Categories

# every inductive argument is __________.

6Deduction and Induction: Putting It All Together

Wavebreakmedia Ltd./Thinkstock and GoldenShrimp/iStock/Thinkstock

Learning Objectives After reading this chapter, you should be able to:

1. Compare and contrast the advantages of deduction and induction.

2. Explain why one might choose an inductive argument over a deductive argument.

3. Analyze an argument for its deductive and inductive components.

4. Explain the use of induction within the hypothetico–deductive method.

5. Compare and contrast falsification and confirmation within scientific inquiry.

6. Describe the combined use of induction and deduction within scientific reasoning.

7. Explain the role of inference to the best explanation in science and in daily life.

har85668_06_c06_207-238.indd 207 4/9/15 11:38 AM

Section 6.1 Contrasting Deduction and Induction

Now that you have learned something about deduction and induction, you may be wondering why we need both. This chapter is devoted to answering that question. We will start by learn- ing a bit more about the differences between deductive and inductive reasoning and how the two types of reasoning can work together. After that, we will move on to explore how scien- tific reasoning applies to both types of reasoning to achieve spectacular results. Arguments with both inductive and deductive elements are very common. Recognizing the advantages and disadvantages of each type can help you build better arguments. We will also investigate another very useful type of inference, known as inference to the best explanation, and explore its advantages.

6.1 Contrasting Deduction and Induction Remember that in logic, the difference between induction and deduction lies in the connec- tion between the premises and conclusion. Deductive arguments aim for an absolute connec- tion, one in which it is impossible that the premises could all be true and the conclusion false. Arguments that achieve this aim are called valid. Inductive arguments aim for a probable connection, one in which, if all the premises are true, the conclusion is more likely to be true than it would be otherwise. Arguments that achieve this aim are called strong. (For a discus- sion on common misconceptions about the meanings of induction and deduction, see A Closer Look: Doesn’t Induction Mean Going From Specific to General?). Recall from Chapter 5 that inductive strength is the counterpart of deductive validity, and cogency is the inductive coun- terpart of deductive soundness. One of the purposes of this chapter is to properly understand the differences and connections between these two major types of reasoning.

There is another important difference between deductive and inductive rea- soning. As discussed in Chapter 5, if you add another premise to an induc- tive argument, the argument may become either stronger or weaker. For example, suppose you are thinking of buying a new cell phone. After looking at all your options, you decide that one model suits your needs better than the others. New information about the phone may make you either more con- vinced or less convinced that it is the right one for you—it depends on what the new information is. With deductive reasoning, by contrast, adding prem- ises to a valid argument can never render it invalid. New information may show that a deductive argument

Fuse/Thinkstock

New information can have an impact on both deductive and inductive arguments. It can render deductive arguments unsound and can strengthen or weaken inductive arguments, such as arguments for buying one car over another.

har85668_06_c06_207-238.indd 208 4/9/15 11:38 AM

Section 6.1 Contrasting Deduction and Induction

is unsound or that one of its premises is not true after all, but it cannot undermine a valid connection between the premises and the conclusion. For example, consider the following argument:

All whales are mammals. Shamu is a whale. Therefore, Shamu is a mammal.

This argument is valid, and there is nothing at all we could learn about Shamu that would change this. We might learn that we were mistaken about whales being mammals or about Shamu being a whale, but that would lead us to conclude that the argument is unsound, not invalid. Compare this to an inductive argument about Shamu.

Whales typically live in the ocean. Shamu is a whale. Therefore, Shamu lives in the ocean.

Now suppose you learn that Shamu has been trained to do tricks in front of audiences at an amusement park. This seems to make it less likely that Shamu lives in the ocean. The addition of this new information has made this strong inductive argument weaker. It is, however, pos- sible to make it stronger again with the addition of more information. For example, we could learn that Shamu was part of a captive release program.

An interesting exercise for exploring this concept is to see if you can keep adding premises to make an inductive argument stronger, then weaker, then stronger again. For example, see if you can think of a series of premises that make you change your mind back and forth about the quality of the cell phone discussed earlier.

Determining whether an argument is deductive or inductive is an important step both in evaluating arguments that you encounter and in developing your own arguments. If an argu- ment is deductive, there are really only two questions to ask: Is it valid? And, are the premises true? If you determine that the argument is valid, then only the truth of the premises remains in question. If it is valid and all of the premises are true, then we know that the argument is sound and that therefore the conclusion must be true as well.

On the other hand, because inductive arguments can go from strong to weak with the addi- tion of more information, there are more questions to consider regarding the connection between the premises and conclusion. In addition to considering the truth of the premises and the strength of the connection between the premises and conclusion, you must also con- sider whether relevant information has been left out of the premises. If so, the argument may become either stronger or weaker when the relevant information is included.

Later in this chapter we will see that many arguments combine both inductive and deductive elements. Learning to carefully distinguish between these elements will help you know what questions to ask when evaluating the argument.

har85668_06_c06_207-238.indd 209 4/9/15 11:38 AM

Section 6.1 Contrasting Deduction and Induction

A Closer Look: Doesn’t Induction Mean Going From Specific to General? A common misunderstanding of the meanings of induction and deduction is that deduction goes from the general to the specific, whereas induction goes from the specific to the gen- eral. This definition is used by some fields, but not by logic or philosophy. It is true that some deductive arguments go from general premises to specific conclusions, and that some induc- tive arguments go from the specific premises to general conclusions. However, neither state- ment is true in general.

First, although some deductive arguments go from general to specific, there are many deduc- tive arguments that do not go from general to specific. Some deductive arguments, for exam- ple, go from general to general, like the following:

All S are M. All M are P. Therefore, all S are P.

Propositional logic is deductive, but its arguments do not go from general to specific. Instead, arguments are based on the use of connectives (and, or, not, and if . . . then). For example, modus ponens (discussed in Chapter 4) does not go from the general to the spe- cific, but it is deductively valid. When it comes to inductive arguments, some—for example, inductive generalizations—go from specific to general; others do not. Statistical syllogisms, for example, go from general to specific, yet they are inductive.

This common misunderstanding about the definitions of induction and deduction is not sur- prising given the different goals of the fields in which the terms are used. However, the defini- tions used by logicians are especially suited for the classification and evaluation of different types of reasoning.

For example, if we defined terms the old way, then the category of deductive reasoning would include arguments from analogy, statistical syllogisms, and some categorical syllogisms. Inductive reasoning, on the other hand, would include only inductive generalizations. In addi- tion, there would be other types of inference that would fit into neither category, like many categorical syllogisms, inferences to the best explanation, appeals to authority, and the whole field of propositional logic.

The use of the old definitions, therefore, would not clear up or simplify the categories of logic at all but would make them more confusing. The current distinction, based on whether the premises are intended to guarantee the truth of the conclusion, does a much better job of simplifying logic’s categories, and it does so based on a very important and relevant distinction.

har85668_06_c06_207-238.indd 210 4/9/15 11:38 AM

Section 6.2 Choosing Between Induction and Deduction

Practice Problems 6.1

1. A deductive argument that establishes an absolute connection between the premises and conclusion is called a __________. a. strong argument b. weak argument c. invalid argument d. valid argument

2. An inductive argument whose premises give a lot of support for the truth of its con- clusion is said to be __________. a. strong b. weak c. valid d. invalid

3. Inductive arguments always reason from the specific to the general. a. true b. false

4. Deductive arguments always reason from the general to the specific. a. true b. false

6.2 Choosing Between Induction and Deduction You might wonder why one would choose to use inductive reasoning over deductive reason- ing. After all, why would you want to show that a conclusion was only probably true rather than guaranteed to be true? There are several reasons, which will be discussed in this sec- tion. First, there may not be an available deductive argument based on agreeable premises. Second, inductive arguments can be more robust than deductive arguments. Third, inductive arguments can be more persuasive than deductive arguments.

