Based on an algebraic set theory called \aggregation theory" developed by the author, a set-theoretic, i.e. an \extensional", model of natural languages is here presented. The syntax is immersed into the semantics by treating the syntactic objects as carriers of \formal sense" { the kind of meaning, which these objects have before they are interpreted to obtain a meaning. Due to this, this model is expected to reect both the syntax and the semantics of natural languages. Associated with this model is a \nominalistic interpretation" of set theory, where the sets are treated as common names of their elements and, in particular, the singletons are treated as proper names.