Linked bibliography for the SEP article "Epistemology of Geometry" by Jeremy Gray

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If everything goes well, this page should display the bibliography of the aforementioned article as it appears in the Stanford Encyclopedia of Philosophy, but with links added to PhilPapers records and Google Scholar for your convenience. Some bibliographies are not going to be represented correctly or fully up to date. In general, bibliographies of recent works are going to be much better linked than bibliographies of primary literature and older works. Entries with PhilPapers records have links on their titles. A green link indicates that the item is available online at least partially.

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  • d’Alembert, J. le Rond, 1784, Encylopédie Méthodique: Mathématique. (Scholar)
  • Badici, E., 2011, “Standards of equality and Hume’s view of geometry”, Pacific Philosophical Quarterly, 92(4): 448–467. (Scholar)
  • Beltrami, E., 1868, “Saggio di interpretazione della geometria non Euclidea”, Giornale di Matematiche, 6: 284–312, in Opere matematiche I: 374–405. English translation in J. Stillwell, 1996, Sources of Hyperbolic Geometry (History of Mathematics 10), American and London Mathematical Societies, p. 7–34. (Scholar)
  • Bioesmat-Martagon, L., 2011, Éléments d’une biographie de l’espace projectif, Nancy: Presses Universitaires de Nancy, Collection histories de geometries, 2.
  • Bolyai, J., 1832, “Appendix scientiam spatii absolute veram exhibens”, in W. Bolyai and J. Bolyai, 1832, Tentamen juventutem studiosam in Elementa Matheosis purae, etc, Maros-Vásérhely, 2 vols. English translation by G.B. Halsted, “The Science Absolute of Space”, Appendix in Bonola 1912 and in J.J. Gray, 2004, János Bolyai, Non-Euclidean Geometry and the Nature of Space, Burndy Library, MIT. (Scholar)
  • Bonola, R., 1906, La geometria non-Euclidea, Bologna: Zanichelli, English translation H.S. Carslaw, preface by F. Enriques, 1912, History of non-Euclidean geometry, Chicago: Open Court; reprint, New York: Dover, 1955. (Scholar)
  • Bottazzini, U., 1999, “Ricci and Levi-Civita: from differential invariants to general relativity”, in J.J. Gray (ed.) The symbolic universe: geometry and physics 1890–1930, Oxford: Oxford University Press. (Scholar)
  • Chasles, M., 1837, Aperçu historique sur l’origine et le développement des méthodes en géométrie …suivi d’un Mémoire de géométrie, etc. Mémoires sur les questions proposées par l’Académie Royale des Sciences et Belles-Lettres de Bruxelles, tom. 11, Bruxelles. (Scholar)
  • Clairaut, A.C., 1741, Elémens de géométrie, Paris: David Fils. Reprinted 1920, Paris: Gauthier-Villars. (Scholar)
  • Cremona, L., 1873, Elementi di geometria projettiva, Turin. English translation by C. Leudesdorf, 1885, Elements of projective geometry, Oxford: Clarendon Press. (Scholar)
  • Enriques, F., 1906, Problemi della Scienza. English translation by K. Royce, 1914, Problems of Science, Chicago: Open Court. (Scholar)
  • Enriques, F., 1907, “Prinzipien der Geometrie”, Encylopädie der Mathematischen Wissenschaften, III.I.1,1–129, Leipzig, Teubner. (Scholar)
  • Euclid, The Thirteen Books of Euclid’s Elements, translation and commentaries by Sir T. L. Heath, New York: Dover Publications, 1956. (Scholar)
  • Gauss, C.F., 1828, “Disquisitiones generales circa superficies curvas”, Commentationes societatis regiae scientiarum Gottingensis recentiores. Reprinted in 1870, Carl Friedrich Gauss Werke, 4: 217–258; and in P. Dombrowski (ed.), 1978, 150 Years After Gauss’ ‘Disquisitiones Generales Circa Superficies Curvas’, Latin original, with a reprint of the English translation by A. Hiltebeitel and J. Morehead, 1902, Astérisque 62, Paris: Société mathématique de France; and in P. Pesic, (ed.), 2005, General investigations of curved surfaces, New York: Dover Books. (Scholar)
  • Gauss, C.F., 1900 Werke 8, Leipzig: Teubner. (Scholar)
  • Gray, J.J., 2008, Plato’s Ghost: The Modernist Transformation of Mathematics, Princeton: Princeton University Press. (Scholar)
  • –––, 2011, Worlds out of Nothing; a course on the history of geometry in the 19th century, 2nd revised ed., London: Springer. (Scholar)
  • –––, 2012, Henri Poincaré: a scientific biography, Princeton: Princeton University Press. (Scholar)
  • Griffin, N., 1991, Russell’s idealist apprenticeship, Oxford: Clarendon Press. (Scholar)
  • Hallett, M. and U. Majer (eds), 2004, David Hilbert’s lectures on the foundations of geometry, 1891–1902, Berlin: Springer. (Scholar)
