The logic of measurement: A realist overview

According to the realist interpretation, measurement commits us not just to the logically independent existence of things in space and time, but also to the existence of quantitatively structured properties and relations, and to the existence of real numbers, understood as relations of ratio between specific levels of such attributes. Measurement is defined as 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 non-extensive 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.