The Language of Argument

1 2 4

C H A P T E R 6 ■ P r o p o s i t i o n a l L o g i c

with “It is not the case that... .” For example, “I did none of the homework”

would be reformulated as “It is not the case that I did any of the homework.”

If the resulting sentence means the same as the original (as it does in this

example), then the original sentence can be symbolized as a propositional

negation. In contrast, “I promise not to leave you” means something very

different from “It is not the case that I promise to leave you,” so “I promise

not to leave you” should not be symbolized as a propositional negation.

Unfortunately, this test will not always work. There is no completely

mechanical procedure for determining whether an English sentence can be

symbolized as a negation. All you can do is think carefully about the sen-

tence’s meaning and context. The best way to get good at this is to practice.

Explain the differences in meaning among “Not everyone loves running,”

“Everyone does not love running,” “Everyone loves not running,” and

“Everyone loves running—not!” For each, is it a negation of “Everyone loves

running”? Why or why not?

Exercise VII

Negative terms or prefixes can often be interpreted in more than one way.

Explain two ways to interpret each of the following sentences. Describe a

context in which it would be natural to interpret it in each way.

1. You may not go to the meeting.


2. I cannot recommend him too highly.


3. He never thought he’d go to the Himalayas.


4. Have you not done all of your homework?


5. All of his friends are not students.


6. I will not go to some football games next season.


7. No smoking section available.


8. The lock on his locker was unlockable.

Exercise VIII

Put each of the following sentences in symbolic form. Be sure to specify exactly

which sentence is represented by each capital letter, and pay special attention

to the placement of the negation. If the sentence could be interpreted in more

Exercise IX

97364_ch06_ptg01_111-150.indd 124 15/11/13 10:15 AM

some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materiallyCopyright 201^3 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights,

affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.