Critical Thinking:
A User’s Manual
Chapter 4
Diagramming Arguments
Argument Diagram
An argument diagram is a visual
representation of the structure of an
argument.
An argument diagram shows the relationship
between the premises.
Relationships between Premises
Convergent premises provide support for the
conclusion independently of one another.
If one premise is removed, the conclusion may
still be supported by the other(s).
Linked premises depend on each other to
provide support for the conclusion.
If one premise is removed, the conclusion is no
longer supported.
How to Diagram Arguments
Step 1: Underline and number each claim.
Step 2: Pay attention to indicator words.
Step 3: Identify the main conclusion.
Step 4: Identify the premises and determine
their relationship.
Step 5: Diagram any subarguments.
Step 6: Check your work.
Numbering Claims
Underline every claim.
Give each claim its own number.
If a claim is repeated, use the same number.
If a conclusion is unstated, write the
conclusion after the passage and give it a
number.
If a claim is implied, underline and number
the non-claim serving as a placeholder and
write the implied claim after the passage.
Using Inference Indicators
Rewrite the argument by substituting
numbers for each claim.
Use the inference indicators to draw a
preliminary diagram of the argument.
Remember that “and” cannot tell you
whether the premises are linked or
convergent.
Drawing Your Diagram
Place the conclusion at the bottom of your
diagram.
Place the premises above the conclusion
Draw an arrow from each convergent premise
to the conclusion.
Connect each linked premise with a “+”,
underline all linked premises, and draw a
single arrow to the conclusion.
Checking Your Work
Read the argument back to yourself to listen
for errors.
“+” means “and”
Substitute an inference indicator for “”
“____ because ____” when reading the argument
from the bottom up
“____ therefore ____” when reading the
argument from the top down
Grace is armed, so she’s dangerous.
 Grace is armed, so  she’s dangerous.
, so .
Here are some reasons why you should
stop smoking cigarettes: smoking is
addictive, and it is bad for your health.
Here are some reasons why  you should
stop smoking cigarettes:  smoking is
addictive, and  it is bad for your health.
Here are some reasons why : , and .
Here are some reasons why  you should
stop smoking cigarettes:  smoking is
addictive, and  it is bad for your health.
You are pregnant, and smoking while
pregnant could hurt the fetus. Therefore,
you should stop smoking cigarettes.
 You are pregnant, and  smoking while
pregnant could hurt the fetus. Therefore,
 you should stop smoking cigarettes.
 and . Therefore .
 You are pregnant, and  smoking while
pregnant could hurt the fetus. Therefore,
 you should stop smoking cigarettes.
Felipe ought to try out for wrestling, since
he is both strong and quick. That’s what I
would do if I were him.
 Felipe ought to try out for wrestling,
since  he is both strong and quick. 
That’s what I would do if I were him.
, since . .
Smoking is not allowed in this restaurant. I
know this is true because I was told to put
my cigarette out the last time I was here.
 Smoking is not allowed in this
restaurant. I know  this is true because
 I was told to put my cigarette out the
last time I was here.
Anyone guilty of leaking classified
government documents is guilty of
treason, and that is just what Julian
Assange has done.
 Anyone guilty of leaking classified
government documents is guilty of
treason, and  that is just what Julian
Assange has done.
 Julian Assange is guilty of treason.
 Anyone guilty of leaking classified
government documents is guilty of
treason, and  that is just what Julian
Assange has done.
 Julian Assange is guilty of treason.
You should bring your lunch to work.
Doesn’t it save you money?
 You should bring your lunch to work. 
Doesn’t it save you money?
 Bringing your lunch to work will save
you money.
Diagramming Multiple Arguments
Arguments with multiple conclusions and
chain arguments can be represented in a
single diagram.
Pay close attention to inference indicators.
The Saints are likely to retain all of their best
starters from last year’s championship team. Thus,
Reggie Bush will be their premier running back,
and Drew Brees will be their quarterback this year.
 The Saints are likely to retain all of their best
starters from last year’s championship team. Thus,
 Reggie Bush will be their premier running back,
and  Drew Brees will be their quarterback this
year.
. Thus,  and .
 The Saints are likely to retain all of their
best starters from last year’s
championship team. Thus,  Reggie Bush
will be their premier running back, and 
Drew Brees will be their quarterback this
year.
Since Reggie Bush was injured last week, he
won’t be able to play in the next game. This
means that Chris Ivory will be the Saints’
starting running back.
Since  Reggie Bush was injured last week, 
he won’t be able to play in the next game. This
means that  Chris Ivory will be the Saints’
starting running back.
Since , . This mean that, .
Since  Reggie Bush was injured in the last
week,  he won’t be able to play in the next
game. This means that  Chris Ivory will be the
Saints’ starting running back.
Your turn!
What is wrong with the following diagram?
+


