Sabrina Brazzo

# The Philosophy of Measurement

Measurement is central to modern science as well as engineering, commerce and daily life. Despite its ubiquity and importance, the necessity of measurement remains a contested issue in philosophy. This article aims to survey some of the main philosophical standpoints on measurement. First, it introduces the basic concepts of measurement and quantitative inquiry. Then, it explains the varying levels of analysis in measurement theory. It finally discusses how a variety of disciplinary and epistemological issues can impact the necessity of measurement.

The central feature of measurement is that it transforms qualitative empirical relations into quantitative mathematical ones. These transformations can then be used to represent objects and events in a number of ways, including as quantities or units. Most of the controversy over the necessity of measurement revolves around the kind of empirical relations that are capable of being mapped to numbers and the conditions under which such mappings can be considered valid.

Mathematical theories of measurement (sometimes referred to collectively as “measurement theory”) focus on the conditions under which numbers and other mathematical entities are adequate for expressing certain kinds of relations, such as equality, sum, difference and ratio. Such theories also address the question of whether or not the relations exhibited by numbers and other mathematical entities actually correspond to real-world properties or to relations between real-world objects.

Early measurement theorists like Helmholtz, Holder and Campbell argued that mathematical operations such as addition and subtraction adequately express qualitative empirical relations between physical magnitudes because these operations mirror the corresponding relation between lengths of rigid rods, for example. This line of reasoning is known as empiricism and is an essential part of the case for the necessity of measurement.

By contrast, realists argue that the use of numbers and other mathematical entities for expressing quantitative relationships among objects is valid in some circumstances even when those numbers do not correspondingly reflect or express any real-world property or relation. This is because the corresponding relation between a physical quantity and its mathematical representation is not always an empirical one, as illustrated by the fact that 60 is twice 30.

In such cases, the criterion for validity can be defined in terms of consistency between measurement outcomes and relevant background theories or other substantive presuppositions about the quantity being measured. This criterion is sometimes referred to as the coherence criterion. More recently, Bas van Fraassen has argued that this criterion should be supplemented by a further requirement, called objectivity. This criterion concerns the coherence of measurement outcomes with respect to a given model, measuring instrument or environment.