Availability Sometimes the best evidence available does not lend itself to a deductive argument. Let us consider a readily accepted fact: Gravity is a force that pulls everything toward the earth. How would you provide an argument for that claim? You would probably pick something up, let go of it, and note that it falls toward the earth. For added effect, you might pick up several things and show that each of them falls. Put in premise–conclusion form, your argument looks something like the following:

My coffee cup fell when I let go of it. My wallet fell when I let go of it. This rock fell when I let go of it. Therefore, everything will fall when I let go of it.

har85668_06_c06_207-238.indd 211 4/9/15 11:38 AM

Section 6.2 Choosing Between Induction and Deduction

When we put the argument that way, it should be clear that it is inductive. Even if we grant that the premises are true, it is not guaranteed that every- thing will fall when you let go of it. Perhaps grav- ity does not affect very small things or very large things. We could do more experiments, but we can- not check every single thing to make sure that it is affected by gravity. Our belief in gravity is the result of extremely strong inductive reasoning. We there- fore have great reasons to believe in gravity, even if our reasoning is not deductive.

All subjects that rely on observation use induc- tive reasoning: It is at least theoretically possible that future observations may be totally different than past ones. Therefore, our inferences based on observation are at best probable. It turns out that there are very few subjects in which we can pro- ceed entirely by deductive reasoning. These tend to be very abstract and formal subjects, such as math- ematics. Although other fields also use deductive reasoning, they do so in combination with inductive reasoning. The result is that most fields rely heavily on inductive reasoning.

Robustness Inductive arguments have some other advantages over deductive arguments. Deductive argu- ments can be extremely persuasive, but they are also fragile in a certain sense. When some- thing goes wrong in a deductive argument, if a premise is found to be false or if it is found to be invalid, there is typically not much of an argument left. In contrast, inductive arguments tend to be more robust. The robustness of an inductive argument means that it is less fragile; if there is a problem with a premise, the argument may become weaker, but it can still be quite persuasive. Deductive arguments, by contrast, tend to be completely unconvincing once they are shown not to be sound. Let us work through a couple of examples to see what this means in practice.

Consider the following deductive argument:

All dogs are mammals. Some dogs are brown. Therefore, some mammals are brown.

As it stands, the argument is sound. However, if we change a premise so that it is no longer sound, then we end up with an argument that is nearly worthless. For example, if you change the first premise to “Most dogs are mammals,” you end up with an invalid argument. Valid- ity is an all-or-nothing affair; there is no such thing as “sort of valid” or “more valid.” The

Alistair Scott/iStock/Thinkstock

Despite knowing that a helium-filled balloon will rise when we let go of it, we still hold our belief in gravity due to strong inductive reasoning and our reliance on observation.

har85668_06_c06_207-238.indd 212 4/9/15 11:38 AM

Section 6.2 Choosing Between Induction and Deduction

argument would simply be invalid and therefore unsound; it would not accomplish its pur- pose of demonstrating that the conclusion must be true. Similarly, if you were to change the second premise to something false, like “Some dogs are purple,” then the argument would be unsound and therefore would supply no reason to accept the conclusion.

In contrast, inductive arguments may retain much of their strength even when there are prob- lems with them. An inductive argument may list several reasons in support of a conclusion. If one of those reasons is found to be false, the other reasons continue to support the conclu- sion, though to a lesser degree. If an argument based on statistics shows that a particular conclusion is extremely likely to be true, the result of a problem with the argument may be that the conclusion should be accepted as only fairly likely. The argument may still give good reasons to accept the conclusion.

Fields that rely heavily on statistical arguments often have some threshold that is typically required in order for results to be publishable. In the social sciences, this is typically 90% or 95%. However, studies that do not quite meet the threshold can still be instructive and pro- vide evidence for their conclusions. If we discover a flaw that reduces our confidence in an argument, in many cases the argument may still be strong enough to meet a threshold.

As an example, consider a tweet made by President Barack Obama regarding climate change.

Although the tweet does not spell out the argument fully, it seems to have the following structure:

A study concluded that 97% of scientists agree that climate change is real, man-made, and dangerous. Therefore, 97% of scientists really do agree that climate change is real, man- made, and dangerous. Therefore, climate change is real, man-made, and dangerous.

Given the politically charged nature of the discussion of climate change, it is not surprising that the president’s argument and the study it referred to received considerable criticism. (You can read the study at http://iopscience.iop.org/1748–9326/8/2/024024/pdf/1748 –9326_8_2_024024.pdf.) Looking at the effect some of those criticisms have on the argument is a good way to see how inductive arguments can be more robust than deductive ones.

One criticism of Obama’s claim is that the study he referenced did not say anything about whether climate change was dangerous, only about whether it was real and man-made. How does this affect the argument? Strictly speaking, it makes the first premise false. But notice that even so, the argument can still give good evidence that climate change is real and

har85668_06_c06_207-238.indd 213 4/9/15 11:38 AM

Section 6.2 Choosing Between Induction and Deduction

man-made. Since climate change, by its nature, has a strong potential to be dangerous, the argument is weakened but still may give strong evidence for its conclusion.

A deeper criticism notes that the study did not find out what all scientists thought; it just looked at those scientists who expressed an opinion in their published work or in response to a voluntary survey. This is a significant criticism, for it may expose a bias in the sampling method (as discussed in Chapters 5, 7, and 8). Even granting the criticism, the argument can retain some strength. The fact that 97% of scientists who expressed an opinion on the issue said that climate change is real and man-made is still some reason to think that it is real and man-made. Of course, some scientists may have chosen not to voice an opposing opinion for reasons that have nothing to do with their beliefs about climate change; they may have simply wanted to keep their views private, for example. Taking all of this into account, we get the fol- lowing argument:

A study found that 97% of scientists who stated their opinion said that cli- mate change is real and man-made. Therefore, 97% of scientists agree that climate change is real and man-made. Climate change, if real, is dangerous. Therefore, climate change is real, man-made, and dangerous.

This is not nearly as strong as the original argument, but it has not collapsed entirely in the way a purely deductive argument would. There is, of course, much more that could be said about this argument, both in terms of criticizing the study and in terms of responding to those criticisms and bringing in other considerations. The point here is merely to highlight the dif- ference between deductive and inductive arguments, not to settle issues in climate science or public policy.

Persuasiveness A final point in favor of inductive reasoning is that it can often be more persuasive than deduc- tive reasoning. The persuasiveness of an argument is based on how likely it is to convince someone of the truth of its conclusion. Consider the following classic argument:

All Greeks are mortal. Socrates was a Greek. Therefore, Socrates was mortal.

Is this a good argument? From the standpoint of logic, it is a perfect argument: It is deduc- tively valid, and its premises are true, so it is sound (therefore, its conclusion must be true). However, can you persuade anyone with this argument?

Imagine someone wondering whether Socrates was mortal. Could you use this argument to convince him or her that Socrates was mortal? Probably not. The argument is so simple and

har85668_06_c06_207-238.indd 214 4/9/15 11:38 AM

Section 6.2 Choosing Between Induction and Deduction

so obviously valid that anyone who accepts the premises likely already accepts the conclu- sion. So if someone is wondering about the conclusion, it is unlikely that he or she will be persuaded by these premises. He or she may, for example, remember that some legendary Greeks, such as Hercules, were granted immortality and wonder whether Socrates was one of these. The deductive approach, therefore, is unlikely to win anyone over to the conclusion here. On the other hand, consider a very similar inductive argument.

Of all the real and mythical Greeks, only a few were considered to be immortal. Socrates was a Greek. Therefore, it is extremely unlikely that Socrates was immortal.

Again, the reasoning is very simple. However, in this case, we can imagine someone who had been wondering about Socrates’s mortality being at least somewhat persuaded that he was mortal. More will likely need to be said to fully persuade her or him, but this simple argument may have at least some persuasive power where its deductive version likely does not.

Of course, deductive arguments can be persuasive, but they generally need to be more com- plicated or subtle in order to be so. Persuasion requires that a person change his or her mind to some degree. In a deductive argument, when the connection between premises and conclu- sion is too obvious, the argument is unlikely to persuade because the truth of the premises will be no more obvious than the truth of the conclusion. Therefore, even if the argument is valid, someone who questions the truth of the conclusion will often be unlikely to accept the truth of the premises, so she or he may be unpersuaded by the argument. Suppose, for example, that we wanted to convince someone that the sun will rise tomorrow morning. The deductive argument may look like this:

The sun will always rise in the morning. Therefore, the sun will rise tomorrow morning.

