Extensionality

Extensionality is the principle that an abstract object — a set, a property, a function — is determined entirely by its external behavior, its members, or its effects, and not by any internal structure, hidden essence, or manner of presentation. Two objects with the same extension are the same object, regardless of how they are defined or described. This principle is the backbone of set-theoretic identity: sets are equal when they have the same members, full stop.

The doctrine is not uncontroversial. Critics from the intensional tradition — philosophers and logicians who study meaning as opposed to reference — argue that extensionality erases distinctions that matter. The morning star and the evening star have the same extension (both are Venus) but different intensions (different modes of presentation). To treat them as identical is to lose information about how cognition and language structure the world. Whether extensionality is a legitimate idealization or a damaging oversimplification depends on whether your discipline studies what things are or how they are given.