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Counterargument Paper
This paper assignment expands upon your Week One Assignment and prepares you for the Final Paper. The expansion is to learn to improve one’s argument after investigating and fairly representing the opposite point of view. The main new tasks are to revise your previous argument created in Week One, to present a counterargument (an argument for a contrary conclusion), and to develop an objection to your original argument.
Here are the steps to prepare to write the counterargument paper:
- Begin reviewing your previous paper paying particular attention to suggestions for improvement made by your instructor.
- Revise your argument, improving it as much as possible, accounting for any suggestions and in light of further material you have learned in the course. If your argument is inductive, make sure that it is strong. If your argument is deductive, make sure that it is valid.
- Construct what you take to be the strongest possible argument for a conclusion contrary to the one you argued for in your Week One paper. This is your counterargument. This should be based on careful thought and appropriate research.
- Consider the primary points of disagreement between the point of view of your original argument and that of the counterargument.
- Think about what you take to be the strongest objection to your original argument and how you might answer the objection while being fair to both sides. Search in the Ashford University Library for quality academic sources that support some aspect of your argument or counterargument.
In your paper,
- Present a revised argument in standard form, with each premise and the conclusion on a separate line.
- Present a counterargument in standard form, with each premise and the conclusion on a separate line.
- Provide support for each premise of your counterargument. Clarify the meaning of the premise and supporting evidence for the premise.
- Pay special attention to those premises that could be seen as controversial. Evidence may include academic research sources, supporting arguments, or other ways of demonstrating the truth of the premise (for more ideas about how to support the truth of premises take a look at the instructor guidance for this week). This section should include at least one scholarly research source. For guidance about how to develop a conclusion see the Ashford Writing Center’s Introductions and Conclusions.
- Explain how the conclusion of the counterargument follows from its premises. [One paragraph]
- Discuss the primary points of disagreement between sincere and intelligent proponents of both sides. [One to two paragraphs]
- For example, you might list any premises or background assumptions on which you think such proponents would disagree and briefly state what you see as the source of the disagreement, you could give a brief explanation of any reasoning that you think each side would find objectionable, or you could do a combination of these.
- Present the best objectionto your original argument. Clearly indicate what part of the argument your objection is aimed at, and provide a paragraph of supporting evidence for the objection. Reference at least one scholarly research source. [One to two paragraphs]
- See the “Practicing Effective Criticism” section of Chapter 9 of your primary textbook for more information about how to present an objection.
For further instruction on how to create arguments, see the How to Construct a Valid Main Argument and Tips for Creating an Inductively Strong Argument documents as well as the video Constructing Valid Arguments.
For an example of how to complete this paper, take a look at the following Week Three Annotated Example. Let your instructor know if you have questions about how to complete this paper.
The Counterargument Paper
- Must be 500 to 800 words in length (not including title and references pages) and formatted according to APA style as outlined in the Ashford Writing Center (for more information about using APA style, take a look at the APA Essay Checklist for Students webpage).
- Must include a separate title page with the following:
- Title of paper
- Student’s name
- Course name and number
- Instructor’s name
- Date submitted
- Must use at least two scholarly sources in addition to the course text.
- The Scholarly, Peer Reviewed, and Other Credible Sources table offers additional guidance on appropriate source types. If you have questions about whether a specific source is appropriate for this assignment, please contact your instructor. Your instructor has the final say about the appropriateness of a specific source for a particular assignment.
- Must document all sources in APA style as outlined in the Ashford Writing Center (for more information about how to create an APA reference list, take a look at the APA References List webpage).
- Must include a separate references page that is formatted according to APA style as outlined in the Ashford Writing Center.
Carefully review the Grading Rubric for the criteria that will be used to evaluate your assignment.
SOCIAL MEDIA EFFECT ON INTERPERSONAL RELATIONSHIPS 2
Social Media Effect on Interpersonal Relationships
The twenty-first century has experienced a sporadic increase in the use and innovation of
technology. There has been much improvement in people’s daily activities due to evolution in
innovations. However, so has been the increase in discussion on the appropriateness and the
costs that the society has had to pay because of the progress. For instance, use of social media
has been an issue that has led scholars to conduct extensive surveys, interviews, and experiments
with the hope of getting a grip on whether it has been of positive or negative influence to the
society. Among the most commonly, asked question is the role it has played in affecting
interpersonal relationships. Different theorists and scholars have had different opinions some of
which can be deduced through logical reasoning. One of the standard forms of expressing an
argument, which I will use in this discussion to draw a conclusion on the issue, would be:
P1: Communication with peer groups primary motivation of social media use
P2: Communication with peers promotes interpersonal relationships
C1: Social media enhances interpersonal relationships.
The first premise has been a result of some of the different studies that have been
influenced by the advent of increased social media use. According to Valerie Barker (2009),
scholarly data on the issue produced results that implied that a significantly high number of
social media users get to use the different platforms with the hope of interacting with their peers
(p. 211). Consequently, the respondents viewed the various platforms as an alternative to calling
their peers or sending them messages on their phones as a way of interaction. Before
popularization of social media, people would use their telephones to call or send messages to
their peers with the hope of engaging in a dialogue that would culminate in improved
relationships. Therefore, social media was seen as an alternative form of communication.
– 2 –
1
1. relationships.
Good format [Teresa Knox]
SOCIAL MEDIA EFFECT ON INTERPERSONAL RELATIONSHIPS 3
The second premise seeks to create a boundary between the first one and the conclusion.
Notably, one cannot engage in communication without expressing his or her ideas or emotions.
After all, communication is the one method using which one can send a message to a different
party. Therefore, in the course of communicating, different people get to learn about others and,
in the process, determine how best to deal with each other under different circumstances. As a
result, the relationship between the two parties improves after some time. In this context,
communication improves the interpersonal relationships between the people involved.
Following a deductive reasoning from the first to the second premise, it is inarguably true
that social media improves interpersonal relationships between the parties involved. According to
the first premise, social media is just but a contemporary means of communication. Therefore, it
plays the role previously played by other communication means such as faxes, telephones, and
letters. On the other hand, the second premise notes that the communication facilitated by the
different channels through which it could be conducted interpersonal relationships. Getting one’s
message across to a particular audience gets the said audience to appreciate how they should
conduct themselves around the sender. In this context, social media is just but another instrument
that facilitates communication. Therefore, communication improves the relationships between
the parties. Connecting the two premises yields an answer to the issue by giving the solution that
social media indeed improves interpersonal relationships.
– 3 –
1
1. relationships.
Good work. [Teresa Knox]
SOCIAL MEDIA EFFECT ON INTERPERSONAL RELATIONSHIPS 4
Reference
Barker, V. (2009). Older adolescents’ motivations for social network site use: The influence of
gender, group identity, and collective self-esteem. CyberPsychology & Behavior, 12(2),
209-213.
1
Running head: THE ETHICS OF ELEPHANTS IN CIRCUSES
The Ethics of Elephants in Circuses
Dr. Christopher Foster
PHI103: Informal Logic
Ashford University
Annotated example for Week Three Assignment
2
THE ETHICS OF ELEPHANTS IN CIRCUSES
Main Argument :
P1: Elephants are highly intelligent animals.
P2: Putting elephants in circuses requires them
to live their lives in extreme confinement.
P3: Anything that requires highly intelligent
animals to live their lives in extreme
confinement is wrong unless it serves a purpose
that outweighs the suffering involved.
P4: Putting elephants in circuses does not serve
a purpose that outweighs the suffering
involved.
C: Therefore, putting elephants in circuses is
wrong.
Counterargument:
P1: Circus elephants provide enjoyment for
humans.
P2: The treatment of circus elephants is not
cruel.
P3: It is morally acceptable to use animals for
human enjoyment provided that their
treatment is not cruel.
C: Therefore it is morally acceptable to have
elephants in circuses.
This is the main argument
in Standard Form.
The main argument is
your argument for your
thesis.
C:
wr
The conclusion of your
main argument is your
thesis statement.
P1
hu
P2
cr
P3
hu
tr
C:
el
r
This is the
counterargument in
standard form, as
indicated in the
instructions.
3
THE ETHICS OF ELEPHANTS IN CIRCUSES
The next three
paragraphs provide
support for each premise
of the counterargument
(as indicated in the
instructions). This would
be added even if the
premise seems obvious.
Clarifying the
meaning of key
terms is often an
important aspect
of defending a
premise.
Notice that it is important
to be as fair as possible to
the other side, representing
the counterargument in the
strongest possible light.
The first premise of the counterargument is an obvious
background fact. If people did not find elephants in
circuses enjoyable, there would be no elephants in circuses.
Circuses exist solely for entertainment. Anything not enjoyable
would be dropped, especially something that requires as much
money and labor as elephants.
The second premise hinges on the meaning of the word “cruel”.
To be cruel is to intentionally inflict pain for the primary purpose of
inflicting pain, or to inflict substantially more pain than is required for the
desired result. Giving a vaccination shot to a child is not cruel, because it is
not done for the purpose of inflicting pain and there is not a substantially less
painful way to get the benefit. Similarly, the mere fact that elephants in circuses suffer to some degree
does not mean they are treated cruelly, provided that suffering is not the goal and that they are not
made to suffer more than is necessary for the intended
purpose.
The third premise is supported by common practice.
Meat, leather, milk, and other animal products are routinely used despite the fact that they require
animals to suffer some pain. Working animals typically suffer various degrees of discomfort or pain, yet
their use is not generally considered unethical if they are treated as well as possible given the goal. Of
course it would be wrong to use humans in this way, but animals do not generally have the rights that
humans do. Carl Cohen, for example, argues that rights come from an agreement between moral
agents. He concludes that animals do not have rights because they cannot make such agreements
4
THE ETHICS OF ELEPHANTS IN CIRCUSES
It is, of course, good to use
scholarly sources to back up
important points.
The first
sentence of
each
paragraph
states the
topic of the
paragraph. This demonstrates
why the conclusion
of the
counterargument
follows from the
premises (as
indicated in the
instructions).
This part of your argument
may not agree with your own
position at all, but it is
important to represent the
argument as well as you can
so that you demonstrate an
appreciation of the best
argument on the other side.
This paragraph
presents a
reasonable and fair
discussion of the
points of
disagreement
between the two
sides (as indicated
in the instructions).
(Cohen, 2001). While the suffering of animals is a
consideration, it does not prohibit their use for the enjoyment of
humans. So long as the use does not seek pain and
suffering as part of the goal, and is carried out as humanely
as possible, using animals for human enjoyment is
morally acceptable.
This counterargument is deductively valid – if all of the premises
are true, then the conclusion must be as well. The third premise sets two
conditions for the moral acceptability of having elephants in circuses. The first
two premises state that both conditions are
met. It follows absolutely then, that having
elephants in circuses is morally acceptable, which is what the conclusion
says.
The primary disagreement between the sides will likely rest on
whether the treatment of elephants is cruel and unnecessary. Certainly,
life as a circus elephant can involve pain and suffering, but so can
life as a wild elephant. Furthermore, the intentional infliction of pain
and suffering is not always wrong, for example, giving a medical shot.
However, many would find the suffering inflicted by the confinement of
5
THE ETHICS OF ELEPHANTS IN CIRCUSES
This objection will be
developed further in
the final paper. A
preview of that
objection is given here
(as indicated in the
instructions).
This paragraph
further develops the
objection, in
preparation for the
final paper.
Again, this point may
(or may not) be
antithetical to your
own view. The point of
this second paper is to
develop and be fair to
the strongest
objection you can
provide to your own
argument.
elephants to be an infliction of suffering for a unnecessary purpose that does not justify the degree of
suffering inflicted. These issues represent the main points of disagreement between the two sides.
The best objection to the original argument is probably
aimed at the fourth premise. Posing such an objection would
require looking at how elephants are actually treated and examining
the degree to which elephants’ presence in circuses contributes to a
further purpose.