One problem with this argument, as with the Socrates argument, is that its premise seems to assume the truth of the conclusion (and therefore commits the fallacy of begging the ques- tion, as discussed in Chapter 7), making the argument unpersuasive. Additionally, however, the premise might not even be true. What if, billions of years from now, the earth is swallowed up into the sun after it expands to become a red giant? At that time, the whole concept of morning may be out the window. If this is true then the first premise may be technically false. That means that the argument is unsound and therefore fairly worthless deductively.

The inductive version, however, does not lose much strength at all after we learn of this trou- bling information:

The sun has risen in the morning every day for millions of years. Therefore, the sun will rise again tomorrow morning.

This argument remains extremely strong (and persuasive) regardless of what will happen billions of years in the future.

har85668_06_c06_207-238.indd 215 4/9/15 11:38 AM

Section 6.3 Combining Induction and Deduction

Practice Problems 6.2

1. Which form of reasoning is taking place in this example?

The sun has risen every day of my life. The sun rose today. Therefore, the sun will rise tomorrow.

a. inductive b. deductive

2. Inductive arguments __________. a. can retain strength even with false premises b. collapse when a premise is shown to be false c. are equivalent to deductive arguments d. strive to be valid

3. Deductive arguments are often __________. a. less persuasive than inductive arguments b. more persuasive than inductive arguments c. weaker than inductive arguments d. less valid than inductive arguments

4. Inductive arguments are sometimes used because __________. a. the available evidence does not allow for a deductive argument b. they are more likely to be sound than deductive ones c. they are always strong d. they never have false premises

6.3 Combining Induction and Deduction You may have noticed that most of the examples we have explored have been fairly short and simple. Real-life arguments tend to be much longer and more complicated. They also tend to mix inductive and deductive elements. To see how this might work, let us revisit an example from the previous section.

All Greeks are mortal. Socrates was Greek. Therefore, Socrates was mortal.

As we noted, this simple argument is valid but unlikely to convince anyone. So suppose now that someone questioned the premises, asking what reasons there are for thinking that all Greeks are mortal or that Socrates was Greek. How might we respond?

We might begin by noting that, although we cannot check each and every Greek to be sure he or she is mortal, there are no documented cases of any Greek, or any other human, living more

har85668_06_c06_207-238.indd 216 4/9/15 11:38 AM

Section 6.3 Combining Induction and Deduction

than 200 years. In contrast, every case that we can document is a case in which the person dies at some point. So, although we cannot absolutely prove that all Greeks are mortal, we have good reason to believe it. We might put our argument in standard form as follows:

We know the mortality of a huge number of Greeks. In each of these cases, the Greek is mortal. Therefore, all Greeks are mortal.

This is an inductive argument. Even though it is theoretically possible that the conclusion might still be false, the premises provide a strong reason to accept the conclusion. We can now combine the two arguments into a single, larger argument:

We know the mortality of a huge number of Greeks. In each of these cases, the Greek is mortal. Therefore, all Greeks are mortal. Socrates was Greek. Therefore, Socrates was mortal.

This argument has two parts. The first argument, leading to the subconclusion that all Greeks are mortal, is inductive. The second argument (whose conclusion is “Socrates was mortal”) is deductive. What about the overall reasoning presented for the conclusion that Socrates was mortal (combining both arguments); is it inductive or deductive?

The crucial issue is whether the prem- ises guarantee the truth of the conclu- sion. Because the basic premise used to arrive at the conclusion is that all of the Greeks whose mortality we know are mortal, the overall reasoning is inductive. This is how it generally works. As noted earlier, when an argu- ment has both inductive and deductive components, the overall argument is generally inductive. There are occa- sional exceptions to this general rule, so in particular cases, you still have to check whether the premises guarantee the conclusion. But, almost always, the longer argument will be inductive.

Fran/Cartoonstock

Sometimes a simple deductive argument needs to be combined with a persuasive inductive argument to convince others to accept it.

har85668_06_c06_207-238.indd 217 4/9/15 11:38 AM

Section 6.4 Reasoning About Science: The Hypothetico–Deductive Method

A similar thing happens when we combine inductive arguments of different strength. In gen- eral, an argument is only as strong as its weakest part. You can think of each inference in an argument as being like a link in a chain. A chain is only as strong as its weakest link.

6.4 Reasoning About Science: The Hypothetico– Deductive Method Science is one of the most successful endeavors of the modern world, and arguments play a central role in it. Science uses both deductive and inductive reasoning extensively. Scientific reasoning is a broad field in itself—and this chapter will only touch on the basics—but dis- cussing scientific reasoning will provide good examples of how to apply what we have learned about inductive and deductive arguments.

At some point, you may have learned or heard of the scientific method, which often refers to how scientists systematically form, test, and modify hypotheses. It turns out that there is not a single method that is universally used by all scientists.

In a sense, science is the ultimate critical thinking experiment. Scientists use a wide variety of reasoning techniques and are constantly examining those techniques to make sure that the conclusions drawn are justified by the premises—that is exactly what a good critical thinker should do in any subject. The next two sections will explore two such methods—the hypothetico–deductive method and inferences to the best explanation—and discover ways that they can improve our understanding of the types of reasoning used in much of science.

The hypothetico–deductive method consists of four steps:

1. Formulate a hypothesis. 2. Deduce a consequence from the hypothesis. 3. Test whether the consequence occurs. 4. Reject the hypothesis if the consequence does not occur.

Although these four steps are not sufficient to explain all scientific reasoning, they still remain a core part of much discussion of how science works. You may recognize them as part of the scientific method that you likely learned about in school. Let us take a look at each step in turn.

Practice Problem 6.3

1. When an argument contains both inductive and deductive elements, the entire argu- ment is considered deductive. a. true b. false

har85668_06_c06_207-238.indd 218 4/9/15 11:38 AM

Section 6.4 Reasoning About Science: The Hypothetico–Deductive Method

Step 1: Formulate a Hypothesis A hypothesis is a conjecture about how some part of the world works. Although the phrase “educated guess” is often used, it can give the impression that a hypothesis is simply guessed without much effort. In reality, scientific hypotheses are formulated on the basis of a back- ground of quite a bit of knowledge and experience; a good scientific hypothesis often comes after years of prior investigation, thought, and research about the issue at hand.

You may have heard the expression “necessity is the mother of invention.” Often, hypotheses are formulated in response to a problem that needs to be solved. Suppose you are unsatisfied with the performance of your car and would like better fuel economy. Rather than buy a new car, you try to figure out how to improve the one you have. You guess that you might be able to improve your car’s fuel economy by using a higher grade of gas. Your guess is not just random; it is based on what you already know or believe about how cars work. Your hypothesis is that higher grade gas will improve your fuel economy.

Of course, science is not really concerned with your car all by itself. Science is concerned with general principles. A scientist would reword your hypothesis in terms of a general rule, something like, “Increasing fuel octane increases fuel economy in automobiles.” The hypothetico–deductive method can work with either kind of hypothesis, but the general hypothesis is more interesting scientifically.

Step 2: Deduce a Consequence From the Hypothesis Your hypothesis from step 1 should have predictive value: Things should be different in some noticeable way, depending on whether the hypothesis is true or false. Our hypothesis is that increasing fuel octane improves fuel economy. If this general fact is true, then it is true for your car. So from our general hypothesis we can deduce the consequence that your car will get more miles per gallon if it is running on higher octane fuel.

It is often but not always the case that the prediction is a more specific case of the hypothesis. In such cases it is possible to infer the prediction deductively from the general hypothesis. The argument may go as follows:

Hypothesis: All things of type A have characteristic B.

Consequence (the prediction): Therefore, this specific thing of type A will have characteristic B.

Since the argument is deductively valid, there is a strong connection between the hypothesis and the prediction. However, not all predictions can be deductively inferred. In such cases we can get close to the hypothetico–deductive method by using a strong inductive inference instead. For example, suppose the argument went as follows:

Hypothesis: 95% of things of type A have characteristic B.

