Self Test on Logic Concepts

Part 1: True or false?

Answers below.

1. Arguments, like statements, are either true or false.

2. Statements, like deductive arguments, are either valid or invalid.

3. An argument can be valid and have a false conclusion.

4. All sound arguments are valid.

5. An argument can have true premises and a true conclusion and yet be unsound.

6. All valid arguments are sound.

7. An argument can be sound and yet have a false conclusion.

8. An inductive, or nondeductive, argument is one in which the arguer claims it is impossible for the premises to be true and the conclusion false.

9. If an argument is valid, its premises must be all true.

10. If an argument is valid, then its conclusion must be true if its premises are true.

11. A sound argument is a valid argument with all true premises.

12. It is impossible for a valid argument to have false premises and a true conclusion.

13. Any argument with false premises and a false conclusion is invalid.

14. If a deductive argument is a substitution instance of a valid argument form, it is a valid argument.

Part 1 ANSWERS

1. Arguments, like statements, are either true or false.

   False. An argument is a set of statements. Each individual statement comprising an argument is true or false, but the argument as a whole is not said to be true or false. Both true and false statements may be found in some arguments. The words "true" and "false" apply to statements only.

2. Statements, like deductive arguments, are either valid or invalid.

   False. Only arguments are said to be valid or invalid. It's true that people often use the words "valid" and "invalid" to apply to statements, but philosophers don't, since we want to be very clear. Statements are "true" or "false"; arguments (and only arguments) are "valid," "invalid," "sound," "unsound," "weak," and "strong."

3. An argument can be valid and have a false conclusion.

   True. If you have the best logic in the world but you start with bad information (false premises), you can get a false conclusion. That's why philosophers aren't satisfied with correct logic alone. We also want the facts to be right. The argument "All bears fly; Lassie is a bear; therefore, Lassie flies" is logically correct (valid). The premises, if they were true, would guarantee the conclusion. But no statement in this argument is true.

4. All sound arguments are valid.

   True. To be sound, a deductive argument must have two characteristics: validity (good logic) and all true premises (good facts).

5. An argument can have true premises and a true conclusion and yet be unsound.

   True. Just because an argument contains all true statements doesn't make it VALID, and you need validity as well as factual correctness for soundness. The argument "Dogs bark; fish swim; therefore West Valley College is in Saratoga" isn't valid, even though all its statements are true. It can't be sound if it's not valid.

6. All valid arguments are sound.

   False. "Valid" just means the logic is right, but soundness requires both good logic and all true premises.

7. An argument can be sound and yet have a false conclusion.

   False. A sound argument is a valid argument with all true premises. If it's valid, the conclusion must be true if the premises are true. In a sound argument, the premises are tue. So a sound argument must have a true conclusion.

8. An inductive, or nondeductive, argument is one in which the arguer claims it is impossible for the premises to be true and the conclusion false.

   False. This is the definition of a deductive argument.

9. If an argument is valid, its premises must be all true.

   "Valid" just means the logic is correct: that is, the conclusion has to be true IF the premises are true. A valid argument can have false premises, but still be valid since the conclusion would have to be true IF the premises were true. Think about the Lassie argument in the answer to number (3) above.

10. If an argument is valid, then its conclusion must be true if its premises are true.

    True. This is the definition of a valid argument.

11. A sound argument is a valid argument with all true premises.

    True. This is the definition of a sound argument.

12. It is impossible for a valid argument to have false premises and a true conclusion.

    False. It IS possible. Consider "All parakeets play basketball very well; Michael Jordan is a parakeet, so Michael Jordan plays basketball very well." The premises imply the conclusion: that is, IF they were true, they would make the conclusion true. So the argument is logically correct (valid). Obviously they're not true, but the conclusion follows and also happens to be true.

13. Any argument with false premises and a false conclusion is invalid.

    False. See the Lassie argument above.

14. If a deductive argument is a substitution instance of a valid argument form, it is a valid argument.

    True. In deduction, validity depends on form.

Part 2: Name the forms of the following arguments, and say if the arguments are valid or invalid, and sound or unsound. Answers below.

