population as a whole.
11. No. You could get a very biased sample by chance, but the likelihood of that happening is very,
very small.
12. Yes. The computer example in Section C.5 of Chapter 14, p. 290.
13. There is a 97% chance that between 39% and 45% of the voters favor that candidate.
14. The sample is big enough. The sample is representative. The sample is studied well.
15. A hasty generalization. The claims about the too-small sample are called "anecdotal evidence."
16. Describing the purported cause and effect with claims:
The cause happened (the claim describing it is true).
The effect happened (the claim describing it is true).
The cause precedes the effect.
It is (nearly) impossible for the cause to happen (be true) and the effect not to happen (be false),
given the normal conditions.
The cause makes a difference—if the cause had not happened (been true), the effect would not
have happened (been true).
There is no common cause.
17. You still have to establish that the cause makes a difference.
18. Reversing cause and effect. Post hoc ergo propter hoc (looking too hard for a cause).
Tracing the cause too far back.
19. Controlled cause-to-effect. Uncontrolled cause-to-effect. Uncontrolled effect-to-cause.
20. Because arguing or persuading badly:
Undermines your own ability to reason well.
Helps destroy democracy.
In the long run doesn't work as well as reasoning well.
Appendix: Using Examples in Reasoning
5. a. Basenjis don't bark.
e. Most Wendy's restaurants have a salad bar.
7. Even if the first premise is true, the argument is bad. This course is a counterexample: The exams are fair, but it's not easy.
8. Unstated premise: You have to inhale marijuana to get high from it. Valid. But that premise is
false: You could eat it.
10. Unstated premise: Almost any professor who's never been late before and is very conscientious
and is late for the first time has been in an accident. Unlikely. He could have been ill, and the
secretary forgot to tell the class. Unstated premise is dubious. Without that premise it's not valid
or strong. So it's unrepairable.
Appendix: Truth-Tables
Sections A and B
1. "and," "or," "not," "if. .. then . . . "
2. The only aspects of claims that we will pay attention to are whether the claim is true or false and how it may be compounded out of other claims.
3. A tautology is a compound claim that is true regardless of the truth-values of its parts.
4. Represent the claim using . Replace the claims with letters. Make a truth-table with
the last column the formal claim. If all the entries in that column are T, then it's a tautology. If
even one is F, it's not a tautology.
5. Form the table for each. They are equivalent if for every row they are both true or both false.
428 Answers to Selected Exercises
6.
8.
11. Tautology.
12. Not a tautology.
14. Not a tautology.
15. Not a tautology.
Answers to Selected Exercises 429
16.
18.
Section C
1.
4. Dick prefers steak Zoe prefers spaghetti ["While" doesn't mean "at the same time" here.]
5. "While" does mean "at the same time," and when a claim is true can't matter when we use the symbols. So the claim can't be represented.
7. Not compound, just two claims. Or: You whine all the time I love you
10. We're going to the movies tonight v we're going out for dinner tonight. However, if you think
the "or" is exclusive then follow Example 3.
13. (Dick takes Spot for a walk Dick will do the dishes) (Dick will take Spot for a walk)
16. Spot barks (there's a skunk in the yard there's a raccoon in the yard)
17. How you formalize this will depend on how you understand "regardless." Here's one
interpretation:
[(You get mad at me) (I will visit your mother)] (You get mad at me)
(I will visit your mother) (You cajole me) (I will visit your mother)
(You cajole me) (I will visit your mother)
18. Can't represent it. It's not. Every student in Dr. E's class is over 18 v every student in Dr. E's class is taking the course while in high school. That could be false and the original true.
[Compare: Every student is male or female.]
20. a.
b.
c.
d.
e.
f.
Section D
1. Every argument that has that form is valid.
2. Not necessarily. It might have another valid argument form. Or it might be a strong argument.
For example: All cats meow. Puff is a cat. So Puff meows. Truth-tables won't show that this is
valid.
430 Answers to Selected Exercises
Valid
Valid. It's not possible for the premises to be true and the conclusion false at the same time.
Invalid. Either circled row shows that.
Valid. Argue that if C E were false, then both C and E would be false. Since B C and D E
are true, both B and D would have to be false. But B vD is true. So one of B or D is true. A
contradiction. So one of C or E is true.
9. Valid.
10. Valid.
11. Spot is a cat Spot meows, (Spot is a cat)
So (Spot meows)
Not valid. Denying the antecedent.
12. The moon is made of green cheese 2 + 2 = 4
(the moon is made of green cheese)
So 2 + 2 = 4
Valid. Excluding possibilities.
Answers to Selected Exercises 431
13. Valid, same as Exercise 12. Sure, the conclusion is false. It's valid, not good.
14. (The students are happy no test is given) (no test is given the students are happy)
The students are happy the professor feels good
The professor feels good (the professor will feel like lecturing)
(the professor feels like lecturing) the professor will give a test
So (the students will be happy)
[Identify "the professor will give a test" with "a test is given."]
