Cognitive Linguistics Language typologists and cognitive linguists have put the notion of the semantic map to great use over the last decade, particularly in the work of Haspelmath (1997, 2003) on indefinite constructions and Croft (2001, 2003) who has 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 polysemies found in the data, so that connections between concepts accord with Croft’s Semantic Map Connectivity Hypothesis. The specific constructions found in any language can subsequently be mapped onto this space in accord with Croft’s hypothesis and the space can be refined if necessary as further languages are added. 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 geometri
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