What do numbers measure? A new approach to fundamental measurement

Mathematical Social Sciences 24:237-276 (1992)
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Abstract

Unlike the standard representational theory of measurement, which takes the real numbers as a pregiven numerical domain, the approach presented in this paper is based on an abstract concept of a procedure of measurement, and ‘values of measurement’ are understood in terms of such procedures. The resulting ‘type approach’ makes use of elementary model-theoretic notions and emphasizes the constructibility of scales. It provides a natural starting point for a systematic discussion of issues that tend to be neglected in the standard framework (such as the relation between measurement and computation). At the same time it is perfectly compatible with the modern representational theory of measurement and helps elucidate a number of issues central to that theory (e.g. the role of Archimedean axioms).

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