Five episodes in the history of quantitative science provided the occasions for changes in the understanding of measurement important for attempts at quantification in the social sciences. First, Euclid's generalization of the ancient concept of measure to the concept of ratio provided a clear rationale for the use of numbers in quantitative science, a rationale that has been important through the history of science and one that contradicts the definition of measurement currently fashionable within the social sciences. Second, Duns Scotus's modelling of qualitative change upon quantitative change provided the opportunity to extend measurement from extensive to intensive attributes, a shift that makes it clear that the possibility of measuring qualitative attributes in the social sciences is not one that can be ruled out a priori. Third, Hölder's specification of the character of quantitative attributes showed that quantitative structure is a specific kind of empirical structure, one that is not logically necessary and, therefore, it shows that it is not necessary that any psychological attributes must be quantitative either. Taking the points emanating from Duns Scotus and Hölder together, the issue of whether psychological attributes are quantitative is shown to be an empirical issue. Fourth, Campbell's delineation of the categories of fundamental and derived measurement, and his subsequent critique of psychophysical measurement, showed that attempts at psychological measurement raised new challenges for measurement theory. Fifth, the articulation of the theory of conjoint measurement by Luce and Tukey reveals one way in which those challenges might be met. Taken as a whole, these episodes show that attempts at measurement in the social sciences are continuous with the rest of science in the sense that the issue of whether social science attributes can be measured raises empirical questions that can be answered only in the light of scientific evidence.
Conjoint measurement undone
