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Article contents
Helmholtz's Naturalized Conception of Geometry and his Spatial Theory of Signs
Published online by Cambridge University Press: 01 April 2022
Abstract
I analyze the two main theses of Helmholtz's “The Applicability of the Axioms to the Physical World,” in which he argued that the axioms of Euclidean geometry are not, as his neo-Kantian opponents had argued, binding on any experience of the external world. This required two argumentative steps: 1) a new account of the structure of our representations which was consistent both with the experience of our (for him) Euclidean world and with experience of a non-Euclidean one, and 2) a demonstration of why geometric propositions are essentially connected to material and temporal aspects of experience. The effect of Helmholtz's discussion is to throw into relief an intermediate category of metrological objects—objects which are required for the properly theoretical activity of doing physical science (in this sense, a priori requirements for doing science), all while being recognizably contingent aspects of experience.
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- Philosophy of Psychology and Cognitive Science
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- Copyright
- Copyright © 1999 by the Philosophy of Science Association
Footnotes
‡
This research was conducted in Toronto, Göttingen, and Berlin, with the support of the Social Science and Humanities Research Council of Canada, the German Academic Exchange Service (DAAD), and the Max-Planck-Institut für Wissenschaftsgeschichte. I am grateful for comments and advice from Ian Hacking, Lorenz Krüger, Ulrich Majer, and Alasdair Urquhart.
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