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Introduction: the classic view of measurement Measurement in science traditionally is defined as an assignment of numbers (or, in some definitions, numerals) to fundamental attributes of an object or event studied (Kyburg 1984). Once such a correspondence between numbers and objective properties is established, the numbers can be manipulated via mathematical operations and the results assigned back to the measured phenomena. The classic conception of measurement can be elaborated to include the entire range of techniques through which geometric models mediate the interpretive relationship between theory and data: ‘Using a geometry, the abstract objects and events of physical theory are composed into models which give a picture of reality and which are used to connect theory by experimental and nonexperimental investigation to sense impressions’ (Willer, 1984: 243). This broadened definition of measurement comprehends a more complex array of practices than simply attaching numbers to objective attributes. The construction of an ‘interpreted diagram’ or model articulates the relevancies under which theoretical expressions are brought into correspondence with empirical properties. A model's constituent symbols and imagery can enable progressive generalisation of a family of models for mapping and measuring diverse phenomena. Despite its emphasis on the dependence of models on theory, this definition retains the classic concept of measurement as a bringing together of symbolic imagery and ‘small bits of information which we receive from the world’ (Willer, 1984: 247).
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