Space, Number, and Geometry from Helmholtz to Cassirer by Francesca Biagioli (En

Description: Space, Number, and Geometry from Helmholtz to Cassirer by Francesca Biagioli However, such later scientific developments as non-Euclidean geometries and Einsteins 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. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description 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 Einsteins 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 Poincaré, and which finds one of its clearest expressions in Hermann von Helmholtzs 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 Cohens account of the aprioricity of mathematics in terms of applicability and Ernst Cassirers 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. Back Cover 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 Einsteins 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 Poincar Author Biography Francesca 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 Hölder. Table of Contents Helmholtzs Relationship to Kant.- The Discussion of Kants Transcendental Aesthetic.- Axioms, Hypotheses, and Definitions.- Number and Magnitude.- Projective Metric and the Concept of Space.- Euclidean and Non-Euclidean Geometries in the Interpretation of Physical Measurements.- Non-Euclidean Geometry and Einsteins General Relativity: Cassirers View in 1921. Review "Francesca Biagiolis Space, Number, and Geometry from Helmholtz to Cassirer is a substantial and pathbreaking contribution to the energetic and growing field of researchers delving into the physics, physiology, psychology, and mathematics of the nineteenth and twentieth centuries. … It is a clear, accurate, and deep account of fascinating and philosophically momentous implications of the move to relativity theory." (Lydia Patton, Journal for General Philosophy of Science, Vol. 50, 2019) Review Quote "Francesca Biagiolis Space, Number, and Geometry from Helmholtz to Cassirer is a substantial and pathbreaking contribution to the energetic and growing field of researchers delving into the physics, physiology, psychology, and mathematics of the nineteenth and twentieth centuries. ... It is a clear, accurate, and deep account of fascinating and philosophically momentous implications of the move to relativity theory." (Lydia Patton, Journal for General Philosophy of Science, Vol. 50, 2019) Feature Offers a new historical reconstruction of the philosophical debate on non-Euclidean geometry in neo-Kantianism Brings a new approach to Helmholtzs philosophy of mathematics Relevance for the current debate about the relativized a priori Details ISBN3319811169 Author Francesca Biagioli ISBN-10 3319811169 ISBN-13 9783319811161 Format Paperback Series Archimedes Year 2018 DEWEY 516 Pages 239 Imprint Springer International Publishing AG Place of Publication Cham Country of Publication Switzerland Publication Date 2018-06-09 Language English Series Number 46 UK Release Date 2018-06-09 Illustrations XX, 239 p. Publisher Springer International Publishing AG Edition Description Softcover reprint of the original 1st ed. 2016 Alternative 9783319317779 Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. 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