10.5: Exercises

Following-From and Implication

In answering the following questions, go light on applying the principle of charity or you will find yourself being so charitable that you can find no examples of bad reasoning. The concept checks and worked exercises can be helpful guides in deciding when to apply the principle.

■ 1. From the fact that all ice melts when placed in a pan above the lit burner of a gas stove, does it follow with certainty that if the president of France places some ice in a pan above the lit burner of a gas stove in Paris next Christmas, his ice will melt?

a. yes
b. no

■ 2. Explain why "no" is an incorrect, or less than adequate, answer to the following question:

Suppose a woman is arrested for a crime, and there are two eyewitnesses who say she is guilty. Does it follow that she is guilty?

3. If Senator Fairchild of New Mexico admits his guilt to the charge of breaking and entering, does it follow that he entered after breaking in? Why?

■ 4. Explain the error in this reasoning:

If Jeremy Irons says, "All U.S. presidents are American citizens" it follows that the current president is an American citizen. Surely that's a mistake. The current president is an American citizen not because Jeremy Irons says something but because of certain Constitutional requirements.

5. Assuming (with the IRS) that all items from column C are to be listed in column F and that all items from column F are to be listed on form 1040 Schedule SA, then

a. it follows with certainty
b. it follows with probability
c. it does not follow

that all items from column C should be listed on form 1040 Schedule SA.

6. Which of the following arguments are deductively valid? Don’t worry about soundness.

a. Whales are mammals, but the biggest living thing in our sea is definitely not a mammal, so it's not a whale either.
b. Potatoes are a kind of produce, and not all of Bob's fattening foods are potatoes, so not all of his fattening foods are produce either.
c. That squirming thing has no backbone, but all fish have backbones. So it's not a fish.
d. All fat fish are good swimmers. No house cat is a fat fish. So no house cats are good swimmers.

7. To ask whether a statement implies another statement is usually to ask an ambiguous question, even if neither statement itself is ambiguous. Briefly explain why.

8. Find a real-life example of a deductively sound argument.

9. Assuming that the following nursery rhyme is an accurate report, which are the only accurate headlines? That is, which can be deduced from the information in the song?

Old MacDonald had a farm. Ee ii ee ii oh.

And on this farm he had some pigs. Ee ii ee ii oh. With an oink! oink! here. And an oink! oink! there. Here an oink! There an oink! Everywhere an oink! oink! Old MacDonald had a farm. Ee ii ee ii oh.

a. Old Man's Farm Overrun by Wild Pigs
b. Cries of Pigs Indicate Animal Abuse on MacDonald Farm
c. MacDonald Animal Farm Teaches Pigs Vowels
d. MacDonald Has Farm That Had Pigs
e. MacDonald Is Man Who Owned Farm That Had Pigs
f. MacDonald Had Farm That Had Animals
g. MacDonald Had Farm That Has Pigs

■ 10. Referring to the previous exercise, does statement (e) logically imply statement (f)?

a. yes
b. no

11. Does statement (e) above logically imply statement (g)?

a. yes
b. no

■ 12. Do the statements in the Old MacDonald song imply statement (e)?

a. yes with certainty
b. yes with probability
c. no, not at all

13. Find three examples of reasoning in which the conclusion is intended to follow from the premises but does not. The sources must be from your own experience outside the college and its classrooms and textbooks. Sources might be newspaper or TV ads, Internet web pages, magazine articles, conversations, books, and so on. Cut out, photocopy, or write up each example on a separate (8.5 x 11 inches) page. On that page, or on the next page if you need more room, identify where the example came from and the date of the publication or the broadcast. Then identify and explain what is illogical about the illogical reasoning that occurs. Staple together your examples in the upper left corner, after adding a cover page containing your name. Don't bother using a fancy binder or notebook. You will be graded on the accuracy and clarity of your identification of the illogical reasoning and on the variety of your examples.

14. Let B = "x is an even number" and let C = "x is 8/2." Then does B logically follows from C?

a. yes
b. no

15. For the previous question, if B is true, then C follows from B with certainty.

a. true
b. false

16. Consider the following proposed argument:

Every man is a potential killer. Everyone who went to the bank is a man. Therefore, everyone who went to the bank is a potential killer.

As long as the ambiguous term bank is referring in both cases to the same financial bank or the same riverbank, does the ambiguity make any difference to whether the conclusion follows from the premises?

17. Assuming that a financial bank is intended in the previous question, does the conclusion follow with certainty from the premises?

18. All cows are mammals and have lanthrobia. All squirrels are mammals and have lanthrobia. All humans are mammals and have lanthrobia. Therefore, all mammals have lanthrobia.

In this argument the conclusion

a. follows with certainty from the premises.
b. follows with probability from the premises.
c. none of the above.

■ 19. All cows are mammals and have lanthrobia. All squirrels are mammals and have lanthrobia. All humans are mammals and have lanthrobia. Therefore, some mammals that are neither cows nor squirrels have lanthrobia.

In this argument the conclusion

a. follows with certainty from the premises.
b. follows with probability from the premises.
c. none of the above

20. The argument about lanthrobia in the previous question is deductively valid.

a. true
b. false

21. If statement A follows from statement B, does statement B thereby follow from statement A?

■ 22. Either you are no friend of Sarah's or you will let me in to borrow your stereo for her. But since you obviously won't let me borrow your stereo for her, therefore you are no friend of hers. This argument is

a. deductively valid.
b. deductively invalid.
c. none of the above.

