Number and measure: Hermann von Helmholtz at the crossroads of mathematics, physics, and psychology.
In 1887 Helmholtz discussed the foundations of measurement in science as a last contribution to his philosophy of knowledge. This essay borrowed from earlier debates on the foundations of mathematics (Grassmann/Du Bois), on the possibility of quantitative psychology (Fechner/Kries, Wundt/Zeller), and on the meaning of temperature measurement (Maxwell,Mach.). Late nineteenth-century scrutinisers of the foundations of mathematics (Dedekind, Cantor, Frege, Russell) made little of Helmholtz's essay. Yet it inspired two mathematicians with an eye on physics (Poincaré and Hölder), and a few philosopher-physicists (Mach, Duhem,Campbell). The aim of the present paper is to situate Helmholtz's contribution in this complex array of nineteenth-century philosophies of number, quantity, and measurement.
Darrigol
Olivier
O
CNRS, Paris, France. darrigol@paris7.jussieu.fr
D005858:Germany; D049672:History, 19th Century; D008433:Mathematics / Q000266:history*; D010684:Philosophy; D010825:Physics / Q000266:history*; D011584:Psychology / Q000266:history*