For example, Ringling Bros. claims that circus elephants are
guaranteed nutritious food, and prompt medical care, that
their training provides a focus for their mental and physical
abilities, and that they are allowed time for play and social
interaction. “A positive, healthy environment is the foundation of training elephants. Therefore, the
cornerstone of all circus elephant training at Ringling Bros. is reinforcement through praise, repetition,
and reward” (elephantcenter, n.d.). If these claims are true, then it
could be argued that their entertainment value to children and
others might be sufficient to outweigh any suffering caused to the
elephants in captivity.
6
THE ETHICS OF ELEPHANTS IN CIRCUSES
References
Cohen, C. (2001). Why animals do not have rights. In The Animal Rights Debate (pp. 27-40). Oxford,
England: Rowman & Littlefield Publishers, Inc.
Elephantcenter (n.d.). Pampered performers. Retrieved from http://www.elephantcenter.com/meet-
our-herd/pampered-performers/
Learning Objectives
After reading this chapter, you should be able to:
1. Define key terms and concepts in inductive logic, including strength and cogency.
2. Differentiate between strong inductive arguments and weak inductive arguments.
3. Identify general methods for strengthening inductive arguments.
4. Identify statistical syllogisms and describe how they can be strong or weak.
5. Evaluate the strength of inductive generalizations.
5Inductive Reasoning
Iakov Kalinin/iStock/Thinkstock
6. Differentiate between causal and correlational relationships and describe various
types of causes.
7. Use Mill’s methods to evaluate causal arguments.
8. Recognize arguments from authority and evaluate their quality.
9. Identify key features of arguments from analogy and use them to evaluate the strength
of such arguments.
When talking about logic, people often think about formal deductive reasoning. However, most of the
arguments we encounter in life are not deductive at all. They do not intend to establish the truth of the
conclusion beyond any possible doubt; they simply try to provide good evidence for the truth of their
conclusions. Arguments that intend to reason in this way are called inductive arguments. Inductive
arguments are not any worse than deductive ones. Often the best evidence available is not final or
conclusive but can still be very good.
For example, to infer that the sun will rise tomorrow because it has every day in the past is inductive
reasoning. The inference, however, is very strongly supported. Not all inductive arguments are as strong
as that one. This chapter will explore different types of inductive arguments and some principles we can
use to determine whether they are strong or weak. The chapter will also discuss some specific methods
that we can use to try to make good inferences about causation. The goal of this chapter is to enable you
to identify inductive arguments, evaluate their strength, and create strong inductive arguments about
important issues.
Age fotostock/SuperStock
Weather forecasters use inductive
reasoning when giving their
predictions. They have tools at their
disposal that provide support for their
arguments, but some arguments are
weaker than others.
5.1 Basic Concepts in Inductive Reasoning
Inductive is a technical term in logic: It has a precise definition, and that definition may be different from
the definition used in other fields or in everyday conversation. An inductive argument is one in which
the premises provide support for the conclusions but fall short of establishing complete certainty. If you
stop to think about arguments you have encountered recently, you will probably find that most of them
are inductive. We are seldom in a position to prove something absolutely, even when we have very good
reasons for believing it.
Take, for example, the following argument:
The odds of a given lottery ticket being the winning ticket are extremely low.
You just bought a lottery ticket.
Therefore, your lottery ticket is probably not the winning ticket.
If the odds of each ticket winning are 1 in millions, then this argument gives very good evidence for the
truth of its conclusion. However, the argument is not deductively valid. Even if its premises are true, its
conclusion is still not absolutely certain. This means that there is still a remote possibility that you
bought the winning ticket.
Chapter 3 discussed how an argument is valid if our premises guarantee the truth of the conclusion. In
the case of the lottery, even our best evidence cannot be used to make a valid argument for the
conclusion. The given reasons do not guarantee that you will not win; they just make it very likely that
you will not win.
This argument, however, helps us establish the likelihood of its conclusion. If it were not for this type of
reasoning, we might spend all our money on lottery tickets. We would also not be able to know whether
we should do such things as drive our car because we would not be able to reason about the likelihood
of getting into a crash on the way to the store. Therefore, this and other types of inductive reasoning are
essential in daily life. Consequently, it is important that we learn how to evaluate their strength.
Inductive Strength
Some inductive arguments can be better or worse than
others, depending on how well their premises increase the
likelihood of the truth of their conclusion. Some arguments
make their conclusions only a little more likely; other
arguments make their conclusions a lot more likely.
Arguments that greatly increase the likelihood of their
conclusions are called strong arguments; those that do not
substantially increase the likelihood are called weak
arguments.
Here is an example of an argument that could be considered
very strong:
A random fan from the crowd is going to race (in a
100 meter dash) against Usain Bolt.
Usain Bolt is the fastest sprinter of all time.
Oksana
Kostyushko/iStock/Thinkstock
Context plays an
important role in
inductive arguments.
What makes an
argument strong in one
context might not be
strong enough in
another. Would you be
more likely to play the
lottery if your chances
of winning were
supported at 99%?
Therefore, the fan is going to lose.
It is certainly possible that the fan could win—say, for example, if Usain Bolt breaks an ankle—but it
seems highly unlikely. This next argument, however, could be considered weak:
I just scratched off two lottery tickets and won $2 each time.
Therefore, I will win $2 on the next ticket, too.
The previous lottery tickets would have no bearing on the likelihood of winning on the next one. Now
this next argument’s strength might be somewhere in between:
The Bears have beaten the Lions the last four times they have played.
The Bears have a much better record than the Lions this season.
Therefore, the Bears will beat the Lions again tomorrow.
This sounds like good evidence, but upsets happen all the time in sports, so its strength is only moderate.
Considering the Context
It is important to realize that inductive strength and weakness are relative
terms. As such, they are like the terms tall and short. A person who is short
in one context may be tall in another. At 6’0”, professional basketball player
Allen Iverson was considered short in the National Basketball Association.
But outside of basketball, someone of his height might be considered tall.
Similarly, an argument that is strong in one context may be considered
weak in another. You would probably be reasonably happy if you could
reliably predict sports (or lottery) results at an accuracy rate of 70%, but
researchers in the social sciences typically aim for certainty upward of 90%.
In highenergy physics, the goal is a result that is supported at the level of 5
sigma—a probability of more than 99.99997%!
The same is true when it comes to legal arguments. A case tried in a civil
court needs to be shown to be true with a preponderance of evidence,
which is much less stringent than in a criminal case, in which the defendant
must be proved guilty beyond reasonable doubt. Therefore, whether the
argument is strong or weak is a matter of context.
Moreover, some subjects have the sort of evidence that allows for extremely
strong arguments, whereas others do not. A psychologist trying to predict
human behavior is unlikely to have the same strength of argument as an
astronomer trying to predict the path of a comet. These are important
things to keep in mind when it comes to evaluating inductive strength.
Strengthening Inductive Arguments
Regardless of the subject matter of an argument, we
generally want to create the strongest arguments we can. In
general, there are two ways of strengthening inductive
arguments. We can either claim more in the premises or
claim less in the conclusion.
Fuse/Thinkstock
The strength of an inductive argument
can change when new premises are
added. When evaluating or presenting
an inductive argument, gather as
many details as possible to have a
more complete understanding of the
strength of the argument.
Claiming more in the premises is straightforward in theory,
though it can be difficult in practice. The idea is simply to
increase the amount of evidence for the conclusion. Suppose
you are trying to convince a friend that she will enjoy a
particular movie. You have shown her that she has liked
other movies by the same director and that the movie is of
the general kind that she likes. How could you strengthen
your argument? You might show her that her favorite actors
are cast in the lead roles, or you might appeal to the reviews
of critics with which she often agrees. By adding these
additional pieces of evidence, you have increased the
strength of your argument that your friend will enjoy the
movie.
However, if your friend looks at all the evidence and still is
not sure, you might take the approach of weakening your conclusion. You might say something like,
“Please go with me; you may not actually like the movie, but at least you can be pretty sure you won’t
hate it.” The very same evidence you presented earlier—about the director, the genre, the actors, and so
on—actually makes a stronger argument for your new, less ambitious claim: that your friend won’t hate
the movie.
It might help to have another example of how each of the two approaches can help strengthen an
inductive argument. Take the following argument:
Every crow I have ever seen has been black.
Therefore, all crows are black.
This seems to provide decent evidence, provided that you have seen a lot of crows. Here is one way to
make the argument stronger:
Studies by ornithologists have examined thousands of crows in every continent in which they
live, and they have all been black.
Therefore, all crows are black.
This argument is much stronger because there is much more evidence for the truth of the conclusion
within the premise. Another way to strengthen the argument—if you do not have access to lots of
ornithological studies—would simply be to weaken the stated conclusion:
Every crow I have ever seen has been black.
Therefore, most crows are probably black.
This argument makes a weaker claim in the conclusion, but the argument is actually much stronger than
the original because the premises make this (weaker) conclusion much more likely to be true than the
original (stronger) conclusion.
By the same token, an inductive argument can also be made weaker either by subtracting evidence from
the premises or by making a stronger claim in the conclusion. (For another way to weaken or strengthen
inductive arguments, see A Closer Look: Using Premises to Affect Inductive Strength.)
A Closer Look: Using Premises to Affect Inductive Strength
Suppose we have a valid deductive argument. That means that, if its premises are all true, then its
conclusion must be true as well. Suppose we add a new premise. Is there any way that the
argument could become invalid? The answer is no, because if the premises of the new argument
are all true, then so are all the premises of the old argument. Therefore, the conclusion still must
be true.
This is a principle with a fancy name; it is called monotonicity: Adding a new premise can never
make a deductive argument go from valid to invalid. However, this principle does not hold for
inductive strength: It is possible to weaken an inductive argument by adding new premises.
The following argument, for example, might be strong:
99% of birds can fly.
Jonah is a bird.
Therefore, Jonah can fly.
This argument may be strong as it is, but what happens if we add a new premise, “Jonah is an
ostrich”? The addition of this new premise just made the argument’s strength plummet. We now
have a fairly weak argument! To use our new big word, this means that inductive reasoning is
nonmonotonic. The addition of new premises can either enhance or diminish an argument’s
inductive strength.
An interesting “game” is to see if you can continue to add premises that continue to flip the
inductive argument’s degree of strength back and forth. For example, we could make the
argument strong again by adding “Jonah is living in the museum of amazing flying ostriches.”
Then we could weaken it again with “Jonah is now retired.” It could be strengthened again with
“Jonah is still sometimes seen flying to the roof of the museum,” but it could be weakened again
with “He was seen flying by the neighbor child who has been known to lie.” The game
demonstrates the sensitivity of inductive arguments to new information.
Thus, when using inductive reasoning, we should always be open to learning more details that
could further serve to strengthen or weaken the case for the truth of the conclusion. Inductive
strength is a neverending process of gathering and evaluating new and relevant information. For
scientists and logicians, that is partly what makes induction so exciting!
Inductive Cogency
Notice that, like deductive validity, inductive strength has to do with the strength of the connection
between the premises and the conclusion, not with the truth of the premises. Therefore, an inductive
argument can be strong even with false premises. Here is an example of an inductively strong argument:
Every lizard ever discovered is purple.
Therefore, most lizards are probably purple.
Of course, as with deductive reasoning, for an argument to give good evidence for the truth of the
conclusion, we also want the premises to actually be true. An inductive argument is called cogent if it is
strong and all of its premises are true. Whereas inductive strength is the counterpart of deductive
validity, cogency is the inductive counterpart of deductive soundness.
5.2 Statistical Arguments: Statistical Syllogisms
The remainder of this chapter will go over some examples of the different types of inductive arguments:
statistical arguments, causal arguments, arguments from authority, and arguments from analogy. You
will likely find that you have already encountered many of these various types in your daily life.
Statistical arguments, for example, should be quite familiar. From politics, to sports, to science and
health, many of the arguments we encounter are based on statistics, drawing conclusions from
percentages and other data.
In early 2013 American actress Angelina Jolie elected to have a preventive double mastectomy. This
surgery is painful and costly, and the removal of both breasts is deeply disturbing for many women. We
might have expected Jolie to avoid the surgery until it was absolutely necessary. Instead, she had the
surgery before there was any evidence of the cancer that normally prompts a mastectomy. Why did she
do this?
