Deck 1: Introduction

Question 1

Consider the following argument:
1. All men are authors.
2. Mark Twain is a man.
$/ \therefore$ 3.Mark Twain is an author.
a. Are all of the premises true?
b. Is the conclusion true or false?
c. Is the argument deductively valid or deductively invalid?
d. Is the argument sound? Explain, giving the definition of a sound argument.

Answer 1

a. No, the first premise is false.
b. True.
c. Valid.
d. No, since a sound argument is an argument that is valid and has all true premises, but this argument has a false premise.

Question 2

Consider the following argument:
1. If George Bush is a Republican, then he is not a Democrat.
2. George Bush is not a Democrat.
3. George Bush is a Republican.
a. Are all of the premises true?
b. Is the conclusion true or false?
c. Is the argument deductively valid or deductively invalid?
d. Is the argument sound? Explain, giving the definition of a sound argument.

Answer 2

a. Yes.
b. True.
c. Invalid, since it is possible that the first two premises are true but the conclusion is false (for example if George Bush were an independent).
d. No, since a sound argument is an argument that is valid and has all true premises, but this argument is invalid.

Question 3

Suppose you know of an argument only that it is valid and has a true conclusion. What, if anything, can you tell about its premises? (Defend your answer, including examples.)

Answer 3

You can't tell anything about its premises. For instance, the valid argument "If Socrates is a man then Socrates is mortal. Socrates is a man. Therefore, Socrates is mortal", has a true conclusion and all true premises. But the valid argument "If Koko (the gorilla) is a man, then Koko is mortal. Koko is a man. Therefore, Koko is mortal", has a true conclusion, and one true and one false premise.

Question 4

Suppose you know of an argument only that it is valid and has a false conclusion. What, if anything, can you tell about its premises? (Defend your answer.)

Question 5

Suppose you know that an argument is sound. What can you determine about its conclusion? (Defend your answer.)

Question 6

Suppose you know of an argument only that it has all true premises and a true conclusion. Can you tell from that whether it is valid or invalid? (Defend your answer.)

Question 7

Suppose you know that argument is invalid. Can you tell from that whether its conclusion is true or false? (Defend your answer.)

Question 8

Suppose you know that an argument is valid. Can you tell from that whether its conclusion is true or false? (Defend your answer.)

Question 9

Suppose you know that a set is consistent. Can you tell from that whether every set member is actually true? (Defend your answer.)

Question 10

Suppose you know every member of a set of sentences is false. Can you tell from that whether the set is inconsistent? (Defend your answer.)