3.9: Exercises

Imprecision

1. Newspaper headline writers are notorious for creating headlines that are ambiguous or have a funny alternative interpretation. The ambiguity can be removed by applying the principle of charity. Do this on the following headlines. Rewrite three of them so that they are unambiguous and don't have a humorous interpretation:

a. Red Tape Holds Up New Bridge
b. Prison Warden Says Inmates May Have 3 Guns
c. 19 Feet Broken in Pole Vault
d. Babies Are What the Mother Eats
e. Police Discover Crack in Australia
f. Sharon to Press His Suit in Israel
g. Buildings Sway from San Francisco to L. A.
h. Cause of AIDS Found—Scientists
i. Potential Witness to Murder Drunk
j. Jerk Injures Neck, Wins Award
k. Terminal Smog Not Lethal

■ 2. (a) Add a comma to disambiguate the following headline and remove the humor. Make no other changes in the headline. (b) Say why the headline is humorous.

Honduran Military Chief Quits Saying He Is Fatigued

■ 3. Suppose a menu states, "You can have eggs and juice or cereal." Replace this ambiguous statement with one of the following statements. The replacement must be a legitimate interpretation of the sentence in the menu, yet it must disambiguate the sentence to make it clear that the customer cannot have both eggs and cereal. The best replacement is:

a. You cannot have both eggs and cereal.
b. You can have eggs, but not juice or cereal.
c. You can have (eggs or juice) and cereal.
d. You can have either eggs and juice, or else cereal.
e. You can have eggs, and you can also have your choice of either juice or cereal.

■ 4. If Mario says, "Some of these grapes have seeds in them," can you be sure he also means that some of them don't, assuming that he intends to make a true statement?

5. The following statement might appear in a recommendation letter:

"In my opinion, you will be very fortunate to get this person to work for you."

How does this statement send two messages?

6. Which one of the following is not an ambiguous recommendation that simultaneously supports and attacks the job candidate? Assume that the sentences occur among many other sentences describing the candidate.

a. I simply cannot recommend this person highly enough.
b. I most enthusiastically recommend this candidate with no qualifications whatsoever.
c. In my opinion you will be very fortunate to get this person to work for you.
d. The recommendation that I can offer for this candidate is that she works hard and is productive.
E. I would urge you to waste no time in making this candidate an offer.

7. If a headline were to say, "New Pill Controls Birth Twice a Month," it would be unintentionally funny. Which one rewriting of it says only what was most probably intended?

a. New Pill Works Twice a Month to Control Pregnancy
b. New Birth Control Pill can be Taken Twice a Month
c. Taking New Pill Twice a Month Promotes Birth
d. Taking New Pill Controls Pregnancy Two Times a Month

8. According to this chapter, what are the greatest obstacles facing the A.I. program of natural language processing? Give examples of the obstacles. Begin your answer by defining both AI and natural language.

■ 9. Suppose a hunter walks all the way around a tree trying to get a shot at a squirrel. Meanwhile, the squirrel never leaves the tree but keeps crawling away from the hunter so that he can never can get a clear shot at the squirrel. In other words, the squirrel keeps the tree between the hunter and itself. When John Brown and Henrietta Lacks discuss this hunting situation, John says the hunter circled the squirrel because the squirrel never left the tree and the hunter got to the north, east, south, and west of the tree. Henrietta disagrees, saying the hunter never circled the squirrel because he never got round to the back of the squirrel. This disagreement between John and Henrietta is about what?

a. Whether John is being honest.
b. Whether the squirrel could have been shot.
c. Whether the hunter would agree with John.
d. Whether the squirrel was circled by the hunter.
e. Whether circling really brings you back to the place where you started.