Jolie explained some of her reasoning in an opinion piece in the New York Times.
I carry a “faulty” gene, BRCA1, which sharply increases my risk of developing breast cancer and
ovarian cancer.
My doctors estimated that I had an 87 percent risk of breast cancer and a 50 percent risk of
ovarian cancer, although the risk is different in the case of each woman. (Jolie, 2013, para. 2–3)
As you can see, Jolie’s decision was based on probabilities and statistics. If these types of reasoning can
have such profound effects in our lives, it is essential that we have a good grasp on how they work and
how they might fail. In this section, we will be looking at the basic structure of some simple statistical
arguments and some of the things to pay attention to as we use these arguments in our lives.
One of the main types of statistical arguments we will discuss is the statistical syllogism. Let us start
with a basic example. If you are not a cat fancier, you may not know that almost all calico cats are
female—to be more precise, about 99.97% of calico cats are female (Becker, 2013). Suppose you are
introduced to a calico cat named Puzzle. If you had to guess, would you say that Puzzle is female or male?
How confident are you in your guess?
Since you do not have any other information except that 99.97% of calico cats are female and Puzzle is a
calico cat, it should seem far more likely to you that Puzzle is female. This is a statistical syllogism: You
are using a general statistic about calico cats to make an argument for a specific case. In its simplest
form, the argument would look like this:
99.97% of calico cats are female.
Puzzle is a calico cat.
Therefore, Puzzle is female.
Clearly, this argument is not deductively valid, but inductively it seems quite strong. Given that male
calico cats are extremely rare, you can be reasonably confident that Puzzle is female. In this case we can
actually put a number to how confident you can be: 99.97% confident.
Of course, you might be mistaken. After all, male calico cats do exist; this is what makes the argument
inductive rather than deductive. However, statistical syllogisms like this one can establish a high degree
of certainty about the truth of the conclusion.
Form
If we consider the calico cat example, we can see that the general form for a statistical syllogism looks
like this:
X% of S are P.
i is an S.
Therefore, i is (probably) a P.
There are also statistical syllogisms that conclude that the individual i does not have the property P.
Take the following example:
Only 1% of college males are on the football team.
Mike is a college male.
Therefore, Mike is probably not on the football team.
This type of statistical syllogism has the following form:
X% of S are P.
i is an S.
Therefore, i is (probably) not a P.
In this case, for the argument to be strong, we want X to be a low percentage.
Note that statistical syllogisms are similar to two kinds of categorical syllogisms presented in Chapter 3
(see Table 5.1). We see from the table that statistical syllogisms become valid categorical syllogisms
when the percentage, X, becomes 100% or 0%.
Table 5.1: Statistical syllogism versus categorical syllogism
Statistical syllogism Similar valid categorical syllogism
Example
99.97% of calico cats are female.
Puzzle is calico.
Therefore, Puzzle is female.
All calico cats are female.
Puzzle is calico.
Therefore, Puzzle is female.
Form
X% of S are P.
i is an S.
Therefore, i is (probably) P.
All M are P.
S is M.
Therefore, S is P.
Example
1% of college males are on the football team.
Mike is a college male.
Therefore, Mike is not on the football team.
No college males are on the football team.
Mike is a college male.
Therefore, Mike is not on the football team.
Form
X% of S are P.
i is an S.
Therefore, i is P.
X% of S are P.
i is an S.
Therefore, i is not P.
When identifying a statistical syllogism, it is important to keep the specific form in mind, since there are
other kinds of statistical arguments that are not statistical syllogisms. Consider the following example:
85% of community college students are younger than 40.
John is teaching a community college course.
Therefore, about 85% of the students in John’s class are under 40.
This argument is not a statistical syllogism because it does not fit the form. If we make i “John” then the
conclusion states that John, the teacher, is probably under 40, but that is not the conclusion of the
original argument. If we make i “the students in John’s class,” then we get the conclusion that it is 85%
likely that the students in John’s class are under 40. Does this mean that all of them or that some of them
are? Either way, it does not seem to be the same as the original conclusion, since that conclusion has to
do with the percentage of students under 40 in his class. Though this argument has the same “feel” as a
statistical syllogism, it is not one because it does not have the same form as a statistical syllogism.
Weak Statistical Syllogisms
There are at least two ways in which a statistical syllogism might not be strong. One way is if the
percentage is not high enough (or low enough in the second type). If an argument simply includes the
premise that most of S are P, that means only that more than half of S are P. A probability of only 51%
does not make for a strong inductive argument.
Another way that statistical syllogisms can be weak is if the individual in question is more (or less) likely
to have the relevant characteristic P than the average S. For example, take the reasoning:
99% of birds do not talk.
My pet parrot is a bird.
Therefore, my pet parrot cannot talk.
The premises of this argument may well be true, and the percentage is high, but the argument may be
weak. Do you see why? The reason is that a pet parrot has a much higher likelihood of being able to talk
than the average bird. We have to be very careful when coming to final conclusions about inductive
reasoning until we consider all of the relevant information.
5.3 Statistical Arguments: Inductive Generalizations
In the example about Puzzle, the calico cat, the first premise said that 99.97% of calico cats are female.
How did someone come up with that figure? Clearly, she or he did not go out and look at every calico cat.
Instead, he or she likely looked at a bunch of calicos, figured out what percentage of those cats were
female, and then reasoned that the percentage of females would have been the same if they had looked
at all calico cats. In this sort of reasoning, the group of calico cats that were actually examined is called
the sample, and all the calico cats taken as a group are called the population. An inductive
generalization is an argument in which we reason from data about a sample population to a claim
about a large population that includes the sample. Its general form looks like this:
X% of observed Fs are Gs.
Therefore, X% of all Fs are Gs.
In the case of the calico cats, the argument looks like this:
99.97% of calico cats in the sample were female.
Therefore, 99.97% of all calico cats are female.
Whether the argument is strong or weak depends crucially on whether the sample population is
representative of the whole population. We say that a sample is representative of a population when the
sample and the population both have the same distribution of the trait we are interested in—when the
sample “looks like” the population for our purposes. In the case of the cats, the strength of the argument
depends on whether our sample group of calico cats had about the same proportion of females as the
entire population of all calico cats.
There is a lot of math and research design—which you might learn about if you take a course in applied
statistics or in quantitative research design—that goes into determining the likelihood that a sample is
representative. However, even with the best math and design, all we can infer is that a sample is
extremely likely to be representative; we can never be absolutely certain it is without checking the
entire population. However, if we are careful enough, our arguments can still be very strong, even if they
do not produce absolute certainty. This section will examine how researchers try to ensure the sample
population is representative of the whole population and how researchers assess how confident they
can be in their results.
Representativeness
The main way that researchers try to ensure that the sample population is representative of the whole
population is to make sure that the sample population is random and sufficiently large. Researchers also
consider a measure called the margin of error to determine how similar the sample population is to the
whole population.
Randomness
Suppose you want to know how many marshmallow treats
are in a box of your favorite breakfast cereal. You do not
have time to count the whole box, so you pour out one cup.
You can count the number of marshmallows in your cup and
then reason that the box should have the same proportion
5xinc/iStock/Thinkstock
To ensure a sample is representative,
participants should be randomly
selected from the larger population.
Careful consideration is required to
ensure selections truly represent the
larger population.
One must be careful when making inductive generalizations
based on statistical data. Consider the examples in this video.
Raw numbers can sound more alarming than percentages.
Likewise, rate statistics can be misleading.
Making Inferences From Statistics
of marshmallows as the cup. You found 15 marshmallows in
the cup, and the box holds eight cups of cereal, so you figure
that there should be about 120 marshmallows in the box.
Your argument looks something like this:
A onecup sample of cereal contains 15
marshmallows.
The box holds eight cups of cereal.
Therefore, the box contains 120 marshmallows.
What entitles you to claim that the sample is
representative? Is there any way that the sample may not
represent the percentage of marshmallows in the whole
box? One potential problem is that marshmallows tend to be
lighter than the cereal pieces. As a result, they tend to rise to the top of the box as the cereal pieces settle
toward the bottom of the box over time. If you just scoop out a cup of cereal from the top, then, your
sample may not be representative of the whole box and may have too many marshmallows.
One way to solve this problem might be to shake the box. Vigorously shaking the box would probably
distribute the marshmallows fairly evenly. After a good shake, a particular piece of marshmallow or
cereal might equally end up anywhere in the box, so the ones that make it into your sample will be
largely random. In this case the argument may be fairly strong.
In a random sample, every member of the population has an equal chance of being included.
Understanding how randomness works to ensure representativeness is a bit tricky, but another example
should help clear it up.
Almost all students at my high school have laptops.
Therefore, almost all high school students in the United States have laptops.
This reasoning might seem pretty strong, especially if you go to a large high school. However, is there a
way that the sample population (the students at the high school) may not be truly random? Perhaps if
the high school is in a relatively wealthy area, then the students will be more likely to have laptops than
random American high schoolers. If the sample population is not truly random but has a greater or
lesser tendency to have the relevant characteristic than a random member of the whole population, this
is known as a biased sample. Biased samples will be discussed further in Chapter 7, but note that they
often help reinforce people’s biased viewpoints (see Everyday Logic: Why You Might Be Wrong).
The principle of randomness applies
to other types of statistical arguments
as well. Consider the argument about
John’s community college class. The
argument, again, goes as follows:
85% of community college
students are younger than
40.
John is teaching a
community college course.
Making Inferences From Statistics
From Title: Evidence in Argument: Critical Thinking
(https://fod.infobase.com/PortalPlaylists.aspx?wID=100753&xtid=49816)
Critical Thinking Questions
1. The characteristics of the sample is an important
consideration when drawing inferences from
statistics. Before reading on, what qualities do you
think an ideal sample possesses?
2. How can one ensure that one is making proper
inferences from evidence?
3. What is the danger of expressing things using rates?
What example is given that demonstrates this
danger?
Therefore, about 85% of the
students in John’s class are
under 40.
Since 85% of community college
students are younger than 40, we
would expect a sufficiently large
random sample of community college
students to have about the same
percentage. There are several ways,
however, that John’s class may not be
a random sample. Before going on to
the next paragraph, stop and see how
many ways you can think of on your
own.
So how is John’s class not a random
sample? Notice first that the
argument references a course at a
single community college. The
average student age likely varies
from college to college, depending on
the average age of the nearby
population. Even within this one
community college, John’s class is not
random. What time is John’s class?
Night classes tend to attract a higher
percentage of older students than
daytime classes. Some subjects also
attract different age groups. Finally,
we should think about John himself.
His age and reputation may affect the kind of students who enroll in his classes.
In all these ways, and maybe others, John’s class is not a random sample: There is not an equal chance
that every community college student might be included. As a result, we do not really have good reason
to think that John’s class will be representative of the general population of community college students.
So we have little reason to expect it to be representative of the larger population. As a result, we cannot
use his class to reliably predict what the population will look like, nor can we use the population to
reliably predict what John’s class will look like.
Everyday Logic: Why You Might Be Wrong
People are often very confident about their views, even when it comes
to very controversial issues that may have just as many people on the
other side. There are probably several reasons for this, but one of
them is due to the use of biased sampling. Consider whether you think
Jakubzak/iStock/Thinkstock
Confirmation bias, or
the tendency to seek
out support for our
beliefs, can be seen in
the friends we choose,
books we read, and
news sources we
select.
your views about the world are shared by many people or by only a
few. It is not uncommon for people to think that their views are more
widespread than they actually are. Why is that?
Think about how you form your opinion about how much of the nation
or world agrees with your view. You probably spend time talking with
your friends about these views and notice how many of your friends
agree or disagree with you. You may watch television shows or read
news articles that agree or disagree with you. If most of the sources
you interact with agree with your view, you might conclude that most
people agree with you.
