The Language of Argument

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R e d u c t i o a d A b s u r d u m

A reductio ad absurdum is deep only if it reveals that a claim implies an ab-

surd result that cannot be avoided without modifying the claim in essential

respects or giving it up entirely.

In sum, then, a reductio ad absurdum argument tries to show that one

claim, X, is false because it implies another claim, Y, that is absurd. To evalu-

ate such an argument, the following questions should be asked:

1. Is Y really absurd?


2. Does X really imply Y?


3. Can X be modified in some minor way so that it no longer implies Y?
   If either of the first two questions is answered in the negative, then the
   reductio fails; if the third question receives an affirmative answer, then
   the reductio is shallow. Otherwise, the reductio ad absurdum argument is
   both successful and deep.

Evaluate the following reductio ad absurdum arguments by asking the above

three questions.

1. Claim to be Refuted: Even the worst of enemies can become friends.
   Reductio: If people are enemies, then they are not friends. If they do
   become friends, then they are not enemies. So it’s absurd to think that
   enemies can be friends.


2. Claim to be Refuted: This ball is both red all over and green all over.
   Reductio: If it is red, it reflects light within a certain range of wavelengths.
   If it is green, it reflects light within a different range of wavelengths. These
   ranges do not overlap, so it is absurd to think that anything can reflect both
   kinds of light. Thus, a ball cannot be both red and green all over.


3. Claim to be Refuted: Most children in Lake Wobegon are above average
   (in intelligence).
   Reductio: If so, the average (intelligence) would really be higher than it
   is; and then it would not be true that most children in Lake Wobegon are
   above the real average (intelligence).


4. Argument to be Refuted: Your brain is mostly empty space, because the
   subatomic particles in it are very far apart.
   Reductio: That’s absurd, because my brain is solid, and it works pretty
   well.


5. Claim to be Refuted: Some things are inconceivable.
   Reductio: Consider something that is inconceivable. Since you are
   considering it, you are conceiving it. But then it is conceivable as well as
   inconceivable. That is absurd. So nothing is inconceivable.

Exercise III

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