Foundational aspects of theories of measurement

It is a scientific platitude that there can be neither precise control nor prediction of phenomena without measurement. Disciplines as diverse as cosmology and social psychology provide evidence that it is nearly useless to have an exactly formulated quantitative theory, if empirically feasible methods of measurement cannot be developed for a substantial portion of the quantitative concepts of the theory. Given a physical concept like that of mass or a psychological concept like that of habit strength, the point of a theory of measurement is to lay bare the structure of a collection of empirical relations which may be used to measure the characteristic of empirical phenomena-corresponding to the concept. Why a collection of relations? From an abstract standpoint, a set of empirical data consists of a collection of relations between specified objects. For example, data on the relative weights of a set of physical objects are easily represented by an ordering relation on the set; additional data, and a fortiori an additional relation, are needed to yield a satisfactory quantitative measurement of the masses of the objects.