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.
