False dilemma

The missing third option

“The forecast says rain on Saturday. So either we cancel the team picnic or we all get soaked.”

There are other options: move it to the pavilion, rent a tent, push it back a week. Canceling might still be the best choice, but the argument makes it look like the only sensible one by leaving out everything else. This is the clear-cut case: the two options offered aren’t exhaustive.

Both can be true

Jordan: Sales dropped because we raised the price.

Casey: No, it’s because customers hate the new packaging.

Jordan: We ran the numbers and the price increase definitely cost us sales. So the packaging isn’t the problem.

Jordan and Casey are treating their explanations as rivals, when both could be contributing. Evidence that the price hurt sales says nothing about whether the packaging did too. Here the options aren’t exclusive, so confirming one doesn’t rule out the other. This version is common when people look for the cause of something that has several.

Opposites that aren’t the only choices

A team lead reviewing a proposal: “Either this plan is solid or it’s worthless. You’ve found a flaw in the budget, so let’s scrap it.”

“Solid” and “worthless” sound like opposites, and in a sense they are: a plan can’t be both. But a plan can be neither, such as good overall with one fixable mistake. The true opposite of “solid” is “not solid”, which covers everything from “needs a tweak” to “hopeless”. The speaker has swapped it for the extreme end, which is a subtler way of leaving options out.

The skeleton is disjunctive syllogism: one of two things is true, one isn’t, so it’s the other. That form is valid: if both premises are true, the conclusion must be. So the fallacy isn’t in the logic. It’s in the first premise, which claims the options are exhaustive when they aren’t. This is exactly the difference between an argument being valid and being sound, and it’s why false dilemma is an informal fallacy rather than a formal one.

The “both can be true” version runs differently: Either P or Q. P. So not Q. That only follows if the “or” means “one or the other, but not both“. If the options can both be true, the conclusion doesn’t follow at all, and logicians call the move affirming a disjunct, a formal fallacy.

Contradictories and contraries. It helps to know which kind of pair you’re looking at.

• Contradictories can’t both be true and can’t both be false: exactly one holds. “The light is on” and “the light is not on” are contradictories. An either/or between contradictories is always true, so it can’t be a false dilemma.
• Contraries can’t both be true, but they can both be false. “The soup is hot” and “the soup is cold” are contraries: it might be lukewarm. An either/or between contraries leaves out the middle.

Many false dilemmas present contraries as if they were contradictories, as in the “solid or worthless” example. Soup has to be hot or not hot, but it doesn’t have to be hot or cold.

A note on names. In everyday use and most textbooks, “false dilemma” and “false dichotomy” mean the same thing, as they do here. Some specialists separate them. Taeda Tomić uses “false dichotomy” for the false either/or statement itself and “false dilemma” for an argument built on one. She further reserves “false dilemma” for arguments shaped like a classical dilemma (“if P, then R; if Q, then S; P or Q; so R or S”), and calls the “not this, so that” version a false disjunctive syllogism.

• Missing option: the options aren’t exhaustive. “You’re either a morning person or a night owl.”
• Overlapping options: the options aren’t exclusive. “Is she a designer or an engineer?” (She could be both.)
• Contraries dressed as contradictories: one extreme stands in for “not the other”. “If it isn’t a success, it’s a failure.”
• The loaded menu: a question or form that offers only some answers, with no argument stated. A feedback survey asks whether the new schedule is “good”, “very good” or “excellent”.
• The two bad horns: both options offered are unpleasant, so any choice looks like a loss. “We either raise prices and lose customers, or keep prices and lose money.” Pointing out a third option is traditionally called going between the horns of the dilemma.

A related pattern in psychology, called all-or-nothing or black-and-white thinking in cognitive behavioral therapy, is a habit of seeing things (often oneself) in extreme categories: a single mistake means total failure. It can produce false dilemmas, but it’s a tendency of thought, not an argument, and it’s a different subject from the fallacy. The Argument from ignorance often takes a false-dilemma shape: “it hasn’t been proven true, so it’s false” leaves out “not yet known”.

A short list of options is fine when the list really is complete, or when the other options have honestly been dealt with.

• The options are contradictories. “The number is even or odd” (for whole numbers), “the package arrived or it didn’t”. One of them has to be true.
• Other options were considered and ruled out. Narrowing to two after checking the rest is good reasoning. It helps to say so, since a listener can’t see the options you eliminated.
• The choice is genuinely forced. A yes-or-no vote, a form with two boxes, or a deadline where not deciding counts as choosing one side. The decision can be binary even when the question behind it isn’t.
• Simplifying openly. “Roughly, there are two approaches here” is fine when it’s offered as a simplification, not used to rule out a third approach.

The test: could both options be false? Could both be true? If so, has anyone shown why not?

Tracking down a dead light

“The kitchen light won’t come on. Either the bulb is dead, or the problem is somewhere else: the fixture, the switch, the wiring or the power. I tried the bulb in another lamp and it works, so the problem is somewhere else.”

This has the “not this, so that” shape, but the two options are built to be contradictories: the bulb is at fault or something other than the bulb is. There’s no third possibility, and the bulb was actually tested, so the conclusion follows.

A real deadline

“The caterer needs a final head count by Friday, so I need a yes or a no from everyone. I can’t send them a ‘maybe’.”

Life has more than two answers to “are you coming?”, but the caterer’s order doesn’t. The choice is genuinely forced by the circumstances, and the speaker says why. Nobody is claiming that “maybe” isn’t a real state of mind, only that it can’t go on the order.

Two options are easier to hold in mind and compare than five. Whoever frames a choice also controls the menu, and people tend to evaluate the options they’re given rather than ask what’s missing, a tendency consistent with what Daniel Kahneman calls “what you see is all there is”.

The reasoning also feels rigorous, because once the menu is accepted, the logic really is valid. Eliminating one option and landing on the other looks like careful deduction, which makes it easy to miss that the work was done by the setup. And the options are often chosen to make one side look bad: offering the alternative in its weakest form (“my plan or doing nothing”) can misrepresent what others actually propose, the same move as a Straw man.

• Ask what’s missing. “Are those really the only two?” Naming even one concrete third option shows the list was incomplete.
• Ask whether both could be true. Especially with explanations: several causes can act at once.
• Find the real opposite. If the options are “solid or worthless”, the real alternative to “solid” is “not solid”, which covers much more.
• Don’t swing to the other extreme. Showing the menu was incomplete doesn’t show that the favored option is wrong. It may still be the best one; the argument just hasn’t shown it.