Traditions in Collision: The Emergence of Logical Empiricism between the Riemannian and Helmholtzian Traditions

Hopos: The Journal of the International Society for the History of Philosophy of Science 7 (2):328-380 (2017)
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Abstract

This paper attempts to explain the emergence of the logical empiricist philosophy of space and time as a collision of mathematical traditions. The historical development of the ``Riemannian'' and ``Helmholtzian'' traditions in 19th century mathematics is investigated. Whereas Helmholtz's insistence on rigid bodies in geometry was developed group theoretically by Lie and philosophically by Poincaré, Riemann's Habilitationsvotrag triggered Christoffel's and Lipschitz's work on quadratic differential forms, paving the way to Ricci's absolute differential calculus. The transition from special to general relativity is briefly sketched as a process of escaping from the Helmholtzian tradition and entering the Riemannian one. Early logical empiricist conventionalism, it is argued, emerges as the failed attempt to interpret Einstein's reflections on rods and clocks in general relativity through the conceptual resources of the Helmholtzian tradition. Einstein's epistemology of geometry should, in spite of his rhetorical appeal to Helmholtz and Poincaré, be understood in the wake the Riemannian tradition and of its aftermath in the work of Levi-Civita, Weyl, Eddington, and others

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Author's Profile

Marco Giovanelli
Università di Torino

Citations of this work

Hermann von Helmholtz.Lydia Patton - 2008 - Stanford Encyclopedia of Philosophy.

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References found in this work

Dynamics of Reason.Michael Friedman - 2001 - Philosophy and Phenomenological Research 68 (3):702-712.
The Rise of Scientific Philosophy.Hans Reichenbach - 1951 - British Journal for the Philosophy of Science 2 (8):334-337.
La Science et l'Hypothèse.Henri Poincaré - 1902 - Revue de Métaphysique et de Morale 11 (1):1-1.
Relativity and Geometry.R. Torretti - 1985 - British Journal for the Philosophy of Science 36 (1):100-104.

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