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An appeal to fear (also called argumentum ad metum or argumentum in terrorem) is a logical fallacy in which a person attempts to create support for their idea by playing on existing fears and prejudices.
For example, "We must raise taxes or else even more hospitals will be closed" or "You should stop drinking unless you want to die young like your father." In both cases, existing fears are exploited to create support for the speaker's proposal. Neither fear is necessarily directly tied to the proposal in question however, and therein lies the fallacy.
The appeal to fear fallacy is closely linked to the false dilemma fallacy, in which a scary situation is often provided as a proposed idea's sole alternative.