Space, Number, and Geometry from Helmholtz...

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Beschreibung

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 Poincaré, 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.

Über den Autor

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.

Zusammenfassung

Offers a new historical reconstruction of the philosophical debate on non-Euclidean geometry in neo-Kantianism

Brings a new approach to Helmholtz's philosophy of mathematics

Relevance for the current debate about the relativized a priori

Inhaltsverzeichnis

Helmholtz's Relationship to Kant.- The Discussion of Kant's 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 Einstein's General Relativity: Cassirer's View in 1921.

Erscheinungsjahr:	2016
Fachbereich:	Allgemeines
Genre:	Philosophie
Jahrhundert:	Antike
Rubrik:	Geisteswissenschaften
Thema:	Lexika
Medium:	Buch
Reihe:	Archimedes
Inhalt:	xx 239 S.
ISBN-13:	9783319317779
ISBN-10:	3319317776
Sprache:	Englisch
Herstellernummer:	978-3-319-31777-9
Ausstattung / Beilage:	HC runder Rücken kaschiert
Einband:	Gebunden
Autor:	Biagioli, Francesca
Auflage:	1st ed. 2016
Hersteller:	Springer Nature Switzerland Springer International Publishing Springer International Publishing AG Archimedes
Maße:	241 x 160 x 20 mm
Von/Mit:	Francesca Biagioli
Erscheinungsdatum:	30.08.2016
Gewicht:	0,559 kg

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