False dilemma

“Either we build the new road or the town dies” offers two futures. A bus line, a smaller road and doing nothing much at all are three more.

Two doors, when the room has more

A false dilemma presents two options as if they were the only ones, so that rejecting one seems to force the other. It is also called a false dichotomy or, in Korean, black-and-white logic. A made-up ad: “Buy our water filter, or keep drinking dirty water.” Tap water that is already safe, a cheaper filter from another company and boiling are left out. The ad wants you to reject the second option and land on the first.

In logical form, a false dilemma usually uses a perfectly valid pattern, the disjunctive syllogism: p ∨ q, ¬q, therefore p. “Either you buy the filter or you drink dirty water. You don’t want dirty water. So buy the filter.” If the first premise were true, the conclusion would follow. The flaw is that the first premise, the either-or, is false. In the terms of the statements course, the argument is valid but unsound.

Where the missing options hide

• In the middle: “Either you love maths or you hate it.” Many people find it fine.
• In both: “Do you want a career or a family?” Plenty of people have both.
• In neither: “Was the film a comedy or a tragedy?” It may be a documentary.
• In later: “Decide now or lose the offer.” Many offers come back.

Some choices really are two-sided. A statement and its negation are a genuine pair: either the shop is open or it is not, and there is no third option. A light switch with two positions has two positions. The test is to ask whether the two options are negations of each other. “Open or not open” passes. “Open or closed for renovation” fails, because the shop might be closed for a holiday.

False dilemmas often come with time pressure or strong feeling, because both make it harder to stop and count the options. The simplest reply is a question: “Are those really the only two choices?” Naming even one more option is enough to break the argument, since the either-or premise is then shown to be false.

There is a mirror image of the false dilemma worth knowing. Sometimes a speaker offers several options and then quietly treats all but one as ruled out without saying why: “We could raise fees, cut staff or borrow, and obviously we can’t raise fees or borrow.” The list may be complete this time, but the eliminations need reasons too. When you meet an either-or, check both parts of the argument: is the list of options complete, and has each rejected option really been shown to fail?