Singular terms and their interpretation

Some formulations of the predicate calculus employ singular terms (‘a’, ‘b’ … etc.) as well as variables. If the quantifiers are to be interpreted substitutionally, of course, the presence of singular terms in the language to supply the appropriate substitution instances is essential. What, in informal argument, corresponds to singular terms in formal logic? Singular terms are usually thought of as the formal analogues of proper names in natural languages. (Where the variables range over numbers, the numerals would correspond to the singular terms.) The formal interpretation of singular terms assigns to each a specific individual in the domain over which the variables range; and, in natural languages, proper names are thought to work in a similar way, each standing for a particular person (or place or whatever).

So while in the case of the quantifiers the main controversy surrounds the question of the most suitable formal interpretation, in the case of singular terms the problems centre, rather, on the understanding of their natural language ‘analogues’. The formal interpretation of singular terms in straightforward extensional languages is uncontroversial; however, rival views about how to understand proper names in natural languages have been used in support of alternative proposals about the formal interpretation of singular terms in less straightforward, e.g. modal, calculi. Among the disputed questions about how, exactly, proper names work are, for instance: just which expressions are bona fide proper names?