Representations of qualitative and quantitative dimensions.

Geometric representations of psychological dimensions are analyzed and compared to an alternative set-theoretical approach. Judgments of similarity between forms and figures reveal the following effects: (a) qualitative attributes are curved relative to quantitative attributes, contrary to intradimensional subtractivity; (b) quantitative attributes augment differences in qualitative attributes, contrary to interdimensional additivity; (c) adding a new dimension with a fixed value increases similarity, contrary to translation invariance. The implications of these results to multidimensional representations of proximity data are discussed.