Extended Arguments
Extended arguments contain several
subarguments.
Break down the passage into small,
manageable parts.
Pay close attention to inference indicators.
The Galaxy Corporation wants to build a casino in St.
Louis, but we should not allow it to be built. First,
gambling is immoral, since gambling is motivated by
greed, and greed is an immoral desire. Second,
communities with casinos have higher crime rates.
This is because casinos attract people who take risks,
and risk-takers are more likely to break the law.
Finally, studies show that people living within 10
miles of a casino have a 90% increased risk of
becoming pathological gamblers. Thus, casinos
encourage psychological problems for the people
that live near them. For all these reasons, the
proposed casino should be opposed.
 The Galaxy Corporation wants to build a casino in
St. Louis, but  we should not allow it to be built.
First,  gambling is immoral, since  gambling is
motivated by greed, and  greed is an immoral
desire. Second,  communities with casinos have
higher crime rates. This is because  casinos attract
people who take risks, and  risk-takers are more
likely to break the law. Finally,  studies show that
people living within 10 miles of a casino have a 90%
increased risk of becoming pathological gamblers.
Thus,  casinos encourage psychological problems
for the people that live near them. For all these
reasons,  the proposed casino should be opposed.
, but . First, , since , and . Second, .
This is because , and . Finally, . Thus, .
For all these reasons, .
First, , since , and .
Second, . This is because , and .
Finally, . Thus, .
For all these reasons, .
First,  gambling is immoral, since  gambling is
motivated by greed, and  greed is an immoral
desire.
First,  gambling is immoral, since  gambling is
motivated by greed, and  greed is an immoral
desire.
Second,  communities with casinos have
higher crime rates. This is because  casinos
attract people who take risks, and  risk-takers
are more likely to break the law.
Second,  communities with casinos have
higher crime rates. This is because  casinos
attract people who take risks, and  risk-takers
are more likely to break the law.
Finally,  studies show that people living within
10 miles of a casino have a 90% increased risk of
becoming pathological gamblers. Thus, 
casinos encourage psychological problems for
the people that live near them.
For all these reasons,  the proposed casino
should be opposed.

+


+





 The Galaxy Corporation wants to build a casino
in St. Louis.
Gambling is immoral.
 Communities with casinos have higher crime
rates.
 Casinos encourage psychological problems for
the people that live near them.
 the proposed casino should be opposed.
 The Galaxy Corporation wants to build a casino in
St. Louis, but  we should not allow it to be built.
First,  gambling is immoral, since  gambling is
motivated by greed, and  greed is an immoral
desire. Second,  communities with casinos have
higher crime rates. This is because  casinos attract
people who take risks, and  risk-takers are more
likely to break the law. Finally,  studies show that
people living within 10 miles of a casino have a 90%
increased risk of becoming pathological gamblers.
Thus,  casinos encourage psychological problems
for the people that live near them. For all these
reasons,  the proposed casino should be opposed.
Basic Analysis with Argument Diagram
Step 1: Write a Basic Analysis of the passage.
Identify the passage.
Analyze the passage.
Step 2: If it is an argument, diagram it.
Verify that your diagram is consistent with your
Basic Analysis.
Since Reggie Bush was injured last week, he
won’t be able to play in the next game. This
means that Chris Ivory will be the Saints’
starting running back.
Since  Reggie Bush was injured last week,
 he won’t be able to play in the next game.
This means that  Chris Ivory will be the
Saints’s starting running back.





Since Reggie Bush was injured last week, he won’t
be able to play in the next game. This means that
Chris Ivory will be the Saints’ starting running back.
This passage contains an argument. The issue is
whether Chris Ivory will be the Saints’ starting
running back. The conclusion is that Chris Ivory will
be the Saints’ starting running back. The premise is
that Reggie Bush won’t be able to play in the next
game.
This passage contains a subargument. The
intermediate conclusion is that Reggie Bush won’t
be able to play in the next game. The premise is that
Reggie Bush was injured last week.