In the field of logic, inductive arguments __________.

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

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.

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.

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

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, 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.

Learning to carefully distinguish between these elements will help you know what questions to ask

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

Click here

(https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems6.1.pdf)

to check your answers.

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.

Twitter/Public Domain

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

and man­made.

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

Click here

(https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems6.2.pdf)

to check your answers.

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.