B. The Conclusion Follows From the Premises
Even if an argument has plausible premises, that's not enough. Consider:
Dr. E teaches critical thinking.
So Dr. E is bald.
There's no connection: The conclusion does not follow from the premises. The
premises do not lead to, support, establish the conclusion.
We all have some intuition about whether a conclusion follows from some
premises. If we didn't, we'd be hopelessly confused in all our reasoning, no more
clever than a four-year old. But most folks have only some bare intuition that they
can't extend to any reasoning outside the subject they're most interested in (music,
sports, car repair, chemistry,. . . ) . We need to come up with a clear understanding
of what it means to say that a conclusion follows from premises, an understanding
we can use in our daily lives and in our work.
SECTION B The Conclusion Follows 39
What would be the best connection between premises and conclusion? If there
were no way at all—no possibility—that both the premises could be true and the
conclusion false, then if the premises are true, the conclusion has to be true, too.
For example,
Every student at this school has paid tuition.
Suzy is a student at this school.
So Suzy has paid tuition.
It's impossible for the premises to be true and the conclusion false. If we then have
good reason to believe that every student at this school has paid tuition, and also that
Suzy is a student at this school, then we have good reason to believe she has paid
tuition—it couldn't be otherwise.
Valid argument An argument is valid if there is no possible way
for its premises to be true and its conclusion false (at the same time).
An argument that is not valid is called invalid.
A valid argument need not be good. For example:
Every elected official in the United States is under thirty-four years old.
So the President of the United States is under thirty-four years old.
This argument is valid: There is no way the premise could be true and the conclusion
false at the same time. Were the premise true—say if tomorrow the laws were
changed and enforced to prohibit people older than thirty-four from holding elective
office—then it would be impossible for the president to be older than thirty-four.
But the argument is bad, since after all it has a false conclusion. And that's because
the premise is false.
So some valid arguments are bad. But is every good argument valid? Does the
idea of validity fully capture what we want "follows from" to mean? Dick heard this
morning that there are parakeets for sale down at the mall. He knows that his
neighbor has a birdcage in her garage, and he wonders if it will be big enough for
one of those parakeets. He makes the following argument:
All parakeets anyone I know has ever seen, or heard, or read about are
under 2 feet tall.
Therefore, the parakeets on sale at the mall are under 2 feet tall.
Surveying all the ways the premise could be true, he thinks that, yes, a new super-
grow bird food could have been formulated and the parakeets at the local mall are
really 3 feet tall, he just hasn't heard about it. Or a rare giant parakeet from the
Amazon forest could have been discovered and brought here. Or a UFO might have
abducted a parakeet by mistake, hit it with growing rays, and it's now gigantic.
40 CHAPTER 3 What Is a Good Argument?
All of these ways that the premise could be true and the conclusion false are
so very unlikely that Dick would have very good reason to believe the conclusion,
even though it's still possible that the conclusion is false. The conclusion does
follow from the premises, even though the argument is not valid.
Strong and weak arguments An argument is strong if there is some way,
some possibility, for its premises to be true and its conclusion false (at the
same time), but every such possibility is extremely unlikely. An argument
is weak if it is possible and not unlikely for its premises to be true and its
conclusion false (at the same time).
We just saw a strong argument that was good. But a weak argument is always
bad. For example,
Dick is a student.
We don't know much about Dick, but we do know that it's not unlikely he could
own a motorcycle—lots of students do, and even if he doesn't, he could have
borrowed one last week to use this semester. This is a bad argument.
The conclusion follows from the premises "The conclusion follows from
the premises" means that the argument is valid or strong.
An argument is either valid or it isn't; there are no degrees to it, no judgment
involved. But evaluating the strength of an argument does involve judgment, for it
depends on how likely certain possibilities appear. The strength of an argument is a
matter of degree, and we classify invalid arguments on a scale from strong to weak.
SECTION B The Conclusion Follows 41
Here is the process involved in analyzing whether the conclusion follows from
the premises of an argument.
To evaluate an argument, you have to imagine possible ways the premises
could be true. You have to be creative. Imagine the possibilities.
Here are some basic points you need to remember.
• Every good argument is valid or strong.
• Not every valid or strong argument is good
(a premise could be implausible).
• Only invalid arguments are classified from strong to weak.
• Every weak argument is bad.
42 CHAPTER 3 What Is a Good Argument?
C. The Tests for an Argument to Be Good
We have three tests for an argument to be good.
Tests for an argument to be good
• The premises are plausible.
