identities

Identities refer to the qualities, attributes, or states by which something is recognized as the same across time or contexts. The term spans philosophical, mathematical, sociological, legal, and technological usage, and it also concerns how people conceive themselves and how they are perceived by others. Across disciplines, identity involves questions of sameness, difference, and continuity.

Philosophical discussions of personal identity investigate what makes a person the same individual across time despite change. The central issue is continuity of existence, with competing theories such as bodily continuity, psychological continuity (notably memory and character), and attempts to combine both. No single account commands universal agreement, and thought experiments abound.

Mathematics treats identity in formal terms. An identity element for a binary operation satisfies a * e = e * a = a for all a. The identity function id maps every element to itself, id(x) = x. In logic and set theory, the identity relation expresses equality, often denoted by =, and is reflexive (x = x).

Social identities are self-ascriptions tied to group memberships such as gender, nationality, ethnicity, religion, or profession, and to how others categorize individuals. They are formed, negotiated, and may change over time. The concept intersects with ideas of intersectionality and identity politics, which focus on collective experiences grounded in shared social positions.

Legal identity denotes recognition by authorities as a person before the law, usually evidenced by official documents. Digital identity covers online credentials and attributes used to verify a person or entity, enabling access to services while raising concerns about privacy, security, and consent. Identity systems underpin finance, health, and public administration.