However, this would be a mistake. Most of us tend to interact more with people and information
sources with which we agree, rather than those with which we disagree. Our circle of friends
tends to be concentrated near us both geographically and ideologically. We share similar
concerns, interests, and views; that is part of what makes us friends. As with choosing friends, we
also tend to select information sources that confirm our beliefs. This is a wellknown
psychological tendency known as confirmation bias (this will be discussed further in Chapter 8).
We seem to reason as follows:
A large percentage of my friends and news sources agree with my view.
Therefore, a large percentage of all people and sources agree with my view.
We have seen that this reasoning is based on a biased sample. If you take your friends and
information sources as a sample, they are not likely to be representative of the larger population
of the nation or world. This is because rather than being a random sample, they have been
selected, in part, because they hold views similar to yours. A good critical thinker takes sampling
bias into account when thinking about controversial issues.
Sample Size
Even a perfectly random sample may not be representative, due to bad luck. If you flip a coin 10 times,
for example, there is a decent chance that it will come up heads 8 of the 10 times. However, the more
times you flip the coin, the more likely it is that the percentage of heads will approach 50%.
The smaller the sample, the more likely it is to be nonrepresentative. This variable is known as the
sample size. Suppose a teacher wants to know the average height of students in his school. He randomly
picks one student and measures her height. You should see that this is not a big enough sample. By
measuring only one student, there is a decent chance that the teacher may have randomly picked
someone extremely tall or extremely short. Generalizing on an overly small sample would be making a
hasty generalization, an error in reasoning that will be discussed in greater detail in Chapter 7. If the
teacher chooses a sample of two students, it is less likely that they will both be tall or both be short. The
more students the teacher chooses for his sample, the less likely it is that the average height of the
sample will be much different than the average height of all students. Assuming that the selection
process is unbiased, therefore, the larger the sample population is, the more likely it is that the sample
will be representative of the whole population (see A Closer Look: How Large Must a Sample Be?).
A Closer Look: How Large Must a Sample Be?
In general, the larger a sample is, the more likely it is to be representative of the population from
which it is drawn. However, even relatively small samples can lead to powerful conclusions if
they have been carefully drawn to be random and to be representative of the population. As of
this writing, the population of the United States is in the neighborhood of 317 million, yet Gallup,
one of the most respected polling organizations in the country, often publishes results based on a
sample of fewer than 3,000 people. Indeed, its typical sample size is around 1,000 (Gallup, 2010).
That is a sample size of less than 1 in every 300,000 people!
Gallup can do this because it goes to great lengths to make sure that its samples are randomly
drawn in a way that matches the makeup of the country’s population. If you want to know about
people’s political views, you have to be very careful because these views can vary based on a
person’s locale, income, race or ethnicity, gender, age, religion, and a host of other factors.
There is no single, simple rule for how large a sample should be. When samples are small or
incautiously collected, you should be suspicious of the claims made on their basis. Professional
research will generally provide clear descriptions of the samples used and a justification of why
they are adequate to support their conclusions. That is not a guarantee that the results are
correct, but they are bound to be much more reliable than conclusions reached on the basis of
small and poorly collected samples.
For example, sometimes politicians tour a state with the stated aim of finding out what the people
think. However, given that people who attend political rallies are usually those with similar
opinions as the speaker, it is unlikely that the set of people sampled will be both large enough and
random enough to provide a solid basis for a reliable conclusion. If politicians really want to find
out what people think, there are better ways of doing so.
Margin of Error
It is always possible that a sample will be wildly different than the population. But equally important is
the fact that it is quite likely that any sample will be slightly different than the population. Statisticians
know how to calculate just how big this difference is likely to be. You will see this reported in some
studies or polls as the margin of error. The margin of error can be used to determine the range of
values that are likely for the population.
For example, suppose that a poll finds that 52% of a sample prefers Ms. Frazier in an election. When you
read about the result of this poll, you will probably read that 52% of people prefer Ms. Frazier with a
margin of error of ±3% (plus or minus 3%). This means that although the real number probably is not
52%, it is very likely to be somewhere between 49% (3% lower than 52%) and 55% (3% higher than
52%). Since the real percentage may be as low as 49%, Ms. Frazier should not start picking out curtains
for her office just yet: She may actually be losing!
Confidence Level
We want large, random samples because we want to be confident that our sample is representative of
the population. The more confident we are that are sample is representative, the more confident we can
be in conclusions we draw from it. Nonetheless, even a small, poorly drawn sample can yield informative
results if we are cautious about our reasoning.
If you notice that many of your friends and acquaintances are out of work, you may conclude that
unemployment levels are up. Clearly, you have some evidence for your conclusion, but is it enough? The
answer to this question depends on how strong you take your argument to be. Remember that inductive
arguments vary from extremely weak to extremely strong. The strength of an argument is essentially the
level of confidence we should have in the conclusion based on the reasons presented. Consider the
following ways you might state your confidence that unemployment levels were up, based on noting
unemployment among your friends and acquaintances.
a. “I’m certain that unemployment is up.”
b. “I’m reasonably sure that unemployment is up.”
c. “It’s more likely than not that unemployment is up.”
d. “Unemployment might be up.”
Clearly, A is too strong. Your acquaintances just are not likely to represent the population enough for
you to be certain that unemployment is up. On the other hand, D is weak enough that it really does not
need much evidence to support it. B and C will depend on how wide and varied your circle of
acquaintances is and on how much unemployment you see among them. If you know a lot of people and
your acquaintances are quite varied in terms of profession, income, age, race, gender, and so on, then
you can have more confidence in your conclusion than if you had only a small circle of acquaintances and
they tended to all be like each other in these ways. B also depends on just what you mean by “reasonably
sure.” Does that mean 60% sure? 75%? 85%?
Most reputable studies will include a “confidence level” that indicates how confident one can be that
their conclusions are supported by the reasons they give. The degree of confidence can vary quite a bit,
so it is worth paying attention to. In most social sciences, researchers aim to reach a 95% or 99%
confidence level. A confidence level of 95% means that if we did the same study 100 times, then in 95 of
those tests the results would fall within the margin of error. As noted earlier, the field of physics
requires a confidence level of about 99.99997%, much higher than is typically required or attained in
the social sciences. On the other end, sometimes a confidence level of just over 50% is enough if you are
only interested in knowing whether something is more likely than not.
Applying This Knowledge
Now that we have learned something about statistical arguments, what can we say about Angelina Jolie’s
argument, presented at the beginning of the prior section? First, notice that it has the form of a statistical
syllogism. We can put it this way, written as if from her perspective:
87% of women with certain genetic and other factors develop breast cancer.
I am a woman with those genetic and other factors.
Therefore, I have an 87% risk of getting breast cancer.
We can see that the argument fits the form correctly. While not deductive, the argument is inductively
strong. Unless we have reason to believe that she is more or less likely than the average person with
those factors to develop breast cancer, if these premises are true then they give strong evidence for the
truth of the conclusion. However, what about the first premise? Should we believe it?
In evaluating the first premise, we need to consider the evidence for it. Were the samples of women
studied sufficiently random and large that we can be confident they were representative of the
population of all women? With what level of confidence are the results established? If the samples were
small or not randomized, then we may have less confidence in them. Jolie’s doctors said that Jolie had an
87% chance of developing breast cancer, but there’s a big difference between being 60% confident that
she has this level of risk and being 99% certain that she does. To know how confident we should be, we
would need to look at the background studies that establish that 87% of women with those factors
develop breast cancer. Anyone making such an important decision would be well advised to look at
these issues in the research before acting.
Practice Problems 5.1
Which of the following attributes might negatively influence the data drawn from the
following samples? Click here
(https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems5.1.pdf)
to check your answers.
1. A teacher surveys the gifted students in the district about the curriculum that should be
adopted at the high school.
a. sample size
b. representativeness of the sample
c. a and b
d. There is no negative influence in this case.
2. A researcher for Apple analyzes a large group of tribal people in the Amazon to
determine which new apps she should create in 2014.
a. sample size
b. representativeness of the sample
c. a and b
d. There is no negative influence in this case.
3. A researcher on a college campus interviews 10 students after a yoga class about their
drug use habits and determines that 80% of the student population probably smokes
marijuana.
a. sample size
b. representativeness of the sample
c. a and b
d. There is no negative influence in this case.
iStock/Thinkstock
Sufficient conditions
are present in
classroom grading
systems. If you need a
total of 850 points to
receive an A, the
sufficient condition to
receive an A is earning
850 points.
5.4 Causal Relationships: The Meaning of Cause
It is difficult to say exactly what we mean when we say that one thing causes another. Think about
turning on the lights in your room. What is the cause of the lights turning on? Is it the flipping of the
switch? The electricity in the wires? The fact that the bulb is not broken? Your initial desire for the lights
to be on? There are many things we could identify as a plausible cause of the lights turning on. However,
for practical purposes, we generally look for the set of conditions without which the event in question
would not have occurred and with which it will occur. In other words, logicians aim to be more specific
about causal relationships by discussing them in terms of sufficient and necessary conditions. Recall that
we used these terms in Chapter 4 when discussing propositional logic. Here we will discuss how these
terms can help us understand causal relationships.
Sufficient Conditions
According to British philosopher David Hume, the notion of cause is based
on nothing more than a “constant conjunction” that holds between
events—the two events always occur together (Morris & Brown, 2014). We
notice that events of kind A are always followed by events of kind B, and we
say “A causes B.” Thus, to claim a causal relationship between events of type
A and B might be to say: Whenever A occurs, B will occur.
Logicians have a fancy phrase for this relationship: We say that A is a
sufficient condition for B. A factor is a sufficient condition for the
occurrence of an event if whenever the factor occurs, the event also occurs:
Whenever A occurs, B occurs as well. Or in other words:
If A occurs, then B occurs.
For example, having a billion dollars is a sufficient condition for being rich;
being hospitalized is a sufficient condition for being excused from jury duty;
having a ticket is a sufficient condition for being able to be admitted to the
concert.
Often several factors are jointly required to create sufficient conditions. For
example, each state has a set of jointly sufficient conditions for being able to
vote, including being over 18, being registered to vote, and not having been
convicted of a felony, among other possible qualifications.
Here is an example of how to think about sufficient conditions when thinking about reallife causation.
We know room lights do not go on just because you flip the switch. The points of the switch must come
into contact with a power source, electricity must be present, a working lightbulb has to be properly
secured in the socket, the socket has to be properly connected, and so forth. If any one of the conditions
is not satisfied, the light will not come on. Strictly speaking, then, the whole set of conditions constitutes
the sufficient condition for the event.
We often choose one factor from a set of factors and call it the cause of an event. The one we call the
cause is the one with which we are most concerned for some reason or other; often it is the one that
represents a change from the normal state of things. A working car is the normal state of affairs; a hole in
Stockbyte/Thinkstock
Although water is a necessary
condition for life, it is not a sufficient
condition for life because humans also
need oxygen and food.
the radiator tube is the change to that state of affairs that results in the overheated engine. Similarly, the
electricity and lightbulb are part of the normal state of things; what changed most recently to make the
light turn on was the flipping of the switch.
Necessary Conditions
A factor is a necessary condition for an event if the event would not occur in the absence of the factor.
Without the necessary condition, the effect will not occur. A is a necessary condition for B if the
following statement is always true:
If A is not present, then neither is B.
This statement happens to be equivalent to the statement that if B is present, then A is present. Thus, a
handy way to understand the difference between necessary and sufficient conditions is as follows:
“A is sufficient for B” means that if A occurs, then B occurs.
“A is necessary for B” means that if B occurs, then A occurs.
Let us take a look at a real example. Poliomyelitis, or polio,
is a disease caused by a specific virus. In only a small
minority of those with poliovirus does the virus infect the
central nervous system and lead to the terrible condition
known as paralytic polio. In the large majority of cases,
however, the virus goes undetected and does not result in
paralysis. Thus, infection with poliovirus is not a sufficient
condition for getting paralytic polio. However, because one
must have the virus to have that condition, being infected
with poliovirus is a necessary condition for getting paralytic
polio (Mayo Clinic, 2014).
