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The Role of Synthetic Geometry in Representational Measurement Theory

Wille, Uta

Inst. Mathematik

Geometric representations of data and the formulation of quantitative models of observed phenomena are of main interest in all kinds of empirical sciences. To support the formulation of quantitative models, {\it representational measurement theory} studies the foundations of measurement. By mathematical methods it is analysed under which conditions attributes have numerical measurements and which numerical manipulations of the measurement values are meaningful (see Krantz et al.~(1971)). In this paper, we suggest to discuss within the measurement theory approach both, the idea of geometric representations of data and the request to provide algebraic descriptions of dependencies of attributes. We show that, within such a broader paradigm of representational measurement theory, synthetic geometry can play a twofold role which enriches the theory and the possibilities of data interpretation.