# advantages of deduction and induction.

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.

6Deduction and Induction: Putting It All Together

Wavebreakmedia Ltd./Thinkstock and GoldenShrimp/iStock/Thinkstock

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 learning 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 scientific reasoning applies to both types of

reasoning to achieve spectacular results. Arguments with both inductive and deductive elements are

arguments. We will also investigate another very useful type of inference, known as inference to the best

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

6.1 Contrasting Deduction and Induction

Remember that in logic, the difference between induction

and deduction lies in the connection between the premises

and conclusion. Deductive arguments aim for an absolute

connection, 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 discussion 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 counterpart 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 reasoning. As discussed in Chapter 5, if you add another premise to an inductive

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 convinced 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 premises to a valid argument can never render it invalid. New

information may show that a deductive argument 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

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, possible 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 argument 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 addition 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 consider 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.

when evaluating the argument.

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 general. 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 inductive arguments

go from the specific premises to general conclusions. However, neither statement is true in

general.

First, although some deductive arguments go from general to specific, there are many deductive

arguments that do not go from general to specific. Some deductive arguments, for example, 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 specific, but it is deductively

valid. When it comes to inductive arguments, some—for example, inductive generalizations—go

Use this video to review deductive and inductive arguments.

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 surprising

given the different goals of the fields in which the terms are used. However, the definitions 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 addition,

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.

Deductive and Inductive Arguments

Deductive and Inductive Arguments

From Title: Logic: The Structure of Reason

(https://fod.infobase.com/PortalPlaylists.aspx?wID=100753&xtid=32714)

Critical Thinking Questions

1. What does it mean when we say that validity is

independent of the truth of the premises and

conclusions in an argument?

2. What are the differences between deductive and

inductive arguments? What is the relationship

between truth and the structure of a deductive

versus an inductive argument?

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

conclusion 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

Alistair Scott/iStock/Thinkstock

Despite knowing that a

helium­filled 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.

6.2 Choosing Between Induction and Deduction

You might wonder why one would choose to use inductive reasoning over deductive reasoning. 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 section. 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.

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

everything will fall when you let go of it. Perhaps gravity does not affect very

small things or very large things. We could do more experiments, but we

cannot 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 therefore have great reasons to believe in gravity, even if our reasoning

is not deductive.

All subjects that rely on observation use inductive 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

proceed entirely by deductive reasoning. These tend to be very abstract and

formal subjects, such as mathematics. 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 arguments can be extremely persuasive, but they are

also fragile in a certain sense. When something 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. Validity is an all­or­nothing affair; there

is no such thing as “sort of valid” or “more valid.” The argument would simply be invalid and therefore

unsound; it would not accomplish its purpose 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 problems 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 conclusion, 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 provide 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, man­made, and

dangerous.

Therefore, 97% of scientists really do agree that climate change is real, man­made, and

dangerous.

Therefore, climate change is real, man­made, 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

(http://iopscience.iop.org/1748­9326/8/2/024024/pdf/1748­9326_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 man­made. 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 man­made. 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 man­made is still some

reason to think that it is real and man­made. 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

following argument:

A study found that 97% of scientists who stated their opinion said that climate change is real

Therefore, 97% of scientists agree that climate change is real and man­made.

Climate change, if real, is dangerous.

Therefore, climate change is real, man­made, 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 difference 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 deductive

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 deductively 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 so obviously valid

that anyone who accepts the premises likely already accepts the conclusion. 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 complicated 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 conclusion 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 question, 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 troubling

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.

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.

Real­life 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 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 premises guarantee the

truth of the conclusion. 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 argument has both inductive and deductive

components, the overall argument is generally inductive.

There are occasional 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.

A similar thing happens when we combine inductive

arguments of different strength. In general, 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.

Practice Problem 6.3

1. When an argument contains both inductive and deductive elements, the entire argument

is considered deductive.

a. true

b. false

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 discussing 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.

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 background 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

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 characteristic B.

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. Essentially, 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 economy 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

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

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 inductive 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 connection

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.

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 hypothesis is false.

It is important to note that although the falsity of the

prediction can demonstrate 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 adequately accounted. Suppose that at the same time

you switch fuel grade, you also get a tune­up 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 reason, 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.

Keystone/Getty Images

Karl Popper, a 20th­

century philosopher

of science, put forth

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).

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 deductive 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 science 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 prevailing philosophy at the time.

Instead, Popper emphasized that claims must be testable and

falsifiable in order to be considered 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

the idea that

unfalsifiable claims

are unscientific.

falsifiability in this video.

Karl Popper and Falsification

Critical Thinking Questions

1. Karl Popper argues that only hypotheses

that can be tested and falsified are

scientific. Do you agree?

2. In addition to being unscientific, Popper

states that unfalsifiable claims tell us

nothing and do not allow us to learn from

our mistakes. Can you make an argument

against Popper’s?

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, unfeelable, 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).

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 matter 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 self­sealing

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 self­sealing

propositions occur within philosophy

itself. There is a philosophical 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 themselves. 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 self­sealing claim (Rachels, 1999). According to Popper’s method, since this claim will

always come out true no matter 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 scientists.

Scientists do their best to avoid making claims that are not falsifiable.

If the hypothetico­deductive 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 hypothetico–deductive

method does not ever specifically prove the hypothesis true, if researchers 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 explanation, 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.

Similarly, if we want to test to see if a certain type of medicine cures a certain type of disease, we test the

product by giving the medicine to a wide variety of patients with the disease, 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 hypothesis 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

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.

Image Asset Management/SuperStock

Sherlock Holmes often used abductive

reasoning, not deductive reasoning, to

solve his mysteries.

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 whichever 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

This type of inference does not occur only in unusual

circumstances like the one described. In fact, we make

inferences 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 better 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 explanation.

Perhaps you are not driving in stop­and­go 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 phenomena, 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.

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 phenomena.

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.

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 northern 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 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 explanation 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 originally 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 observations 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.

Collection

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.

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.)

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 actually

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 possible 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 Descartes. 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 philosophy’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 experiences.

Consider these competing explanations of our experiences:

• We are dreaming this whole thing.

• We are hallucinating all of this.

• 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 something

else or nothing at all. The third option seems to assume that there is a real world somewhere

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.

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 roommate’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 phenomena. This principle is

called fecundity. Galileo’s explanation of the orbits of the planets 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.

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 explanation 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.

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

explanation 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 Turnitin.

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.

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 human.

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 far­leaning

radio host claims that the downturn in the economy is the direct result of the president’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 __________.

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.

b. demonstrating that the argument is valid

d. valid arguments cannot be made invalid

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 technology. 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.”

Summary and Resources

Chapter Summary

Although induction and deduction are treated differently in the field of logic, they are frequently

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 combine 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 orchestrated 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 prevent 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?

Web Resources

PMM)

Watch Ashford professor Justin Harrison lecture on the difference between inductive and deductive

arguments.

v=VXW5mLE5Y2g)

Shmoop offers an animated video on the difference between induction and deduction.

http://www.ac4d.com/2012/06/03/abductive­reasoning­in­airport­security­and­profiling

(http://www.ac4d.com/2012/06/03/abductive­reasoning­in­airport­security­and­profiling)

>Design expert Jon Kolko applies abductive reasoning to airport security in this blog post.

Key Terms

abductive reasoning

See inference to the best explanation.

falsifiable

Describes a claim that is conceivably possible to prove false. That does not mean that it is false; only

that prior to testing, 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 phenomena, the simpler the explanation the

better.

self-sealing propositions

Claims that cannot be proved false because they are interpreted in a way that protects them against

any possible counterexample.

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