First note that the last three premises yield, via reasoning in a chain, A B.
So we've reduced it to:
Thus we have both A B and A B. And so from Exercise 4 we have A. So it's valid.
15. Dick and Zoe visit his family at Christmas they will fly
Dick and Zoe visit Zoe's mother at Christmas they will fly
Dick and Zoe visit his family at Christmas
Dick and Zoe visit Zoe's mother at Christmas
So they will fly. [Identify "They will fly"
with "Dick and Zoe will travel by plane."]
Valid. Valid
16. (Tom is from New York Tom is from Virginia)
Tom is from Syracuse (Tom is from New York Tom is from Virginia)
So, (Tom is from Syracuse) ["Tom is from the East Coast" isn't needed.]
Valid.
If it were possible to have D false, and so D true, with these premises true, then by the direct
way of reasoning with conditionals, B C would be true. But the first premise gives us that
is true. A contradiction. So D is false. So D is true.
17. The government is going to spend less on health and welfare.
The government is going to spend less on health and welfare (the government is going to cut
the Medicare budget v the government is going to slash spending on the elderly)
&nbs
p; The government is going to cut the Medicare budget the elderly will protest
The government is going to slash spending on the elderly advocates of the poor will protest
So: The elderly will protest advocates of the poor will protest
Valid.
From the first two premises we get B C. Then if we want we can do a table. Or we can argue as
follows. Suppose D E were false. Then both D and E are false. So by the indirect way of
reasoning with conditionals, both B and C would have to be false. So B C would have to be
false. But we already have that B C is true. So D E isn't false.
432 Answers to Selected Exercises
Appendix: Aristotelian Logic
Section B
2. To use a term in a categorical syllogism, there must be at least one thing that term stands for.
7. Whether the claim is universal or particular.
8. Whether the claim is affirmative or negative.
10. Categorical? Yes.
Subject: Cats.
Predicate: Carnivores.
Quantity: Particular. Quality: Negative.
11. Categorical? Yes.
Subject: Tom.
Predicate: Football players.
Quantity: Universal. Quality: Affirmative.
13. Categorical? Yes. All donkeys are meat eaters.
Subject: Donkeys.
Predicate: Meat eaters.
Quantity: Universal. Quality: Affirmative.
16. Categorical? Yes (though it's a stretch). No knowers of critical thinking are things that will ever starve.
Subject: Knowers of critical thinking.
Predicate: Things that will ever starve.
Quantity: Universal. Quality: Negative.
17. Categorical? No. Nearly every all. Nearly every some.
18. Categorical? No. It's a compound.
23. Categorical? Yes. Dr. E is not a cat owner.
Subject: Dr. E.
Predicate: Cat owners.
Quantity: Universal. Quality: Negative.
25. Categorical? No. You can't make comparisons in categorical claims, or at least not in a way that's useful for reasoning.
28. Categorical? Yes. Some professor at this school is a person known to have failed all students in his class.
Subject: Professors at this school.
Predicate: People known to have failed all students in his class.
Quantity: Particular.
Quality: Affirmative.
Section C
2. a. In no possible circumstance can they both be true, though they can both be false.
3. a. In no possible circumstance can they both be false, though they can both be true.
4. a. If "All dogs bark" is true, then "Some dogs bark" is true. If "Some dogs bark" is false, then
"All dogs bark" is false,
b. If "No cats bark" is true, then "Some cats do not bark" is true. If "Some cats do not bark" is false, then "No cats bark" is false.
5. a. A claim equivalent to one in the form "All S are P."
b. A claim equivalent to one in the form "No S is P."
c. A claim equivalent to one in the form "Some S is P."
d. A claim equivalent to one in the form "Some S is not P."
Answers to Selected Exercises 433
8. Contrary.
9. Contrary, but not via categorical form.
10. Contradictory.
11. Subalternate.
12. Subcontrary.
16. Contrary, but neither are categorical.
Section D
4. The term that appears in both premises.
5. The premise that uses the major term.
6. The premise that uses the minor term.
8. Invalid. Reasoning backwards with "no."
9. All S are M. All M are P. So all S are P. Valid. Reasoning in a chain with "all."
10. All S are M. No M is P. So some S is not P. Valid.
11. Some S is M. All Mare P. So some S is not P. Invalid.
12. Some S is M. Some M is P. So some S is P. Invalid. Reasoning in a chain with "some."
13. All S are M. No M are P. So no S are P. Valid.
14. All S are M. Some M is not P. So some S is not P. Invalid.
15. All S are M. All M are P. So some S are P. Valid.
17. All wasps are stingers (A). Some bumblebees are not stingers (O).
So some bumblebee is not a wasp (O). Valid.
