9.8: Exercises

Inconsistency

■ 1. Which of these signs, if any, gets its humor from an appeal to inconsistency?

a. On a California freeway: “Fine for Littering.”
b. On the wall of a Canadian cleaning service: “Able to Do the Worst Possible Job.”
c. In a Boston fast-food parking lot: “Parking for Drive-Through Customers Only.”
d. At a Florida bookstore: “Rare, out-of-print, and nonexistent books.”
e. Posted at a New Hampshire library honoring the poet Robert Frost: “Frost Free Library.”

■ 2. If somebody says to you that it is raining and it is not, then by applying the principle of charity you can reasonably assume that the person intends to say something logically inconsistent—something that is really so and not so in the same sense at the same time.

a. true
b. false

3. The principle of charity for inconsistency

a. is a technique of thought for revealing or uncovering a contradiction in one's own thinking.
b. says to be charitable to your principles regardless of the inconsistency in other people's principles.
c. is applied to consistent sets of statements to turn them into inconsistent sets.
d. says to try to find a consistent interpretation.

■ 4. If Sarah says, "Andre Agassi from Las Vegas once won the French Open Tennis

Tournament," and if you reply with, "No, he didn't," then you’ve contradicted Sarah

a. true
b. false

5. Read the following newspaper editorial.

Tfiineo Sakai won't be attending classes at the University of Rochester's William E. Simon School of Business this fall. He was admitted all right, but that was before the Eastman Kodak Company found out he worked for Fuji Photo Film in Japan and would actually be associating right there in the same classroom with some of its own employees in a two-year master's degree program for middle-level businessmen. Kodak doesn't approve of that kind of fraternization with its business rivals, and Sakai has been sent packing.

When Kodak barks, Rochester jumps. The film and camera company isn't just the city's leading industry; it's also the reason why the university has one of the ten largest endowments in the country. Other American universities have run into criticism for undertaking research under proprietary contracts with private companies or for accepting funds from foreign countries or other sources of beneficence with strings attached specifying what's going to be taught with that money. But only in Rochester, so far as anyone knows, can a corporate benefactor actually reach right down into the admissions process to determine who's fit to be educated.

Japanese companies like to send their employees to study here so that they can learn more about American business principles and practices. Sakai certainly obtained a terrific object lesson at the Simon school, which has heretofore loudly proclaimed its commitment to free markets and an absence of regulatory oversight. Kodak, for its part, says it was only concerned that some of its people might have felt constrained from talking in school while Sakai was around for fear that they might give away some company trade secrets. Meanwhile, Kodak has announced that it's giving the Simon school another $36,000 a year to train business executives in how to take creative risks. Obviously, there's no connection between the two events.

In the above passage, is the following remark true? The writer reports that Kodak's contributions to the university are the real reason why the university has one of the ten largest endowments in the country, yet the article itself contradicts this claim by suggesting between the lines that this is not the real reason why the university has one of the ten largest endowments in the country.

a. true
b. false

6. The writer of the editorial in the previous question explicitly says there's no connection between the two events (requesting the student rejection and donating $36,000) but implies between the lines that there really is a connection, so the writer accuses Kodak of committing a contradiction between what they say is so and what is really so.

a. true
b. false

7. Given your common knowledge, and paying attention to the source of the information in the above editorial, it is reasonable to be skeptical and say it is fairly improbable that Kodak really intends to give $36,000 more a year to the University of Rochester.

a. true
b. false

8. The writer of the editorial about Kodak says the Simon business school at the University of Rochester has publicly proclaimed a commitment to free markets and an absence of regulatory oversight, yet the writer suggests that the school's actions show they don't actually have that commitment, so the editor indirectly accuses the Simon school of an inconsistency between what they say and what they do.

a. true
b. false

9. Notice in the following dialogue how Emilio slowly uncovers Washington's inconsistent set of moral beliefs.

Emilio: Listen to what it says here in the paper. "David Jones was especially bitter after the experience. After commenting on the incident, he said I don't see why having sex with your mother is wrong. If it feels good, then it's OK. Of course, I would never do it; I wouldn't want to go to jail. Besides, in my own case I never really liked my mother, God rest her soul, but I don't believe it's unethical.'" Damn. Can you believe Jones really said that? I think he ought to get what he deserves.

