Abstract
The formal or mathematical theory of representation has as its primary goal such an enrichment of the understanding, although there are other goals of representation of nearly as great importance—for instance, the use of numerical representations of measurement procedures to make computations more efficient. A conceptual analysis of measurement can properly begin by formulating the two fundamental problems of any measurement procedure. The first problem is that of representation, justifying the assignment of numbers to objects or phenomena. What one must show is that the structure of a set of phenomena under certain empirical operations and relations is the same as the structure of some set of numbers under corresponding arithmetical operations and relations. Solution of the representation problem for a theory of measurement does not completely lay bare the structure of the theory, for there is often a formal difference between the kind of assignment of numbers arising from different procedures of measurement. This is the second fundamental problem, determining the scale type of a given procedure. The scale type is based on the proof of an invariance theorem for the representation. This is another way of stating the second fundamental problem.
Published Version
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