Consequence: Therefore, a specific thing of type A will probably have charac- teristic B.

har85668_06_c06_207-238.indd 219 4/9/15 11:38 AM

Section 6.4 Reasoning About Science: The Hypothetico–Deductive Method

In such cases the connection between the hypothesis and the prediction is less strong. The stronger the connection that can be established, the better for the reliability of the test. Essen- tially, you are making an argument for the conditional statement “If H, then C,” where H is your hypothesis and C is a consequence of the hypothesis. The more solid the connection is between H and C, the stronger the overall argument will be.

In this specific case, “If H, then C” translates to “If increasing fuel octane increases fuel econ- omy in all cars, then using higher octane fuel in your car will increase its fuel economy.” The truth of this conditional is deductively certain.

We can now test the truth of the hypothesis by testing the truth of the consequence.

Step 3: Test Whether the Consequence Occurs Your prediction (the consequence) is that your car will get better fuel economy if you use a higher grade of fuel. How will you test this? You may think this is obvious: Just put better gas in the car and record your fuel economy for a period before and after changing the type of gas you use. However, there are many other factors to consider. How long should the period of time be? Fuel economy varies depending on the kind of driving you do and many other factors. You need to choose a length of time for which you can be reasonably confident the driving conditions are similar on average. You also need to account for the fact that the first tank of better gas you put in will be mixed with some of the lower grade gas that is still in your tank. The more you can address these and other issues, the more certain you can be that your conclusion is correct.

In this step, you are constructing an inductive argument from the outcome of your test as to whether your car actually did get better fuel economy. The arguments in this step are induc- tive because there is always some possibility that you have not adequately addressed all of the relevant issues. If you do notice better fuel economy, it is always possible that the increase in economy is due to some factor other than the one you are tracking. The possibility may be very small, but it is enough to make this kind of argument inductive rather than deductive.

Step 4: Reject the Hypothesis If the Consequence Does Not Occur We now compare the results to the prediction and find out if the prediction came true. If your test finds that your car’s fuel economy does not improve when you use higher octane fuel, then you know your prediction was wrong.

Does this mean that your hypothesis, H, was wrong? That depends on the strength of the con- nection between H and C. If the inference from H to C is deductively certain, then we know for sure that, if H is true, then C must be true also. Therefore, if C is false, it follows logically that H must be false as well.

In our specific case, if your car does not get better fuel economy by switching to higher octane fuel, then we know for sure that it is not true that all cars get better fuel economy by doing so. However, if the inference from H to C is inductive, then the connection between H and C is less than totally certain. So if we find that C is false, we are not absolutely sure that the hypothesis, H, is false.

har85668_06_c06_207-238.indd 220 4/9/15 11:38 AM

Section 6.4 Reasoning About Science: The Hypothetico–Deductive Method

For example, suppose that the hypothesis is that cars that use higher octane fuel will have a higher tendency to get better fuel mileage. In that case if your car does not get higher gas mileage, then you still cannot infer for certain that the hypothesis is false. To test that hypothesis adequately, you would have to do a large study with many cars. Such a study would be much more complicated, but it could provide very strong evidence that the hypoth- esis is false.

It is important to note that although the falsity of the prediction can dem- onstrate that the hypothesis is false, the truth of the prediction does not prove that the hypothesis is true. If you find that your car does get better fuel economy when you switch gas, you cannot conclude that your hypothesis is true.

Why? There may be other factors at play for which you have not ade- quately accounted. Suppose that at the same time you switch fuel grade, you also get a tune-up and new tires and start driving a completely different route to work. Any one of these things might be the cause of the improved gas mileage; you cannot conclude that it is due to the change in fuel (for this rea- son, when conducting experiments it is best to change only one variable at a time and carefully control the rest). In

other words, in the hypothetico–deductive method, failed tests can show that a hypothesis is wrong, but tests that succeed do not show that the hypothesis was correct.

This logic is known as falsification; it can be demonstrated clearly by looking at the structure of the argument. When a test yields a negative result, the hypothetico–deductive method sets up the following argument:

If H, then C. Not C. Therefore, not H.

You may recognize this argument form as modus tollens, or denying the consequent, which was discussed in the chapter on propositional logic (Chapter 4). This argument form is a valid, deductive form. Therefore, if both of these premises are true, then we can be certain that the conclusion is true as well; namely, that our hypothesis, H, is not true. In the specific case at hand, if your test shows that higher octane fuel does not increase your mileage, then we can be sure that it is not true that it improves mileage in all vehicles (though it may improve it in some).

IPGGutenbergUKLtd/iStock/Thinkstock

At best, the fuel economy hypothesis will be a strong inductive argument because there is a chance that something other than higher octane gas is improving fuel economy. The more you can address relevant issues that may impact your test results, the stronger your conclusions will be.

har85668_06_c06_207-238.indd 221 4/9/15 11:38 AM

Section 6.4 Reasoning About Science: The Hypothetico–Deductive Method

Contrast this with the argument form that results when your fuel economy yields a positive result:

If H, then C. C. Therefore, H.

This argument is not valid. In fact, you may recognize this argument form as the invalid deduc- tive form called affirming the consequent (see Chapter 4). It is possible that the two premises are true, but the conclusion false. Perhaps, for example, the improvement in fuel economy was caused by a change in tires or different driving conditions instead. So the hypothetico –deductive method can be used only to reject a hypothesis, not to confirm it. This fact has led many to see the primary role of science to be the falsification of hypotheses. Philosopher Karl Popper is a central source for this view (see A Closer Look: Karl Popper and Falsification in Science).

A Closer Look: Karl Popper and Falsification in Science Karl Popper, one of the most influential philosophers of sci- ence to emerge from the early 20th century, is perhaps best known for rejecting the idea that scientific theories could be proved by simply finding confirming evidence—the prevail- ing philosophy at the time. Instead, Popper emphasized that claims must be testable and falsifiable in order to be consid- ered scientific.

A claim is testable if we can devise a way of seeing if it is true or not. We can test, for instance, that pure water will freeze at 0°C at sea level; we cannot currently test the claim that the oceans in another galaxy taste like root beer. We have no realistic way to determine the truth or falsity of the second claim.

A claim is said to be falsifiable if we know how one could show it to be false. For instance, “there are no wild kangaroos in Georgia” is a falsifiable claim; if one went to Georgia and found some wild kangaroos, then it would have been shown to be false. But what if someone claimed that there are ghosts in Georgia but that they are imperceptible (unseeable, unfeel- able, unhearable, etc.)? Could one ever show that this claim is false? Since such a claim could not conceivably be shown to be false, it is said to be unfalsifiable. While being unfalsifiable might sound like a good thing, according to Popper it is not, because it means that the claim is unscientific.

Following Popper, most scientists today operate with the assumption that any scientific hypothesis must be testable and must be the kind of claim that one could possibly show to be false. So if a claim turns out not to be conceivably falsifiable, the claim is not really scientific—and some philosophers have gone so far as to regard such claims as meaningless (Thornton, 2014).

Keystone/Getty Images

Karl Popper, a 20th- century philosopher of science, put forth the idea that unfalsifiable claims are unscientific.

(continued)

har85668_06_c06_207-238.indd 222 4/9/15 11:38 AM

Section 6.4 Reasoning About Science: The Hypothetico–Deductive Method

As an example, suppose a friend claims that “everything works out for the best.” Then suppose that you have the worst month of your life, and you go back to your friend and say that the claim is false: Not everything is for the best. Your friend might then reply that in fact it was for the best because you learned from the experience. Such a statement may make you feel better, but it runs afoul of Popper’s rule. Can you imagine any circumstance that your friend would not claim is for the best? Since your friend would probably say that it was for the best no mat- ter what happens, your friend’s claim is unfalsifiable and therefore unscientific.

In logic, claims that are interpreted so that they come out true no matter what happens are called self-sealing propositions. They are understood as being internally protected against any objections. People who state such claims may feel that they are saying something deeply meaningful, but according to Popper’s rule, since the claim could never be falsified no matter what, it does not really tell us anything at all.