Washington: What's that?
Emilio: About twenty years making license plates in the prison factory.
Washington: Who's to judge?
Emilio: What do you mean by that? I'm to judge, that's who!
Washington: I doubt it. It's not your place. Are you planning on playing God here? It's for God to decide these things.
Emilio: Are you saying that no ordinary person is supposed ever to make any moral judgments of right and wrong about anybody else's behavior?
Washington: You got it.
Emilio: You don't really believe that. I know what you’ve done.
Washington: What are you talking about? Done what, when?
Emilio: Remember the little boy you found in the psychology building when we were on our way to class?
Washington: Yes.
Emilio: Well, you made a moral decision right there. You could tell he was lost, and you helped him find his way back to his family. He had gotten off the elevator on the wrong floor. You were fifteen minutes late to your psych class.
Washington: Just because I helped him doesn't mean I made any moral judgment of him.
Emilio: Right, you didn't judge him, but you did judge your own action. You acted to help, but you could have acted by doing nothing. A decision not to get involved is a moral decision, too. You chose. You weren't playing God. You just judged between the two ways for you to act.
Washington: OK, but I judged my own actions, I didn't judge anyone else's.
Emilio: Suppose I'd been alone and had found the same boy.
Washington: Then it would have been your problem.
Emilio: Wouldn't you have expected me to do the same thing you did?
Washington: Yeah, I'd have predicted that. I know you're apt to do that kind of thing just because you're you. It comes natural.
Emilio: But wouldn't you have thought badly of me if I'd not done what you expected? You do believe I have the free will to do something you don't expect, right?
Washington: Uh, yes. OK, I'd approve if you did help the kid. Which reminds me, you never paid back the money I gave you when we both had turkey sandwiches at lunch the day before Thanksgiving.
Emilio: Oh. Well, your memory is as good as any elephant in your herd.
Washington: Why is it easier to remember who owes you money than who you owe money to?
Emilio: Maybe because it's easier to judge than to be judged.

Identify the inconsistent set of Washington's moral beliefs that Emilio uncovered with his questioning.

10. If a set of statements is inconsistent, then any addition to the set that doesn't revise the original statements will preserve inconsistency.

a. true
b. false

11. Create a sentence that contains an oxymoron that was not used or mentioned in this chapter.

■ 12. Is this group of three statements logically inconsistent? (In this problem, interpret the word some to mean "at least one and possibly all.")

Every dog chases some cat.
Some cats chase no dogs.
Some dogs chase all the cats.

■ 13. The following statement is false:

A rose is not a rose

a. true
b. false

■ 14. The following statement is self-contradictory:

A rose is not a rose.

a. true
b. false

■ 15. If a person is being inconsistent, as we have been using this term, then the person has irregular patterns of behavior or frequently changes his or her beliefs.

a. true
b. false

16. Are these four statements logically consistent?

• Only bears sleep in this house.
• Goldilocks is not a bear.
• Smokey is a bear.
• Goldilocks and Smokey both sleep in this house although Smokey sleeps downstairs and Goldilocks sleeps upstairs.

17. Consider this list of three statements:

i. x + 1 = 10
ii. x is unequal to 7
iii. x < 3

If the following statement is added to the above three, will the resultant set of four statements be consistent?

x = 9

18. Consider this list of three statements:

i. Modern works of art are not romantic.
ii. But they are occasionally erotic.
iii. However, an erotic work of art could be romantic.

Which statement(s) below, if added separately to the above list, would cause the list to be inconsistent?

a. More than one romantic work of art is erotic.
b. Only one romantic work of art is erotic.
c. Two romantic works of art are modern works.
d. Romantic works of art are not modern.
e. All of the above.

■ 19. Is this set of statements inconsistent, provided there is no equivocation?

The human body is totally a material thing.
The human mind is totally a spiritual thing.
Mind and body can interact.
Spirit and matter cannot interact.

20. Which of the following statements, if added to the four statements in the previous question, would make the new list of five statements be consistent?

a. Spirit and matter do interact.
b. The human body is both a material and a spiritual thing.
c. Sometimes the human body is a material thing and sometimes it is not.
d. None of the above.

■ 21. What logical inconsistency, if any, occurs in this hypothetical news story?

The Russian Military says that it sold 150 bear missiles for $3 million to Central American freedom fighters last month. It says the USSR received full payment. The guerrillas say they paid $3 million to a representative of Soviet intelligence last month; they say they were promised they would receive 150 bear missiles, but only 50 missiles were ever delivered.