■ 10. The disagreement between John and Henrietta mentioned in the previous question

a. is not merely a semantic dispute.
b. turns on the ambiguity of "circled the squirrel."
c. turns on the difference between a hunter and a killer.
d. is one that a logical reasoner would have no trouble in adjudicating in favor of John. ^[101]

11. Explain why the following passage contains a semantic disagreement rather than a substantial disagreement.

Emilio: When you think about American foreign policy, you've got to admit that Andre is a real American. He is always first to fly the flag. He supports America when other Americans are bad-mouthing it.
Juanita: Andre is a citizen of Argentina who is living here and hoping to become a citizen. So, he's not a real American. He just happens to support American foreign policy.
Emilio: You’ve got to admit that Andre would support America against its enemies.
Juanita: What about his not being an American citizen?

12. The following four choices for completing the sentence vary in their precision. Rank them, beginning with the most precise. Starting with the new budget, our country will be

a. focusing more on the unemployment problem.
b. making changes for the better.
c. changing the definition of unemployment as far as statistics are concerned for computing the percentage of workers who are unemployed.
d. reconsidering the unemployment calculations.

■ 13. Rewrite the following statement in a way (your choice) that makes it less vague:

You have to get more centered and in touch with yourself.

■ 14. Rewrite the following statement in a way (your choice) that makes it vaguer:

You have to get more centered and in touch with yourself.

15. Rewrite the following sentence to make it vaguer.

Pele died of asphyxiation during the Brazil-Argentina soccer championship in 1987.

16. As far as logical reasoning is concerned, identify the most significant difficulty with the following astrological forecast:

May 20 is an unusually bad time for a Leo or a Scorpio to make major decisions.

a. Some astrologers might not like either a Leo or a Scorpio.
b. A bad time for a Leo is usually a good time for a Scorpio.
c. Ambiguity occurs with time because it could mean time of day or time of week or time in music.
d. The difficulty is with not specifying which major decisions.
e. There have been some bad times at Ridgemont High School, says Beyoncé.

17. Use a vague term in two contexts. Make it clear, without saying so directly, that vagueness is not a problem in the first but is a problem in the second.

18. Find a vague word or phrase in a recent daily newspaper. Clip the article, paste it to a regular-size page, and write on the page why the statement is vague. Say whether the vagueness interferes with the communication, and why.

19. Create an original sentence that is too imprecise for the context because it is too general. Say why it is too general.

■ 20. Rewrite the following sentence to make it less precise:

Federer was defeated by Nadal in some U.S. Open tennis tournament or other.

21. Take your answer to the previous question and rewrite it to make it even less precise.

■ 22. Rewrite the imprecise sentence "It is raining fairly hard over there right now" to make it less precise. Explain why it is less precise.

23. The following statement is from an astrology forecast. It is imprecise. Why? What are the sources of imprecision?

Soon, you will be involved in an unusual relationship.

24. Why would a critical thinker say the following report from the planning commission is odd?

If traffic density continues to grow as predicted, then the flow at Howe Avenue and Marconi Boulevard should become congested in two years from next December 21st.

25. [difficult question] Consider the following political problem, and choose the best amendment to the law below. The treasurer Jesse Unruh of the State of California died in office in 1988, and the governor nominated a replacement, his friend Dan Lungren. Lungren’s nomination was voted on by the two houses of the State Legislature—the Senate and the Assembly. The vote occurred within 90 days of the governor's submission of the nomination to the two houses, and the Senate approved the nominee but the Assembly disapproved. The problem this raised was whether Dan Lungren could go ahead and take office. The following is the relevant part of the Constitution of the State of California, Article V, Section 5:

(a) [T]he Governor may fill a vacancy in office by appointment until a successor qualifies.

(b) Whenever there is a vacancy in the office of the Superintendent of Public Instruction, the Lieutenant Governor, Secretary of State, Controller, Treasurer, or Attorney General, or the State Board of Equalization, the Governor shall nominate a person to fill the vacancy who shall take office upon confirmation by a majority of the membership of the Senate and a majority of the membership of the Assembly and who shall hold office for the balance of the unexpired term.

(c) In the event the nominee is neither confirmed nor refused confirmation by both the Senate and the Assembly within 90 days of the submission of the nomination, the nominee shall take office as if he or she had been confirmed by a majority of the Senate and Assembly; provided, that if such 90-day period ends during a recess of the Legislature, the period shall be extended until the sixth day following the day on which the Legislature reconvenes.

