Introductory Logic

Assignment 1

Answer each of the following questions as comprehensively as possible.

1. Using the material you've learned so far and the reading "Inductive Reasoning - Part 1," explain the difference between a sound argument and a cogent argument. Give an example of each.

2. To the best of your ability, explain the difference between "certainty" and "objectively probable." Give examples.

3. Explain the difference between probabilities and statistics and how one is used to inform the other. Give examples.

4. In your own words, explain the difference between inductive and deductive logic.

5. Using the video, "Why Probability is Important," list five reasons to study probability theory. Choose two of these reasons and explain why each is either a compelling reason for you or not a compelling reason for you.

6. To the best of your ability, explain the difference between the classical and logical interpretations of probability.

7. In your own words and to the best of your ability, explain a significant problem for the classical interpretation of probability. (I am not looking for a technical, mathematical answer here. Feel free to explain the problem in informal terms using examples if you need to.)

8. Using the video, "Probability - The Logical Interpretation," explain the concept of conditional probability.

9. In your own words, what is the benefit of the frequency interpretation of probability over the other two covered in this unit?

10. Choose one of the objections to the frequency interpretation of probability and explain it in your own words.

Assignment 2

I. Complete each of the following inductive generalizations by supplying the conclusion. Be precise.

1.

1. Almost all politicians lie.
2. Blake is a politician.
3. Hence, ...

2.

1. We surveyed 80% of the school, and all of them agreed with the class president.
2. John goes to our school.
3. Therefore,...

3.

1. You haven't liked anything you've tried at that restaurant.
2. Therefore, this time...

4.

1. Most of the philosophers we met at the conference were arrogant.
2. And those two we met at the bar weren't any better.
3. Oh no, here comes another. I bet...

5.

1. In the first experiment, sugar turned black when heated.
2. In experiments two through fifty, sugar turned black when heated.
3. Therefore, probably...

6.

1. We surveyed 90% of the city, and only 35% approve of the mayor's proposal.
2. Thus, most people probably...

7.

1. Every time you have pulled the lever on the slot machine, you've lost.
2. So, ...

8.

1. 65% of 10% of citizens get married.
2. Terri is a citizen.
3. Hence, ...

9.

1. Every girl I met at the bar last night snubbed me.
2. Every girl I met at the bar so far tonight has snubbed me.
3. Therefore, ...

10.

1. All the politicians at the convention last year were jerks.
2. All the politicians we've met at the convention this year were jerks.
3. Hence, probably, ...

II. For each of the following examples, explain a way that the method of data collecting could undermine the strength of an inductive generalization. There is more than one problem with some examples.

1. Marvin county schools offered any child who is interested the opportunity to change schools to a school with a new curriculum in order to test the effectiveness of the new curriculum.

2. Interested in the eighth grade pop culture, surveyors interviewed eighth graders from twelve girls' schools and three co-ed schools.

3. To find out what typical Americans think of the current political client, 785 college students were polled from a variety of campuses all over the U.S.

4. To determine how many students at University of California were engaged in unsafe sex, researchers interviewed every student in Professor Grant's economics class.

5. To find out how well Georgians think the Georgia governor is doing in office, researchers polled 90% of the population of the largely Republican Rabun County.

6. Interviewers set up a booth outside the local Walmart to ask anyone who approached them whether they thought Walmart's hiring policies are discriminatory.

7. Tameeka says, "I've known two people who have visited Europe, and they both say that Europeans hate Americans. It seems that people outside the U.S. do not like us."

8. In order to determine the attitudes of college students to the government's foreign policy on terrorism, researchers asked college students the following question: "Are you in favor of the imperialist policy of treating all foreigners as terror suspects?"

9. A survey question asks, "Given the numerous gun-related accidents and homicides, and the recent horrifying school shootings, are you in favor of more gun regulation?"

10. Veronica says, "I've had three employees who claim to be Christian work for me, and none was a team player. I just won't hire someone if they claim to be Christian because I need team players."

III. Explain why each of the following arguments from analogy is weak by explaining whether there are more dissimilarities than similarities between the compared objects or events, whether thesimilarities are not relevant to the feature in the conclusion, or both.

1.

1. Our college has a basketball team, a sports arena, and two head coaches, and we're number 1 in the nation.
2. Your college has a basketball team, a sports arena, and two head coaches.
3. Therefore, your college is probably also number 1 in the nation.

2.

1. That guy is 6'1" tall, has brown hair, was born in Tennessee, and has cancer.
2. I am 6'1" tall, have brown hair, and was born in Tennessee.
3. So, I probably have cancer.

3.

