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Of course, from one point of view the final effect in King Lear is nihilistic, but opinions may differ as points of view differ. The effect may also be interpreted as Existentialist angst, that is, meaninglessness of life in itself.
The term is sometimes used in association with anomie to explain the general mood of despair at a perceived pointlessness of existence that one may develop upon realising there are no necessary norms, rules, or laws. Movements such as Futurism and deconstruction among others, have been identified by commentators as "nihilistic" at various times in various contexts.