Introduction to Logic – Exercises

For each of the following arguments, rewrite them in “canonical form,” i.e., identify premises and conclusion and write in order - with premises first. Then evaluate whether the arguments are valid or invalid, strong or weak. Provide some reason for why you think this.

1. Mad cow disease is spread by feeding cows with infected parts and this practice has yet to be eliminated. So, mad cow disease continues to be a problem for people who eat meat.

2. Whenever you drive faster than the speed limit, you risk a ticket or an accident. So, you’d better drive the speed limit!

3. The sun has risen every day of human history. So, the sun will rise tomorrow.

4. No one can predict baseball. So, you can’t know that the Giants are going to win the World Series.

5. John deserves to be free. After all, John is a human being and every human being deserves to be free.

6. Based on my experience of blog comments and social media, I can truly say that humanity is much more ignorant and angry than we used to be.

7. This year the Republicans will win back the legislature. After all, the pendulum swings from the left to the right and the Democrats have one in recent years.

8. It always rains in San Francisco in January, so if you’re traveling to San Francisco in January, prepare for rain.

9. The following conversation between a four-year-old and her mother:
Amy: “Mommy, what color are violets?”
Mother: “Purple.”
Amy: “I saw some violets.” [What argument is Amy using in order to draw this conclusion?]

10. Conclusive proof that the earth is spherical is provided by these two observations: (1) spheres cast curved shadows; and (2) the earth casts a curved shadow [on the moon during a lunar eclipse].

11. Fish like to swim. I like to swim. So, I am a fish.

12. I know he was involved. Only a guilty person accepts a pardon.

13. All apples are delicious and this is an apple. So, this must be delicious!

14. If you fail the course, you will not receive credit. But you received credit. So, you must have passed.

15. I had two choices – I could swallow a handful of sleeping pills, or I could declare myself bankrupt. My father was a minister, and he didn’t believe in suicide. Neither do I. I chose bankruptcy.

16. Two old bankers are talking:
If God hadn’t wanted there to be poor people, He would have made us rich people more generous. [This argument will require you to add additional sentences in order to make it clear.]

17. The third-century church father Origen made the following (paraphrased argument):
If the creation story is a true literal description, then for the first three days of the earth’s existence there was no sun. The concept of “day” is defined by reference to the sun. It cannot be the case that both the concept is so defined and the earth existed three days before the sun was created. From this, it follows that the creation story in Genesis is not a true literal description.

18. Historian of science, A. C. Crombie writes:
Some later Greek writers had used erosion by water as evidence for the temporal origin of the earth, for, they argued if the earth had existed from eternity all mountains and other features would by now have disappeared.

19. Adam Nordwall, an American Chippewa Indian chief, had the occasion to visit Rome. When he arrived, in full tribal regalia, he said the following:
“I proclaim this day the day of the discovery of Italy... What right did Columbus have to discover American when it had already been inhabited for thousands of years? The same right that I have to come now to Italy and proclaim the discovery of your country.”

20. A conversation between two students:
First student: “Did you go to Spanish yesterday?
 Second student: “Did you? Oh, you wouldn’t be asking me.” [What argument is the Second student making here?]

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1. Mad cow disease is spread by feeding cows with infected parts and this practice has yet to be eliminated. So, mad cow disease continues to be a problem for people who eat meat.

1. Mad cow disease is spread by feeding cows with infected parts.
2. If the practice of feeding cows with infected parts is not eliminated, then the problem of mad cow disease will spread.
3. The practice has not been eliminated.
4. Therefore, the problem of mad cow disease will spread.
This argument conforms to modus ponens (If P, then Q. P. Therefore, Q.) Modus ponens is a valid argument form. This is a valid argument....
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