The Language of Argument

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Reductio Ad Absurdum

REDUCTIO AD AbSURDUm

Particular counterexamples can normally be used to refute claims only if

those claims are universal, so how can we refute claims that are not univer-

sal? One method is to show that the claim to be refuted implies something

that is ridiculous or absurd in ways that are independent of any particular

counterexample. This mode of refutation is called a reductio ad absurdum,

which means a reduction to absurdity. Reductios, as they are called for short,

can refute many different kinds of propositions. They are sometimes directed

at a premise in an argument, but they can also be used to refute a conclusion.

This method of refutation will not show exactly what is wrong with the argu-

ment for that conclusion, but it will show that something is wrong with the

argument, because it cannot be sound if its conclusion is false. That might be

enough in some situations.

For example, suppose someone argues that because there is a tallest

mountain and a heaviest human, there must also be a largest integer. We

might respond by arguing as follows: Suppose there is a largest integer. Call

it N. Since N is an integer, N + 1 is also an integer. Moreover, N + 1 is larger

than N. But it is absurd to think that any integer is larger than the largest

integer. Therefore, our supposition—that there is a largest integer—must

be false.

In this mathematical example a contradiction is derived, but absurdity

also comes in other forms. Suppose a neighbor tells a parent, “The local pub-

lic schools are so bad that you ought to send your kids to private school,”

and the parent responds, “Do you think I’m rich?” The point of this rhetori-

cal question is that it is absurd to think that the parent is rich, presumably

because of her lifestyle or house, which the neighbor can easily see. Without

being rich, the parent cannot afford a private school, so the neighbor ’s ad-

vice is useless.

Often the absurdity is derived indirectly. A wonderful example occurred

in the English parliamentary debate on capital punishment. One member

of Parliament was defending the death penalty on the grounds that the

alternative—life in prison—was much more cruel than death. This claim

was met with the following reply: On this view, those found guilty of first-

degree murder ought to be given life in prison, and the death penalty should

2. Is the Morgenbesser retort a shallow counterexample or a deep counterex-
   ample? Why?


3. When theologians claim that God can do anything, atheists sometimes re-
   spond that God cannot make a stone that is so large that God cannot lift it,
   or that God cannot make a circle with four sides. Are these really counterex-
   amples to the theologians’ claim? Why or why not?

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