Measurement Theory: History and Philosophy

Measurement theory is the philosophical account of the practice of measurement in science. Its main historical landmarks parallel the history of quantitative science. First, Euclid liberalized the concept of ratio to explain how incommensurable quantities are measured via (whole) numbers. Second, medieval philosophers broadened the concept of quantity by distinguishing the concept of extensive quantity from that of intensive quantity. Third, Hölder axiomatized the concept of continuous quantity, making explicit the isomorphism between ratios of magnitudes of a continuous quantity and the positive real numbers. Fourth, Helmholtz identified the two modes of quantification in physical science (what Campbell later called ‘fundamental’ and ‘derived’ measurement), thereby helping to identify the kinds of evidence sustaining quantification in physics. Fifth, Luce and others developed the theory of conjoint measurement as a mode of quantification suitable for sciences, such as psychology, where neither fundamental nor derived measurement (in Campbell's sense) applies. External to science, nonempirical conceptions of number in the philosophy of mathematics stimulated development of the now generally accepted representational approach to measurement, and the radical empiricist philosophy of science, operationism, shaped Stevens' understanding of measurement, an understanding influential within psychology.