Other examples of self-sealing propositions occur within philosophy itself. There is a philo- sophical theory known as psychological egoism, for example, which teaches that everything everyone does is completely selfish. Most people respond to this claim by coming up with examples of unselfish acts: giving to the needy, spending time helping others, and even dying to save someone’s life. The psychological egoist predictably responds to all such examples by stating that people who do such things really just do them in order to feel better about them- selves. It appears that the word selfish is being interpreted so that everything everyone does will automatically be considered selfish by definition. It is therefore a self-sealing claim (Rachels, 1999). According to Popper’s method, since this claim will always come out true no mat- ter what, it is unfalsifiable and unscientific. Such claims are always true but are actually empty because they tell us nothing about the world. They can even be said to be “too true to be good.”

Popper’s explorations of scientific hypotheses and what it means to confirm or disconfirm such hypotheses have been very influential among both scientists and philosophers of scien- tists. Scientists do their best to avoid making claims that are not falsifiable.

A Closer Look: Karl Popper and Falsification in Science (continued)

If the hypothetico-deductive method cannot be used to confirm a hypothesis, how can this test give evidence for the truth of the claim? By failing to falsify the claim. Though the hypo- thetico–deductive method does not ever specifically prove the hypothesis true, if research- ers try their hardest to refute a claim but it keeps passing the test (not being refuted), then there can grow a substantial amount of inductive evidence for the truth of the claim. If you repeatedly test many cars and control for other variables, and if every time cars are filled with higher octane gas their fuel economy increases, you may have strong inductive evidence that the hypothesis might be true (in which case you may make an inference to the best explana- tion, which will be discussed in Section 6.5).

Experiments that would have the highest chance of refuting the claim if it were false thus provide the strongest inductive evidence that it may be true. For example, suppose we want to test the claim that all swans are white. If we only look for swans at places in which they are known to be white, then we are not providing a strong test for the claim. The best thing to do (short of observing every swan in the whole world) is to try as hard as we can to refute the claim, to find a swan that is not white. If our best methods of looking for nonwhite swans still fail to refute the claim, then there is a growing likelihood that perhaps all swans are indeed white.

har85668_06_c06_207-238.indd 223 4/9/15 11:38 AM

Section 6.4 Reasoning About Science: The Hypothetico–Deductive Method

Similarly, if we want to test to see if a certain type of medicine cures a certain type of dis- ease, we test the product by giving the medicine to a wide variety of patients with the dis- ease, including those with the least likelihood of being cured by the medicine. Only by trying as hard as we can to refute the claim can we get the strongest evidence about whether all instances of the disease are treatable with the medicine in question.

Notice that the hypothetico–deductive method involves a combination of inductive and deductive reasoning. Step 1 typically involves inductive reasoning as we formulate a hypoth- esis against the background of our current beliefs and knowledge. Step 2 typically provides a deductive argument for the premise “If H, then C.” Step 3 provides an inductive argument for whether C is or is not true. Finally, if the prediction is falsified, then the conclusion—that H is false—is derived by a deductive inference (using the deductively valid modus tollens form). If, on the other hand, the best attempts to prove C to be false fail to do so, then there is growing evidence that H might be true.

Therefore, our overall argument has both inductive and deductive elements. It is valuable to know that, although the methodology of science involves research and experimentation that goes well beyond the scope of pure logic, we can use logic to understand and clarify the basic principles of scientific reasoning.

Practice Problems 6.4

1. A hypothesis is __________. a. something that is a mere guess b. something that is often arrived at after a lot of research c. an unnecessary component of the scientific method d. something that is already solved

2. In a scientific experiment, __________. a. the truth of the prediction guarantees that the hypothesis was correct b. the truth of the prediction negates the possibility of the hypothesis being correct c. the truth of the prediction can have different levels of probability in relation to

the hypothesis being correct d. the truth of the prediction is of little importance

3. The argument form that is set up when a test yields negative results is __________. a. disjunctive syllogism b. modus ponens c. hypothetical syllogism d. modus tollens

4. A claim is testable if __________. a. we know how one could show it to be false b. we know how one could show it to be true c. we cannot determine a way to prove it false d. we can determine a way to see if it is true or false

(continued)

har85668_06_c06_207-238.indd 224 4/9/15 11:38 AM

Section 6.5 Inference to the Best Explanation

5. Which of the following claims is not falsifiable? a. The moon is made of cheese. b. There is an invisible alien in my garage. c. Octane ratings in gasoline influence fuel economy. d. The Willis Tower is the tallest building in the world.

Practice Problems 6.4 (continued)

6.5 Inference to the Best Explanation You may feel that if you were very careful about testing your fuel economy, you would be entitled to conclude that the change in fuel grade really did have an effect. Unfortunately, as we have seen, the hypothetico–deductive method does not support this inference. The best you can say is that changing fuel might have an effect; that you have not been able to show that it does not have an effect. The method does, however, lend inductive support to which- ever hypothesis withstands the falsification test better than any other. One way of articulating this type of support is with an inference pattern known as inference to the best explanation.

As the name suggests, inference to the best explanation draws a conclusion based on what would best explain one’s observations. It is an extremely important form of inference that we use every day of our lives. This type of inference is often called abductive reasoning, a term pioneered by American logician Charles Sanders Peirce (Douven, 2011).

Suppose that you are in your backyard gazing at the stars. Suddenly, you see some flashing lights hovering above you in the sky. You do not hear any sound, so it does not appear that the lights are coming from a helicopter. What do you think it is? What happens next is abductive reasoning: Your brain searches among all kinds of possibilities to attempt to come up with the most likely explanation.

One possibility is that it is an alien spacecraft coming to get you (one could joke that this is why it is called abductive reasoning). Another possibility is that it is some kind of military vessel or a weather balloon. A more extreme hypothesis is that you are actually dreaming the whole thing.

Notice that what you are inclined to believe depends on your existing beliefs. If you already think that alien spaceships come to Earth all the time, then you may arrive at that conclusion with a high degree of certainty (you may even shout, “Take me with you!”). However, if you are somewhat skeptical of those kinds of theories, then you will try hard to find any other explanation. Therefore, the strength of a particular inference to the best explanation can be measured only in relation to the rest of the things that we already believe.

har85668_06_c06_207-238.indd 225 4/9/15 11:38 AM

Section 6.5 Inference to the Best Explanation

This type of inference does not occur only in unusual circumstances like the one described. In fact, we make infer- ences to the best explanation all the time. Returning to our fuel economy example from the previous section, suppose that you test a higher octane fuel and notice that your car gets bet- ter gas mileage. It is possible that the mileage change is due to the change in fuel. However, as noted there, it is possible that there is another expla- nation. Perhaps you are not driving in stop-and-go traffic as much. Perhaps you are driving with less weight in the car. The careful use of inference to the best explanation can help us to discern what is the most likely among many possibilities (for more examples, see A Closer Look: Is Abductive Reasoning Everywhere?).

If you look at the range of possible explanations and find one of them is more likely than any of the others, inference to the best explanation allows you to conclude that this explanation is likely to be the correct one. If you are driving the same way, to the same places, and with the same weight in your car as before, it seems fairly likely that it was the change in fuel that caused the improvement in fuel economy (if you have studied Mill’s methods in Chapter 5, you should recognize this as the method of difference). Inference to the best explanation is the engine that powers many inductive techniques.

The great fictional detective Sherlock Holmes, for example, is fond of claiming that he uses deductive reasoning. Chapter 2 suggested that Holmes instead uses inductive reasoning. However, since Holmes comes up with the most reasonable explanation of observed phe- nomena, like blood on a coat, for example, he is actually doing abductive reasoning. There is some dispute about whether inference to the best explanation is inductive or whether it is an entirely different kind of argument that is neither inductive nor deductive. For our purposes, it is treated as inductive.

