristics to many forms of psilo cybin mushrooms. Therefore, it is likely that this form of mushroom has compounds th at have neurological effects. a. argument from analogy b. statistical syllogism c. inductive generalization d. causal argument 35. A recent survey at work indicates that 60% of the employees bel ieve that they do not make enough money for the work that they do. It is likely that a m ajority of the people that work for this company are unhappy in their jobs. a. argument from analogy b. statistical syllogism c. inductive generalization d. causal argument 36. A family is committed to buying Hondas because every Honda th ey have owned has had few problems and been very reliable. They believe that all Hon das must be reliable. a. argument from analogy b. statistical syllogism c. inductive generalization d. causal argument Summary and Resources Chapter Summary The key feature of inductive arguments is that the support they provide for a conclusion is always less than perfect. Even if all the premises of an inductiv e argument are true, there is at least some possibility that the conclusion may be false. Of course, when an i nductive argument is very strong, the evidence for the conclusion may still be overwhelming. Even our be st scientific theories are supported by inductive arguments.

This chapter has looked at four broad types of inducti ve arguments: statistical arguments, causal arguments, arguments from authority, and arguments fro m analogy. We have seen that each type can be quite strong, very weak, or anywhere in between. The key to success in evaluating their strength is to be able to (a) identify the type of argument being used , (b) know the criteria by which to evaluate its strength, and (c) notice the strengths and weaknesses of the specific argument in question within the context that it is given. If we can perform all of t hese tasks well, then we should be good evaluators of inductive reasoning. Critical Thinking Questions 1. What are some ways that you can now protect yourself from making hasty generalizations through inductive reasoning?

2. Can you think of an example that relates to each one of Mill’s m ethods of determining causation? What are they, and how did you determine that it fit with Mill’ s methods?

3. Think of a time where you reasoned improperly about correla tion and causation. Have you seen anyone in the news or in your place of employment fall into impr oper analysis of causation? What did they do, and what errors did they make?

4. Learning how to evaluate arguments is a great way to empower the mind. What are three forms of empowerment that result when people understand how to ident ify and evaluate arguments? 5. Why do you believe that superstitions are so prevalent in many societies? What forms of illogical reasoning lead to belief in superstitions? Are there a ny superstitions that you believe are true? What evidence do you have that supports your claims?

6. Think of an example of a strong inductive argument, then thi nk of a premise that you can add that significantly weakens the argument. Now think of a new pre mise that you can add that strengthens it again. Now find one that makes it weaker, and so on. Repeat this process several times to notice how the strength of inductive arguments can ch ange with new premises. Web Resources http://austhink.com/critical/pages/stats_prob.html (http://austhink.com/critical/pages/stats_prob.html) This website offers a number of resources and essays design ed to help you learn more about statistics and probability.

http://www.nss.gov.au/nss/home.nsf/pages/Sample+size+cal culator (http://www.nss.gov.au/nss/home.nsf/pages/Sample+size+calculator) The Australian government hosts a sample size calculator that allows users to approximate how large a sample they need.

http://www.gutenberg.org/ebooks/27942 (http://www.gutenberg.org/ebooks/27942) Read John Stuart Mill’s A System of Logic, which is where Mill first introduces his methods for i dentifying causality.

Key Terms appeal to authority See argument from authority . argument from analogy Reasoning in which we draw a conclusion about something based on characteristics of other similar things. argument from authority An argument in which we infer that something is true because someo ne (a purported authority) said that it was true. causal argument An argument about causes and effects. cogent An inductive argument that is strong and has all true premises. confidence level In an inductive generalization, the likelihood that a rando m sample from a population will have results that fall within the estimated margin of error. correlation An association between two factors that occur together frequently or that vary in relation to each other. inductive arguments Arguments in which the premises increase the likelihood of the c onclusion being true but do not guarantee that it is. inductive generalization An argument in which one draws a conclusion about a whole popula tion based on results from a sample population. joint method of agreement and difference A way of selecting causal candidates by looking for a factor that is present in all cases in which the effect occurs and absent in all cases in which it does not. margin of error A range of values above and below the estimated value in which i t is predicted that the actual result will fall. method of agreement A way of selecting causal candidates by looking for a factor that is present in all cases in which the effect occurs. method of concomitant variation A way of selecting causal candidates by looking for a factor that is highly correlated with the effect in question. method of difference A way of selecting causal candidates by looking for a factor that is present when effect occurs and absent when it does not. necessary condition A condition for an event without which the event will not occu r; A is a necessary condition of B if A occurs whenever B does. population In an inductive generalization, the whole group about which the generalization is made; it is the group discussed in the conclusion. proximate cause See trigger cause . random sample A group selected from within the whole population using a select ion method such that every member of the population has an equal chance of being included. sample A smaller group selected from among the population. sample size The number of individuals within the sample. statistical arguments Arguments involving statistics, either in the premises or in the conclusion. statistical syllogism An argument of the form X% of S are P; i is an S; Therefore, i is (prob ably) a P. strong arguments Inductive arguments in which the premises greatly increase the likelihood that the conclusion is true. sufficient condition A condition for an event that guarantees that the event will occur; A is a sufficient condition of B if B occurs whenever A does. trigger cause The factor that completes the cause chain resulting in the effe ct. Also known as proximate cause. weak arguments Inductive arguments in which the premises only minimally incre ase the likelihood that the conclusion is true. Choose a Study Mode 