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Books > Science & Mathematics > Science: general issues > History of science
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Space, Number, and Geometry from Helmholtz to Cassirer (Hardcover, 1st ed. 2016)
Loot Price: R3,568
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Space, Number, and Geometry from Helmholtz to Cassirer (Hardcover, 1st ed. 2016)
Series: Archimedes, 46
Expected to ship within 12 - 19 working days
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This book offers a reconstruction of the debate on non-Euclidean
geometry in neo-Kantianism between the second half of the
nineteenth century and the first decades of the twentieth century.
Kant famously characterized space and time as a priori forms of
intuitions, which lie at the foundation of mathematical knowledge.
The success of his philosophical account of space was due not least
to the fact that Euclidean geometry was widely considered to be a
model of certainty at his time. However, such later scientific
developments as non-Euclidean geometries and Einstein's general
theory of relativity called into question the certainty of
Euclidean geometry and posed the problem of reconsidering space as
an open question for empirical research. The transformation of the
concept of space from a source of knowledge to an object of
research can be traced back to a tradition, which includes such
mathematicians as Carl Friedrich Gauss, Bernhard Riemann, Richard
Dedekind, Felix Klein, and Henri Poincare, and which finds one of
its clearest expressions in Hermann von Helmholtz's epistemological
works. Although Helmholtz formulated compelling objections to Kant,
the author reconsiders different strategies for a philosophical
account of the same transformation from a neo-Kantian perspective,
and especially Hermann Cohen's account of the aprioricity of
mathematics in terms of applicability and Ernst Cassirer's
reformulation of the a priori of space in terms of a system of
hypotheses. This book is ideal for students, scholars and
researchers who wish to broaden their knowledge of non-Euclidean
geometry or neo-Kantianism.
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