Image Asset Management/SuperStock

Sherlock Holmes often used abductive reasoning, not deductive reasoning, to solve his mysteries.

har85668_06_c06_207-238.indd 226 4/9/15 11:38 AM

Section 6.5 Inference to the Best Explanation

A Closer Look: Is Abductive Reasoning Everywhere? Some see inference to the best explanation as the most common type of inductive inference. A few of the inferences we have discussed in this book, for example, can potentially be cast as examples of inferences to the best explanation.

For example, appeals to authority (discussed in Chapter 5) can be seen as implicitly using inference to the best explanation (Harman, 1965). If you accept something as true because someone said it was, then you can be described as seeing the truth of the claim as the best explanation for why he or she said it. If we have good reason to think that the person was deluded or lying, then we are less certain of this conclusion because there are other likely explanations of why the person said it.

Furthermore, it is possible to see what we do when we interpret people’s words as a kind of inference to the best explanation of what they probably mean (Hobbs, 2004). If your neighbor says, “You are so funny,” for instance, we might use the context and tone to decide what he means by “funny” and why he is saying it (and whether he is being sarcastic). His comment can be seen as either rude or flattering, depending on what explanation we give for why he said it and what he meant.

Even the classic inductive inference pattern of inductive generalization can possibly be seen as implicitly involving a kind of inference to the best explanation: The best explanation of why our sample population showed that 90% of students have laptops is probably that 90% of all students have laptops. If there is good evidence that our sample was biased, then there would be a good competing explanation of our data.

Finally, much of scientific inference may be seen as trying to provide the best explanation for our observations (McMullin, 1992). Many hypotheses are attempts to explain observed phe- nomena. Testing them in such cases could then be seen as being done in the service of seeking the best explanation of why certain things are the way they are.

Take a look at the following examples of everyday inferences and see if they seem to involve arriving at the conclusion because it seems to offer the most likely explanation of the truth of the premise:

• “John is smiling; he must be happy.” • “My phone says that Julie is calling, so it is probably Julie.” • “I see a brown Labrador across the street; my neighbor’s dog must have gotten out.” • “This movie has great reviews; it must be good.” • “The sky is getting brighter; it must be morning.” • “I see shoes that look like mine by the door; I apparently left my shoes there.” • “She still hasn’t called back yet; she probably doesn’t like me.” • “It smells good; someone is cooking a nice dinner.” • “My congressperson voted against this bill I support; she must have been afraid of

offending her wealthy donors.” • “The test showed that the isotopes in the rock surrounding newly excavated bones had

decayed X amount; therefore, the animals from which the bones came must have been here about 150 million years ago.”

These examples, and many others, suggest to some that inference to the explanation may be the most common form of reasoning that we use (Douven, 2011). Do you agree? Whether you agree with these expanded views on the role of inference or not, it clearly makes an enormous contribution to how we understand the world around us.

har85668_06_c06_207-238.indd 227 4/9/15 11:38 AM

Section 6.5 Inference to the Best Explanation

Form Inferences to the best explanation generally involve the following pattern of reasoning:

X has been observed to be true. Y would provide an explanation of why X is true. No other explanation for X is as likely as Y. Therefore, Y is probably true.

One strange thing about inferences to the best explanation is that they are often expressed in the form of a common fallacy, as follows:

If P is the case, then Q would also be true. Q is true. Therefore, P is probably true.

This pattern is the logical form of a deductive fallacy known as affirming the consequent (discussed in Chapter 4). Therefore, we sometimes have to use the principle of charity to determine whether the person is attempting to provide an inference to the best explanation or making a simple deductive error. The principle of charity will be discussed in detail in Chapter 9; however, for our purposes here, you can think of it as giving your opponent and his or her argument the benefit of the doubt.

For example, the ancient Greek philosopher Aristotle reasoned as follows: “The world must be spherical, for the night sky looks different in the northern and southern regions, and that would be the case if the earth were spherical” (as cited in Wolf, 2004). His argument appears to have this structure:

If the earth is spherical, then the night sky would look different in the north- ern and southern regions. The night sky does look different in the northern and southern regions. Therefore, the earth is spherical.

It is not likely that Aristotle, the founding father of formal logic, would have made a mistake as silly as to affirm the consequent. It is far more likely that he was using inference to the best explanation. It is logically possible that there are other explanations for southern stars moving higher in the sky as one moves south, but it seems far more likely that it is due to the shape of the earth. Aristotle was just practicing strong abductive reasoning thousands of years before Columbus sailed the ocean blue (even Columbus would have had to use this type of reasoning, for he would have had to infer why he did not sail off the edge).

In more recent times, astronomers are still using inference to the best explanation to learn about the heavens. Let us consider the case of discovering planets outside our solar system, known as “exoplanets.” There are many methods employed to discover planets orbiting other stars. One of them, the radial velocity method, uses small changes in the frequency of light a

har85668_06_c06_207-238.indd 228 4/9/15 11:38 AM

Section 6.5 Inference to the Best Explanation

star emits. A star with a large planet orbiting it will wobble a little bit as the planet pulls on the star. That wobble will result in a pattern of changes in the frequency of light coming from the star. When astronomers see this pattern, they conclude that there is a planet orbiting the star. We can more fully explicate this reasoning in the following way:

That star’s light changes in a specific pattern. Something must explain the changes. A large planet orbiting the star would explain the changes. No other explanation is as likely as the explanation provided by the large planet. Therefore, that star probably has a large planet orbiting it.

The basic idea is that if there must be an explanation, and one of the available explanations is better than all the others, then that explanation is the one that is most likely to be true. The key issue here is that the explanation inferred in the conclusion has to be the best explana- tion available. If another explanation is as good—or better—then the inference is not nearly as strong.

Virtue of Simplicity Another way to think about inferences to the best explanation is that they choose the simplest explanation from among otherwise equal explanations. In other words, if two theories make the same prediction, the one that gives the simplest explanation is usually the best one. This standard for comparing scientific theories is known as Occam’s razor, because it was origi- nally posited by William of Ockham in the 14th century (Gibbs & Hiroshi, 1997).

A great example of this principle is Galileo’s demonstration that the sun, not the earth, is at the center of the solar system. Galileo’s theory provided the simplest explanation of observa- tions about the planets. His heliocentric model, for example, provides a simpler explanation for the phases of Venus and why some of the planets appear to move backward (retrograde motion) than does the geocentric model. Geocentric astronomers tried to explain both of these with the idea that the planets sometimes make little loops (called epicycles) within their orbits (Gronwall, 2006). While it is certainly conceivable that they do make little loops, it seems to make the theory unnecessarily complex, because it requires a type of motion with no independent explanation of why it occurs, whereas Galileo’s theory does not require such extra assumptions.

Therefore, putting the sun at the center allows one to explain observed phenomena in the most simple manner possible, without making ad hoc assumptions (like epicycles) that today seem absurd. Galileo’s theory was ultimately correct, and he demonstrated it with strong inductive (more specifically, abductive) reasoning. (For another example of Occam’s razor at work, see A Closer Look: Abductive Reasoning and the Matrix.)

har85668_06_c06_207-238.indd 229 4/9/15 11:38 AM

Section 6.5 Inference to the Best Explanation

A Closer Look: Abductive Reasoning and the Matrix One of the great questions from the history of philosophy is, “How do we know that the world exists outside of us as we perceive it?” We see a tree and we infer that it exists, but do we actu- ally know for sure that it exists? The argument seems to go as follows:

I see a tree. Therefore, a tree exists.

This inference, however, is invalid; it is possible for the premise to be true and the conclusion false. For example, we could be dreaming. Perhaps we think that the testimony of our other senses will make the argument valid:

I see a tree, I hear a tree, I feel a tree, and I smell a tree. Therefore, a tree exists.

However, this argument is still invalid; it is pos- sible that we could be dreaming all of those things as well. Some people state that senses like smell do not exist within dreams, but how do we know that is true? Perhaps we only dreamed that someone said that! In any case, even that would not rescue our argument, for there is an even stronger way to make the premise true and the conclusion false: What if your brain is actually in a vat somewhere attached to a computer, and a scientist is directly controlling all of your perceptions? (Or think of the 1999 movie The Matrix, in which humans are living in a simulated reality created by machines.)

