False Dichotomy
Framing a choice as two options when more exist.
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In plain terms
A false dichotomy presents an "either/or" when the real answer includes neither, both, or something between. The move works because the brain accepts the framing before it checks whether the framing is complete.
Also called a false dilemma. Sometimes the two options are genuinely the only ones. Often they aren't, and the third option is exactly what should have been discussed.
Why it's fallacious
Valid reasoning requires that the listed options actually exhaust the possibilities. If a third option exists and got quietly dropped, the argument hasn't proven anything about what's true. It has only proven something about what fits inside the frame the speaker chose.
The fallacy is especially sneaky because it often comes attached to a true claim. "One of these two must happen" might be false while "one of at least three things might happen" is obviously true. The narrowness is where the error lives.
Canonical example
"You either support the new border policy, or you want open borders. Which is it?"
There are more than two positions on border policy. Between "support this specific policy" and "support no policy" lie an enormous number of alternatives: different enforcement priorities, different asylum rules, different resource allocations, different timelines. The framing erases every one of them and forces a picked-team answer to a question with many possible answers.
Counter-example (not a fallacy)
"Either the light is on or it's off. If it's on, the bulb is working. If it's off, either the bulb is out, the switch is off, or the power is down."
This isn't a false dichotomy, for two reasons. The first either/or really is exhaustive (the light is binary), and the downstream branches properly enumerate the additional cases. A genuine dichotomy is fine. The fallacy is only present when options are missing.
How to respond when you see it
Name the missing option. "There's a third choice, which is [X]. Can we talk about that?" If the speaker treats X as unavailable, ask why. The answer will reveal whether X was actually ruled out on the merits, or just left out for effect.