18. No badly managed business is profitable (E).
No oyster cultivating business in North Carolina is badly managed (E).
So some oyster cultivating business in North Carolina is profitable (I).
Invalid.
19. Not categorical because "most" "all" and "most" "some." Invalid, but strong.
20. No straightforward way to view this as categorical. But valid.
21. Not categorical, because compounds aren't categorical. Invalid, weak, affirming the consequent.
22. EAE. Valid.
23. Police chiefs who interfere with the arrest of city officials are always fired. (A)
People who are fired are people who collect unemployment. (A)
So some police chiefs who interfere with the arrest of city officials are people who collect
unemployment (I).
Valid.
24. No obvious rewrite as categorical. But valid.
Appendix: Diagramming Arguments
Section A
The answers here are not definitive. When an argument is incomplete and doesn't have enough
indicator words, there are likely to be different ways to repair it.
1. 1 + 2 2. No one under sixteen has a driver's license. 1
So Zoe must be over sixteen. 2 Zoe has a driver's license, a
3
434 Answers to Selected Exercises
3. If an animal is such that 2 and 3, then it is the dumbest animal in the world, a
4. I'm on my way to school. 1 I left five minutes late. 2 Traffic is heavy. 3 I'll be late for class. 4 I might as well stop and get breakfast. J Whenever I'm on my way to school and I'm
five minutes late and traffic is heavy, I will be late for my classes, a If I'm late for classes, I might as well be very late or miss the class, b
5. Pigs are very intelligent animals. 1 They make great pets. 2
They learn to do tricks as well as any dog can. 3 They can be
housetrained. 4 And they are affectionate 5. They like to cuddle. 6
Pigs are known as one of the smartest animals there are. 7
If you get bored with them or they become unruly, you can eat
them. 8 Anything that is intelligent, can be housetrained, and is
affectionate is a great pet. a
6. Smoking is disgusting. 1 It makes your breath smell horrid. 2 If you've ever kissed someone after they smoked a cigarette you feel as though you're going to vomit. 3 Besides, it will kill you. 4 You should not do anything that is disgusting and can kill you. a You should not smoke, b
7. You're good at numbers. 1 You sort of like business. 2 You should major in accounting 3—
accountants make really good money. 4 If you're good at numbers and sort of like business,
you'll be good at accounting, a If you're an accountant you'll make good money, b You should major in something that you'll enjoy, be good at, and make good money at. c
Accounting is the only thing that you'll enjoy, be good at, and make good money at. d
8. Not an argument.
Section B
1. You should not take illegal drugs. 1 They can kill you. 2 If you overdose, you can die. 3
If you share a needle, you could get AIDS. 4 If you get AIDS, then you die. 5
If you don't die (not 3), you may end up a vegetable or otherwise permanently incapacitated. 6
Answers to Selected Exercises 435
By using drugs you run the risk of getting arrested and possibly going to jail or having a hefty
fine
against you. 7
Some think the "high" from drugs is worth all the risks. 8 They are addicted. 9
They are only trying to justify supporting their habit. 10
You shouldn't do anything that has a high risk of killing you or permanently incapacitating you
or putting you in jail or having a fine against you. a
People who are addicted to drugs and are trying to justify their habit shouldn't be believed, b
Sex is the answer to almost everyone's problems. 1
It takes away your tensions. 2
It doesn't if you're involved with someone you don't like. 3
Sex makes you feel better. 4
It doesn't if it's against your morals. 5 Heroin makes you feel good. 6
It's healthy, natural, just like eating and drinking. 7
You can catch terrible diseases. 8 Sex should be confined to marriage. 9
Just looking at the diagram, we can see that Zoe has not
established her conclusion: Every one of her premises has
been brought into doubt (by a plausible claim).
This is an example in which the counterargument is
intended to do more than throw doubt on the
conclusion: It's meant to establish another claim.
(Though it's missing premises for that.)
3. Nixon was a crook/criminal. 1 He said he wasn't in the famous "Checkers" speech. 2
That was just political evasion. 3 You can't just take someone's word that he's not a criminal, especially if he's a politician. 4
He directed the break-in at the Democratic Party Headquarters. 5
They never showed that he did that. 6
His accomplices like Haldemann were
covering up. 7
That's why they got pardoned. 8
Nixon used the FBI against his enemies. 9
It was stupid for Clinton to make a speech
honoring Nixon when Nixon died. 10
Clinton was doing it so that when he dies
someone will make a speech for him. 11
It is stupid to make a speech honoring
someone who was a criminal, a
(Don't add "Clinton is a criminal." There's no
reason to believe that Zoe thinks that's plausible.)
Index
Italic page numbers indicate a definition.
Abd-el-Kadr, 99
Aristotelian logic, 373-384
accepting or rejecting claims, criteria
Aristotle, 373,382-383
Richard L Epstein Page 55