The Language of Argument

9 2

cH A Pt eR 5 ■ D e e p A n a l y s i s

Contrast this example with a different argument:

(1) All senators are paid.

(2) Sam is paid.

∴(3) Sam is a senator. (from 1–2)

Here the premises and the conclusion are all in fact true, let’s assume, but

that is still not enough to make the argument valid, because validity con-

cerns what is possible or impossible, not what happens to be true. This con-

clusion could be false even when the premises are true, for Sam could leave

the Senate but still be paid for some other job, such as lobbyist. That possi-

bility shows that this argument is invalid.

Another very common form of argument is called modus ponens:

(1) If it is snowing, then the roads are slippery.

(2) It is snowing.

∴(3) The roads are slippery. (from 1–2)

This argument is valid, because it is not possible for its premises to be true

when its conclusion is false. We can show that by assuming that the con-

clusion is false and then reasoning backwards. Imagine that the roads are

not slippery. Then there are two possibilities. Either it is snowing or it is not

snowing. If it is not snowing, then the second premise is false. If it is snow-

ing, then the first premise must be false, since we are supposing that it is

snowing and that the roads are not slippery. Thus, at least one premise has

to be false when the conclusion is false. Hence, this argument is valid.

This argument might seem similar to another:

(1) If it is snowing, then the roads are slippery.

(2) It is not snowing.

∴(3) The roads are not slippery. (from 1–2)

This argument is clearly invalid, because there are several ways for its

premises to be true when its conclusion is false. It might have just stopped

snowing or ice might make the roads slippery. Then the roads are slippery,

so the conclusion is false, even if both premises are true.

Yet another form of argument is often called process of elimination:

(1) Either Joe or Jack or Jim or Jerry committed the murder.

(2) Joe didn’t do it.

(3) Jack didn’t do it.

(4) Jim didn’t do it.

∴(5) Jerry committed the murder. (from 1–4)

The first premise asserts that at least one of these four suspects is guilty. That

couldn’t be true if all of the other premises were true and the conclusion

were false, because that combination would exclude all four of these sus-

pects. So this argument is valid.

97364_ch05_ptg01_079-110.indd 92 15/11/13 9:53 AM

some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materiallyCopyright 201^3 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights,

affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.