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, in particular by using the semantic map model. But the semantic map model, while theoretically well-motivated in typology, is not mathematically well-defined or computationally tractable, making it impossible to use with large and highly variable crosslinguistic datasets. 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 Haspelmath's semantic map analysis of indefinite pronouns, and reanalyze Dahl's (1985) large tense-aspect dataset. MDS works best with large datasets, demonstrating 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.
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