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Philosophy of Geometry from Riemann to Poincaré - R. Torretti
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R. Torretti:

Philosophy of Geometry from Riemann to Poincaré - pocketboek

ISBN: 9789027718372

Geometry has fascinated philosophers since the days of Thales and Pythagoras. In the 17th and 18th centuries it provided a paradigm of knowledge after which some thinkers tried to pattern… Meer...

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Philosophy of Geometry from Riemann to Poincaré (Episteme, v. 7) (Episteme, 7, Band 7) - Roberto Torretti
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Philosophy of Geometry from Riemann to Poincaré (Episteme, v. 7) (Episteme, 7, Band 7) - eerste uitgave

1984, ISBN: 9789027718372

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D. Reidel Publishing, Taschenbuch, Auflage: 1. 459 Seiten, Publiziert: 1984-12-31T00:00:01Z, Produktgruppe: Buch, Hersteller-Nr.: Illustrations, 3.24 kg, Verkaufsrang: 9827, Geometrie, Na… Meer...

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Philosophy of Geometry from Riemann to Poincaré (Episteme, v. 7) (Episteme, 7, Band 7) - Roberto Torretti
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Roberto Torretti:
Philosophy of Geometry from Riemann to Poincaré (Episteme, v. 7) (Episteme, 7, Band 7) - eerste uitgave

1984

ISBN: 9789027718372

pocketboek

D. Reidel Publishing, Taschenbuch, Auflage: 1. 459 Seiten, Publiziert: 1984-12-31T00:00:01Z, Produktgruppe: Buch, Hersteller-Nr.: Illustrations, 3.24 kg, Verkaufsrang: 9827, Geometrie, Na… Meer...

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Philosophy of Geometry from Riemann to Poincaré (Episteme, v. 7) (Episteme, 7, Band 7) - Roberto Torretti
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Roberto Torretti:
Philosophy of Geometry from Riemann to Poincaré (Episteme, v. 7) (Episteme, 7, Band 7) - eerste uitgave

1984, ISBN: 9789027718372

pocketboek

D. Reidel Publishing, Taschenbuch, Auflage: 1. 459 Seiten, Publiziert: 1984-12-31T00:00:01Z, Produktgruppe: Book, Hersteller-Nr.: Illustrations, 3.24 kg, Verkaufsrang: 9419, Geometrie, Na… Meer...

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Philosophy of Geometry from Riemann to Poincare - R. Torretti
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R. Torretti:
Philosophy of Geometry from Riemann to Poincare - pocketboek

1984, ISBN: 9789027718372

Buch, Softcover, Softcover reprint of the original 1st ed. 1984, [PU: Kluwer Academic Publishers], Kluwer Academic Publishers, 1984

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Bijzonderheden over het boek
Philosophy of Geometry from Riemann to Poincaré (Episteme, v. 7) (Episteme, 7, Band 7)

...a carefull and scholarly discussion of the history and philosophy of geometry from the 1850's, marked by Riemann's generalized conception of space, and ending with Hilbert's axiomatics and PoincarA(c)'s conventionalism at the beginning of the century.' The Modern Schoolman This is a deeply learned, scrupulously careful, very informative book which was well worth writing... In sum, Toretti has written carefully, with much insight, deep and broad learning, and sober judgement on a topic of profound difficulty and interest.' Australian Journal of Philosophy Torretti has written a very useful book which helps fill a large gap in the literature on the philosophy of mathematics.' The Philosophical Quarterly It delves into the contributions of many neglected writers and dispells myths concerning the contributions of others, which have too often been perpetuated in the philosophical literature... I suggest that it deserves to become a standard word.' Dialogue

Gedetalleerde informatie over het boek. - Philosophy of Geometry from Riemann to Poincaré (Episteme, v. 7) (Episteme, 7, Band 7)


EAN (ISBN-13): 9789027718372
ISBN (ISBN-10): 9027718377
pocket book
Verschijningsjaar: 1984
Uitgever: D. Reidel Publishing
480 Bladzijden
Gewicht: 0,713 kg
Taal: eng/Englisch

Boek bevindt zich in het datenbestand sinds 2007-03-06T07:09:57+01:00 (Amsterdam)
Detailpagina laatst gewijzigd op 2021-10-21T21:43:54+02:00 (Amsterdam)
ISBN/EAN: 9027718377

ISBN - alternatieve schrijfwijzen:
90-277-1837-7, 978-90-277-1837-2


Gegevens van de uitgever

Auteur: R. Torretti
Titel: Episteme; Philosophy of Geometry from Riemann to Poincaré - A Series in the Foundational, Methodological, Philosophical, Psychological, Sociological, and Political Aspects of the Sciences, Pure and Applied
Uitgeverij: Springer; Springer Netherland
461 Bladzijden
Verschijningsjaar: 1984-12-31
Dordrecht; NL
Gewicht: 1,470 kg
Taal: Engels
234,33 € (DE)
240,90 € (AT)
258,50 CHF (CH)
POD

