Inferring Universals from Grammatical Variation: Multidimensional Scaling for Typological Analysis

Abstract

A fundamental fact about grammatical structure is that it is highly variable both across languages and within languages. Typological analysis has drawn language universals from grammatical variation through implicational universals, implicational hierarchies, and more recently, semantic maps. With larger-scale crosslinguistic studies and high levels of grammatical variation, these methods are inadequate, and the most sophisticated of these, semantic maps, while theoretically well-motivated in typology, is not mathematically well-defined. We argue that multidimensional scaling (MDS), in particular the Optimal Classification nonparametric unfolding algorithm, offers a powerful, formalized tool that allows linguists to infer language universals from highly complex and large-scale datasets. We compare our approach to previous work, including Haspelmath's semantic map analysis of indefinite pronouns, Levinson et al.'s dissimilarity MDS analysis of spatial adpositions, and Dahl's (1985) analysis of tense and aspect. We offer a new analysis of the relationship between lexical and grammatical aspect using MDS and a phasal model of event structure. MDS works best with large-scale datasets, implying the centrality of grammatical variation in inferring language universals and the importance of examining as wide a range of grammatical behavior as possible both within and across languages.