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 (Poincare and Holder), 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.
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DOI 10.1016/S0039-3681(03)00043-8
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Olivier Darrigol (2007). A Helmholtzian Approach to Space and Time. Studies in History and Philosophy of Science Part A 38 (3):528-542.
Francesca Biagioli (2014). What Does It Mean That “Space Can Be Transcendental Without the Axioms Being So”? Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 45 (1):1-21.
Joel Michell (2006). Psychophysics, Intensive Magnitudes, and the Psychometricians' Fallacy. Studies in History and Philosophy of Science Part C 37 (3):414-432.

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