On the other hand, being squashed by a steamroller is a
sufficient condition for death, but it is not a necessary
condition. Whenever someone has been squashed by a
steamroller, that person is quite dead. However, it is not the
case that anyone who is dead has been run over by a
steamroller.
If our purpose in looking for causes is to be able to produce an effect, it is reasonable to look for
sufficient conditions for that effect. If we can manipulate circumstances so that the sufficient condition is
present, the effect will also be present. If we are looking for causes in order to prevent an effect, it is
reasonable to look for necessary conditions for that effect. If we prevent a necessary condition from
materializing, we can prevent the effect.
The eradication of yellow fever is a striking example. Research showed that being bitten by a certain
type of mosquito was a necessary condition for contracting yellow fever (though it was not a sufficient
condition, for some people who were bitten by these mosquitoes did not contract yellow fever).
Consequently, a campaign to destroy that particular species of mosquito through the widespread use of
insecticides virtually eliminated yellow fever in many parts of the world (World Health Organization,
2014).
Necessary and Sufficient Conditions
The most restrictive interpretation of a causal relationship consists of construing “cause” as a condition
both necessary and sufficient for the occurrence of an event. If factor A is necessary and sufficient for the
occurrence of event B, then whenever A occurs, B occurs, and whenever A does not occur, B does not
occur. In other words:
If A, then B, and if notA, then notB.
For example, to produce diamonds, certain very specific conditions must exist. Diamonds are produced if
and only if carbon is subjected to immense pressure and heat for a certain period of time. Diamonds do
not occur through any other process. If all of the conditions exist, then diamonds will result; diamonds
exist only when all of those conditions have been met. Therefore, carbon subjected to the right
combination of pressure, heat, and time constitutes both a necessary and sufficient condition for
diamond production.
This construction of cause is so restrictive that very few actual relationships in ordinary experience can
satisfy it. However, some scientists think that this is the kind of invariant relationship that scientific laws
must express. For instance, according to Newton’s law of gravitation, objects attract each other with a
force proportional to the inverse of the square of their distance. Therefore, if we know the force of
attraction between two bodies, we can calculate the distance between them (assuming we know their
masses). Conversely, if we know the distance between them, we can calculate the force of attraction.
Thus, having a certain degree of attraction between two bodies constitutes both a necessary and
sufficient condition for the distance between them. It happens frequently in math and science that the
values assigned to one factor determine the values assigned to another, and this relationship can be
understood in terms of necessary and sufficient conditions.
Other Types of Causes
The terms necessary condition and sufficient condition give us concrete and technical ways to describe
types of causes. However, in everyday life, the factor we mention as the cause of an event is rarely one
we consider sufficient or even necessary. We frequently select one factor from a set and say it is the
cause of the event. Our aims and interests, as well as our knowledge, affect that choice. Thus, practical,
moral, or legal considerations may influence our selection. There are three principal considerations that
may lead us to choose a single factor as “the cause,” although this is not an exhaustive listing.
Trigger cause. The trigger cause, or the factor that initiates an event, is often designated the cause of the
event. Usually, this is the factor that occurs last and completes a causal chain—the set of sufficient
conditions—producing the effect. Flipping the switch triggers the lights. All the other factors may be
present and as such constitute the standing conditions that allow the event to be triggered. The trigger
factor is sometimes referred to as the proximate cause since it is the factor nearest the final event (or
effect).
Unusual factor. Let us suppose that someone turns on a light and an explosion follows. Turning on the
light caused an explosion because the room was full of methane gas. Now being in a room is fairly
Hagen/Cartoonstock
Variables, such as buffalo and White
men, can be correlated in two
ways—directly and inversely. Which
type of correlation is being discussed
in this cartoon?
normal, turning on lights is fairly normal, having oxygen in a room is fairly normal, and having an
unsealed light switch is fairly normal. The only condition outside the norm is the presence of a large
quantity of explosive gas. Therefore, the presence of methane is referred to as the cause of the explosion.
What is unusual, what is outside the norm, is the cause. If we are concerned with fixing moral or legal
responsibility for an effect, we are likely to focus on the person who left the gas on, not the person who
turned on the lights.
Controllable factor. Sometimes we call attention to a controllable factor instrumental in producing the
event and point out that since the factor could have been controlled, so could the event. Thus, although
smoking is neither a sufficient nor a necessary condition for lung cancer, it is a controllable factor.
Therefore, over and above uncontrollable factors like heredity and chance, we are likely to single out
smoking as the cause. Similarly, drunk driving is neither a sufficient nor a necessary condition for getting
into a car accident, but it is a controllable factor, so we are likely to point to it as a cause.
Correlational Relationships
In both the case of smoking and drunk driving, neither were necessary nor sufficient conditions for the
subsequent event in question (lung cancer and car accidents). Instead, we would say that both are highly
correlated with the respective events. Two things can be said to be correlated, or in correlation, when
they occur together frequently. In other words, A is correlated with B, so B is more likely to occur if A
occurs, and vice versa. For example, having gray hair is correlated with age. The older someone is, the
more likely he or she is to have gray hair, and vice versa. Of course, not all people with gray hair are old,
and not all old people have gray hair, so age is neither a necessary nor a sufficient condition for gray
hair. However, the two are highly correlated because they have a strong tendency to go together.
Two things that vary in the same direction are said to be
directly correlated or to vary directly; the higher one’s age,
the more gray hair. Things that are correlated may also vary
in opposite directions; these are said to vary inversely. For
example, there is an inverse correlation between the size of
a car and its fuel economy. In general, the bigger a car is, the
lower its fuel economy is. If you want a car that gets high
miles per gallon, you should focus on cars that are smaller.
There are other factors to consider too, of course. A small
sports car may get lower fuel economy than a larger car
with less power. Correlation does not mean that the
relationship is perfect, only that variables tend to vary in a
certain way.
You may have heard the phrase “correlation does not imply
causation,” or something similar. Just because two things
happen together, it does not necessarily follow that one
causes the other. For example, there is a wellknown
correlation between shoe size and reading ability in
elementary children. Children with larger feet have a strong
tendency to read better than children with smaller feet. Of
course, no one supposes that a child’s shoe size has a direct
effect on his or her reading ability, or vice versa. Instead,
both of these things are related to a child’s age. Older children tend to have bigger feet than younger
children; they also tend to read better. Sometimes the connection between correlated things is simple, as
in the case of shoe size and reading, and sometimes it is more complicated.
Whenever you read that two things have been shown to be linked, you should pay attention to the
possibility that the correlation is spurious or possibly has another explanation. Consider, for example, a
study showing a strong correlation between the amount of fat in a country’s diet and the amount of
certain types of cancer in that country (such as K. K. Carroll’s 1975 study, as cited in Paulos, 1997). Such
a correlation may lead you to think that eating fat causes cancer, but this could potentially be a mistake.
Instead, we should consider whether there might be some other connection between the two.
It turns out that countries with high fat consumption also have high sugar consumption—perhaps sugar
is the culprit. Also, countries with high fat and sugar consumption tend to be wealthier; fat and sugar are
expensive compared to grain. Perhaps the correlation is the result of some other aspect of a wealthier
lifestyle, such as lower rates of physical exercise. (Note that wealth is a particularly common
confounding factor, or a factor that correlates with the dependent and independent variables being
studied, as it bestows a wide range of advantages and difficulties on those who have it.) Perhaps it is a
combination of factors, and perhaps it is the fat after all; however, we cannot simply conclude with
certainty from a correlation that one causes the other, not without further research.
Sometimes correlation between two things is simply random. If you search through enough data, you
may find two factors that are strongly correlated but that have nothing at all to do with each other. For
example, consider Figure 5.1. At first glance, you might think the two factors must be closely connected.
But then you notice that one of them is the divorce rate in Maine and the other is the per capita
consumption of margarine in the United States. Could it be that by eating less margarine you could help
save the marriages of people in Maine?
Figure 5.1: Are these two factors correlated?
Although it may seem like two factors are correlated, we sometimes have to look harder
to understand the relationship.
Source: www.tylervigen.com (http://www.tylervigen.com) .
On the other hand, although correlation does not imply causation, it does point to it. That is, when we
see a strong correlation, there is at least some reason to suspect a causal connection of some sort
between the two correlates. It may be that one of the correlates causes the other, a third thing causes
them both, there is some more complicated causal relation between them, or there is no connection at
all.
However, the possibility that the correlation is merely accidental becomes increasingly unlikely if the
sample size is large and the correlation is strong. In such cases we may have to be very thoughtful in
seeking and testing possible explanations of the correlation. The next section discusses ways that we
might find and narrow down potential factors involved in a causal relationship.
5.5 Causal Arguments: Mill’s Methods
Reasoning about causes is extremely important. If we can correctly identify what causes a particular
effect, then we have a much better chance of controlling or preventing the effect. Consider the search for
a cure for a disease. If we do not understand what causes a particular disease, then our chances of being
able to cure it are small. If we can identify the cause of the disease, we can be much more precise in
searching for a way to prevent the disease. On the other hand, if we think we know the cause when we
do not, then we are likely to look in the wrong direction for a cure.
A causal argument—an argument about causes and effects—is almost always an inductive argument.
This is because, although we can gather evidence about these relationships, we are almost never in a
position to prove them absolutely.
The following four experimental methods were formally stated in the 19th century by John Stuart Mill in
his book A System of Logic and so are often referred to as Mill’s methods. Mill’s methods express the
most basic underlying logic of many current methods for investigating causality. They provide a great
introduction to some of the basic concepts involved—but know that modern methods are much more
rigorous.
Used with caution, Mill’s methods can provide a guide for exploring causal connections, especially when
one is looking at specific cases against the background of established theory. It is important to
remember that although they can be useful, Mill’s methods are only the beginning of the study of
causation. By themselves, they are probably most useful as methods for identifying potential subjects for
further study using more robust methods that are beyond the scope of this book.
Method of Agreement
In 1976 an unknown illness affected numerous people in Philadelphia. Although it took some time to
fully identify the cause of the disease, a bacterium now called Legionella pneumophila, the first step in
the investigation was to find common features of those who became ill. Researchers were quick to note
that sufferers had all attended an American Legion convention at the BellevueStratford Hotel. As you
can guess, the focus of the investigation quickly narrowed to conditions at the hotel. Of course, the
convention and the hotel were not the actual cause of getting sick, but neither was it mere coincidence
that all of the ill had attended the convention. By finding the common elements shared by those who
became ill, investigators were able to quickly narrow their search for the cause. Ultimately, the
bacterium was located in a fountain in the hotel.
The method of agreement involves comparing situations in which the same kind of event occurs. If the
presence of a certain factor is the only respect in which the situations are the same (that is, they agree),
then this factor may be related to the cause of the event. We can represent this with something like
Table 5.2. The table indicates whether each of four factors was present in a specific case (A, B, or C) and,
in the last column, whether the effect manifested itself (in the earlier case of what is now known as
Legionnaires’ disease, the effect we would be interested in is whether infection occurred).
Table 5.2: Example of method of agreement
Case Factor 1 Factor 2 Factor 3 Factor 4 Effect
A No Yes Yes No Yes
Case Factor 1 Factor 2 Factor 3 Factor 4 Effect
B No No Yes Yes Yes
C Yes Yes Yes Yes Yes
The three cases all resulted in the same effect but differed in which factors were present—with the
exception of Factor 3, which was present in all three cases. We may then suspect that Factor 3 may be
causally related to the effect. Our notion of cause here is that of sufficient condition. The common factor
is sufficient to account for the effect.
In general, the method of agreement works best when we have a large group of cases that is as varied as
possible. A large group is much more likely to vary across many different factors than a small group.
Unfortunately, the world almost never presents us with two situations wholly unlike except for one
factor. We may have three or more situations that are greatly similar. For example, all of the afflicted in
the 1976 outbreak were members of the American Legion, all were adults, all were men, all lived in
Pennsylvania. Here is where we have to use common sense and what we already know. It is unlikely that
merely being a member of an organization is the cause of a disease. We expect diseases to be caused by
environmental factors: bacteria, viruses, contaminants, and so on. As a result, we can focus our search on
those similarities that seem most likely to be relevant to the cause. Of course, we may be wrong; that is a
hallmark of inductive reasoning generally, but by being as careful and as reasonable as we can, we can
often make great progress.
