A PROBLEM AND SOME SOLUTIONS

Although soundness guarantees a true conclusion, we usually expect even more from an argument than soundness. In the first place, an argument can be sound but trivially uninteresting:

(1) Nigeria is in Africa.

(2) Nigeria is in Africa. (from 1)

Compare these arguments:

(1) Al Gore was president. (1*) George W. Bush was president.

(2) Frogs are frogs. (2*) Frogs are frogs.

Are these arguments valid? Why or why not? Are they sound? Why or why not? Is anything wrong with the argument on the right side? If so, what?

Discussion Question

3. All teenagers are my children.

All my children are students.

All teenagers are students.

4. All teenagers are students.

All my children are students.

All my children are students.

Indicate whether each of the following sentences is true. For those that are true, explain why they are true. For those that are false, show why they are false by giving a counterexample.

1. Every argument with a false conclusion is invalid.

2. Every argument with a false premise is invalid.

3. Every argument with a false premise and a false conclusion is invalid.

4. Every argument with a false premise and a true conclusion is invalid.

5. Every argument with true premises and a false conclusion is invalid.

6. Every argument with a true conclusion is sound.

7. Every argument with a false conclusion is unsound.