Sameness

Sameness refers to the relation or quality of being the same as something else. In ordinary use it often means numerical identity—the idea that two labels refer to the same object—and, more broadly, qualitative identity, where two things share the same properties. The term is often contrasted with similarity or difference.

In philosophy, sameness is tied to the concept of identity. Numerical identity is the relation of being the very same thing: if x is identical to y, then every property of x is a property of y (Leibniz's law). Distinctions are drawn between identity over time (objects persisting through change) and qualitative sameness (distinct objects sharing all relevant properties). The Ship of Theseus illustrates questions about whether gradual replacement preserves sameness.

In logic and mathematics, sameness is modeled by identity relations or equivalence relations. Two mathematical objects can be said to be the same in a given structure if there is an isomorphism or if they are identical as tokens, even if they occupy different positions in a diagram or memory.

In computing, identity and equality are separate notions: an object's identity refers to its unique reference or memory location, while equality tests compare content or value, which may or may not coincide with identity.

In cognition and linguistics, humans recognize sameness under transformations, such as rotation or scaling, and assign meaning to words that express sameness or synonymy. Across domains, questions about sameness address when two things count as one and the same, when they merely resemble, and how such judgments are grounded in theory, perception, or convention.