• The premises are more plausible than the conclusion.
• The argument is valid or strong.
Each of these tests is independent of the others: Each can fail while the other
two hold. So in evaluating whether an argument is good, we can start with
whichever of these tests is easiest to determine.
But why should we be interested in whether the argument is valid or strong if
we don't know whether the premises are true? Compare evaluating an argument
whose premises we don't know to be true to applying for a home loan. A couple
goes in and fills out all the forms. The loan officer looks at their answers. She might
tell them right then that they don't qualify. That is, even though she doesn't know if
the claims they made about their income and assets are true, she can see that even if
they are true, the couple won't qualify for a loan. So why bother to investigate
whether what they said is true? On the other hand, she could tell them that they'll
qualify if those claims are true. Then she goes out and makes phone calls, checks
credit references, and so on, and finds out if they were telling the truth.
With an argument that is valid or strong you can say about the premises: Grant
me this and the conclusion follows. Good reasoning is concerned with what follows
from what, as well as with what is true.
Evaluating whether an argument passes these tests requires skills
, which is
what this course is meant to teach you. But evaluating whether an argument is good
also depends on your knowledge, for as you know more, you become better at
evaluating whether premises are plausible and whether possibilities are likely.
E x a m p l e s Are the following arguments valid? If not valid, where on the scale
from strong to weak does the example lie? If the argument is valid or strong, is it
also good?
Example 1 Dr. E is a philosophy professor. All philosophy professors are bald.
So Dr. E is bald.
Analysis The argument is valid: There is no possible way the premises could be
true and the conclusion false at the same time. The conclusion is true, too. But it's
a bad argument, because the second premise is false. We have no more reason to
believe the conclusion than we did before we heard the argument.
SECTION C The Tests for an Argument to Be Good 43
Example 2 Maria (to her supervisor): I was told that I would earn a bonus if I put
in 100 hours of overtime and had a perfect attendance record for two months. I have
since put in 110 hours of overtime and have a perfect attendance record for the last
ten weeks. So I'm entitled to a bonus.
Analysis This is a valid argument. It's not possible for the premises to be true and
the conclusion false. But we don't know if the argument is good because we don't
know if the premises are true.
Example 3 Student athletes should not be given special leniency in assigning their
course marks, because that wouldn't be treating all students equally.
Analysis This is how Maria answered her first writing lesson. But what does
"treating all students equally" mean? It means "treat everyone the same way." So
the argument is: You shouldn't treat athletes differently, because you should treat
everyone the same way. The premise may be true, but it's just a restatement of the
conclusion. The argument begs the question, so it's bad.
Example 4 Dick is a bachelor. So Dick was never married.
Analysis This is not valid: Dick could have been divorced. This argument is
weak: Given what we know, it's not unlikely that the premise could be true and
the conclusion false. So the argument is bad.
Example 5 Good teachers give fair exams, and Dr. E gives fair exams. So Dr. E
is a good teacher.
Analysis The premises of the argument are true. And the conclusion is true, too!
But is it a good argument? Can we imagine a way in which the premises could be
true and the conclusion false? Yes: Dr. E might bore his students to tears and just
copy fair exams from the instructor's manual of the textbook. After all, the premise
doesn't say that only good teachers give fair exams. So the argument is weak, and
hence bad.
Example 6 Maria's hair is naturally black. Today Maria's hair is red. So Maria
dyed her hair.
Analysis Could the premises be true and the conclusion false? Perhaps: Maria
might be taking a new medication that has a strong effect, or she might have gotten
too close to the machinery when they were painting her car, or . . . . These are all
extremely unlikely, but still possible. So the argument is strong, not valid. Since
we know that Maria's hair is black, it's a good argument.
How do we show an argument is weak? We describe at least one likely
way in which the premises could be true and the conclusion false.
44
CHAPTER 3 What Is a Good Argument?
Example 7 Harry: Every time I can remember eating eggs I've broken out in a
rash. It couldn't be the butter or oil they're fried in, 'cause I remember it happening
when I had hard-boiled eggs, too. I must be allergic to eggs.
Analysis This is a strong argument, and we can trust that Harry isn't lying. So it's
a good argument. But it's not valid: There could be a strange new virus that Harry
caught whose only symptom is that it makes him sick when he eats eggs. In a week
or two he might be fine.
Example 8 Prosecuting attorney: The defendant intended to kill Louise. He bought
a gun three days before he shot her. He practiced shooting at a target that had her
name written across it. He staked out her home for two nights. He shot her twice.
