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Titulos:
Space, Number, and Geometry from Helmholtz to Cassirer by Francesca Biagioli.
ISBN:
3-319-31779-2
Lugar de Edición:
Editor:
Fecha de Edición:
Edición #:
1st ed. 2016.
Notas Formateada:
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.
Nota de contenido:
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.
Palabras clave:
Philosophy (General).; Geometry.; History of Philosophy.; History and Philosophical Foundations of Physics.; Geometry.

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Campo 100:
1 ^aBiagioli, Francesca.^eauthor.^4aut^4http://id.loc.gov/vocabulary/relators/aut
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10^aSpace, Number, and Geometry from Helmholtz to Cassirer^h[electronic resource] /^cby Francesca Biagioli.
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Campo 250:
^a1st ed. 2016.
Campo 300:
^a1 online resource (XX, 239 p.)
Campo 490:
1 ^aArchimedes, New Studies in the History and Philosophy of Science and Technology,^x1385-0180 ;^v46
Campo 505:
0 ^aHelmholtzs 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.
Campo 520:
^aThis 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.
Campo 650:
0^aPhilosophy (General).
Campo 650:
0^aGeometry.
Campo 650:
14^aHistory of Philosophy.^0http://scigraph.springernature.com/things/product-market-codes/E15000
Campo 650:
24^aHistory and Philosophical Foundations of Physics.^0http://scigraph.springernature.com/things/product-market-codes/P29000
Campo 650:
24^aGeometry.^0http://scigraph.springernature.com/things/product-market-codes/M21006
Proveniencia:
^aUniversidad de San Andrés - Biblioteca Max Von Buch
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Institucion:
Universidad de San Andrés
Dependencia:
Biblioteca Max Von Buch

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