Marco, Giovanelli
(2013)
Collision of Traditions. The Emergence of Logical Empiricism Between
the Riemannian and Helmholtzian Traditions.
[Preprint]
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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Collision of Traditions. The Emergence of Logical Empiricism Between
the Riemannian and Helmholtzian Traditions. (deposited 08 Nov 2013 16:34)
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