One individual who struggled with these types of questions (though there were no computers back then) was a French philosopher named René Des- cartes. He sought a deductive proof that the world outside of us is real, despite these types of disturbing possibilities (Descartes, 1641/1993). He eventually came up with one of philoso- phy’s most famous arguments, “I think, therefore, I am” (or, more precisely, “I am thinking, therefore, I exist”), and from there attempted to prove that the world must exist outside of him.

Many philosophers feel that Descartes did a great job of raising difficult questions, but most feel that he failed in his attempt to find deductive proof of the world outside of our minds. Other philosophers, including David Hume, despaired of the possibility of a proof that we know that there is a world outside of us and became skeptics: They decided that absolute knowledge of a world outside of us is impossible (Hume, 1902).

However, perhaps the problem is not the failure of the particular arguments but the type of reasoning employed. Perhaps the solution is not deductive at all but rather abductive. It is not that it is logically impossible that tables and chairs and trees (and even other people) do not really exist; it is just that their actual existence provides the best explanation of our experi- ences. Consider these competing explanations of our experiences:

• We are dreaming this whole thing. • We are hallucinating all of this.

In The Matrix, we learn that our world is simulated by machines, and although we can see X, hear X, and feel X, X does not exist.

(continued)

har85668_06_c06_207-238.indd 230 4/9/15 11:38 AM

Section 6.5 Inference to the Best Explanation

• Our brains are in a vat being controlled by a scientist. • Light waves are bouncing off the molecules on the surface of the tree and entering our

eyeballs, where they are turned into electrical impulses that travel along neurons into our brains, somehow causing us to have the perception of a tree.

It may seem at first glance that the final option is the most complex and so should be rejected. However, let us take a closer look. The first two options do not offer much of an explanation for the details of our experience. They do not tell us why we are seeing a tree rather than some- thing else or nothing at all. The third option seems to assume that there is a real world some- where from which these experiences are generated (that is, the lab with the scientist in it). The full explanation of how things work in that world presumably must involve some complex laws of physics as well. There is no obvious reason to think that such an account would require fewer assumptions than an account of the world as we see it. Hence, all things considered, if our goal is to create a full explanation of reality, the final option seems to give the best account of why we are seeing the tree. It explains our observations without needless extra assumptions.

Therefore, if knowledge is assumed only to be deductive, then perhaps we do not know (with absolute deductive certainty) that there is a world outside of us. However, when we consider abductive knowledge, our evidence for the existence of the world as we see it may be rather strong.

A Closer Look: Abductive Reasoning and the Matrix (continued)

How to Assess an Explanation There are many factors that influence the strength of an inference to the best explanation. However, when testing inferences to the best explanation for strength, these questions are good to keep in mind:

• Does it agree well with the rest of human knowledge? Suggesting that your room- mate’s car is gone because it floated away, for example, is not a very credible story because it would violate the laws of physics.

• Does it provide the simplest explanation of the observed phenomena? According to Occam’s razor, we want to explain why things happen without unnecessary complexity.

• Does it explain all relevant observations? We cannot simply ignore contradicting data because it contradicts our theory; we have to be able to explain why we see what we see.

• Is it noncircular? Some explanations merely lead us in a circle. Stating that it is raining because water is falling from the sky, for example, does not give us any new information about what causes the water to fall.

• Is it testable? Suggesting that invisible elves stole the car does not allow for empirical confirmation. An explanation is stronger if its elements are potentially observable.

• Does it help us explain other phenomena as well? The best scientific theories do not just explain one thing but allow us to understand a whole range of related phenom- ena. This principle is called fecundity. Galileo’s explanation of the orbits of the plan- ets is an example of a fecund theory because it explains several things all at once.

An explanation that has all of these virtues is likely to be better than one that does not.

har85668_06_c06_207-238.indd 231 4/9/15 11:38 AM

Section 6.5 Inference to the Best Explanation

A Limitation One limitation of inference to the best explanation is that it depends on our coming up with the correct explanation as one of the candidates. If we do not think of the correct explana- tion when trying to imagine possible explanation, then inference to the best explanation can steer us wrong. This can happen with any inductive argument, of course; inductive arguments always carry some possibility that the conclusion may be false even if the premises are true. However, this limitation is a particular danger with inference to the best explanation because it relies on our being able to imagine the true explanation.

This is one reason that it is essential to always keep an open mind when using this technique. Further information may introduce new explanations or change which explanation is best. Being open to further information is important for all inductive inferences, but especially so for those involving inference to the best explanation.

Practice Problems 6.5

1. This philosopher coined the term abductive reasoning. a. Karl Popper b. Charles Sanders Peirce c. Aristotle d. G. W. F. Hegel

2. Sherlock Holmes is often said to be engaging in this form of reasoning, even though from a logical perspective he wasn’t. a. deductive b. inductive c. abductive d. productive

3. In a specific city that happens to be a popular tourist destination, the number of residents going to the emergency rooms for asthma attacks increases in the summer. When the winter comes and tourism decreases, the number of asthma attacks goes down. What is the most probable inference to be drawn in this situation? a. The locals are allergic to tourists. b. Summer is the time that most people generally have asthma attacks. c. The increased tourism leads to higher levels of air pollution due to traffic. d. The tourists pollute the ocean with trash that then causes the locals to get sick.

4. A couple goes to dinner and shares an appetizer, entrée, and dessert. Only one of the two gets sick. She drank a glass of wine, and her husband drank a beer. What is the most probable inference to be drawn in this situation? a. The wine was the cause of the sickness. b. The beer protected the man from the sickness. c. The appetizer affected the woman but not the man. d. The wine was rotten.

(continued)

har85668_06_c06_207-238.indd 232 4/9/15 11:38 AM

Section 6.5 Inference to the Best Explanation

5. You are watching a magic performance, and there is a woman who appears to be floating in space. The magician passes a ring over her to give the impression that she is floating. What explanation fits best with Occam’s razor? a. The woman is actually floating off the ground. b. The magician is a great magician. c. There is some sort of unseen physical object holding the woman.

6. You get a stomachache after eating out at a restaurant. What explanation fits best with Occam’s razor? a. You contracted Ebola and are in the beginning phases of symptoms. b. Someone poisoned the food that you ate. c. Something was wrong with the food you ate.

7. In order to determine how a disease was spread in humans, researchers placed two groups of people into two rooms. Both rooms were exactly alike, and no people touched each other while in the rooms. However, researchers placed someone who was infected with the disease in one room. They found that those who were in the room with the infected person got sick, whereas those who were not with an infected person remained well. What explanation fits best with Occam’s razor? a. The disease is spread through direct physical contact. b. The disease is spread by airborne transmission. c. The people in the first room were already sick as well.

8. There is a dent in your car door when you come out of the grocery store. What expla- nation fits best with Occam’s razor? a. Some other patron of the store hit your car with their car. b. A child kicked your door when walking into the store. c. Bad things tend to happen only to you in these types of situations.

9. A student submits a paper that has an 80% matching rate when submitted to Tur- nitin. There are multiple sites that align exactly with the content of the paper. What explanation fits best with Occam’s razor? a. The student didn’t know it was wrong to copy things word for word without

citing. b. The student knowingly took material that he did not write and used it as his

own. c. Someone else copied the student’s work.

10. You are a man, and you jokingly take a pregnancy test. The test comes up positive. What explanation fits best with Occam’s razor? a. You are pregnant. b. The test is correct. c. The test is defective.

11. A bomb goes off in a supermarket in London. A terrorist group takes credit for the bombing. What explanation fits best with Occam’s razor? a. The British government is trying to cover up the bombing by blaming a terrorist

group. b. The terrorist group is the cause of the bombing. c. The U.S. government actually bombed the market to get the British to help them

fight terrorist groups.

Practice Problems 6.5 (continued)

(continued)

har85668_06_c06_207-238.indd 233 4/9/15 11:38 AM

Section 6.5 Inference to the Best Explanation

12. You have friends and extended family over for Thanksgiving dinner. There are kids running through the house. You check the turkey and find that it is overcooked because the temperature on the oven is too high. What explanation fits best with Occam’s razor? a. The oven increased the temperature on its own. b. Someone turned up the heat to sabotage your turkey. c. You bumped the knob when you were putting something into the oven.

