Answers to Practice Logic Quiz

Part I: True or False?

1. Every sound argument is valid. True. By definition a sound argument is a valid argument in which all the premises are true.

2. If the premises and the conclusion of an argument are true, then the argument is sound. false. The argument must also be valid. The following argument has a true premise and conclusion yet is unsound: (1) UW is in Wisconsin; therefore (2) Most humans die before age 100.

3. If an argument is sound, then its premises and conclusions are true. True. Since all the premises of a sound argument are true and the conclusion follows logically from the premises, the conclusion must be true, too.

4. It is impossible to produce a valid argument for a false conclusion. False. All it takes is at least one false premise. Example: 1. All philosophers are 12 foot tall. 2. D.H. is a philosopher. Therefore 3. D.H. is 12 foot tall.

5. If an argument is invalid, then its conclusion is false. False. To say that an argument is invalid is to say only that the conclusion doesn't follow. For a counterexample, see #2 above.

6. Unless I am confused about logic, I cannot be wrong about whether an argument is rationally persuasive to me. True. If I'm not confused about logic, then I will believe that an argument is valid if and only if it is in fact valid. And I will then believe that it is sound if and only if I believe that its premises are true. Since an argument is rationally persuasive to me if and only if it is valid and I believe its premises, an argument will be rationally persuasive to me if and only if I think it is, and so I cannot be wrong about this.

7. If the premises in an argument are controversial, then the argument can still be sound. True. An argument is sound if it is valid and its premises are true. To say that a premise is controversial is to say that people disagree about whether it is true or false and does not imply that the premise is false. Controversial premises are sometimes true.

8. Sound arguments are true arguments. False. There is no such thing as a true argument, because an argument is not a statement, and only statements can be true or false. Statements can be true or false, but arguments cannot be.

9. To judge whether an argument is valid, you do not need to know whether the premises or the conclusion are true or false. True. Whether an argument is valid depends on the logical relation between the premises and conclusion, not on whether the premises or conclusion are true or false.

10. If two people agree about what an argument says and disagree about whether it is sound, then one of them must be wrong. True. Unless there is an ambiguity, so that there is no fact of the matter about what the argument says, either the argument is sound or it isn't, and if people disagree only one of them can be right.

II. Reconstructing an argument

Consider the following apparent argument: "Since it is obviously unobjectionable to permit people to sell blood or hair, there can be no objection to a woman charging "rent" for the use of her womb." Reformulate this as a valid argument for the conclusion that surrogate motherhood should be legally permissible and comment on whether it is sound.

This is not easy! Here are three possibilities.

The simplest is:

1. If it is legally permissible to sell blood and hair, then surrogate motherhood should be legally permissible.

2. It is legally permissible to sell blood and hair.

thus 3. Surrogate motherhood should be legally permissible.

The validity obvious, the soundness is not. Premise 1 is dubious and arbitrary.

Here's a more complicated possibility.

1. Other things being equal, it should be legally permissible for individuals to sell or rent parts of their bodies.

2. Surrogate motherhood involves the selling or renting of parts of people's bodies.

thus 3. Other things being equal, surrogate motherhood should be legally permissible.

4. Other things are equal (i.e. there are no other considerations counting against permitting surrogate motherhood).

thus 5. Surrogate motherhood should be legally permissible.

The reference to the sale of blood and hair functions as evidence supporting premise 1. One could bring it explicitly into the argument as follows:

A. If it were not the case that, other things being equal, it should be legally permissible for individuals to sell or rent parts of their bodies, then it would not be legal to sell hair or blood.

B. It is legal to sell hair and blood.

thus 1. Other things being equal, it should be legally permissible for individuals to sell or rent parts of their bodies.

and the argument could then continue from there.

Since premise 1 and 4 both appear to be false, this argument appears to be unsound.

Here's a third possibility.

1. If it is not true that surrogate motherhood should be legally permissible, then it should not be legally permissible to sell body parts such as hair and blood.

2. It is legally permissible to sell body parts such as hair and blood.

thus 3. Surrogate motherhood should be legally permissible.

Premise 1 seems to be false, and so this argument is valid but unsound.