Natural language is often used to say what the actual world is like, and we refer not only to this actual world but also to the things that we find in there, and that strike us as distinguished and relevant enough to talk about. All known languages have devices to refer to things in the world, our world, if you want. It seems to be a characteristic property of language that a special category of expressions serves especially this device of reference: names. This chapter is not on names though. It is on the role that reference plays according to prevailing theories of the meaning of natural language expressions, that is, in formal semantics.
We take it for granted that it is clear to the reader what we mean when we say things such as the following.
(1) The name “Barack Obama” refers to the current president of the United States, and the phrase “the name ‘Barack Obama’ ” has his name as its referent.
(2) When Wittgenstein referred to the author of the Tractatus he was referring to himself.
(3) The referent IM(a) of a proper name a in a model M is the individual in the domain of M assigned to a by the interpretation function IM of the model.
The word reference is taken here not as in a “reference manual”, in the “references section” of an article, or in the “professional references” in your CV, although the expressions are of course lexically related. Reference is considered from a linguistic perspective, as a phenomenon related to language.We will mostly speak of the reference of linguistic items, be they words, phrases, sentences, or uses or utterances thereof. Often it is associated with a specific syntactic category, that of noun phrases, or with a specific type of linguistic items, most particularly names and singular or plural nouns. The references of the expressions are taken to be individuals, objects, sets of objects, or any kind of things one can, indeed, refer to. The objects can be physical, perceptible objects, times, places, events, as well as abstract objects, imaginary objects, objects of any kind. Briefly, but not very informatively, we could say that objects thus conceived of can be anything one can refer to, or equivalently that anything one can refer to is an object.