Meanings as Conceptual Structures

Cognitive semantics relates linguistic expressions to conceptual structures. The purpose of this paper is to present a framework for such a cognitive structure. As a preparation, Putnam’s argument against intensional semantics as a theory of meaning is presented. Some of the main tenets of cognitive semantics as it has developed during the last years are outlined. The notion of a conceptual space is proposed as a central tool for representing semantic information. It is outlined how conceptual spaces can be used as a basis for a formal cognitive semantics.The model is then applied to some problems in lexical semantics, such as the effect of varying contrast classes. 1. WHAT IS A SEMANTICS? A very general answer, that I think everybody can agree on, to the question of what a semantics is, is that it specifies a relation between linguistic expressions and the referents of the expressions. But soon afterwards, opinions diverge. There is, in particular, no agreement on what kind of entities the meanings of various words are. Some say that the referents of language are things in the world, some say they are things, but maybe not in this world, and some say they are mental constructions without any posit that these constructions coalesce with reality. I want to contrast two general traditions in semantics, one realistic and one cognitivistic. According to the realistic approach to semantics the meaning of a word or expression is something out there in the world. Realistic semantics comes in two flavors: extensional and intensional. In the extensional type of semantics, one starts out from a language L, which may or may not be defined in formal terms, and maps the constitutents of L onto a “world.” Names are mapped onto objects, predicates are mapped onto sets of objects or relations between objects, etc. By compositions of these mappings sentences end up being mapped onto truth values. The main objective of this kind of semantics is to determine truth conditions for the sentences in L. A consequence of this approach is that the meaning of an expression is independent of how individual users understand it. The first developed theory of this type is Frege’s semantics, but it gets a more precise form in Tarski’s theory of truth. Schematically, the mappings can be illustrated as in Figure 1. Figure 1: The ontology of extensional semantics The extensional theory of reference implicit in this kind of semantics was soon found to be wanting on account of several phenomena in natural languages. In order to handle some of these problems, so called intensional semantics was developed by logicians and linguists. In this brand, the language L is mapped onto a set of possible worlds instead of only a single world. Still, the goal of the semantics is to provide truth conditions for the sentences in L. The meaning