The procedure of establishing a measure of an attribute consists of the assignment of numbers to objects whose attributes show some variability according to rules. These rules are chosen so that the assigned numbers contain some ‘information’ about the differing variants of the attribute. In the article, we discuss a heuristic, a scaling, and a representational approach. Within the heuristic approach, rules can be based on a verbal argument heuristically linking the variability in the attribute to differences in the measurements. In this case, the specific information that is represented by the measurements is very hard to determine due to the lack of a formal model. Within the scaling approach, a formal model is used to derive rules for the assignment of numbers to the variants of the attribute. From a scaling model, conclusions about the specific information assumed to be represented in the measurements can be derived. Both approaches depend on the assumption that there is something to measure, namely that the attribute that is going to be measured exists in a realm different from the numerical one. Within the representational approach, one tries to clarify what conditions must be met by an attribute to be considered measurable so that relations between the measurements can be interpreted as reflecting relations between the variants of the attribute. By specifying the conditions an attribute must meet to be measurable at all, measurement theory opens an alternative way to rules and thus to measurements. Following this approach, it is no longer necessary only to assume that there is some measurable attribute, but one can find out whether this indeed is the case. Moreover, the interdependence of the definition of an attribute and its measurability, as well as the role theory plays in defining certain attributes, can be clarified.