Analysis The argument is strong. If there's good reason to believe the premises,
then the argument is good and establishes beyond a reasonable doubt "The defendant
intended to kill Louise." But it's not valid: We don't know the defendant's thoughts,
and the conclusion might be false.
Example 9
Analysis The defendant may be telling the truth. All he says may be true, yet the
argument is weak, and hence bad. What he says shouldn't create reasonable doubt.
Example 10 Tom: You didn't have eggs in the house this morning, did you?
Dick: No. Why?
Tom: Well, you've got some in the refrigerator now.
Dick: Zoe must have bought eggs, since she knew we were out.
Analysis This isn't valid. Zoe's mom could have brought over the eggs; when they
were out, the landlord might have brought them over; a guest who was staying with
them might have bought them; . . . . There are so many likely possibilities for the
premises to be true and the conclusion false that the argument is weak.
Example 11 Tom: You didn't have eggs in the house this morning, did you?
Dick: No. Why?
Tom: Well, you've got some in the refrigerator now.
Dick: Zoe must have bought eggs, since she knew we were out.
Tom: Are you sure?
SECTION C The Tests for an Argument to Be Good 45
Dick: Sure. No one else has a key to the apartment. And Zoe didn't
plan to have any guests over today.
Analysis This argument is stronger than the last one, because some of the possible
ways the premises could be true and the conclusion false have been ruled out. But
it's still not very strong.
Example 12 Tom: You didn't have eggs in the house this morning, did you?
Dick: No. Why?
Tom: Well, you've got some in the refrigerator now.
Dick: Zoe must have bought eggs, since she knew we were out.
Tom: Are you sure?
Dick: Sure. No one else has a key to the apartment. And we never
let anyone else in.
Tom: But didn't your neighbor Mrs. Zzzyzzx say she had some eggs
from her cousins' farm?
Dick: Yes, but Zoe said we should only bring food into the house
that we'd purchased ourselves at the health-food store. And
she always keeps her word.
Analysis This argument is a lot stronger because so many of the ways in which the
premises could be true and the conclusion false have been ruled out. Still, it's not
valid: The landlord could have gotten a locksmith to open the door, and then before
he went out put eggs in the refrigerator; or a burglar could have broken in and left
some eggs behind; or Zoe could have bought a chicken and left it in the refrigerator
and it laid eggs there; or . . . . These are possible ways that the premises could be
true and the conclusion false, but they are all so unlikely that the argument is strong.
And since we can trust Dick's word, it is good. So Tom and Dick have good reason
to believe that Zoe bought the eggs.
Though we can't say exactly where Example 11 lies on the sca
le from strong to
weak, we can say that Example 10 is weak, and Example 12 is strong. But if we
can't say exactly how strong an argument is, isn't the whole business of classifying
46 CHAPTER 3 What Is a Good Argument?
arguments worthless? That would be a drawing the line fallacy. There may be some
fuzziness in the middle, but we can distinguish strong arguments from weak ones.
We've seen good arguments and we've seen bad arguments. A good argument
gives us good reason to believe the conclusion. A bad argument tells us nothing
about whether the conclusion is true or false. If we encounter a bad argument, we
have no more reason to believe or disbelieve the conclusion than we had before.
Exercises for Sections A-C
1. What is an argument?
2. What does it mean to say an argument is valid?
3. What does it mean to say an argument is strong?
4. If an argument is valid or strong, does that mean it's a good argument? Explain.
5. a. How can you show that an argument is not valid?
b. How can you show that an argument is weak?
6. If an argument is valid and its premises are true, is its conclusion true, too? Explain.
7. If an argument is bad, what does that show about its conclusion?
8. If an argument is strong and its premises are true, is its conclusion true, too? Explain.
9. To be classified as good, an argument must pass three tests. What are they?
10. What does it mean to say the three tests for an argument to be good are independent?
11. a. Make up an example of an argument that is valid and good,
b. Make up an example of an argument that is valid and bad.
12. a. Make up an example of an argument that is strong and good,
b. Make up an example of an argument that is strong and bad.
13. Make up an example of an argument that is weak. Is it good?
14. Can we show that an argument is not valid by showing that its conclusion is false?
Give an example or explanation.
15. To decide whether an argument is good, does it depend on whether it convinced anyone?
16. Can an argument be both valid and strong?
17. What do we call an argument with a clearly false premise?
18. Which of the following uses of the words "valid" and "invalid" accord with the definition in this chapter?
a. Your parking sticker is invalid.
b. That's not a valid answer to my question.