Provided the two houses do vote on a nominee, the trouble is that for the nominee to take office, paragraph (b) appears to state that the nominee needs to be approved by both houses, but paragraph (c) implies that the nominee does not need to be. If the intent is really as paragraph (b) appears to state, then the constitution should be amended to clear up the ambiguity. Assuming the intent is also to leave intact the notion that the nominee may take office if neither house actually votes on the nomination, the best amendment woulda.

a. Replace in paragraph (b) "shall take office upon confirmation by a majority of the membership of the Senate and a majority of the membership of the Assembly" with "shall not take office upon confirmation by a majority of the membership of the Senate and a majority of the membership of the Assembly unless voted upon."
b. Replace in paragraph (c) "neither confirmed nor refused confirmation" with "not confirmed."
c. replace "is neither confirmed nor refused confirmation by both the Senate and the Assembly" with "is neither refused confirmation by the Senate and the Assembly."
d. replace "neither confirmed nor refused confirmation" with "not refused confirmation."

■ 26. "Some women volleyball players are taller than some men volleyball players of the same age." This sentence expresses

a. no generalization.
b. a universal generalization.
c. a non-universal generalization.

27. Create a true, explicitly universal generalization about racism that uses the word racism.

28. Create a true, explicitly non-universal generalization about racism that uses the word racism.

■ 29. Give one original example of a true universal generalization about the class of fish and one example of a true non-universal generalization about fish.

30. Suppose Brad’s height is determined to be 5.1147 feet. It was, let's say, measured by using the following operation. Scientists placed a horizontal bar on Brad’s head while he stood next to a vertical beam. They marked on the vertical beam where the floor was and then marked on the beam how high the bottom of the horizontal bar reached. Using very precise instruments, the scientists then measured the distance between the marks.

What did you notice that was unusual, from a critical thinking perspective, in the previous paragraph?

31. Comment on the most significant operationalization problem of the following statement from a scientific report: "People who lie are more likely to have been born in May than people who don't."

32. For the following disagreement, answer these questions: (a) Is the disagreement factual or merely verbal? (b) If it is factual, state the fact in dispute and then state what observation, test, or discovery would settle the dispute. If it is verbal, identify the key term in the dispute and state the different senses in which the two persons are using it.

Leonard: I visited Elvis Presley's grave in Tennessee last summer. I know the King is dead, but it is hard to believe.
Angela: The King isn't dead. He is still influencing music. He is alive and well and living in London where he works as a ghost writer.
Leonard: Ha! A ghost maybe, but not a ghost writer. Elvis departed this world in Las Vegas and was buried at Graceland in Tennessee. Why do you say he's ghost writing?

Angela: A music magazine I read said he is. Everyone in the article said he is still active musically.

■ 33. Read the following dialogue and decide whether the dispute is merely verbal (a semantic disagreement) or factual (substantial disagreement):

Serena: Did you hear that Andrea is in Kaiser Hospital with brain injuries from that motorcycle accident? She is alive but so lifeless lying there, so pitiful, no brain activity, just a slowly beating heart and a faint breath. David, you’ve really got to visit her before she dies.

David: No, she has already died, because she has no brain activity. I heard this from Jesse, who talked to the doctor. I'll go to the funeral instead.

34. Create an original example of equivocation. Underline or italicize the term that changes meaning.

35. "When a liquid turns to vapor, it loses heat and gets colder." In the previous sentence, what is the antecedent (referent) of the word it? Is the word referring to the liquid or the vapor or both? The sentence won’t be clear or understandable to a reader who does not have scientific background knowledge about the principle behind the refrigerator. Rewrite the sentence to remove the ambiguity in the antecedent.

36. (a) Your instructor will supply you with a blank sheet of paper. Use it to list six statements that you believe to be true about your state or its government. Put your name on the paper. You won't be graded on the quality of your answers but only on your participation, (b) When asked by the instructor, exchange your paper with someone else. On the other person's paper, place an asterisk next to the statement that you believe is the least precise or most vague, (c) On the paper, place a question mark next to any statement that you believe to be questionable because it is either false or susceptible to a false interpretation, (d) Your instructor will ask the class to provide examples of statements from the papers that are imprecise and that are questionable, (e) When asked by the instructor, get together with the person whose paper you have and explain why you made the assessments you did in parts (b) and (c). (f) When asked by the instructor, hand in the paper containing your assessments.

