Department of Philosophy (PHI)

Constructive Dilemmas

General form:

If P, then Q. If R, then S. P or R. Therefore Q or S.

Example. If I get a new car, I'll have to make many payments. If I get a very old car, I'll have to endure occasional breakdowns. I will get either a new car or a very old car. So either I'll have to make many payments or I'll have to endure occasional breakdowns.

Variation: sometimes three or more alternatives are considered in a "di"-lemma, as in the form

If P, then Q. If R, then S. If T, then U. P or R or T. Therefore Q or S or U.

Simpler forms of constructive dilemma:

If P, then S. If R, then S. P or R. Therefore S.

If it rains, the game will be cancelled. If it snows, the game will be cancelled. It will rain or snow. So the game will be cancelled.

If P, then R. If not P, then S. Therefore R or S.

If exactly eight people show up for the party, we'll play bridge. Otherwise we'll play hearts. Hence, either we'll play bridge or we'll play hearts.

If P, then S. If not P, then S. Therefore S.

If you take pills for a cold, you'll recover. If you don't, you'll recover. So you'll recover.

Destructive Dilemmas

General form:

If P, then Q. If R, then S. Not Q or not S. Therefore not P or not R.

Example. If Abigail is to be a great athlete, she'll have to train constantly. If she is to be a great scientist, she'll have to study constantly. Either she won't train constantly or she won't study constantly. Hence, either she won't be a great athlete or she won't be a great scientist.

Note: 'Not both X and Y' is equivalent to 'Not X or not Y' and is often substituted for it.

Example. If Abigail is to be a great athlete, she'll have to train constantly. If she is to be a great scientist, she'll have to study constantly. She can't both train constantly and study constantly. Hence, she can't be both a great athlete and a great scientist.

Simpler forms of destructive dilemma:

If P, then Q. If P, then S. Not Q or not S. Therefore not P.

Example. If I am to finish my psychology major this spring, I must take Statistics at 3 p.m. In order to finish, I must also take Abnormal Psychology at 3 p.m. I can't take both courses at 3 p.m. Consequently, I will not finish my psychology major this spring.

If P, then R. If P, then not R. Therefore not P.

Example. To please my boss, I must always agree with him. To please my boss, I must sometimes disagree with him. So I can't please my boss.

Fallacy of false dilemma. Any dilemma in which a questionable 'OR' statement is used as a premise, i.e., where viable alternatives are overlooked.

Example: The psychology major argument might involve this fallacy if the student doesn't know that the two requirements can only be satisfied by being in two places at once. Maybe there is an alternative way of satisfying one of the requirements than by attending that class at 3 p.m.