compound claim
sufficient condition
"or" claim
direct way of reasoning
alternative
with conditionals
contradictory of a claim
indirect way of reasoning
excluding possibilities
with conditionals
false dilemma
affirming the consequent
conditional
denying the antecedent
antecedent
reasoning in a chain
consequent
with conditionals
contrapositive
slippery slope argument
necessary condition
reasoning from hypotheses
EXERCISES for Chapter 6 135
Exercises for Chapter 6
1. Make a list of the valid argument forms we studied in this chapter.
2. Make a list of the weak argument forms we studied in this chapter.
3. Make a list of the bad argument types we studied in this chapter.
4. What does it mean to say someone is reasoning in a chain with conditionals?
5. What is a slippery slope argument?
6. Rewrite the credit card argument on p. 133 to show that it is reasoning in a chain.
7. Assume these three claims are true:
• If Dr. E wins the lottery, then Dr. E will be rich.
• If Dr. E's book sells one million copies, then Dr. E will be rich.
• If Dr. E marries a rich woman, then Dr. E will be rich.
a. Write an equivalent contrapositive for each.
b. Write the contradictory of each.
c. Give an example of each of the valid and weak forms of arguments using
conditionals, except reasoning in a chain.
d. State which claims are sufficient for which others.
e. State which claims are necessary for which others.
8. Make flash cards to practice recognizing the forms of arguments we saw in this chapter.
• On the back of a card, put the form (for example, If A then B; not A; so not B ) .
• Write whether it's valid or weak. On the front, put an example you've made up.
• Make three cards for each form, each card showing a different example. Some of the
examples should have a conditional that isn't already in "if . . . then . . ." form.
• Practice with your own cards.
• Trade with a fellow student.
• If you're not sure that your examples illustrate the forms, ask your instructor.
Here's some more of Tom's homework, with Dr. E's comments.
Suzy: If you apologize to Zoe, I'm sure she'll help you look for Spot.
Dick: It's her fault he got loose. I won't apologize.
Suzy: Then she won't help you look for Spot.
Argument? (the whole dialogue) (yes or no) Yes.
Conclusion (if unstated, add it): Zoe won't help Dick look for Spot.
Premises: If you apologize to Zoe, she'll help you go look for Spot.
It's Zoe's fault Spot got loose. Dick won't apologize to Zoe.
Additional premises needed (if none, say so): None.
Classify (with the additional premises): Valid.
Form: It's the direct way of reasoning with conditionals.
Good argument? (yes or no, with an explanation) Good.
No . It's a exist of denying the antecedent. The premises are true, all right,
but Zoe did go help Dick. She felt guilty.
136 CHAPTER 6 Compound Claims
If you don't give to charity, you're selfish. If you pay all your bills on time with
nothing left over, you can't give to charity. Since you don't want to be selfish,
you shouldn't pay all your bills on time.
Argument? (yes or no) Yes.
Conclusion (if unstated, add it): You shouldn't pay all your bills on time.
Premises: If you don't give to charity, you're selfish. If you pay all your bills
on time with nothing left over, you can't give to charity. You don't
want to be selfish.
Additional premises needed (if none, say so): When you pay your bills, you
have nothing left over.
Classify (with the additional premises): Valid.
Form: Reasoning in a chain and indirect way.
Good argument? (yes or no, with an explanation) It looks O.K. if the
premises apply to the person, but something seems wrong.
Good. You recognized the form, and you're getting good at spotting what
unstated premises are needed. 'What's wrong here is that "selfish" is too vague.
The first premise isn't true. 'What is true, perhaps, is "If you don't give to charity
whenyou have more money than you need for your essentials, then you're selfish."
For Exercises 9-26, answer the questions below.
Argument! (yes or no)
Conclusion:
Premises:
Additional premises needed to make it valid or strong (if none, say so):
Classify: valid very strong weak
One of the forms we studied in this chapter! (state which one)
Good argument! (check one)
• It's good (passes the three tests).
• It's valid or strong, but you don't know if the premises are true,
so you can't say if it's good or bad.
• It's bad because it's unrepairable (state which of the reasons apply).
9. If Suzy breaks up with Tom, then she'll have to return his letter jacket. But there is no
way she'll give up that jacket. So she won't break up with Tom.
10. Steve Pearce is a congressman who meets with his constituents regularly. If someone is
a good congressman, he meets with his constituents regularly. So Mr. Pearce is a good
congressman.
11. To take issue with current Israeli policy is to criticize Israel. To criticize Israel is to be
anti-Israel. To be anti-Israel is to be anti-Semitic. So if you take issue with current
Israeli policy, you're an anti-Semite.
