History and Philosophy of Measurement: a Realist View

− According to the realist interpretation, measurement is the estimation of numerical relations (or ratios) between magnitudes of a quantitative attribute and a unit. The history of scientific measurement, from antiquity to the present may be interpreted as revealing a progressive deepening in the understanding of this position. First, the concept of ratio was broadened to include ratios between incommensurable magnitudes; second, the concept of a quantitative attribute was broadened to include nonextensive quantities; third, quantitative structure and its relations to ratios and real numbers were elaborated; and finally, the issue of empirically distinguishing between quantitative and non-quantitative structures was addressed. This interpretation of measurement understands it in a way that is continuous with scientific investigation in general, i.e., as an attempt to discover independently existing facts.