23. Write an essay of three pages (typed double-spaced, if possible) that answers the following question. (Background: Many liberals say “no" and many conservatives say "yes," so be sure to consider all sides of the issue).

Does it follow from the Bill of Rights of the U.S. Constitution that individuals have the right to bear arms?

24. If the premises of an argument are true, and if their being true makes it improbable that the conclusion is false, then the argument is inductively strong.

a. true
b. false

25. If you knew that all fast swimmers have good lung capacity, and if you knew that some fast swimmers have bad politics, would it follow for certain that every student who has good politics and is a fast swimmer has good lung capacity?

■ 26. Is it possible to have a deductively sound argument that is also deductively valid?

■ 27. Is it possible to have an inductively strong argument that is deductively invalid?

28. "John isn't a good waiter because all good waiters have pleasant smiles, but John doesn't have a pleasant smile." If you were to learn that John really is a good waiter, then you could say that

a. the argument is deductively invalid and unsound.
b. the argument is deductively valid and sound.
c. the argument is deductively invalid and sound.
d. a premise is false.

29. Create an obviously deductively valid argument for the conclusion that the Bible is the word of God. One of your key premises must be that the Bible was written by one or more Christian prophets.

30. Create an obviously deductively invalid argument for the conclusion that the Bible is the word of God, using the following as one of your key premises: the Bible was written by the Christian prophets.

31. Suppose that a medical team has examined 21 randomly selected children of the Zambezi Desert and discovered that all of them have malaria or else once had it. It follows

a. with certainty
b. with probability
c. neither with probability nor certainty

that the next three randomly selected children of the Zambezi Desert will be found to have malaria or else to have once had it, if they are examined for malaria. You may assume that there are approximately 8,000 children in the Zambezi Desert.

32. Premise: A survey of major corporate executives indicates that 60 percent believe that some American businesses often engage in price fixing.

Conclusion: If you were to randomly pick five of the surveyed major corporate executives, you could reasonably expect that three of them would believe that all American businesses engage in some form of price fixing.

The conclusion

a. follows.
b. does not follow.

33. President Kennedy was murdered. So, if Oswald did not kill Kennedy, then someone else did.

a. true
b. false

34. President Kennedy was murdered. So, if Oswald had not killed Kennedy, then someone else would have.

a. true
b. false

35. (a) If only great works of art are owned by the Crocker Gallery, does it follow with certainty that the only great works of art are owned by the Crocker Gallery? (b) How about vice versa? Assume that the gallery does own works of art.

■ 36. Bacteria use only an asexual form of reproduction. So, it

a. follows with certainty
b. follows with probability
c. does not follow

that bacteria do not use a sexual form of reproduction. By the way, you did take the required biology course that is a pre-requisite for this course, didn’t you?

37. If the club members are not adults, and only adults have rights, then

a. it follows with certainty
b. it follows with probability
c. it does not follow

that the club members have no rights at all.

38. If a researcher proved that certain bacteria will cause pneumonia in any large animal because 100 percent of the tested animals given the bacteria caught pneumonia whereas none of the animals who weren't given the bacteria caught pneumonia, this proof would be

a. a deductively sound argument
b. an inductively strong argument

39. For the following argumentation, you may assume that the meaning of the words tort and sequestration are taught in every law school, (a) Identify any premise indicators and any conclusion indicators (these terms were defined in an earlier chapter). (b) Is this argument deductively valid? (c) Discuss the question of the argument's soundness, (d) How would you improve the argument if you believe it does need improvement?

Any lawyer knows what the words tort and sequestration mean. Surprisingly, this so-called "friend” of yours doesn't know what the words mean. It follows that your friend is not a lawyer.

40. In a recent issue of your daily newspaper, find a letter to the editor that contains an argument, (a) What is the issue? (b) What conclusion is the writer arguing for? (c) Briefly list the main reasons offered, and number them, (d) Which of the reasons can the average reader tell are true? (e) Is the argument probably intended to be inductive or deductive, or isn't there enough information to tell? (f) Briefly discuss the quality of the argument. Are there weak spots in the argument? Where? Why? (g) Attach a copy of the letter to your answer.

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1 Answer (a). If all ice melts, then the president's ice melts, too

2 The correct answer is "Yes and no." No, it doesn't follow with certainty, but yes, it does follow with significant probability. The mere fact that the person is arrested is some reason to increase your degree of belief in the person's guilt. More often than not, the police arrest the correct persons. However, police do make mistakes, so even if it does follow, from the person's being arrested, that the person is guilty, it doesn't follow with strong enough probability that a member of the jury should vote for conviction on this evidence alone.

4 It follows from what Jeremy Irons says but it doesn't follow from his saying it. The two need to be distinguished. The reasoning in the paragraph doesn't distinguish them.

10 Answer (a). This is the correct answer because, if you own it, you certainly have it, and if it's a pig, it's certainly an animal. In questions like this, it is expected that you will use your common knowledge as background assumptions when they are needed; in this case, for example, you are using the assumption that all pigs are animals

12 Answer (b). Given when the song was created, and your background knowledge that in those times, unlike in the twenty-first century, most farms were family owned, it is probable that he actually owns the farm rather than is a tenant farmer or leases the land, though you cannot be sure that he owns it

19 Answer (a). It is deductively valid because the conclusion is forced to be true whenever the premises are. Of course, we have no way of knowing whether the premises are actually true, so we cannot judge the argument's soundness.

22 Answer (a).

26 Yes, every sound argument is valid

27 Yes, they all are deductive invalid.

36 Answer (a). It's just a matter of what the word asexual means