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About this product
- DescriptionThis book offers a reconstruction of the debate on n-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 kwledge. The success of his philosophical account of space was due t 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 n-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 kwledge 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 kwledge of n-Euclidean geometry or neo-Kantianism.
- Author BiographyFrancesca Biagioli completed her PhD in philosophy and history of science at the University of Turin, Italy, in 2012. Her areas of specialization are Kant, neo-Kantianism, and the history of philosophy of science in the 19th Century. She is the author of articles about the philosophy of science of neo-Kantians such as Hermann Cohen, Alois Riehl and Ernst Cassirer, and scientists and mathematicians such as Hermann von Helmholtz and Otto Holder.
- Author(s)Francesca Biagioli
- PublisherSpringer International Publishing AG
- Date of Publication22/08/2016
- SubjectScience: General & Reference
- Series TitleArchimedes
- Series Part/Volume Number46
- Place of PublicationCham
- Country of PublicationSwitzerland
- ImprintSpringer International Publishing AG
- Content Notebiography
- Weight555 g
- Width155 mm
- Height235 mm
- Spine16 mm
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