Steven J

Introduction Language typologists and cognitive linguists have put the notion of the semantic map to great use over the last decade, particularly in such works as Haspelmath (1997) on indefinite constructions. Croft (2001, 2003) has also developed the notion of conceptual space in his typological and construction grammar work. Thus far, semantic maps have been the result of empirical research involving laborious consideration of cross-linguistic data in order to identify the relevant categories and then to arrange those categories into a conceptual space. The arrangement of these categories reflects the actual overlapping polysemy found in the data, so that connections between concepts accord with Croft’s (2001, 2003) Semantic Map Connectivity Hypothesis. A conceptual space such as that found in Haspelmath (1997, 2003) emerges (Figure 1) and the indefinite constructions of all languages can subsequently be mapped onto this space (Figures 2 and 3) in accord with Croft’s hypothesis. If exceptions are found as new languages are added, the semantic map can be further refined. The connections between categories in the conceptual space have validity, but the specific geometrical arrangement and distance between categories lack theoretical import. However, the recent work of Croft and Poole (forthcoming) revolutionizes the semantic map and introduces a meaningful notion of quantitative semantic distance as well as a precisely defined geometric arrangement, through the use of a mathematically well-defined model, Multidimensional Scaling (MDS), more specifically utilizing Poole's Optimal Classifcation (OC) method. MDS techniques have long been used by researchers in psychology, economics, and political science among other disciplines. Additionally, MDS analysis allows the linguist interested in semantic maps to consider much larger conceptual spaces, where the