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Logical Thought – Homework 02
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Logical Thought
Fall 2004
Homework 02
A. Identifying Statements
For each of the following sentences, indicate how many statements it contains (if any),
and paraphrase those statements.
Example: The store promises to refund your money if you are unsatisfied with the
service.
This sentence contains two statements: (i) The store promises to refund your
money, and (ii) you are unsatisfied with the service.
1. Don’t forget to let the dog out when you get home!
This is not a declarative sentence, and hence does not contain a statement.
2. Oil has been discovered deep below the artic tundra.
One statement: Oil has been discovered deep below the artic tundra.
Note that this sentence should not be rendered as two statements:
(1) Oil has been discovered.
(2) Oil is deep below the artic tundra.
Because (1) and (2) might not be talking about the same oil, yet the original
sentence is.
3. Charlie visited her aunt, read a book, and wrote a letter to her congressional
representative.
Three statements: (i) Charlie visited her aunt, (ii) Charlie read a book, and (iii)
Charlie wrote a letter to her congressional representative.
4. A student may enroll for this class only if she satisfies the prerequisites or has
permission of the instructor.
Three statements: (i) A student may enroll for this class, (ii) A student satisfies the
prerequisites, and (iii) A student has permission of the instructor.
Logical Thought – Homework 02
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5. In the event of inclement weather, the reception will be held indoors.
Two statements: (i) The weather is inclement, and (ii) The reception will be held
indoors. (When paraphrased as a conditional, the two statements are obvious: If
the weather is inclement, then the reception will be held indoors.)
6. Despite feeling a bit ill, Terence decided to attend the concert.
Two statements: (i) Terence felt a bit ill, and (ii) Terence decided to attend the
concert.
B. Paraphrasing
Each of the following passages can be interpreted as containing a single argument (i.e.,
one conclusion, and one or more premises). For each passage, paraphrase the argument,
breaking down compound statements into their atomic components when doing so does
not misrepresent the argument. Use complete sentences, and present the paraphrased
argument in standard form.
7. Every art and every inquiry, and similarly every action and pursuit, is thought to
aim at some good; and for this reason the good has rightly been declared to be that
at which all things aim. (Aristotle)
The most straightforward paraphrase is:
(1) Every art and every inquiry, and similarly every action and pursuit, is thought
to aim at some good.
(2) Therefore, the good is that at which all things aim.
However, (1) can be broken down into component statements. So a more
thorough paraphrase is:
(1) Every art is thought to aim at some good.
(2) Every inquiry is thought to aim at some good.
(3) Every action is thought to aim at some good.
(4) Every pursuit is thought to aim at some good.
(5) Therefore, the good is that at which all things aim.
8. Profit serves a very crucial function in a free enterprise economy, such as our
own. High profits are the signal that consumers want more of the output of the
industry. High profits provide the incentive for firms to expand output and for
more firms to enter the industry in the long run. For a firm of above-average
efficiency, profits represent the reward for greater efficiency.
Logical Thought – Homework 02
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(1) High profits are the signal that consumers want more of the output of the
industry.
(2) High profits provide the incentive for firms to expand output and for more
firms to enter the industry in the long run.
(3) For a firm of above-average efficiency, profits represent the reward for greater
efficiency.
(4) Therefore, Profit serves a very crucial function in a free enterprise economy,
such as our own.
9. Though it is possible that REM sleep and dreaming are not necessary in the adult,
REM deprivation studies seem to suggest otherwise. Why would REM pressure
increase with deprivation if the system is unimportant in the adult?
(1) REM pressure increases with deprivation.
(2) Therefore, REM sleep and dreaming are necessary (or important) in the adult.
10. Since the secondary light (from the moon) does not inherently belong to the
moon, and is not received from any star or from the sun, and since in the whole
universe there is no other body left but the earth, what must we conclude? What
is to be proposed? Surely we must assert that the lunar body is illuminated by the
earth.
(1) The secondary light (from the moon) is not produced by the moon itself.
(2) The secondary light (from the moon) is not received from any star or from the
sun.
(3) The only remaining possible object that could supply light to the moon is the
earth.1
(4) Therefore, the moon is illuminated by the earth.
1
This is one way to paraphrase the claim that “in the whole universe there is no other body left but the
earth.”