22. Defend your evaluation of the quality of the following explanation:

Approximately two-thirds of the doctor's patients caught Barre's disease. This fact can be explained by pointing out that the doctor breathed directly on all his patients, that the doctor had Barre's disease, too, and that whenever a person with Barre's disease breathes directly on another person the other person will catch it, too.

23. Is the following sentence self-contradictory?

Voters must be club members, but some club members are nonvoters.

24. Is the following sentence self-contradictory?

Voters must be club members, but no club members are nonvoters.

■ 25. Are these two statements inconsistent? (Assume the term the senator refers to the same person in both statements so there is no equivocation.)

a. The wife of the senator is an interesting person.
b. The senator has no wife.

■ 26. If two statements are consistent, then they’ve got to be true.

a. true
b. false

27. If a group of two statements is consistent, then at least one of them must be true.

a. true
b. false

■ 28. It is impossible for contradictory statements to accurately characterize the physical world, although people could hold contradictory beliefs about the world.

a. true
b. false

■ 29. My friend Stan told me that yesterday he had met my wife's friend Kate at a political meeting. He said they were going out to dinner this Saturday. My wife told me that she talked to Kate earlier today and Kate said she had met Stan at a political meeting; Kate told her that she and Stan were going to play tennis together on Saturday. What inconsistency, if any, is there here?

■ 30. The statement that Barack Obama was the first president of the United States of America is false. It is also

a. self-contradictory
b. an oxymoron
c. inconsistent with our background knowledge
d. contrary to the claim that Abraham Lincoln was not the first president of the United States of America.

31. Why is inconsistency at the heart of logical reasoning?

■ 32. Are these two statements logically inconsistent?

Hell doesn't exist. Yet in a different sense it really does.

■ 33. Suppose Alex says, "Any oxide will melt if heated to at least 2000 degrees," and Linda says "Yttrium barium oxide melts only above 2300 degrees." Has Linda made a claim inconsistent with Alex's?

a. can't tell (briefly say why)
b. yes
c. no

34. Referring to the previous question, explain why you cannot tell whether Linda has refuted Alex.

35. If three statements are inconsistent (with each other), then at least one of them must be false.

a. true
b. false

36. If John says something that contradicts what Sandra says, does it follow that either John or Sandra is lying?

37. Is the following sentence, which contains three sub-statements, self-contradictory?

An asterique is an emulator; all emulators can transverse-bilateralize, and an asterique cannot transverse-bilateralize.

■ 38. Which of the following statement pairs are logically inconsistent?

1. That cereal is at least 20 percent sugar.
2. That cereal is at most 20 percent sugar.
3. That soft drink is at least 10 percent sugar.
4. That soft drink is at least 15 percent sugar.
5. Some of them are.
6. Some of them aren’t.

a. 1 and 2.
b. 3 and 4.
c. 5 and 6.
d. None of the above.

39. You are asked to find out if the following statement is true. What should a good critical thinker do? "A few dinosaurs lived on Earth before the first sharks, and some sharks were on Earth millions of years before any of the dinosaurs, but there are still many other kinds of sharks in today's oceans, although no dinosaurs that we’ve so far detected." Yes, the instructions are imprecise.

40. If I’ve contradicted what the manager of the New York Giants says, then I’ve thereby refuted what the manager says.

a. true
b. false

■ 41. Are these four statements inconsistent?

• Either the U.S. or Russia will start a global thermonuclear war; nobody else can.
• If Russia starts it, then we will all die.
• Yet if the U.S. starts it, then we will all die, too.
• However, God has given us the knowledge that we won't all die, no matter what happens.

42. Create two graphs—one, a bar graph; the other, a pie chart. Make the two graphs be inconsistent with each other but contain as much of the same information as possible.

43. Write a short essay discussing whether the following two quotations are really inconsistent. Mention why somebody might say they are and why somebody else might say they aren't. Then try to resolve the issue of consistency. Stick to the issue; do not discuss the issue of whether slavery is morally wrong.

"Slavery is morally wrong." (Abraham Lincoln for the Union)
"Slavery is not morally wrong." (Jefferson Davis for the Confederacy)

44. Are these three statements logically consistent with each other?

Only bears sleep in these woods.
Squirrels sleep at night, but not in these woods.
If a thing sleeps in these woods, then it's a bear.
All bears and only bears sleep in these woods.