1. That object is round, inflatable, white, and used for volleyball.
2. This object is round, inflatable, and striped. (But it is a weather balloon.)
3. It follows that it is probably used for volleyball.

4.

1. Last semester I took a philosophy course with Dr. Arp in room 208 and it was super easy.
2. The philosophy class Dr. Arp is offering next semester is also in room 208.
3. This implies that that class will be super easy, as well.

5.

1. The last book I read by that author had a male protagonist.
2. That book was over 600 pages and terribly boring.
3. Her new work also has a male protagonist and is at least as long.
4. Therefore, it will probably be terribly boring.

IV. Identify the mistake made in each of the following arguments by explaining(not merely stating) whether the argument mistakes correlation for causation, mistakes temporal order for causal order, or mistakes coincidence for causation.

1.

1. Every time I have worn this ring, my choir performances are excellent.
2. Therefore, this ring is responsible for my excellent performances.

(So, I'm definitely wearing this ring during the next performance.)

2.

1. I always get nervous just before I go on stage.
2. So, nervousness causes me to perform publically.

(In that case, I should definitely stop getting nervous, so I won't have to perform.)

3.

1. That girl is here at the library every time I come in.
2. She must be interested in me.

4.

1. The last three times I played golf, my knee has hurt.
2. And today, while playing golf, my knee is hurting.
3. Golf must cause knee problems.

5.

1. As it turns out, people who write a will tend to live longer.
2. Hence, writing a will leads to long life.

(So, if you want to live longer, you should probably write a will.)

Assignment 3

I. In each of the following exercises, identify the informal fallacy that is committed, and explain why each is an example of that fallacy. (1 pt. each)

1. "The surgeon general says that smoking is linked to cancer. But I know lots of people who smoke and don't have cancer. So, it easy to see that it is false that everyone who smokes will get cancer. Thus, the surgeon general is just wrong."

2. We either nuke that country, or we continually deal with the terrorist attacks against our people all over the world.

3. "All the reports of alien abductions come from people of exceptionally low intelligence. This is further supported by the fact that they make claims about alien abductions."

4. That evolutionary principle works at the population level, so it affects each and every member of that species.

5. Dale Earnhardt, Jr. says: "I only drink Budweiser." [Of course, this is before he dropped their endorsement.]

6. "Introducing the Lexus HS 250h: The World's Only Dedicated Luxury Hybrid." (Found on the Lexus website.)

7. Child: "Why do I have to do it?"

Mother: "You will not be happy if you don't!"

8. Of course aliens exist. There is no evidence that they don't exist!

9. "GatorAde-is it in you?"

10. "No one has ever shown me any evidence for evolution. Therefore, it must be false."

11. "Of course we should invade Austria. Everyone thinks so!"

12. "These diamonds would really set you apart. Your family would be so jealous. You should get them!"

13. "All of the evidence points to a correlation between eating fast food and obesity. You should probably not eat very much of that, if any."

14. "You know you shouldn't believe your brother about those investments. He is the most self-centered, arrogant jerk on the planet."

15. "I can't believe my pastor that adultery is really all that bad. I mean, he had an affair for goodness sake!"

16. "Oh, honey, we should help that man. Because... well, just look at him. He's so sad and lonely. I bet he could use some money."

17. "Neil DeGrasse Tyson, a well-respected physicist, says that soil must have a certain amount of acidity to grow orchids. So, that's what I believe, too."

18. "My Aunt Tilley, a noted horticulturist, says that the universe is around 13 billion years old. So, that's what I believe, too."

19. "Of course scientists are right about the age of the universe! They're scientists for crying out loud!"

20. "The current administration wants to cut funding for military airplanes. But this is a wonton disregard for national security. Anyone who cares about the safety of our country should be outraged."

21. Jury Foreperson: "Listen people, we've been here for a month. Do you want to spend another month here? Let's find him guilty of the crime already!"

22. Lawyer: "That guy's a rapist. Why should you believe anything he says?"

23. Lawyer: "My client is the victim of incest himself. How can you convict him of this crime of incest?"

24. "My doctor says the first test showed no cancer. So, I'm cancer-free!"

25. Your parents say: "Einstein's theory of special relativity is a load of nonsense."

II. Look through the Wikipedia entry, "List of Cognitive Biases," and answer the following questions.

List of Cognitive Biases - Wikipedia

1. Choose two biases, one from the "Social biases" section and one from the "Memory errors and biases" section. Explain both biases and two examples, either from your own life or from popular culture or media where these biases may explain someone's behavior. (150-300 words;)

2. Develop a strategy for helping people avoid these fallacies. What would you recommend? Would you change education? Would you change the law? Would you require more regulation over advertising and product information? If so, how would you know how much regulation would help? (100-300 words;)