Uniqueness

Definition
Uniqueness is a distinguishing property of singular definite descriptions. The sentence The present king of France is bald entails that there is a king of France (existence) and that there is exactly one (uniqueness). A point of debate has been the question whether existence and uniqueness should be treated as part of the assertion (as Russell did) or as a presupposition (as Strawson proposed).

Links

 * Utrecht Lexicon of Linguistics