Answer & Explanation:300-400 wordsOne of the most common inferences in life is the inference to the best explanation (sometimes called abductive reasoning). We use this type of reasoning to infer what would best explain the things that we see. Chapter 6 in our book demonstrates ways in which this type of reasoning helps us to explain the world around us.Prepare: To prepare for this lesson take a close look at the sections from Chapter 6 on “Inference to the Best Explanation,” “Form,” “Virtue of Simplicity,” and “How to Assess an Explanation.” Choose a topic that is difficult or controversial to explain. Some good topics include hoaxes, unusual sightings (e.g. UFOs, bigfoot, the Loch Ness monster), the supernatural or paranormal, events that are the subject of conspiracy theories, unsolved crimes or other court cases, etc. Reflect: Do a little research to find a specific topic and learn about explanations on both sides. Consider what you think might best explain the observed facts of the case.Write: Explain the topic you chose and why it is interesting or controversial. Present good arguments on more than one side of the issue (e.g. competing explanations of the facts). Analyze both arguments that you have presented. Then present your own argument for your theory that you feel will best explain this phenomenon. Are there any holes in your theory? Is there any information that would be likely to strengthen or weaken your case?
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Deduction and Induction:
Putting It All Together
6
Wavebreakmedia Ltd./Thinkstock and GoldenShrimp/iStock/Thinkstock
Learning Objectives
After reading this chapter, you should be able to:
1. Compare and contrast the advantages of deduction and induction.
2. Explain why one might choose an inductive argument over a deductive argument.
3. Analyze an argument for its deductive and inductive components.
4. Explain the use of induction within the hypothetico–deductive method.
5. Compare and contrast falsification and confirmation within scientific inquiry.
6. Describe the combined use of induction and deduction within scientific reasoning.
7. Explain the role of inference to the best explanation in science and in daily life.
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Section 6.1
Contrasting Deduction and Induction
Now that you have learned something about deduction and induction, you may be wondering
why we need both. This chapter is devoted to answering that question. We will start by 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.
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.
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.
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
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Contrasting Deduction and Induction
Section 6.1
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.
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Contrasting Deduction and Induction
Section 6.1
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 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.
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Choosing Between Induction and Deduction
Section 6.2
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
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.
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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.
Alistair Scott/iStock/Thinkstock
Despite knowing that a helium-filled
balloon will rise when we let go of it,
we still hold our belief in gravity due
to strong inductive reasoning and our
reliance on observation.
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 all-or-nothing affair; there is no such thing as “sort of valid” or “more valid.” The
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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,
man-made, and dangerous.
Therefore, 97% of scientists really do agree that climate change is real, manmade, and dangerous.
Therefore, climate change is real, man-made, and dangerous.
Given the politically charged nature of the discussion of climate change, it is not surprising
that the president’s argument and the study it referred to received considerable criticism.
(You can read the study at http://iopscience.iop.org/1748–9326/8/2/024024/pdf/1748
–9326_8_2_024024.pdf.) Looking at the effect some of those criticisms have on the argument
is a good way to see how inductive arguments can be more robust than deductive ones.
One criticism of Obama’s claim is that the study he referenced did not say anything about
whether climate change was dangerous, only about whether it was real and man-made.
How does this affect the argument? Strictly speaking, it makes the first premise false. But
notice that even so, the argument can still give good evidence that climate change is real and
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man-made. Since climate change, by its nature, has a strong potential to be dangerous, the
argument is weakened but still may give strong evidence for its conclusion.
A deeper criticism notes that the study did not find out what all scientists thought; it just
looked at those scientists who expressed an opinion in their published work or in response
to a voluntary survey. This is a significant criticism, for it may expose a bias in the sampling
method (as discussed in Chapters 5, 7, and 8). Even granting the criticism, the argument can
retain some strength. The fact that 97% of scientists who expressed an opinion on the issue
said that climate change is real and man-made is still some reason to think that it is real and
man-made. Of course, some scientists may have chosen not to voice an opposing opinion for
reasons that have nothing to do with their beliefs about climate change; they may have simply
wanted to keep their views private, for example. Taking all of this into account, we get the following argument:
A study found that 97% of scientists who stated their opinion said that climate change is real and man-made.
Therefore, 97% of scientists agree that climate change is real and man-made.
Climate change, if real, is dangerous.
Therefore, climate change is real, man-made, and dangerous.
This is not nearly as strong as the original argument, but it has not collapsed entirely in the
way a purely deductive argument would. There is, of course, much more that could be said
about this argument, both in terms of criticizing the study and in terms of responding to those
criticisms and bringing in other considerations. The point here is merely to highlight the 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
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