Method of Difference
The method of difference involves comparing a situation in which an event occurs with similar
situations in which it does not. If the presence of a certain factor is the only difference between the two
kinds of situations, it is likely to be causally related to the effect.
Suppose your mother comes to visit you and makes your favorite cake. Unfortunately, it just does not
turn out. You know she made it in the same way she always does. What could the problem be? Start by
looking at differences between how she made the cake at your house and how she makes it at hers.
Ultimately, the only difference you can find is that your mom lives in Tampa and you live in Denver.
Since that is the only difference, that difference is likely to be causally related to the effect. In fact,
Denver is both much higher and much drier than Tampa. Both of these factors make a difference in
baking cakes.
Let us suppose we are interested in two cases, A and B, in which A has the effect we are interested in
(the cake not turning out right) and B does not. This is outlined in Table 5.3. If we can find only one
factor that is different between the two cases—in this case, Factor 1—then that factor is likely to be
causally related to the effect. This does not tell us whether the factor directly causes the effect, but it
does suggest a causal link. Further investigation might reveal just exactly what the connection is.
Table 5.3: Example of method of difference
Case Factor 1 Factor 2 Factor 3 Factor 4 Effect
A Yes No No Yes Yes
B No No No Yes No
In this example, Factor 1 is the one factor that is different between the two cases. Perhaps the presence
of Factor 1 is related to why Case A had the effect but Case B did not. Here we are seeing Factor 1 as a
necessary condition for the effect.
The method of difference is employed frequently in clinical trials of experimental drugs. Researchers
carefully choose or construct two situations that resemble each other in as many respects as possible. If
a drug is employed in one but not the other, then they can ascribe to the drug any change in one
situation not matched by a change in the other. Note that the two sets must be as similar as possible,
since variation could introduce other possible causal links. The group in which change is expected is
often referred to as the experimental group, and the group in which change is not expected is often
referred to as the control group.
The method of difference may seem obvious and its results reliable. Yet even in a relatively simple
experimental setup like this one, we may easily find grounds for doubting that the causal claim has been
adequately established.
One important factor is that the two cases, A and B, have to be as similar as possible in all other respects
for the method of difference to be used effectively. If your 8yearold son made the cake without
supervision, there are likely to be a whole host of differences that could explain the failure. The same
principle applies to scientific studies. One thing that can subtly skew experimental results is
experimental bias. For example, if the experimenters know which people are receiving the experimental
drug, they might unintentionally treat them differently.
To prevent such possibilities, socalled blind experiments are often used. Those conducting the
experiment are kept in ignorance about which subjects are in the control group and which are in the
experimental group so that they do not even unintentionally treat the subjects differently.
Experimenters therefore, do not know whether they are injecting distilled water or the actual drug. In
this way the possibility of a systematic error is minimized.
We also have to keep in mind that our inquiry is guided by background beliefs that may be incorrect. No
two cases will ever be completely the same except for a single factor. Your mother made the cake on a
different day than she did at home, she used a different spoon, different people were present in the
house, and so on. We naturally focus on similarities and differences that we expect to be relevant.
However, we should always realize that reality may disagree with our expectations.
Causal inquiry is usually not a matter of conducting a single experiment. Often we cannot even control
for all relevant factors at the same time, and once an experiment is concluded, doubts about other
factors may arise. A series of experiments in which different factors are kept constant while others are
varied one by one is always preferable.
Joint Method of Agreement and Difference
The joint method of agreement and difference is, as the name suggests, a combination of the methods
of agreement and difference. It is the most powerful of Mill’s methods. The basic idea is to have two
groups of cases: One group shows the effect, and the other does not. The method of agreement is used
within each group, by seeing what they have in common, and the method of difference is used between
the two groups, by looking for the differences between the two. Table 5.4 shows how such a chart would
look, if we were comparing three different cases (1, 2, and 3) among two groups (A and B).
Table 5.4: Example of joint method of agreement and difference
Case/group Factor 1 Factor 2 Factor 3 Factor 4 Effect
1/A Yes No No Yes Yes
2/A No No Yes Yes Yes
3/A No Yes No Yes Yes
1/B No Yes Yes No No
2/B Yes Yes No No No
3/B Yes No Yes No No
As you can see, within each group the cases agree only on Factor 4 and the effect. But when you compare
the two groups, the only consistent differences between them are in Factor 4 and the effect. This result
suggests the possibility that Factor 4 may be causally related to the effect in question. In this method, we
are using the notion of a necessary and sufficient condition. The effect happens whenever Factor 4 is
present and never when it is absent.
The joint method is the basis for modern randomized controlled experiments. Suppose you want to see
if a new medicine is effective. You begin by recruiting a large group of volunteers. You then randomly
assign them to either receive the medicine or a placebo. The random assignment ensures that each
group is as varied as possible and that you are not unknowingly deciding whether to give someone the
medicine based on some common factor. If it turns out that everyone who gets the medicine improves
and everyone who gets the placebo stays the same or gets worse, then you can infer that the medicine is
probably effective.
In fact, advanced statistics allow us to make inferences from such studies even when there is not perfect
agreement on the presence or absence of the effect. So, in reading studies, you may note that the
discussion talks about the percentage of each group that shows or does not show the effect. Yet we may
still make good inferences about causation by using the method of concomitant variation.
Method of Concomitant Variation
The method of concomitant variation is simply the method of looking for correlation between two
things. As we noted in our discussion of correlation, this cannot be used to conclude conclusively that
one thing causes the other, but it is suggestive that there is perhaps some causal connection between the
two. Stronger evidence can be found by further scientific study.
You may have noticed that, in discussing causes, we are trying to explain a phenomenon. We observe
something that is interesting or important to us, and we seek to know why it happened. Therefore, the
study of Mill’s methods, as well as correlation and concomitant variation, can be seen as part of a
broader type of reasoning known as inference to the best explanation, the effort to find the best or most
accurate explanation of our observations. Because this type of reasoning is sometimes classified as a
separate type of reasoning (sometimes called abductive reasoning), it will be covered in Chapter 6.
In summary, Mill’s methods provide a framework for exploring causal relationships. It is important to
remember that although they can be useful, they are only the beginning of this important field. By
themselves, they are probably most useful as methods for identifying potential subjects for further study
using more robust methods that are beyond the scope of this book.
Practice Problems 5.2
Identify which of Mill’s methods discussed in the chapter relates to the following
examples. Click here
(https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems5.2.pdf)
to check your answers.
1. After going to dinner, all the members of a family came down with vomiting. They all had
different entrées but shared a salad as an appetizer. The mother of the family determines
that it must have been the salad that caused the sickness.
a. method of agreement
b. method of difference
c. joint method
d. method of concomitant variation
2. A couple goes to dinner and shares an appetizer, entrée, and dessert. Only one of the two
gets sick. She drank a glass of wine, and her husband drank a beer. She believes that the
wine was the cause of her sickness.
a. method of agreement
b. method of difference
c. joint method
d. method of concomitant variation
3. In a specific city, the number of people going to emergency rooms for asthma attacks
increases as the level of pollution increases in the summer. When the winter comes and
pollution goes down, the number of people with asthma attacks decreases.
a. method of agreement
b. method of difference
c. joint method
d. method of concomitant variation
4. In the past 15 years there has never been a safety accident in the warehouse. Each day
for the past 15 years Lorena has been conducting the morning safety inspections.
However, today Lorena missed work, and there was an accident.
a. method of agreement
b. method of difference
c. joint method
d. method of concomitant variation
5. Since we have hired Earl, productivity in the office has decreased by 20%.
a. method of agreement
b. method of difference
c. joint method
d. method of concomitant variation
6. In the past, lead was put into many paints. It was found that the number of infant
fatalities increased in relation to the amount of exposure these infants had to leadbased
paints that were used on their cribs.
a. method of agreement
b. method of difference
c. joint method
d. method of concomitant variation
7. It appears that the likelihood of catching the Zombie virus increases the more one is
around people who have already been turned into zombies.
a. method of agreement
b. method of difference
c. joint method
d. method of concomitant variation
8. In order to determine how a disease was spread in humans, researchers placed two
groups of people into two rooms. Both rooms were exactly alike. However, in one room
they placed someone who was infected with the disease. The researchers 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.
a. method of agreement
b. method of difference
c. joint method
d. method of concomitant variation
9. In a certain IQ test, students in a specific group performed at a much higher level than
those of the other groups. After analyzing the group, the researchers found that the high
performing students all smoked marijuana before the exam.
a. method of agreement
b. method of difference
c. joint method
d. method of concomitant variation
badahos/iStock/Thinkstock
The ability to think critically about an
authority’s argument will allow you to
determine reliable sources from
unreliable ones, which can be quite
helpful when writing research papers,
reading news articles, or taking advice
from someone.
5.6 Arguments From Authority
An argument from authority, also known as an appeal to authority, is an inductive argument in which
one infers that a claim is true because someone said so. The general reasoning looks like this:
Person A said that X is true.
Person A is an authority on the subject.
Therefore, X is true.
Whether this type of reasoning is strong depends on the issue discussed and the authority cited. If it is
the kind of issue that can be settled by an argument from authority and if the person is actually an
authority on the subject, then it can actually be a strong inductive argument.
Some people think that arguments from authority in general are fallacious. However, that is not
generally the case. To see why, try to imagine life without any appeals to authority. You could not believe
anyone’s statements, no matter how credible. You could not believe books; you could not believe
published journals, and so on. How would you do in college if you did not listen to your textbooks,
teachers, or any other sources of information?
Even in science class, you would have to do every
experiment on your own because you could not believe
published reports. In math, you could not trust the book or
teacher, so you would have to prove every theorem by
yourself. History class would be a complete waste of time
because, unless you had a time machine, there would be no
way to verify any claims about what happened in the past
without appeal to historical records, newspapers, journals,
and so forth. You would also have a hard time following
medical advice, so you might end up with serious health
problems. Finally, why would you go to school or work if
you could not trust the claim that you were going to get a
degree or a paycheck after all of your efforts?
Therefore, in order to learn from others and to succeed in
life, it is essential that we listen to appropriate authorities.
However, since many sources are unreliable, misleading, or
even downright deceptive, it is essential that we learn to
distinguish reliable sources of authority from unreliable
ones. Chapter 7 will discuss how to distinguish between
legitimate and fallacious appeals to authority.
Here are some examples of legitimate arguments from authority:
“The theory of relativity is true. I know because my physics professor and my physics textbook
teach that it is true.”
“Pine trees are not deciduous; it says so right here in this tree book.”
“The Giants won the pennant! I read it on ESPN.com.”
“Mike hates radishes. He told me so yesterday.”
All of these inferences seem pretty strong. For examples of arguments to authority that are not as strong,
or even downright fallacious, visit Chapter 7.
5.7 Arguments From Analogy
An argument from analogy is an inductive argument that draws conclusions based on the use of
analogy. An analogy is a comparison of two items. For example, many object to deficit spending (when
the country spends more money than it takes in) based on the reasoning that debt is bad for household
budgets. The person’s argument depends on an analogy that compares the national budget to a
household budget. The two items being compared may be referred to as analogs (or analogues,
depending on where you live) but are referred to technically as cases. Of the two analogs, one should be
well known, with a body of knowledge behind it, and so is referred to as the familiar case; the second
analog, about which much less is known, is called the unfamiliar case.
The basic structure of an argument from analogy is as follows:
B is similar to A.
A has feature F.
Therefore, B probably also has feature F.
Here, A is the familiar case and B is the unfamiliar case. We made an inference about thing B based on its
similarity to the more familiar A.
