Chapter 1 On the Type-Token Relationships

Abstract

Taking into account the dual ontological status of linguistic objects as tokens (material, concrete objects) and types (abstract objects), the paper outlines two different but equivalent, axiomatic approaches to the formalization of the theories of concrete and abstract words (the Tk of word tokens theory and the theory Tp of word types). Theories Tk and Tp are formalized on two levels. The first level of formalization of the theory Tk are tokens whose primary existence is assumed here, and the second level are types having derivative existence. The formalization levels for the theory Tp are the opposite. It can be proved that the two theories Tk and Tp are equivalent, which leads to the conclusion that in the syntactic research of language one can omit the assumption of the primary existence of linguistic types. These two different approaches to the ontology of language are fully presented in the author’s work in Polish: “O dwóch podejściach do formalizacji teorii napisów” (Zeszyty Naukowe WSP w Opolu, Matematyka 27 (1990), 33–48). The ideas contained in this work are also used in the other works of this volume.