■ 37. Comment on the following passage:

Because of the influx of Hispanics and Asians, only about 16 percent of the United States will be white (and non-Hispanic) by the year 2020, according to statistics produced by the scientific research firm.

a. The term United States is pseudoprecise.
b. The term Asian was operationalized improperly.
c. The year is vague.
d. The term statistics is ambiguous.
E. None of the above.

■ 38. Occasionally in disputes about the theory of evolution, someone will say it is a theory and someone else will disagree, saying that evolution is, instead, a fact. This is probably an example of a semantic disagreement. Explain why.

39. What is the first and what is the last general claim made in the U.S. Declaration of Independence? Defend or explain your choices.

■40. How do you tell the difference between a big person and a not so big person?

41. A reporter who is accused of quoting a politician "out of context" is being accused of taking a phrase one way when the context indicates it should be taken another way. Create an original example of this.

■ 42. The italicized phrases in the following items are vague. Are they too vague, given the likely context in which they are expressed, or are they OK?

a. The government wastes millions of dollars every week. I can think of a lot better things to do with that money. Let's use those millions for education and health care instead.

b. Stop right there! Put your hands up slowly, or I'll shoot you in the back.

c. Nurse, please give the patient some of that pain killer.

d. Add milk even though the recipe doesn't call for it. Go ahead. Do it now.

e. Mom, I know you’ve already given me $500, but I still don't have enough money to buy the car. Can I have more ?

f. Letter to the editor of a medical journal: Medicare payment limits for outpatient prescriptions need to be raised by 10 percent because our study indicates that the elderly use a sizeable percent of all outpatient prescriptions.

g. Letter to the editor of a medical journal: Last year, our state's poison control centers handled 338,304 telephone calls at an average cost of $18.24 per call. The state's health department has rigorously evaluated and analyzed the state poison center system by conducting onsite visits to each local poison center operation. They confirm the $18.24 figure, and have recommended continued funding for another five years. The legislature should take the health department's advice.

43. All creationists agree that the universe was created during six days by God's design. After a careful reading of the Bible in 1658, one creationist, Irish Anglican Archbishop James Ussher, calculated the origin of the world to be at 9 am, Sunday, October 23, 4004 B.C., Greenwich Mean Time. Referring to the chapter's definition of pseudoprecision, did the Archbishop probably make a mistake of type 1, 2, or 3?

■ 44. Is more better than less?

■ 45. Discuss the following dialogue:

Philosopher: What do you think of working with gray clay?

Artist: I hate all pieces of clay. They are too hard to work with; I like paint.

Philosopher: Do you hate that statue of David?

Artist: No, it’s magnificent.

Philosopher: But it’s a piece of clay! So, you hate it and don’t hate it.

Artist: Wait a minute!

Definitions

■ 1. Operationalize the term acid. Make it sufficient for a junior high school science text.

■ 2. Describe what is wrong with this lexical definition:

By definition, a vixen is a kind of fox.

3. Create a non-operational definition of acid that would be appropriate for third graders.

■ 4. Which kind of definition is this? (lexical, stipulative, operational, ostensive, etc.)

“I defined Republican,” the pollster said, "to mean anybody who checked the Republican box on the enclosed form.”

5. Suppose you define liquid water to a six-year-old in the following way:

(Liquid) water means the wet stuff that comes out of your faucet when you wash your hands. It is also the stuff in rivers and lakes and puddles.

This definition

a. commits the error of failure to elucidate.

b. is circular.

c. is a definition by example.

d. is stipulative and lexical.

e. is an operational definition.

6. Suppose you define ( liquid) water to a five-year-old as "the wet stuff." The definition is

a. too narrow.

b. circular.

c. too broad.

d. autonomous.

