Reference, Kinds and Predicates
Marie La Palme Reyes, John Macnamara, Gonzalo E. Reyes · 1994
Abstract The aim of this paper is to present a theory of reference for proper names (PNs), count nouns (CNs) and predicables (mainly adjectives, adjectival phrases, verbs, verb phrases). The paper is divided into three sections and an Appendix. In the first, we describe briefly some theses on reference. These theses express the logical prerequisites for reference to take place. The second section, which is the core of the paper, describes a mathematical theory that is based on these theses. This theory, the theory of reference mentioned above, constitutes the foundation for the semantics of kinds and predicates. The third section, which is devoted to some applications of the theory, is divided into three parts. In the first, we discuss and apply the notion of an underlying map which is directly linked to reference and kinds. In the second, we discuss some transformations that such parts of speech as CNs, MNs (mass nouns) and predicables may undergo and we provide semantical counterparts for these transformations. In the third, we mention some problems and possible developments of our theory. In the Appendix, we sketch a proof of a soundness theorem for the formal system introduced in the second section.