347
348 Cartoon Writing Lesson F
4.
Harry's rabbit was pregnant.
Dr. E grew a beard.
A. The man at the car in the parking lot is the person who ran over the bicycle.
B. The man in the car knew he ran over the bicycle and purposely didn't stop.
Writing Lesson 12
Let's see how much you've learned in this course. Write an argument for or against
the following.
Student athletes should be given special leniency when the instructor
assigns course marks.
349
Making Decisions
The skills you've learned in this course can help you make better decisions.
Making a decision is making a choice. You have options. When making a
decision you can start as you would on a writing exercise: Make a list for and against
the choice—all the pros and cons you can think of. Make the best argument for each
side. Then your decision should be easy: Choose the option for which there is the
best argument. Making decisions is no more than being very careful in constructing
arguments for your choices.
But there may be more than two choices. Your first step should be to list all
the options and give an argument that these really are the only options, and not a
false dilemma.
Suppose you do all that, and you still feel there's something wrong. You see
that the best argument is for the option you feel isn't right. You have a gut reaction
that it's the wrong decision. Then you're missing something. Don't be irrational.
You know that when confronted with an argument that appears good yet whose
conclusion seems false, you must show that the argument is weak or a premise is
implausible. Go back to your pro and con lists.
Now at the end of this course your reasoning has been sharpened, you can
understand more, you can avoid being duped. And, I hope, you will reason well with
those you love and work with and need to convince. And you can make better
decisions. But whether you will do so depends not just on method, not just on the
tools of reasoning, but on your goals, your ends. And that depends on virtue.
Exercises on Making Decisions
1. Decide whether you should cook dinner at home tonight.
2. Decide whether and what kind of dog you should get.
3. Decide whether you should buy a car during this next year.
4. Decide whether you should recommend this course to a friend.
351
352 Making Decisions
5. If you don't have a job, decide whether you should get one next semester.
If you have a job, decide whether you should quit.
6. Decide what career you should have.
7. If you're not married, decide whether you should ever get married.
If you are married, decide whether you should get divorced.
8. If you have children, decide whether you should have more.
If you don't have children, decide whether you ever should.
9. If you're doing drugs, decide whether you should stop.
10. If you have slept with your friend's lover, decide whether you should tell your friend.
11. Decide whether you should be honest for the rest of your life.
12. Decide whether you should believe in God.
13. Decide whether you should keep this book or sell it back at the end of the term.
Key W o r d s virtue
the love of wisdom
APPENDICES
Using Examples in Reasoning
A. Examples for Definitions and Methods 355
B. Showing a General Claim is False 356
C. Showing an Argument is Not Valid 356
Summary 357
• Exercises on Examples 357
A. Examples for Definitions and Methods
When I defined "valid argument" in Chapter 3,1 gave an example of a valid
argument. So there really are such things. Then I showed that not every argument
is valid by giving another example. So the definition wasn't vacuous: Some
arguments fit the definition, some don't.
Then I gave examples so you could see the difference between valid arguments
and similar notions, such as strong arguments and good arguments.
We need examples when we make definitions in order to be sure we've got the
right definition. Compare the attempt to define "school cafeteria" on p. 30.
We need examples with definitions to:
• Show that something fits the definition.
• Show that not everything fits the definition.
• Show the difference between the definition
and other notions we already know.
The first two points are essential when the term we're defining, like "school
cafeteria," is one we supposedly all understand. We want to be sure the definition
fits our usual way of talking. Getting definitions of ordinary words is very important
in insurance policies and courts of law.
On the other hand, suppose we want to make a vague term precise:
A classic car is one that was built before 1959 and is in mint condition.
So a 1956 Chevy Bel Air in mint condition would be a classic car. A 1965 Corvette
in perfect condition would not be a classic car by this definition, even if some people
might call it one. And a classic car might not be an antique, for no car built in the
355
356 APPENDIX: Using Examples in Reasoning
50s would normally count as an antique. Nor would a 1932 Ford in lousy condition,
which is an antique, be called a classic car.
I've shown that there are classic cars that aren't antiques, and antiques that
aren't classic cars. That is, I showed that neither definition included the other.
Note what I did after listing the three reasons for using examples with
definitions above: I showed how to use the method. I showed that the method made
sense and gave you an idea how to use it by giving an example. Whenever I've
introduced a new method in this book, I've given you an example of how to use it.
