The formal fallacy of false dilemma—also known as false choice, false dichotomy, falsified dilemma, fallacy of the excluded middle, black and white thinking, false correlative, either/or fallacy, and bifurcation—involves a situation in which two alternative statements are held to be the only possible options, when in reality there exist one or more other options which have not been considered. The fallacy relies on a misuse of the or operator. For misuse of the and operator, see Package-deal fallacy.
The dilemma need not be limited to two choices; it may involve three possibilities, in which case it is known as a trifurcation. There may be even more choices involved, in which case the fallacy may arise simply by accidental omission—possibly through a form of wishful thinking—rather than by deliberate deception.
When two alternatives are presented, they are often, though not always, two extreme points on some spectrum of possibilities. This can lend credence to the larger argument by giving the impression that the options are mutually exclusive, even though they need not be. Furthermore, the options are typically presented as being collectively exhaustive, in which case the fallacy can be overcome, or at least weakened, by considering other possibilities, or perhaps by considering the whole spectrum of possibilities, as in fuzzy logic.

Examples
Very often a Morton's Fork, a choice between two equally unpleasant options, is a false dilemma. The phrase originates from an argument for taxing English nobles:
"Either the nobles of this country appear wealthy, in which case they can be taxed for good; or they appear poor, in which case they are living frugally and must have immense savings, which can be taxed for good."
This is a false dilemma, because some members of the nobility may in fact lack liquid assets.

Black and white thinking

Correlative-based fallacies
Descartes' Error
Law of the excluded middle, whose misapplication is sometimes the cause of this fallacy
Pascal's Wager
Nolan chart
Half-truths