1. All parakeets play basketball very well. Michael Jordan is a parakeet. Therefore, Michael Jordan plays basketball very well.

2. All members of the WVC football team play football better than Dr. LaFave. Steve Young is not a member of the WVC football team. Therefore, Steve Young does not play football better than Dr. LaFave.

3. Any student who gets an A in this class passes the class. Jack, a student, gets an A in this class. Therefore Jack passes the class.

4. If the moon revolves around the earth, then Jimmy Carter is the current US President. The moon does revolve around the earth, so Jimmy Carter must be the current US President.

5. Either Carter or Ford is the current US President. Carter is not the current US President, so it must be Ford.

6. If you win an Olympic Gold Medal, then you're an excellent athlete. Terry, a ballet dancer, is an excellent athlete. Therefore, Terry wins an Olympic Gold Medal.

7. If you win an Olympic gold medal, then you're an excellent athlete. Terry, a ballet dancer, is not an excellent athlete. Therefore Terry has never won an Olympic gold medal.

8. If you jump off the Empire State Building, you float gently to the ground. If you float gently to the ground, then you're not injured. Therefore, if you jump off the Empire State Building, you're not injured.

9. If you marry, you'll get bored. If you stay single, you'll be lonely. You've got to be either married or single. So you're going to be either bored or lonely.

Part 2 ANSWERS

1. All parakeets play basketball very well. Michael Jordan is a parakeet. Therefore, Michael Jordan plays basketball very well.

   The argument form is modus ponens. Modus ponens is a valid form; this means any argument in modus ponens form is valid. So this argument is valid (the conclusion has to be true if the premises are true), but unsound (one or more premises are false).

2. All members of the WVC football team play football better than Dr. LaFave. Steve Young is not a member of the WVC football team. Therefore, Steve Young does not play football better than Dr. LaFave.

   The argument form is denying the antecedent. Denying the antecedent is an invalid form, so this argument is invalid (the conclusion does not have to be true if the premises are true). The argument is also automatically unsound since it is invalid; soundness requires both validity (correct logic) and all true premises.

3. Any student who gets an A in this class passes the class. Jack, a student, gets an A in this class. Therefore Jack passes the class.

   The argument form is modus ponens. It is valid (the conclusion has to be true if the premises are true), and sound, assuming Jack gets an A in the class.

4. If the moon revolves around the earth, then Jimmy Carter is the current US President. The moon does revolve around the earth, so Jimmy Carter must be the current US President.

   The argument form is modus ponens. It is valid (the conclusion has to be true if the premises are true), but unsound (the conditional premise is false).

5. Either Carter or Ford is the current US President. Carter is not the current US President, so it must be Ford.

   The argument form is disjunctive syllogism. Disjunctive syllogism is a valid form, so this argument is valid (the conclusion has to be true if the premises are true). However, this argument is unsound, since the disjunctive premise is false (there are other options besides the ones mentioned).

6. If you win an Olympic Gold Medal, then you're an excellent athlete. Terry, a ballet dancer, is an excellent athlete. Therefore, Terry wins an Olympic Gold Medal.

   The argument form is affirming the consequent. Affirming the consequent is an invalid form, so this argument is invalid (the conclusion does not have to be true if the premises are true). The argument is unsound because it is invalid.

7. If you win an Olympic gold medal, then you're an excellent athlete. Terry, a ballet dancer, is not an excellent athlete. Therefore Terry has never won an Olympic gold medal.

   The argument form is modus tollens. Modus tollens is a valid form, so the argument is valid (the conclusion must be true if the premises are true). The argument is sound if the premises are also true.

8. If you jump off the Empire State Building, you float gently to the ground. If you float gently to the ground, then you're not injured. Therefore, if you jump off the Empire State Building, you're not injured.

   The argument form is hypothetical syllogism. It is valid (the conclusion must be true if the premises are true), but unsound because the premises are false.

9. If you marry, you'll get bored. If you stay single, you'll be lonely. You've got to be either married or single. So you're going to be either bored or lonely.

   The argument form is constructive dilemma. It is valid (the conclusion must be true if the premises are true), but unsound because the premises are false (we hope).