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Definition of inexplicable : Not explicable; not explainable; incapable of being explained, interpreted, or accounted for; as, an inexplicable mystery.

Synonyms:

secret, cryptical, mystical, unexplained, occult, unfathomed, dark, incomprehensible, mystic, puzzling, abstruse, unfathomable, enigmatical, hidden, explain, paradoxical, transcendental, difficult, cryptic, mysterious, uncomprehensible, mystifying, unknown, cabalistic, recondite, obscure, self-contradictory, unaccountable, inscrutable, deep, unexplainable

Usage examples:

• " My dear child," said the Abbe Gondrin, " learn to understand that saying which seems to you so inexplicable. - "The Lesser Bourgeoisie", Honore de Balzac.
• That a man, otherwise more than sane, should value a jewel for its own sake was to him an inexplicable thing. - "The Gem Collector", P. G. Wodehouse.
• So, deeply considered, all nature is inexplicable to us also. - "The Captain of the Gray-Horse Troop", Hamlin Garland.