binarity

The representation of something as a pair (or set) of binary oppositions.

The binarity of even an obvious pair of opposites like male:female rests on a restricted domain that excludes hermaphrodites, beings with no sex organs (for whatever reason) and so on. While binarity is undoubtedly an essential feature of oppositeness, it is not, on its own, sufficient. There are many situations where a domain is construed with only two members, but oppositeness seems to be absent.

The state of existing as a binary system.