BC; Book; Hardcover, Softcover / Philosophie/Allgemeines, Lexika; Wissenschaftsphilosophie und -theorie; Verstehen; 19th century; Albert Einstein; Ernst Waldfried Josef Wenzel Mach; Interpretation; science; C; Philosophy of Science; History and Philosophical Foundations of Physics; History, general; Philosophy of Science; Philosophical Foundations of Physics and Astronomy; History; Religion and Philosophy; Geschichte der Naturwissenschaften; Geschichte; Geschichtsschreibung, Historiographie; BB

1 / Background.- 1.0.1 Greek Geometry and Philosophy.- 1.0.2 Geometry in Greek Natural Science.- 1.0.3 Modern Science and the Metaphysical Idea of Space.- 1.0.4 Descartes’ Method of Coordinates.- 2 / Non-Euclidean Geometries.- 2.1 Parallels.- 2.1.1 Euclid’s Fifth Postulate.- 2.1.2 Greek Commentators.- 2.1.3 Wallis and Saccheri.- 2.1.4 Johann Heinrich Lambert.- 2.1.5 The Discovery of Non-Euclidean Geometry.- 2.1.6 Some Results of Bolyai-Lobachevsky Geometry.- 2.1.7 The Philosophical Outlook of the Founders of Non-Euclidean Geometry.- 2.2 Manifolds.- 2.2.1 Introduction.- 2.2.2 Curves and their Curvature.- 2.2.3 Gaussian Curvature of Surfaces.- 2.2.4 Gauss’ Theorema Egregium and the Intrinsic Geometry of Surfaces.- 2.2.5 Riemann’s Problem of Space and Geometry.- 2.2.6 The Concept of a Manifold.- 2.2.7 The Tangent Space.- 2.2.8 Riemannian Manifolds, Metrics and Curvature.- 2.2.9 Riemann’s Speculations about Physical Space.- 2.2.10 Riemann and Herbart. Grassmann.- 2.3 Projective Geometry and Projective Metrics.- 2.3.1 Introduction.- 2.3.2 Projective Geometry: An Intuitive Approach.- 2.3.3 Projective Geometry: A Numerical Interpretation.- 2.3.4 Projective Transformations.- 2.3.5 Cross-ratio.- 2.3.6 Projective Metrics.- 2.3.7 Models.- 2.3.8 Transformation Groups and Klein’s Erlangen Programme.- 2.3.9 Projective Coordinates for Intuitive Space.- 2.3.10 Klein’s View of Intuition and the Problem of Space-Forms.- 3 / Foundations.- 3.1 Helmholtz’s Problem of Space.- 3.1.1 Helmholtz and Riemann.- 3.1.2 The Facts which Lie at the Foundation of Geometry.- 3.1.3 Helmholtz’s Philosophy of Geometry.- 3.1.4 Lie Groups.- 3.1.5 Lie’s Solution of Helmholtz’s Problem.- 3.1.6 Poincaré and Killing on the Foundations of Geometry.- 3.1.7 Hilbert’s Group-Theoretical Characterization of the Euclidean Plane.- 3.2 Axiomatics.- 3.2.1 The Beginnings of Modern Geometrical Axiomatics.- 3.2.2 Why are Axiomatic Theories Naturally Abstract?.- 3.2.3 Stewart, Grassmann, Plücker.- 3.2.4 Geometrical Axiomatics before Pasch.- 3.2.5 Moritz Pasch.- 3.2.6 Giuseppe Peano.- 3.2.7 The Italian School. Pieri. Padoa.- 3.2.8 Hilbert’s Grundlagen.- 3.2.9 Geometrical Axiomatics after Hilbert.- 3.2.10 Axioms and Definitions. Frege’s Criticism of Hilbert.- 4 / Empiricism, Apriorism, Conventionalism.- 4.1 Empiricism in Geometry.- 4.1.1 John Stuart Mill.- 4.1.2 Friedrich Ueberweg.- 4.1.3 Benno Erdmann.- 4.1.4 Auguste Calinon.- 4.1.5 Ernst Mach.- 4.2 The Uproar of Boeotians.- 4.2.1 Hermann Lotze.- 4.2.2 Wilhelm Wundt.- 4.2.3 Charles Renouvier.- 4.2.4 Joseph Delboeuf.- 4.3 Russell’s Apriorism of 1897.- 4.3.1 The Transcendental Approach.- 4.3.2 The ‘Axioms of Projective Geometry’.- 4.3.3 Metrics and Quantity.- 4.3.4 The Axiom of Distance.- 4.3.5 The Axiom of Free Mobility.- 4.3.6 A Geometrical Experiment.- 4.3.7 Multidimensional Series.- 4.4 Henri Poincaré.- 4.4.1 Poincaré’s Conventionalism.- 4.4.2 Max Black’s Interpretation of Poincaré’s Philosophy of Geometry.- 4.4.3 Poincaré’s Criticism of Apriorism and Empiricism.- 4.4.4 The Conventionality of Metrics.- 4.4.5 The Genesis of Geometry.- 4.5.6 The Definition of Dimension Number.- 1. Mappings.- 2. Algebraic Structures. Groups.- 3. Topologies.- 4. Differentiable Manifolds.- Notes.- To Chapter 1.- To Chapter 2.- 2.1.- 2.2.- 2.3.- To Chapter 3.- 3.1.- 3.2.- To Chapter 4.- 4.1.- 4.2.- 4.3.- 4.4.- References.

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