Francesca Biagioli
University of Turin
Hermann von Helmholtz’s geometrical papers have been typically deemed to provide an implicitly group-theoretical analysis of space, as articulated later by Felix Klein, Sophus Lie, and Henri Poincaré. However, there is less agreement as to what properties exactly in such a view would pertain to space, as opposed to abstract mathematical structures, on the one hand, and empirical contents, on the other. According to Moritz Schlick, the puzzle can be resolved only by clearly distinguishing the empirical qualities of spatial perception from those describable in terms of axiomatic geometry. This paper offers a partial defense of the group-theoretical reading of Helmholtz along the lines of Ernst Cassirer in the fourth volume of The Problem of Knowledge of 1940. In order to avoid the problem raised by Schlick, Cassirer relied on a Kantian view of space not so much as an object of geometry, but as a precondition for the possibility of measurement. Although the concept of group does not provide a description of space, the modern way to articulate the concept of space in terms of transformation groups reveals something about the structure and the transformation of spatial concepts in mathematical and natural sciences.
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DOI 10.15173/jhap.v6i3.3436
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References found in this work BETA

An Essay on the Foundations of Geometry.BERTRAND A. W. RUSSELL - 1897 - Revue de Métaphysique et de Morale 6 (3):354-380.
Philosophy of Geometry From Riemann to Poincaré.Nicholas Griffin - 1981 - Philosophical Quarterly 31 (125):374.
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Citations of this work BETA

Hermann von Helmholtz.Lydia Patton - 2008 - Stanford Encyclopedia of Philosophy.
Francesca Biagioli: Space, Number, and Geometry From Helmholtz to Cassirer: Springer, Dordrecht, 2016, 239 Pp, $109.99 , ISBN: 978-3-319-31777-9. [REVIEW]Lydia Patton - 2019 - Journal for General Philosophy of Science / Zeitschrift für Allgemeine Wissenschaftstheorie 50 (2):311-315.

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