7. In an ordinary conversation, if you were to define steam as the white stuff given off in the air when water is boiled, your definition would probably be acceptable. However, to a scientist, this definition would be incorrect. Find out why, then write an explanation of why your first definition was unacceptable. Hint: Steam is not white.

■ 8. Analyze the errors in the following reasoning:

According to the dictionary definition of science, a science is a body of knowledge amassed in a systematic way. Because a telephone book and a repair manual both are systematized bodies of knowledge, it follows that they, too, are sciences. Thus, the following is a correct listing of some of the sciences: physics, botany, repair manual, chemistry, geology, psychology, telephone book, astronomy, anthropology.

Is the definition too broad, too narrow, or both? How would you improve on the dictionary definition?

9. Construct a definition of bat that is too broad but not too narrow.

10. Construct definitions of the terms ballistic missile and cruise missile that make it clear whether a cruise missile is a ballistic missile. Do not use the term cruise missile in your definition of ballistic missile. This exercise may require additional research.

11. Consider this argument: "Today it will rain or snow there, but not both. Since it is raining there, it’s not snowing. Here is an analysis of it in sentential logic:

R is the sentence "It will rain there."
S is the sentence "It will snow there."

Then the pattern of the above argument is

R or S, but not both R and S.
R
So, Not-S

and that is the form of a valid argument in sentential logic.

In this analysis of the argument, the definitions are

a. lexical.
b. stipulative.
c. circular.
d. inconsistent.
e. vague

Explain why your answer is correct. One major part of this question is to find the definitions.

12. Define the phrase legal right to privacy, then create an argument defending your definition. You are encouraged to use outside research to enrich your answer.

13. Give an operational definition of water for an adult audience.

14. Describe any flaws you notice in the following definitions.

a. By tall woman, I mean "a woman over 5'9"."
b. "History is an account, mostly false, of unimportant events which are brought about by rulers, mostly knaves, and soldiers, mostly fools." (Ambrose Bierce)
c. Apple pie means a pastry with apple filling.
d. The definition of likes better that I used in my report on whether rich women like sex better than poor women was to count the number of "yes" answers from women who answered my question "Do you like sex?"
e. The definition of busybody: a curious person.

