The dimensionality of grammatical variation

Recent approaches to variability have focused on the rank ordering of linguistic objects (e.g. noun-phrase transformations, environments of phonological reduction rules) or sociolinguistic objects (e.g. speakers, speech communities). These one-dimensional orderings can take various forms, such as implicational scales, squishes, or the ranking of variable constraints. It is suggested here that sometimes a higher dimensional configuration might better represent the variation. Computer-based heuristic procedures, notably multidimensional scaling techniques, are available for investigating the dimensionality of large data sets. In applying such methods to some well-known data, we confirm the one-dimensionality of Ross' collection of tests of noun-phrasiness as well as of the classes of fake NP's; and we confirm the two-dimensionality of the complementizer QUE-deletion rule in Montreal French. The linguistic environment of syllable-final S-reduction for speakers of Panamanian Spanish is shown to be three-dimensional. Phonological data are used to find two sociolinguistically significant dimensions of the speech community.