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 on indefinite constructions and Croft 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 (in manuscript) 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), long used by researchers in psychology and political science among other disciplines. Additionally, MDS analysis allows for the consideration of much larger conceptual spaces, where the necessary permutations of possible category arrangements would be onerous if not impossible if undertaken by hand. The conceptual spaces identified through empirical consideration and MDS analysis are understood to reflect something of the topology of linguistic concepts and how these concepts are structured mentally. These semantic maps also provide predictive power for language change, identifying the meanings that are more or less likely to be encompassed by polysemous words and morphemes under diachronic development.
The present paper will extend the work of Croft and Pool (in manuscript) using MDS analysis to reveal the semantic space of Slavic case, giving consideration to case semantics in Russian, Czech, and Polish. The semantic maps thus produced will then be considered in light of Jakobson’s classic analyses of Russian case semantics as well as Janda and Clancy’s analyses of Slavic case semantics in The Case Book for Russian, The Case Book for Czech, and The Case Book for Polish in order to confirm, refine, or challenge those analyses. It is hoped that MDS analysis in linguistic research will provide a powerful tool for analyzing large samples of linguistic data while also providing a rigorously defined mathematical method that gives teeth to the powerful insights of cognitive linguistics.
References
Croft, William, and Keith T. Poole. In Manuscript. Inferring universals
from grammatical variation: multidimensional scaling for typological analysis.
Haspelmath, Martin. 1997. Indefinite pronouns. Oxford: Oxford University
Press.
_____. 2003. The geometry of grammatical meaning: semantic maps and crosslinguistic
comparison. The new psychology of language, vol. 2, ed. Michael Tomasello,
211-42.Mahwah, NJ: Lawrence Erlbaum Associates.