Analogical reasoning proceeds from this premise: Since the analogs are similar either in many ways or in
some very important ways, they are likely to be similar in other ways as well. If there are many
similarities, or if the similarities are significant, then the analogy can be strong. If the analogs are
different in many ways, or if the differences are important, then it is a weak analogy. Conclusions arrived
at through strong analogies are fairly reliable; conclusions reached through weak analogies are less
reliable and often fallacious (the fallacy is called false analogy). Therefore, when confronted with an
analogy (“A is like B”), the first question to be asked is this: Are the two analogs very similar in ways that
are relevant to the current discussion, or are they different in relevant ways?
Analogies occur in both arguments and explanations. As we saw in Chapter 2, arguments and
explanations are not the same thing. The key difference is whether the analogy is being used to give
evidence that a certain claim is true—an argument—or to give a better understanding of how or why a
claim is true—an explanation. In explanations, the analogy aims to provide deeper understanding of the
issue. In arguments, the analogy aims to provide reasons for believing a conclusion. The next section
provides some tips for evaluating the strength of such arguments.
Evaluating Arguments From Analogy
Again, the strength of the argument depends on just how much A is like B, and the degree to which the
similarities between A and B are relevant to F. Let us consider an example. Suppose that you are in the
market for a new car, and your primary concern is that the car be reliable. You have the opportunity to
buy a Nissan. One of your friends owns a Nissan. Since you want to buy a reliable car, you ask a friend
how reliable her car is. In this case you are depending on an analogy between your friend’s car and the
car you are looking to buy. Suppose your friend says that her car is reliable. You can now make the
following argument:
The car I’m looking at is like my friend’s car.
My friend’s car is reliable.
Therefore, the car I’m looking at will be reliable.
How strong is this argument? That depends on how similar the two cases are. If the only thing the cars
have in common is the brand, then the argument is fairly weak. On the other hand, if the cars are the
same model and year, with all the same options and a similar driving history, then the argument is
stronger. We can list the similarities in a chart (see Table 5.5). Initially, the analogy is based only on the
make of the car. We will call the car you are looking at A and your friend’s car B.
Table 5.5: Comparing cars by make
Car Make Reliable?
B Nissan Yes
A Nissan ?
The make of a car is relevant to its reliability, but the argument is weak because that is the only
similarity we know about. To strengthen the argument, we can note further relevant similarities. For
example, if you find out that your friend’s car is the same model and year, then the argument is
strengthened (see Table 5.6).
Table 5.6: Comparing cars by make, model, and year
Car Make Model Year Reliable?
B Nissan Sentra 2000 Yes
A Nissan Sentra 2000 ?
The more relevant similarities there are between the two cars, the stronger the argument. However, the
word relevant is critical here. Finding out that the two cars have the same engine and similar driving
histories is relevant and will strengthen the argument. Finding out that both cars are the same color and
have license plates beginning with the same letter will not strengthen the argument. Thus, arguments
from analogy typically require that we already have some idea of which features are relevant to the
feature we are interested in. If you really had no idea at all what made some cars reliable and others not
reliable, then you would have no way to evaluate the strength of an argument from analogy about
reliability.
Another way we can strengthen an argument from analogy is by increasing the number of analogs. If you
have two more friends who also own a car of the same make, model, and year, and if those cars are
reliable, then you can be more confident that your new car will be reliable. Table 5.7 shows what the
chart would look like. The more analogs you have that match the car you are looking at, the more
confidence you can have that the car you’re looking at will be reliable.
Table 5.7: Comparing multiple analogs
Car Make Model Year Reliable?
B Nissan Sentra 2000 Yes
C Nissan Sentra 2000 Yes
D Nissan Sentra 2000 Yes
A Nissan Sentra 2000 ?
In general, then, analogical arguments are stronger when they have more analogous cases with more
relevant similarities. They are weaker when there are significant differences between the familiar cases
and the unfamiliar case. If you discover a significant difference between the car you are looking at and
the analogs, that reduces the strength of the argument. If, for example, you find that all your friends’ cars
have manual transmission, whereas the one you are looking at has an automatic transmission, this
counts against the strength of the analogy and hence against the strength of the argument.
Another way that an argument from analogy can be weakened is if there are cases that are similar but do
not have the feature in question. Suppose you find a fourth friend who has the same model and year of
car but whose car has been unreliable. As a result, you should have less confidence that the car you are
looking at is reliable.
Here are a couple more examples, with questions about how to gauge the strength.
“Except for size, chickens and turkeys are very similar birds. Therefore, if a food is good for
chickens, it is probably good for turkeys.”
Relevant questions include how similar chickens and turkeys are, whether there are significant
differences, and whether the difference in size is enough to allow turkeys to eat things that would be too
big for chickens.
“Seattle’s climate is similar, in many ways to the United Kingdom’s. Therefore, this plant is
likely to grow well in Seattle, because it grows well in the United Kingdom.”
Just how similar is the climate between the two places? Is the total about of rain about the same? How
about the total amount of sun? Are the low and high temperatures comparable? Are there soil
differences that would matter?
“I am sure that my favorite team will win the bowl game next week; they have won every game
so far this season.”
This example might seem strong at first, but it hides a very relevant difference: In a bowl game, college
football teams are usually matched up with an opponent of approximately equal strength. It is therefore
likely that the team being played will be much better than the other teams played so far this season. This
difference weakens the analogy in a relevant way, so the argument is much weaker than it may at first
appear. It is essential when studying the strength of analogical arguments to be thorough in our search
for relevant similarities and differences.
Analogies in Moral Reasoning
Analogical reasoning is often used in moral reasoning and moral arguments. Examples of analogical
reasoning are found in ethical or legal debates over contentious or controversial issues such as abortion,
gun control, and medical practices of all sorts (including vaccinations and transplants). Legal arguments
are often based on finding precedents—analogous cases that have already been decided. Recent
arguments presented in the debate over gun control have drawn conclusions based on analogies that
compare the United States with other countries, including Switzerland and Japan. Whether these and
similar arguments are strong enough to establish their conclusions depends on just how similar the
cases are and the degree and number of dissimilarities and contrary cases. Being aware of similar cases
Jupiterimages/BananaStock/Thinkstock
Retailers such as bookstores
commonly use arguments from
analogy when they suggest purchases
that have already occurred or that are occurring in other areas can vastly improve one’s wisdom about
how best to address the topic at hand.
The importance of analogies in moral reasoning is sometimes captured in the principle of equal
treatment—that if two things are analogous in all morally relevant respects, then what is right (or
wrong) to do in one case will be right (or wrong) to do in the other case as well. For example, if it is right
for a teacher to fail a student for missing the final exam, then another student who does the same thing
should also be failed. Whether the teacher happens to like one student more than the other should not
make a difference, because that is not a morally relevant difference when it comes to grading.
The reasoning could look as follows:
Things that are similar in all morally relevant respects should be treated the same.
Student A was failed for missing the final exam.
Student B also missed the final exam.
Therefore, student B should be failed as well.
It follows from the principle of equal treatment that if two things should be treated differently, then
there must be a morally relevant difference between them to justify this different treatment. An example
of the application of this principle might be in the interrogation of prisoners of war. If one country wants
to subject prisoners of war to certain kinds of harsh treatments but objects to its own prisoners being
treated the same way by other countries, then there need to be relevant differences between the
situations that justify the different treatment. Otherwise, the country is open to the charge of moral
inconsistency.
This principle, or something like it, comes up in many other types of moral debates, such as about
abortion and animal ethics. Animal rights advocates, for example, say that if we object to people harming
cats and dogs, then we are morally inconsistent to accept to the same treatment of cows, pigs, and
chickens. One then has to address the question of whether there are differences in the beings or in their
use for food that justify the differences in moral consideration we give to each.
Other Uses of Analogies
Analogies are the basis for parables, allegories, and forms of
writing that try to give a moral. The phrase “The moral of
the story is . . .” may be featured at the end of such stories, or
the author may simply imply that there is a lesson to be
learned from the story. Aesop’s Fables are one wellknown
example of analogy used in writing. Consider the fable of the
ant and the grasshopper, which compares the hardworking,
industrious ant with the footloose and fancyfree
grasshopper. The ant gathers and stores food all summer to
prepare for winter; the grasshopper fiddles around and
plays all summer, giving no thought for tomorrow. When
winter comes, the ant lives warm and comfortable while the
grasshopper starves, freezes, and dies. The fable argues that
we should be like the ant if we want to survive harsh times.
The ant and grasshopper are analogs for industrious people
and lazy people. How strong is the argument? Clearly, ants
based on their similarity to other
items.
and grasshoppers are quite different from people. Are the
differences relevant to the conclusion? What are the
relevant similarities? These are the questions that must be
addressed to get an idea of whether the argument is strong or weak.
Practice Problems 5.3
Determine whether the following arguments are inductive or deductive. Click here
(https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems5.3.pdf)
to check your answers.
1. All voters are residents of California. But some residents of California are Republican.
Therefore, some voters are Republican.
a. deductive
b. inductive
2. All doctors are people who are committed to enhancing the health of their patients. No
people who purposely harm others can consider themselves to be doctors. Therefore,
some people who harm others do not enhance the health of their patients.
a. deductive
b. inductive
3. Guns are necessary. Guns protect people. They give people confidence that they can
defend themselves. Guns also ensure that the government will not be able to take over its
citizenry.
a. deductive
b. inductive
4. Every time I turn on the radio, all I hear is vulgar language about sex, violence, and drugs.
Whether it’s rock and roll or rap, it’s all the same. The trend toward vulgarity has to
change. If it doesn’t, younger children will begin speaking in these ways and this will
spoil their innocence.
a. deductive
b. inductive
5. Letting your kids play around on the Internet all day is like dropping them off in
downtown Chicago to spend the day by themselves. They will find something that gets
them into trouble.
a. deductive
b. inductive
6. Many people today claim that men and women are basically the same. Although I believe
that men and women are equally capable of completing the same tasks physically as well
as mentally, to say that they are intrinsically the same detracts from the differences
between men and women that are displayed every day in their social interactions, the
way they use their resources, and the way in which they find themselves in the world.
a. deductive
b. inductive
7. Too many intravenous drug users continue to risk their lives by sharing dirty needles.
This situation could be changed if we were to supply drug addicts with a way to get clean
needles. This would lower the rate of AIDS in this highrisk population as well as allow
for the opportunity to educate and attempt to aid those who are addicted to heroin and
other intravenous drugs.
a. deductive
b. inductive
8. I know that Stephen has a lot of money. His parents drive a Mercedes. His dogs wear
cashmere sweaters, and he paid cash for his Hummer.
a. deductive
b. inductive
9. Dogs are better than cats, since they always listen to what their masters say. They also
are more fun and energetic.
a. deductive
b. inductive
10. All dogs are warmblooded. All warmblooded creatures are mammals. Hence, all dogs
are mammals.
a. deductive
b. inductive
11. Chances are that I will not be able to get in to see Slipknot since it is an over 21 show, and
Jeffrey, James, and Sloan were all carded when they tried to get in to the club.
a. deductive
b. inductive
12. This is not the best of all possible worlds, because the best of all possible worlds would
not contain suffering, and this world contains much suffering.
a. deductive
b. inductive
13. Some apples are not bananas. Some bananas are things that are yellow. Therefore, some
things that are yellow are not apples.
a. deductive
b. inductive
14. Since all philosophers are seekers of truth, it follows that no evil human is a seeker after
truth, since no philosophers are evil humans.
a. deductive
b. inductive
15. All squares are triangles, and all triangles are rectangles. Therefore, all squares are
rectangles.
a. deductive
b. inductive
16. Deciduous trees are trees that shed their leaves. Maple trees are deciduous trees.
Therefore, maple trees will shed their leaves at some point during the growing season.
a. deductive
b. inductive
17. Joe must make a lot of money teaching philosophy, since most philosophy professors are
rich.
a. deductive
b. inductive
18. Since all mammals are coldblooded, and all coldblooded creatures are aquatic, all
mammals must be aquatic.
a. deductive
b. inductive
19. I felt fine until I missed lunch. I must be feeling tired because I don’t have anything in my
stomach.