13. Researchers recently mapped the genome of a human skeleton that was 45,000 years old. They found long fragments of Neanderthal DNA integrated into this human genome. What explanation fits best with Occam’s razor? a. Humans and Neanderthals interbred at some point prior to the life of this hu-

man. b. The scientists used a faulty method in establishing the genetic sequence. c. This was actually a Neanderthal skeleton.

14. There is a recent downturn in employment and the economy. A politically far-leaning radio host claims that the downturn in the economy is the direct result of the presi- dent’s actions. What explanation fits best with Occam’s razor? a. The downturn in employment is due to many factors, and more research is in

order. b. The downturn in employment is due to the president’s actions. c. The downturn in employment is really no one’s fault.

15. In order for an explanation to be adequate, one should remember that __________. a. it should agree with other human knowledge b. it should include the highest level of complexity c. it should assume the thing it is trying to prove d. there are outlying situations that contradict the explanation

16. The fecundity of an explanation refers to its __________. a. breadth of explanatory power b. inability to provide an understanding of a phenomenon c. lack of connection to what is being examined d. ability to bear children

17. Why might one choose to use an inductive argument rather than a deductive argument? a. One possible explanation must be the correct one. b. The argument relates to something that is probabilistic rather than absolute. c. An inductive argument makes the argument valid. d. One should always use inductive arguments when possible.

18. This is the method by which one can make a valid argument invalid. a. adding false supporting premises b. demonstrating that the argument is valid c. adding true supporting premises d. valid arguments cannot be made invalid

(continued)

Practice Problems 6.5 (continued)

har85668_06_c06_207-238.indd 234 4/9/15 11:38 AM

Section 6.5 Inference to the Best Explanation

19. This form of inductive argument moves from the general to the specific. a. generalizations b. statistical syllogisms c. hypothetical syllogism d. modus tollens

Questions 20–24 relate to the following passage:

If I had gone to the theater, then I would have seen the new film about aliens. I didn’t go to the theater though, so I didn’t see the movie. I think that films about aliens and supernatural events are able to teach people a lot about what the future might hold in the realm of tech- nology. Things like cell phones and space travel were only dreams in old movies, and now they actually exist. Science fiction can also demonstrate new futures in which people are more accepting of those that are different from them. The different species of characters in these films all working together and interacting with one another in harmony displays the unity of different people without explicitly making race or ethnicity an issue, thereby bringing people into these forms of thought without turning those away who do not want to explicitly confront these issues.

20. How many arguments are in this passage? a. 0 b. 1 c. 2 d. 3

21. How many deductive arguments are in this passage? a. 0 b. 1 c. 2 d. 3

22. How many inductive arguments are in this passage? a. 0 b. 1 c. 2 d. 3

23. Which of the following are conclusions in the passage? Select all that apply. a. If I had gone to the theater, then I would have seen the new film about aliens. b. I didn’t go to the theater. c. Films about aliens and supernatural events are able to teach people a lot about

what the future might hold in the realm of technology. d. The different species of characters in these films all working together and

interacting with one another in harmony displays the unity of different people without explicitly making race or ethnicity an issue.

24. Which change to the deductive argument would make it valid? Select all that apply. a. Changing the first sentence to “If I would have gone to the theater, I would not

have seen the new film about aliens.” b. Changing the second sentence to “I didn’t see the new film about aliens.” c. Changing the conclusion to “Alien movies are at the theater.” d. Changing the second sentence to “I didn’t see the movie, so I didn’t go to the theater.”

Practice Problems 6.5 (continued)

har85668_06_c06_207-238.indd 235 4/9/15 11:38 AM

Summary and Resources

Summary and Resources

Chapter Summary Although induction and deduction are treated differently in the field of logic, they are fre- quently combined in arguments. Arguments with both deductive and inductive components are generally considered to be inductive as a whole, but the important thing is to recognize when deduction and induction are being used within the argument. Arguments that com- bine inductive and deductive elements can take advantage of the strengths of each. They can retain the robustness and persuasiveness of inductive arguments while using the stronger connections of deductive arguments where these are available.

Science is one discipline in which we can see inductive and deductive arguments play out in this fashion. The hypothetico–deductive method is one of the central logical tools of science. It uses a deductive form to draw a conclusion from inductively supported premises. The hypothetico–deductive method excels at disconfirming or falsifying hypotheses but cannot be used to confirm hypotheses directly.

Inference to the best explanation, however, does provide evidence supporting the truth of a hypothesis if it provides the best explanation of our observations and withstands our best attempts at refutation. A key limitation of this method is that it depends on our being able to come up with the correct explanation as a possibility in the first place. Nevertheless, it is a powerful form of inference that is used all the time, not only in science but in our daily lives.

Critical Thinking Questions

1. You have probably encountered numerous conspiracy theories on the Internet and in popular media. One such theory is that 9/11 was actually plotted and orches- trated by the U.S. government. What is the relationship between conspiracy theories and inference to the best possible explanation? In this example, do you think that this is a better explanation than the most popular one? Why or why not?

2. What are some methods you can use to determine whether or not information represents the best possible explanation of events? How can you evaluate sources of information to determine whether or not they should be trusted?

3. Descartes claimed that it might be the case that humans are totally deceived about all aspects of their existence. He went so far as to claim that God could be evil and could be making it so that human perception is completely wrong about everything. However, he also claimed that there is one thing that cannot be doubted: So long as he is thinking, it is impossible for him to doubt that it is he who is thinking. Hence, so long as he thinks, he exists. Do you think that this argument establishes the inherent existence of the thinking being? Why or why not?

4. Have you ever been persuaded by an argument that ended up leading you to a false conclusion? If so, what happened, and what could you have done differently to pre- vent yourself from believing a false conclusion?

5. How can you incorporate elements of the hypothetico–deductive method into your own problem solving? Are there methods here that can be used to analyze situations in your personal and professional life? What can we learn about the search for truth from the methods that scientists use to enhance knowledge?

har85668_06_c06_207-238.indd 236 4/9/15 11:38 AM

Summary and Resources

abductive reasoning See inference to the best explanation.

falsifiable Describes a claim that is conceiv- ably possible to prove false. That does not mean that it is false; only that prior to test- ing, it is possible that it could have been.

falsification The effort to disprove a claim (typically by finding a counterexample to it).

hypothesis A conjecture about how some part of the world works.

hypothetico–deductive method The method of creating a hypothesis and then attempting to falsify it through experimentation.

inference to the best explanation The process of inferring something to be true because it is the most likely explanation of some observations. Also known as abductive reasoning.

Occam’s razor The principle that, when seeking an explanation for some phenom- ena, the simpler the explanation the better.

self-sealing propositions Claims that can- not be proved false because they are inter- preted in a way that protects them against any possible counterexample.

Web Resources https://www.youtube.com/watch?v=RauTW8F-PMM Watch Ashford professor Justin Harrison lecture on the difference between inductive and deductive arguments.

https://www.youtube.com/watch?v=VXW5mLE5Y2g Shmoop offers an animated video on the difference between induction and deduction.

http://www.ac4d.com/2012/06/03/abductive-reasoning-in-airport-security-and-profiling Design expert Jon Kolko applies abductive reasoning to airport security in this blog post.

Key Terms

Answers to Practice Problems Practice Problems 6.1

1. d 2. a

3. b 4. b

Practice Problems 6.2

1. a 2. a

3. a 4. a

Practice Problem 6.3

1. b

har85668_06_c06_207-238.indd 237 4/9/15 11:38 AM

Summary and Resources

Practice Problems 6.4

1. b 2. c 3. d

4. d 5. b

Practice Problems 6.5

1. b 2. a 3. c 4. a 5. c 6. c 7. b 8. a 9. b

10. c 11. b 12. c

13. a 14. a 15. a 16. a 17. b 18. d 19. b 20. d 21. b 22. c 23. c 24. d

har85668_06_c06_207-238.indd 238 4/9/15 11:38 AM