B. Showing a General Claim is False
Dick: All dogs hate cats.
Zoe: No way. Remember Zelda on Elm Street when we were growing up?
She had a dog and cat that got along fine.
Zoe has shown that Dick's general claim is false by providing an example.
Harry: No car built before 1992 had an airbag.
Tom: That's not right. My buddy's 1991 Volvo has an airbag.
Tom's example shows that Harry's general claim is false.
Suzy: Almost all students at this university live on campus.
Harry: No they don't. I know lots of guys who go to night classes
who don't.
Suzy: Well, anyway, all my friends live on campus.
For Harry to show that Suzy's "almost all" claim is false he has to give not one, but a
lot of examples.
People often generalize badly, too quickly from too few examples. You can
bring them back to earth with well-chosen examples.
C. Showing an Argument is Not Valid
How do we show an argument is invalid? Consider:
Dick is a bachelor.
Therefore, Dick was never married.
We could say, no, that's not valid because Dick could be divorced, and we call a
divorced man a bachelor. That's giving an example of a possible case where the
premises are true and the conclusion false.
Or we could say the argument's not valid because I know someone, Ralph,
who's a bachelor and he was married. And his name could have been "Dick."
That's giving an actual example (with the names changed).
EXERCISES on Examples 357
When we want to show an argument is not valid we give a possible or actual
example in which the premises are true and the conclusion false.
We do the same when we want to show that an argument is not strong.
Zoe and Dick have each gone out for the day. Dick returns, sees that Zoe
is gone, and finds that there's a roast cooking in the oven. So (he thinks)
Zoe has started dinner.
Viewing the first three sentences as premises, we can say that Dick's argument is not
valid: A burglar might have broken in and left a roast in the oven. That's extremely
unlikely, but it will do to show that the argument isn't valid.
But is the argument strong? Well, Dick's friend Jose has been visiting for a
week, and maybe he decided to help out and started dinner. That's an example of a
possibility that isn't so unlikely. So we conclude the argument is weak. That's how
we show an argument is weak: We look for one or more (possible) examples that
aren't unlikely where the premises are true and the conclusion false.
Summary We've reviewed some of the ways we can use examples in reasoning:
• To make sure we've given a good definition and to clarify how to use
the definition.
• To show how to use a new method.
• To show that a general claim is false.
• To show that an argument is not valid.
• To show that an argument is weak.
You should get good at using examples, because theory without examples isn't
understood—it's unusable, and sometimes just plain wrong.
Exercises on Examples
1. Detail how examples were used in making the definition of "argument" in Chapter 1
(look at the three reasons for using examples with definitions).
2. Define "professional athlete." Use examples to contrast professional athletes with
college athletes who receive scholarships, and amateur athletes, who are supported by
governments to participate in the Olympics.
3. Define "student financial aid" and use examples to make your definition clear.
4. Detail how examples were used in Chapter 4 to show how to use the Guide to Repairing
Arguments.
5. Show that the following are false or at least dubious:
a. All dogs bark.
b. All sheep are raised for meat.
c. Nearly everyone who is at this college is on financial aid.
d. No teacher at this school gives good lectures.
e. No fast-food restaurant serves healthy food.
358 APPENDIX: Using Examples in Reasoning
For each argument below, if it is meant to be valid but is invalid, give an example to show
that. If it's meant to be strong but it's weak, give enough examples to show that. If the
argument is valid but not good, give an example to show why.
6. All good teachers give fair exams. Professor Zzzyzzx gives fair exams. So Professor
Zzzyzzx is a good teacher.
7. If this course were easy, the exams would be fair. The exams are fair. So this course
is easy.
8. President Clinton didn't inhale marijuana. So President Clinton never got high from
marijuana.
9. Almost all teachers at this school speak English as their first language. So the
mathematics professor you're going to have for calculus next semester speaks English
as his or her first language.
10. Professor Zzzyzzx was late for class. He's never been late for class before. He's always
conscientious in all his duties. So he must have been in an accident.
11. Dick: I'm telling you I'm not at fault. How could I be? She hit me from the rear.
Anytime you get rear-ended it's not your fault.
Truth-Tables
A. Symbols and Truth-Tables 359
B. The Truth-Value of a Compound Claim 362
• Exercises for Sections A and B 364
C. Representing Claims 365
• Exercises for Section C 367
D. Checking for Validity 368
• Exercises for Section D 370
Summary 372
A. Symbols and Truth-Tables
The ancient Greek philosophers were the first to analyze arguments using compound
claims. From then until the mid-19th century the analysis of compound claims
wasn't much different from what you saw in Chapter 6, though many more valid and
invalid argument forms had been catalogued, with Latin names attached.