a. deductive
b. inductive
20. If you drive too fast, you will get into an accident. If you get into an accident, your
insurance premiums will increase. Therefore, if you drive too fast, your insurance
premiums will increase.
a. deductive
b. inductive
21. The economy continues to descend into chaos. The stock market still moves down after it
makes progress forward, and unemployment still hovers around 10%. It is going to be a
while before things get better in the United States.
a. deductive
b. inductive
22. Football is the best sport. The athletes are amazing, and it is extremely complex.
a. deductive
b. inductive
23. We should go to see Avatar tonight. I hear that it has amazing special effects.
a. deductive
b. inductive
24. Pigs are smarter than dogs. It’s easier to train them.
a. deductive
b. inductive
25. Seventy percent of the students at this university come from upperclass families. The
school budget has taken a hit since the economic downturn. We need funding for the
three new buildings on campus. I think it’s time for us to start a phone campaign to raise
funds so that we don’t plunge into bankruptcy.
a. deductive
b. inductive
26. Justin was working at IBM. The last person we got from IBM was a horrible worker. I
don’t think that it’s a good idea for us to go with Justin for this job.
a. deductive
b. inductive
27. If she wanted me to buy her a drink, she would’ve looked over at me. But she never
looked over at me. So that means that she doesn’t want me to buy her a drink.
a. deductive
b. inductive
28. Almost all the people I know who are translators have their translator’s license from the
ATA. Carla is a translator. Therefore, she must have a license from the ATA.
a. deductive
b. inductive
29. The economy will not recover anytime soon. Big businesses are struggling to keep their
profits high. This is due to the fact that consumers no longer have enough money to
purchase things that are luxuries. Most of them buy only those things that they need and
don’t have much left over. Those same businesses have been firing employees left and
right. If America’s largest businesses are losing employees, then there won’t be any jobs
for the people who are already unemployed. That means that these people will not have
money to pump back into the system, and the circle will continue to descend into
recession.
a. deductive
b. inductive
Determine which of the following forms of inductive reasoning are taking place.
30. The purpose of ancient towers that were discovered in Italy are unknown. However,
similar towers were discovered in Albania, and historical accounts in that country
indicate that the towers were used to store grain. Therefore, the towers in Italy were
probably used for the same purpose.
a. argument from analogy
b. statistical syllogism
c. inductive generalization
d. causal argument
31. After the current presidential administration passes a bill that increases the amount of
time people can be on unemployment, the unemployment rate in the country increases.
Economists studying the bill claim that there is a direct relation between the bill and the
unemployment rate.
a. argument from analogy
b. statistical syllogism
c. inductive generalization
d. causal argument
32. When studying a group of electricians, it was found that 60% of them did not have
knowledge of the new safety laws governing working on power lines. Therefore, 60% of
the electricians in the United States probably do not have knowledge of the new laws.
a. argument from analogy
b. statistical syllogism
c. inductive generalization
d. causal argument
33. In the state of California, studies found that violent criminals who were released on
parole had a 68% chance of committing another violent crime. Therefore, a majority of
violent criminals in society are likely to commit more violent crimes if they are released
from prison.
a. argument from analogy
b. statistical syllogism
c. inductive generalization
d. causal argument
34. Psilocybin mushrooms cause hallucinations in humans who ingest them. A new species of
mushroom shares similar visual characteristics to many forms of psilocybin mushrooms.
Therefore, it is likely that this form of mushroom has compounds that have neurological
effects.
a. argument from analogy
b. statistical syllogism
c. inductive generalization
d. causal argument
35. A recent survey at work indicates that 60% of the employees believe that they do not
make enough money for the work that they do. It is likely that a majority of the people
that work for this company are unhappy in their jobs.
a. argument from analogy
b. statistical syllogism
c. inductive generalization
d. causal argument
36. A family is committed to buying Hondas because every Honda they have owned has had
few problems and been very reliable. They believe that all Hondas must be reliable.
a. argument from analogy
b. statistical syllogism
c. inductive generalization
d. causal argument
Summary and Resources
Chapter Summary
The key feature of inductive arguments is that the support they provide for a conclusion is always less
than perfect. Even if all the premises of an inductive argument are true, there is at least some possibility
that the conclusion may be false. Of course, when an inductive argument is very strong, the evidence for
the conclusion may still be overwhelming. Even our best scientific theories are supported by inductive
arguments.
This chapter has looked at four broad types of inductive arguments: statistical arguments, causal
arguments, arguments from authority, and arguments from analogy. We have seen that each type can be
quite strong, very weak, or anywhere in between. The key to success in evaluating their strength is to be
able to (a) identify the type of argument being used, (b) know the criteria by which to evaluate its
strength, and (c) notice the strengths and weaknesses of the specific argument in question within the
context that it is given. If we can perform all of these tasks well, then we should be good evaluators of
inductive reasoning.
Critical Thinking Questions
1. What are some ways that you can now protect yourself from making hasty generalizations
through inductive reasoning?
2. Can you think of an example that relates to each one of Mill’s methods of determining causation?
What are they, and how did you determine that it fit with Mill’s methods?
3. Think of a time where you reasoned improperly about correlation and causation. Have you seen
anyone in the news or in your place of employment fall into improper analysis of causation?
What did they do, and what errors did they make?
4. Learning how to evaluate arguments is a great way to empower the mind. What are three forms
of empowerment that result when people understand how to identify and evaluate arguments?
5. Why do you believe that superstitions are so prevalent in many societies? What forms of
illogical reasoning lead to belief in superstitions? Are there any superstitions that you believe
are true? What evidence do you have that supports your claims?
6. Think of an example of a strong inductive argument, then think of a premise that you can add
that significantly weakens the argument. Now think of a new premise that you can add that
strengthens it again. Now find one that makes it weaker, and so on. Repeat this process several
times to notice how the strength of inductive arguments can change with new premises.
Web Resources
http://austhink.com/critical/pages/stats_prob.html
(http://austhink.com/critical/pages/stats_prob.html)
This website offers a number of resources and essays designed to help you learn more about statistics
and probability.
http://www.nss.gov.au/nss/home.nsf/pages/Sample+size+calculator
(http://www.nss.gov.au/nss/home.nsf/pages/Sample+size+calculator)
The Australian government hosts a sample size calculator that allows users to approximate how large a
sample they need.
http://www.gutenberg.org/ebooks/27942 (http://www.gutenberg.org/ebooks/27942)
Read John Stuart Mill’s A System of Logic, which is where Mill first introduces his methods for identifying
causality.
Key Terms
appeal to authority
See argument from authority.
argument from analogy
Reasoning in which we draw a conclusion about something based on characteristics of other similar
things.
argument from authority
An argument in which we infer that something is true because someone (a purported authority) said
that it was true.
causal argument
An argument about causes and effects.
cogent
An inductive argument that is strong and has all true premises.
confidence level
In an inductive generalization, the likelihood that a random sample from a population will have
results that fall within the estimated margin of error.
correlation
An association between two factors that occur together frequently or that vary in relation to each
other.
inductive arguments
Arguments in which the premises increase the likelihood of the conclusion being true but do not
guarantee that it is.
inductive generalization
An argument in which one draws a conclusion about a whole population based on results from a
sample population.
joint method of agreement and difference
A way of selecting causal candidates by looking for a factor that is present in all cases in which the
effect occurs and absent in all cases in which it does not.
margin of error
A range of values above and below the estimated value in which it is predicted that the actual result
will fall.
method of agreement
A way of selecting causal candidates by looking for a factor that is present in all cases in which the
effect occurs.
method of concomitant variation
A way of selecting causal candidates by looking for a factor that is highly correlated with the effect in
question.
method of difference
A way of selecting causal candidates by looking for a factor that is present when effect occurs and
absent when it does not.
necessary condition
A condition for an event without which the event will not occur; A is a necessary condition of B if A
occurs whenever B does.
population
In an inductive generalization, the whole group about which the generalization is made; it is the group
discussed in the conclusion.
proximate cause
See trigger cause.
random sample
A group selected from within the whole population using a selection method such that every member
of the population has an equal chance of being included.
sample
A smaller group selected from among the population.
sample size
The number of individuals within the sample.
statistical arguments
Arguments involving statistics, either in the premises or in the conclusion.
statistical syllogism
An argument of the form X% of S are P; i is an S; Therefore, i is (probably) a P.
strong arguments
Inductive arguments in which the premises greatly increase the likelihood that the conclusion is true.
sufficient condition
A condition for an event that guarantees that the event will occur; A is a sufficient condition of B if B
occurs whenever A does.
trigger cause
The factor that completes the cause chain resulting in the effect. Also known as proximate cause.
weak arguments
Inductive arguments in which the premises only minimally increase the likelihood that the conclusion
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.
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
Click here
(https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems6.3.pdf)
to check your answers.
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
know or believe about how cars work. Your hypothesis is that higher grade gas will improve your fuel
economy.
Of course, science is not really concerned with your car all by itself. Science is concerned with general
principles. A scientist would reword your hypothesis in terms of a general rule, something like,
“Increasing fuel octane increases fuel economy in automobiles.” The hypothetico–deductive method can
work with either kind of hypothesis, but the general hypothesis is more interesting scientifically.
Step 2: Deduce a Consequence From the Hypothesis
Your hypothesis from step 1 should have predictive value: Things should be different in some noticeable
way, depending on whether the hypothesis is true or false. Our hypothesis is that increasing fuel octane
improves fuel economy. If this general fact is true, then it is true for your car. So from our general
hypothesis we can deduce the consequence that your car will get more miles per gallon if it is running on
higher octane fuel.
It is often but not always the case that the prediction is a more specific case of the hypothesis. In such
cases it is possible to infer the prediction deductively from the general hypothesis. The argument may go
as follows:
Hypothesis: All things of type A have characteristic B.
Consequence (the prediction): Therefore, this specific thing of type A will have characteristic B.
Since the argument is deductively valid, there is a strong connection between the hypothesis and the
prediction. However, not all predictions can be deductively inferred. In such cases we can get close to the
hypothetico–deductive method by using a strong inductive inference instead. For example, suppose the
argument went as follows:
Hypothesis: 95% of things of type A have characteristic B.
Consequence: Therefore, a specific thing of type A will probably have 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
your conclusion is correct.
IPGGutenbergUKLtd/iStock/Thinkstock
At best, the fuel economy hypothesis
will be a strong inductive argument
because there is a chance that
something other than higher octane
gas is improving fuel economy. The
more you can address relevant issues
that may impact your test results, the
stronger your conclusions will be.
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.
Learn more about Karl Popper’s criterion of
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
Click here
(https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems6.4.pdf)
to check your answers.
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
that we already believe.
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.
©Warner Bros./Courtesy Everett
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
Click here
(https://ne.edgecastcdn.net/0004BA/constellation/PDFs/PHI103_2e/Answers_PracticeProblems6.5.pdf)
to check your answers.
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 __________.
a. breadth of explanatory power
b. inability to provide an understanding of a phenomenon
c. lack of connection to what is being examined
d. ability to bear children
17. Why might one choose to use an inductive argument rather than a deductive argument?
a. One possible explanation must be the correct one.
b. The argument relates to something that is probabilistic rather than absolute.
c. An inductive argument makes the argument valid.
d. One should always use inductive arguments when possible.
18. This is the method by which one can make a valid argument invalid.
a. adding false supporting premises
b. demonstrating that the argument is valid
c. adding true supporting premises
d. valid arguments cannot be made invalid
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
https://www.youtube.com/watch?v=RauTW8FPMM (https://www.youtube.com/watch?v=RauTW8F
PMM)
Watch Ashford professor Justin Harrison lecture on the difference between inductive and deductive
arguments.
https://www.youtube.com/watch?v=VXW5mLE5Y2g (https://www.youtube.com/watch?
v=VXW5mLE5Y2g)
Shmoop offers an animated video on the difference between induction and deduction.
http://www.ac4d.com/2012/06/03/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.
Choose a Study Mode
is true.
