A patient who lost his left arm in an accident several years ago describes ongoing, sometimes painful sensations that feel as though they are coming from the missing limb. What is this?

This is an organic hallucination, specifically a phantom limb: a hallucination with a clear, identifiable physical cause, here altered nerve signalling following amputation, exactly as described. It is not a functional hallucination, which requires a real, simultaneous sensory trigger in the same channel rather than arising from an underlying disease process — there is no such concurrent stimulus here. It is not an illusion, since an illusion always has a real stimulus behind it, and there is no genuine current stimulus in the missing limb to be misperceived. And while it is felt as a bodily sensation, calling it simply a tactile hallucination misses what defines it: organic hallucination differs from a hallucination in a primary psychiatric illness mainly by the presence of an identifiable physical cause, not by the perceptual quality of the experience itself, and phantom limb specifically has a well-documented mechanism related to altered nerve signalling.