Abstract: Addressing the perennial question “under what conditions can real objects, attributes or relations be represented by numbers?” Hermann von Helmholtz gave an answer in his 1887 lecture “Zählen und Messen” which diverged from the predominant Kantian understanding of quantity and number. Unlike Kant, Helmholtz defined numbers prior to quantities, and regarded the concepts of homogeneity, unit, equality and addition as not having to do with necessary stages of human cognition, but physically determined in specific experimental contexts. Furthermore, Helmholtz did not define measurability by reference to measurement of space, time and mass, which made his views different from his contemporaries, such as the neo-Kantian philosopher Hermann Cohen, the mathematician Paul Du Bois Reymond and the physicist James Clerk Maxwell. The current paper argues that Helmholtz’s epistemology in “Zählen und Messen” closely mirrored the practices of measurement in electricity and magnetism, and was shaped by his involvement in efforts to establish an international electrical standard leading up to the 1881 International Congress of Electricians. The divergence between practice and theory, the lengthy process of calibration leading up to the definition and manufacture of units, and the ambiguous role of the measurement of length, mass and time in defining electromagnetic standards, all played a part in Helmholtz’s 1887 article.
