Work on the semantics and pragmatics of indefinite nominals has grown in the last thirty years to form a subfield of its own within the already focused field of nominal semantics. In this area of study, clearly circumscribing the domain of inquiry amounts to giving a theory of its object. Defining indefinites, therefore, cannot be a first step in a chapter like the present one, whose aim is to provide an overview of some of the solutions developed to the semantic and pragmatic problems they raise. Instead of attempting a definition of indefinites, then, we begin with a quick empirical tour of the type of nominals that are uncontroversially or arguably indefinite, after which we outline the issues the rest of the chapter focuses on.
As a first step, we can divide determiner phrases (DPs) into definite and indefinite based on whether they are headed by a definite or an indefinite D(eterminer). In English then, the expressions in (1) count as indefinite while those in (2) count as definite.
(1) Mary visited a garden, some garden(s), some of the gardens, a certain garden.
(2) Maurice visited the / this garden, these gardens / the capital of Albania / the largest museum in the world.
Within formal semantics, rooted in Aristotelian logic, the italicized DPs in these examples share the interpretive property of being existential, a property that distinguishes them from universal DPs such as every garden or each garden. Definite existentials are distinguished from their indefinite sisters in that their referent is supposed to be uniquely identified somehow, either because it is familiar or unique in context, or because it is inherently unique.
Classifying further types of nominals as definite or indefinite is intimately connected with analytic choices. Staying again with English, the italicized nominals below are uncontroversially accepted among the indefinite group even though this is a definite D and the plural in (4) is bare.
(3) We visited this splendid garden in Suzhou that was offered to a Chinese scholar by his disciples.
(4) Muriel visited gardens when she traveled to France this summer.