In the early 1900s a simple method was devised for checking whether an
argument form using compound claims is valid. Using it we can easily justify the
validity and invalidity of the argument forms we studied in Chapter 6.
We can analyze many arguments using compound claims by concentrating on
how compound claims can be built up from just four English words or phrases:
and, or, not, i f . . . then . . .
These words are used in many different ways in English, too many for us to
investigate every possible way they could be used in arguments. We will concentrate
on just one aspect of them: How compound claims that use them depend on the
truth or falsity (truth-value) of the claims from which they are built. We won't
care how plausible a claim is, or how we might happen to know it, or its subject
matter, or any other aspect of it. We make the following assumption.
The classical abstraction The only aspects of a claim we'll pay attention to are
whether the claim is true or false, and how it is compounded from other claims.
359
360 APPENDIX: Truth-Tables
So long as the argument we are analyzing makes sense in terms of this assumption,
the methods we develop here will allow us to check for validity. To remind us that
we're making this assumption, we're going to use special symbols to represent the
words we're interested in.
Now we can be precise about how we will understand these words in
arguments, relative to the classical abstraction. Let's start with "and".
Spot is a dog and Puff is a cat.
When is this true? When both "Spot is a dog" is true and "Puff is a cat" is true.
That's the only way it can be true. Let's summarize that in a table, where A and B
stand for any claims:
A conjunction (^-claim) is true (T)
when both parts are true. Otherwise
it is false (F).
Now we'll look at "not".
Spot is not a dog.
This is true if "Spot is a dog" is false, and false if "Spot is a dog" is true. That's simple to formalize:
A negation ( -claim) is true if its part is
false; it is false if its part is true.
How about "or"?
London is the capital of England or Paris is the capital of France.
Is this true? There's going to be disagreement. Some say it isn't, because "London
is the capital of England" and "Paris is the capital of France" are both true. Others
say the compound is true. The question is whether an "or" claim can be true if both
parts are true.
It turns out to be simplest to use to formalize "or" in the inclusive sense:
One or the other or both parts are true. Later we'll see how to formalize "or" in the
exclusive sense: One or the other but not both parts are true.
SECTION A Symbols and Truth-Tables 361
> A disjunction ( -claim) is false
if both parts are false. Otherwise
it is true.
Finally, we have "if. . . then . . .". These words have so many connotations
and uses in English that it's hard to remember that we're going to pay attention only
to whether the parts of the compound claim are true or false. The following table is
the one that's best:
A conditional ( -claim) is false if the
antecedent is true and consequent false.
Otherwise it is true.
Why do we choose this table? Let's look at it row by row.
We said the direct way of reasoning with conditionals is valid:
If A then B, A, so B.
So if A B is true, and A is true, then B is true {the first row).
Suppose A is true and B is false (the second row). In a valid form we can't get
a false conclusion (B) from true premises. Since there are only two premises, it must
be that A B is false.
But why should A B be true in the last two rows? Suppose Dr. E says to
Suzy,
If you get 90% on the final exam, you'll pass this course.
It's the end of the term. Suzy gets 58% on the final. Dr. E fails her. Can we say that
Dr. E lied? No. So the claim is still true, even though the antecedent is false and the
consequent is false (the fourth row).
But suppose Dr. E relents and passes Suzy anyway. Can we say he lied? No,
for he said "if", not "only if". So the claim is still true, even though the antecedent is false and the consequent is true (the third row).
The formalization of "if. . . then . . ." in this table is the best we can do when
we adopt the classical abstraction. We deal with cases where the antecedent "does
not apply" by treating the claim as vacuously true.
362 APPENDIX: Truth-Tables
B. The Truth-Value of a Compound Claim
With these tables to interpret "and", "or", "not", and "if . . . then . . ." we can calculate the truth-value of a compound claim fairly easily. For example,
If Dick goes to the movies and Zoe visits her mother, then no one will
walk Spot tonight.
We can formalize this as:
(Dick goes to the movies Zoe visits her mother)
no one will walk Spot tonight
I had to use parentheses to mark off the antecedent. They do the work that commas
Richard L Epstein Page 45