Counterexamples

1. If statement A is a counterexample to B, then B is a counterexample to A

a. true
b. false

■ 2. (a) Create an original generalization about AIDS or about being HIV positive. (b) Give an example that is consistent with it and supports it. (c) Create a successful counterexample that is inconsistent with it and that refutes it.

■ 3. If it is possible, create an original statement that is easily recognized to be a universal generalization with no counterexamples.

4. If it is possible, create an original statement that is easily recognized to be a universal generalization but that has a counterexample.

5. Create a statement that would be a counterexample to the claim that all things in the universe are cooler than a candle flame.

■ 6. Give a counterexample to the claim that all promises should be kept.

7. Identify the claim below that is a generalization but that has no counterexamples.

a. There is no there there. (Said by Gertrude Stein when she was talking about her home in Oakland, California.)
b. All professional basketball players in the U.S. like to eat Cheerios.
c. Every planet around the sun is held in orbit primarily by the force of gravity.
d. In general, General Abrams has more clout than General Franklin.

8. Here is a refutation of the astrologers' claim that the stars determine every person's destiny. It is from the Confessions of St. Augustine, a Roman, who was a Catholic father born in North Africa and who wrote in about 400 A. D. First, briefly explain why his challenge is a successful refutation. Then revise and weaken the claim by making it less precise so that St. Augustine's remarks won't refute the revised claim.

Firminus had heard from his father that when his mother had been pregnant with him a slave belonging to a friend of his father's was also about to bear. It happened that since the two women had their babies at the same instant, the men were forced to cast exactly the same horoscope for each newborn child down to the last detail, one for his [father's] son, the other for the little slave. Yet Firminus, born to wealth in his parents' house, had one of the more illustrious careers in life whereas the slave had no alleviation of his life's burden.

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Inconsistency

1 All of them. For example in the first sign, there is an inconsistency between one interpretation of the ambiguous sign and your expectation. The one interpretation is that the littering is fine in the sense of OK, but that’s inconsistent with your expectation that the littering is not OK and thus deserving of a financial fine.

2 Answer (b). Perhaps the person means that it is raining in some place but not raining in some other place. That could be true. Using the principle of charity, you would assume that the person intends to say something true; logically inconsistent statements cannot all be true.

4 Answer (a). Your remark contradicts her statement, but doesn’t refute it until you go on to show you are correct and she is not

5 From The Sacramento Bee, September 9, 1987, p. B6.

12 The three could all be true, so they are consistent.

13 Answer (a).

14 Answer (a).

15 Answer (b).

19 Yes, because the statement that spirit and matter cannot interact implies that no spiritual thing can interact with any material thing.

21 No inconsistency. However, it is likely that either the guerrillas were lying or they were cheated by the representative.

25 Yes; (a) presupposes what (b) denies.

26 Answer (b). All that is required is that they could be true as far as their meanings are concerned. These two sentences are consistent even though both are false: George Washington was assassinated by Benedict Arnold. It has never snowed in the United Kingdom.

28 Answer (a).

29 No inconsistency.

30 Answer (c).

32 No, because of that phrase “in a different sense.” If exist can have different senses, then hell might not exist literally as a place you can go to after you die, but it might exist here on Earth in people's minds. However, if exist cannot have this latter sense, then the second statement is simply false, but still not inconsistent with the first.

33 Answer (b).

35 It follows that one of them said something false. It doesn't follow that anyone was intending to say something false—that is, lying.

38 Answer (d).

41 Yes, they are inconsistent. From the first three statements, it follows that we will all die. From the fourth, it follows that we won't. This is an inconsistency. If you know something, then it is true; that idea is applied to the fourth statement.

Counterexamples

2 (a) All past basketball players were HIV positive, (b) Magic Johnson (a basketball player who played for the Los Angeles Lakers) was HIV positive, (c) Johnny Dawkins (a basketball player who played for the Philadelphia 76ers) was not HIV positive.

3 All even numbers are integers.

6 Consider the example of a promise you made to your friend to return the knife you borrowed. In the situation in which he rushes up to you raving mad and saying he wants his knife back so he can kill his mother, you should break your promise. Saying "You should not keep promises that might hurt someone" is a relevant answer. It is in the ballpark, but it is inadequate because it provides no specific example of a promise. A counterexample is always a specific example from the category that the generalization is about.