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Imprecision

1. From Red Tape Holds Up New Bridge and More Flubs from the Nation's Press, edited by Gloria Cooper, collected by the Columbia Journalism Review, Putnam Publishing Group, copyright by Columbia University of New York, 1987.
2. "Honduran Military Chief Quits, Saying He Is Fatigued." In other words, what he said when he quit was, “I am tired." The silly interpretation that the comma helps remove is "Honduran military chief has been saying he is tired, but now he has stopped saying this."
3. Answer (d). Choice (a) is incorrect because it is not a way to interpret the original sentence, although it is an implication of the sentence when it is interpreted as (d).
4. You cannot be sure. Maybe Mario ate two grapes from a bowl of a hundred grapes, found seeds in both, didn't examine any others, and then made a cautious statement about what he knew for sure at that point.
9. Answer (d).
10. Answer (b). Since the dispute is merely verbal, answer (a) is not correct.
13. In rewriting the sentence, you will have to add information that was not specifically contained in it. For example: You have to decide which of your interests are more important than others; rank these interests; then change your life so that you try hardest to satisfy the highest ranking ones.
14. You need to focus
20. Somebody beat somebody in a tennis tournament.
22. You might have rewritten it as follows: "It is raining now." This reduces the information conveyed by the sentence and thereby makes it less precise.
26. Answer (c). The sentence expresses a non-universal generalization about women volleyball players. To be a universal generalization the first “Some” would need to be replaced with “All.”
29. A universal generalization uses all or its equivalent; a non-universal generalization uses a term that is less universal, such as many or most or some or two-thirds. For example, here is a universal generalization: All (healthy) fish can swim. Here is a non-universal generalization: Many fish are smaller than the typical house cat. Both generalizations are true.
33. The dispute is merely verbal. The disputed term is dead. If the two would just agree on what dead means, they would resolve their conflict, because there are no other facts in dispute. Samantha believes that dead means there is no heartbeat or breath, but David believes that dead means there is no brain activity.
37. Answer (e).
38. The first person could mean theory in the sense of a set of general principles, but the second person could mean theory in the sense of an uncertain statement, one not backed up by evidence. Both persons would be correct with their own usage of the term. A Texas law that was on the books from 1974 to 1984 required that all state-supported school textbooks clearly distinguish scientific fact from mere theory. In particular, the Texas law required the theory of evolution to be taught as a hypothesis on an equal par with the creationist "theory." This law perpetuated an error in the philosophy of science that turns on the three-way ambiguity of the word theory. When a detective says, "My theory is that the butler committed the crime," the word theory means (1) the same as "hypothesis" or "educated guess." The word theory can also mean (2) a general explanation or general system of accepted laws. In addition, the term can also mean (3) unjustified opinion or mere hypothesis. The theory of evolution is a theory in sense (2), not the other two. The legislators were probably confusing the three senses. When we distinguish fact from opinion, we mean that a factual claim is an opinion backed up with a solid justification. If a claim is a fact, then it is not just somebody's opinion—it is a true opinion, as far as the experts can tell. It is important here that the vast majority of experts agree; if they disagree with each other, it would be jumping to conclusions to call a theory a "fact." The theory of evolution is sufficiently well justified scientifically that it deserves to be called a "fact." Creationist theory, on the other hand, is without a solid scientific justification, despite the loud objections of a few of its advocates. It has many religious supporters but no significant scientific support. Although the theory of evolution is a fact in the sense in which we say that anything we have good reason to call "true" we also call a "fact," the theory of evolution is not a specific fact as is "This water boiled at about 212 degrees." The theory of evolution is a moral general fact because it is so wide-ranging. It is general because it is a comprehensive system of principles that is used for explaining a wide range of specific facts, such as the fact that dinosaur bones are buried more deeply than human bones, the fact that DNA proteins in human cells are more like those in monkeys than those in tomatoes, and hundreds of other specific facts. Creationism is also a theory in the sense of being general and not specific. It is general, but it is not a general fact. So, what is the answer to the question, Is evolution a theory or a fact? The answer is that it all depends on how the terms are being defined. It could be both; it might also be neither; or it could be one but not the other. The theory of evolution is a fact in the sense of being true. Yet the theory of evolution is not a specific fact because it's a general truth and not a specific truth. The theory of evolution is a theory because it's an integrated set of principles. Yet the theory of evolution is not a theory in the sense of being a mere opinion without a solid scientific justification.
42. Here are answers to parts (b) and (c).
b. Not too vague. There is no need for more precision in such a situation. Turning around and saying, "How far up do you mean?" would be likely to be answered with a bullet.
c. The answer depends on the nurse's background knowledge. The phrase would be too vague if the nurse has no access to more precise directions as to the kind and exact amount of the painkiller that the doctor expects to be administered. The phrase would not be too vague if the doctor could presume that the nurse already had access to such directions, say, on the patient's chart. A simple answer to part (c) such as "Not too vague" or "Too vague" would not adequately demonstrate depth of insight into the exercise.
44. It all depends on what you are comparing. More pain is not better than less pain. More happiness is better than less happiness
45. The philosopher is being unfair to the artist. When saying, “I hate all pieces of clay,” the artist did not mean to be taken literally; the artist meant, “I hate working with all pieces of clay,” and this is consistent with liking a piece of clay that someone else has worked with.

Definitions

1. Perform the litmus test. Take a strip of purple litmus paper and dip it into the liquid. If, when removed, the paper is red, then call the liquid an acid.
2. The definition is too broad. It is imprecise because it does not say what kind of fox, and it should say what kind because not all foxes are vixens
4. An operational definition.
8. The definition of science is too broad because it includes too many things among the sciences. Being systematic is only one of the requirements for science. The definition of science could be improved to prevent phone books and repair manuals from being included by noting that science is a systematic way of explaining and predicting events. Science is not merely a systematic collection of facts.
10b. Too figurative, and thus too imprecise for seriously conveying the meaning of history.