12. Dr. E (on an exam day): If students don't like me, they won't show up. But all of them
showed up today. So they must really like me.
EXERCISES for Chapter 6 137
13. Manuel: Look here in the paper. People in Uganda are dying of some fever where they
hemorrhage a lot.
Maria: If people in Uganda are dying of hemorrhagic fever, it must be the ebola virus.
Manuel: So it's the ebola virus!
14. Maria: Professor, professor, why wouldn't you answer my question in class?
Professor Zzzyzzx: Questions in my class I do not allow. If one student I am allowing
to ask a question, then others I must allow. Und then I will have lots and lots of
questions to answer. Und time I won't have for my lecture.
15. Maria: Lee will take care of Spot Tuesday if Dick will help him with his English paper.
Manuel: (later) Dick didn't help Lee with his English paper, so I guess Lee didn't take
care of Spot on Tuesday.
16. Dick: If Freud was right, then the only things that matter to a man are fame, riches,
and the love of beautiful women.
Zoe: But Ralph is poor, single, never married, and uninterested in women.
And he's certainly not famous. Yet he's happy. So Freud was wrong.
17. Only if Columbus landed in a place with no people in it could you say that he discovered
it. But the Americas, especially where he landed, were populated. He even met natives.
So Columbus didn't discover America. He just discovered a route to America.
18. Tom: If Dick loves Zoe, he'll give her an engagement ring.
Harry: But Dick loves Spot a lot more than Zoe.
Suzy: So Dick won't give Zoe an engagemen
t ring.
19. Every criminal either is already a hardened repeat offender or will become one because
of what he'll learn in jail. We don't want any hardened criminals running free on our
streets. So if you lock up someone, he should be locked up forever.
20. Mary Ellen: If I go on Jane Fonda's workout and diet plan, I'll lose weight.
Suzy: (later) Did you see how much weight Mary Ellen lost?
Zoe: She must have gone on that workout plan by Jane Fonda.
21. Dick: I heard that Tom's going to get a pet. I wonder what he'll get?
Zoe: The only pets you're allowed in this town are dogs or cats or fish.
Dick: Well, I know he can't stand cats.
Zoe: So he'll get a dog or fish.
Dick: Not fish. He isn't the kind to get a pet you just contemplate.
Zoe: So let's surprise him and get him a leash.
22. Mom: For a marriage to work, people have to have a lot in common.
Zoe: Wrong! I know lots of miserable marriages where the people had a lot in
common.
23. Lee: If Maria's paycheck comes in on time, she can pay the rent this month.
Manuel: I saw Maria at the bank this afternoon. She said she was depositing her
paycheck.
Lee: Great! So the rent will be paid!
138 CHAPTER 6 Compound Claims
24. Aid to third-world countries? Why should we care more about starving children there
than here?
25. Zoe: I can't believe you let Spot run away on your walk.
Dick: We'll just have to wait for him to come home. I searched everywhere for him.
Zoe: {later) Did you let Spot back in the yard?
Dick: No.
Zoe: So someone else must have let him in. The gate's latched.
Dick: Maybe he got back in by himself.
Zoe: No. If he could get in, he could get out. And if he could get out, he would,
because he loves to run around the neighborhood. But he never gets out
anymore when the gate is latched.
26. Maria: Listen to this argument I read in Steen's Practical Philosophy for the Life
Sciences, "If the population density of a species is high in some area, then the
species will not reproduce in that area. If a species doesn't reproduce in some
area, it will go extinct in that area. Therefore, if the population density of a
species is very high in some area, it will go extinct in that area."
Lee: Gosh, that explains why there aren't any alligators in New York: there used to be
too many of them.
27. You've worked hard enough. Take some time off. Go to a bar or a patty or a church
gathering. Listen. And bring back examples of the valid and weak forms of reasoning
we studied in this chapter.
Additional Exercise
28. Assume that all the claims below are true:
• If a 250 ton meteor crashes into earth, then mankind will become extinct.
• If scientists are put in charge of nuclear weapons, then mankind will become extinct.
• If the ebola virus breaks out in Africa, then mankind will become extinct.
• If an ice age freezes all the seas, then mankind will become extinct.
Using them:
a. Write the contradictory of each "if. . . then . . ." claim.
b. Write the contrapositive of each "if. . . then . . ." claim.
c. Give an example of each of the valid and weak forms of arguments using
conditionals, except reasoning in a chain.
d. State which claims are sufficient for which others.
e. State which claims are necessary for which others.
F u r t h e r Study Propositional logic is the study of how to analyze arguments solely in
terms of their structure as composed of compound claims using "and," "or," "not,"
" i f . . . then . . .". The appendix on truth-tables is a short introduction to it. A course on formal logic will spend several weeks on the subject.
