 Scientific developments during the nineteenth century challenged the distinction between extensive and intensive magnitudes. Thermodynamics and wave optics showed that differences in temperature and hue corresponded to differences in spatio-temporal magnitudes such as velocity and wavelength. Electrical magnitudes such as resistance and conductance were shown to be capable of addition and division despite not being extensive in the Kantian sense, i.e., not synthesized from spatial or temporal parts. Moreover, early experiments in psychophysics suggested that intensities of sensation such as brightness and loudness could be represented as sums of “just noticeable differences” among stimuli, and could therefore be thought of as composed of parts (see  Section 3.3).  These findings, along with advances in the axiomatization of branches of mathematics, motivated some of the leading scientists of the late nineteenth century to attempt to clarify the mathematical foundations of measurement (Maxwell 1873; von Kries 1882; Helmholtz 1887; Mach 1896; Poincaré 1898; Hölder 1901; for historical surveys see Darrigol 2003; Michell 1993, 2003; Cantù and Schlaudt 2013; Biagioli 2016: Ch. 4, 2018). These works are viewed today as precursors to the body of scholarship known as “measurement theory”.