1640s, "treating of a thing as the same as another; act of making or proving to be the same," from French identification, probably from identifier (see identify). Psychological sense of "becoming or feeling oneself one with another" is from 1857. Meaning "act or process of determining the identity of something" is from 1859. Meaning "object or document which marks identity" is from 1947 (short for identification tag, card, etc.).
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Harper, D. (n.d.). Etymology of I.D.. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/I.D.