Writing Lesson 6
You've learned about filling in unstated premises, indicator words, what counts as a
plausible premise, and reasoning with compound claims.
Write an argument either for or against the following:
For any course at this school, if a student attends every class, takes all
the exams, and hands in all the assignments, then the professor should
give the student a passing mark.
Check whether your instructor has chosen a different topic for this assignment.
In order to improve your new skills, the directions for this assignment are a
little different. You should hand in two pages:
First page: A list of premises and the conclusion.
Second page: The argument written as an essay with indicator words.
We should be able to see at a glance from the list of premises whether your
argument is good. The essay form should read just as clearly, if you use indicator
words well. Remember, there should be no claims in the essay form that aren't listed
as premises.
Note that the topic is a conditional. You need to understand how to form the
contradictory in order to make up your pro and con lists and to write your argument.
Be very clear in your mind about what you consider to be necessary as opposed to
sufficient conditions to get a passing mark.
To show you some of the problems students have, I'm including Suzy's
argument on a different topic, as well as Tom's. Lee wrote a better one, so I've
included his, too.
139
140 Writing Lesson 6
Suzy Queue
Critical Thinking
Issue: If a professor's colleagues do not consider his exams to be well written,
then marks for the course should be given on a curve, not on percentage.
Premises:
1. A grade on a test reflects just how students are doing on that subject. If a test is
not clearly understood, then the reflection of the scores will be lower.
2. Every student deserves to be treated fairly if the test is not clearly written the
opportunity is not equal.
3. Due to the unclear test, the grading should start with the highest scored test in the
class and the other test scores behind that.
4. Unclear tests should not be given in the first place, so to compensate for the
strain on your brain for trying to decipher the test, grades should be curved to
compensate.
5. The test is a direct reflection of how the teacher is getting through to his students,
so in order to have an accurate idea, grading on the curve would show him the
relation of all the students scores together.
Conclusion: Teachers who give poorly written exams should grade on the curve.
Writing Lesson 6 141
Suzy Queue
page 2
A grade on a test reflects just how students are doing on that subject. If the test is
not clearly understood, then the reflection of the scores will be lower. Every student
deserves to be treated fairly if the test is not clearly written the opportunity is not
equal. Due to the unclear test, the grading should start with the highest scored test
and the other test score behind that. Unclear tests should not be given in the first
place, so to compensate for the strain on your brain for trying to decipher the test,
grades should be curved to compensate. The test is a direct reflection of how the
teacher is getting through to his students, so in order to have an accurate idea,
grading on a curve would show him the relation of all the students scores tog
ether.
Teachers who give poorly written exams should grade on the curve.
Some serious problems here, for (1), what does "reflect" mean? And "clearly
understood"? By whom? That's the point. Besides, it's not one premise— it's two
claims, for (2) you apparently have two claims, but it's incoherent, Your (4) is an
argument (that word "so" is the clue), not a premise. And (5) is two claims, too.
You almost proved the conclusion you've stated. 'But you missed the point. It's a lot
easier to prove what you stated than the issue you were supposed to write on. 'Who
decides what "poorly written" means? 'Where is anything about his colleagues?
It's pretty clear to me that you wrote the essay first, and then tried to figure out
what you said.
142 Writing Lesson 6
Tom Wyzyczy
Critical Thinking
Section 4
Writing Lesson 6
Issue: Every student should be required to take either critical thinking or freshman
composition, but not both.
Definition: I'll understand the issue as "University students should be required to
take either a freshman course on critical thinking or freshman composition,
but not both."
Premises:
Critical thinking courses teach how to write. 1
Freshman composition teaches how to write. 2
Critical thinking courses teach how to read an essay. 3
Freshman composition teaches how to read an essay. 4
Credit should not be given for taking two courses that teach roughly the same
material. 5
If credit shouldn't be given for taking a course, students shouldn't be required to
take it. 6
Conclusion: Every student should be required to take either critical thinking or
freshman composition, but not both.
continued on next page
This is sloppy workcompared to what you've done in the past. You've shown, more or
[ess, that a student should not have to take both courses. But you haven't shown that
he should take one or the other, which is also part of the issue [ (A or B) and not C].
So you've established neither the original claim nor its contradictory.
You need a claim that links 1-4 with 5 and 6, like "Freshman composition and
criticalthinking courses teach the same material." (I see on the next page you do have
that claim.)
But worse is that 6 is at Best dubious: How about those students who have to take-
remedial math for which no credit is given? And l and 2 are too vague. Both courses
Richard L Epstein Page 18
