Answers to exercise A on p. 3-4
1. Premises: If a person's desk is organized, her mind is organized. Susan's desk is organized. Conclusion: Susan's mind is organized.
2. Premises: Abortion involves the taking of human life. Anything that involves the taking of human life raises serious moral questions. Conclusion: Abortion raises serious moral questions.
3. Premises: All living things need some external source of energy. The sun is the only external source of energy for living things on earth. Conclusion: All living things on earth need the sun.
4. Premises: No man has any natural authority over his fellows. Force produces no right to any natural authority of a man over his fellows. Conclusion: All justifiable authority amoung men must be established on the basis of conventions.
5. Not an argument. It is simply a conditional (if ... then) statement.
6. Premises: The existence of God provides the only satisfactory explanation of the existence of changing things. There must be a satisfactory explanation of whatever exists. Conclusion: God exists.
7. Not an argument (in our sense of the term).
8. Not an argument. In this case "thus" means "for example".
9. Premises: If health were the only desirable characteristic in a human being, then healthy people would always be happier than unhealthy people. It is not the case that healthy people are always happier than unhealthy people Conclusion: Health is not the only desirable characteristic in a human being.
10. Not an argument.
11. Premise: A prince is not able to exercise this virtue of liberality without risk if it be known. Conclusion: If a prince is prudent, he must not object to being called miserly
Answers to exercises on p. 10
1. An instance of MTT
2. Not an instance of any of the modi. (Note that "Self-sacrifice is often not wise" is not the negation of "Self-sacrifice is sometimes wise.")
3. Not an instance of any of the modi--Fallacy of Affirming the Consequent.
4. An instance of MTT
5. Not an instance of any of the modi--Fallacy of Affirming the Consequent
6. An instance of MTP (Note that you can treat a statement and its double negation as interchangeable.)
7. An instance of MPP
8. An instance of MPP
9. An instance of MPT
10. An instance of MTP
Answers to Exercises on p. 11
1. The world might be like this:
There is a constitutional referendum and all lovers of Canada will vote yes. But a number of people who do not love Canada will also vote yes, because they were bribed to do so. Tom Smith is one of the people who do not love Canada and who votes yes, because he was bribed to do so.
If the world were like that, the premises of the argument would be true and the conclusion false.
2. The world might be like this:
It is always wrong to kill innocent human beings. But it is sometimes right to kill human beings who are not innocent. Capital punishment is sometimes the rightful killing of human beings who are not innocent.
If the world were like that, the premise of the argument would be true and its conclusion false.
3. The world might be like this:
There are exactly three people, A, B, and C. A loves B but does not love C. B loves C but does not love A. C loves B but does not love A.
If the world were like that, the premise of the argument would be true and its conclusion false.
4. The world might be like this:
Judy has thought long and hard about whether capital punishment is wrong, but has failed to do any research or to look into the facts about capital punishment. Judy is furthermore very emotional about the subject of capital punishment. Judy has concluded that capital punishment is wrong.
If the world were like that, the premise of the argument would be true, and its conclusion false.
Exercise B
The only combination that is not possible is that the argument is valid, all the premises are true and the conclusion is false. All the other cases are possible. Here is an example of a valid argument with a false premise and a true conclusion: If Stephen Harper is a woman, then Stephen Harper is a human being; Stephen Harper is a woman; therefore, Stephen Harper is a human being.