  • Helmholtz, H. von, 1868, “Über die thatsächlichen Grundlagen der Geometrie”, Nachrichten K. Ges. Wissenschaften zu Göttingen, 9. English translation by M. F. Lowe, 1921, “On the facts underlying geometry”, Epistemological Writings, R. S. Cohen and Y. Elkana (eds), Boston Studies in the Philosophy of Science, Boston: Reidel, volume 37, 39–57. (Scholar)
  • –––, 1870, “Über den Ursprung und die Bedeutung der geometrischen Axiome”, Vorträge und Reden, vol. 2, 1–31. English translation “On the origin and significance of the axioms of geometry”, in Epistemological Writings, pp. 1–25. (Scholar)
  • –––, 1921, Schriften zur Erkenntnistheorie, Berlin: Springer, P. Hertz and M. Schlick (eds), 1977, translated by M.F. Lowe as Epistemological Writings, R.S. Cohen and Y. Elkana (eds), Reidel. (Scholar)
  • Herbart, J.F., 1824–1825, Psychologie als Wissenschaft neu gegründet auf Erfahrung, Metaphysik, und Mathematik, 2 vols, Königsberg: A.W. Unzer. (Scholar)
  • Hilbert, D., 1899, Grundlagen der Geometrie, Festschrift zur Feier der Enthüllung des Gauss-Weber-Denkmals in Göttingen, Leipzig: Teubner, many subsequent editions. English translation of 10th edition by L. Unger, 1971, Foundations of geometry, Chicago: Open Court. (Scholar)
  • –––, 1901, “Über Flächen von konstanter Gaussscher Krümmung”, Transactions of the American Mathematical Society 2: 87–99. In Gesammelte Abhandlungen, 2: 437–448. (Scholar)
  • Hume, D., 1739–1740, A Treatise of Human Nature, London. Searchable text at A Treatise of Human Nature by David Hume, reprinted from the Original Edition in three volumes and edited, with an analytical index, by L.A. Selby-Bigge, M.A. (Oxford: Clarendon Press, 1896). [online searchable Hume 1739] (Scholar)
  • Kant, I., 1781, 1787, Kritik der reinen Vernunft; translator Norman Kemp Smith, 1929, Immanuel Kant’s Critique of Pure Reason, 2nd ed. rep. 1970, London: Macmillan. (Scholar)
  • Klein, C.F., 1871, “Ueber die sogenannte Nicht-Euklidische Geometrie”, Mathematische Annalen, 4: 573–625. Also in Gesammelte Mathematische Abhandlungen 1, (no. XVI): 254–305, Berlin: Springer. (Scholar)
  • –––, 1872, Vergleichende Betrachtungen über neuere geometrische Forschungen, Programm zum Eintritt in die philosophische Facultät und den Senat der Universität zu Erlangen, Deichert, Erlangen, in Gesammelte Mathematische Abhandlungen 1, (no. XXVII): 460–497. English translation by M.W. Haskell, 1892–1893, Bulletin of the New York Mathematical Society 2: 215–249, Berlin, Springer. (Scholar)
  • –––, 1873, “Ueber die sogenannte Nicht-Euklidische Geometrie. (Zweiter Aufsatz)”, Mathematische Annalen, 6: 112–145, in Gesammelte Mathematische Abhandlungen 1, (no. XVIII): 311–343, Berlin: Springer. (Scholar)
  • Laplace, P.-S., 1796, “Exposition du système du monde,” Paris: Crapelet, in Oeuvres VI, Paris, Gauthier-Villars, 1884 (Scholar)
  • Legendre, A.-M., 1794, Éléments de géométrie, Paris: Fermin Didot Frères, several editions.
  • Levi-Civita, T., 1917, “Nozione de parallelismo in una varietà qualunque”, Rendiconto del Circolo Matematico di Palermo, 42: 173–205. (Scholar)
  • Lobachevskii, N.I., 1835, “Neue Anfangsgrunde der Geometrie mit einer vollständigen Theorie der parallellinien”, German translation in Lobachetschefskij, N.I. 1899 Zwei geometrische Abhandlungen, tr. F. Engel, Leipzig, Teubner. (Scholar)
  • –––, 1840, Geometrische Untersuchungen zur Theorie der Parallellinien, Berlin, rep. Mayer & Müller, 1887, English tr. G.B. Halsted, Geometric Researches in the Theory of Parallels, Appendix in (Bonola 1912). (Scholar)
  • –––, 1856, Pangéométrie, ou précis de géométrie fondée sur une théorie générale des paralleles, Kasan. English translation with commentary, Pangeometry, A. Papadopoulos (ed.), European Mathematical Society, 2010. (Scholar)
  • Locke, J., 1690, An Essay Concerning Human Understanding, London. [Locke 1690 available online] (Scholar)
  • Marchisotto, E. and J.T. Smith, 2007, The legacy of Mario Pieri in geometry and arithmetic, Boston: Birkhäuser. (Scholar)
  • Mueller, I., 1981, Philosophy of Mathematics and Deductive Structure in Euclid’s Elements, Cambridge: MIT Press. (Scholar)
  • Nabonnand, P., 2000, “La polémique entre Poincaré et Russell au sujet du statut des axiomes de la géométrie,” Revue d’histoire des mathématiques, 6: 219–269. (Scholar)
  • Newton, Sir I., 1687, Philosophiæ Naturalis Principia Mathematica. English translation The Principia: Mathematical Principles of Natural Philosophy, tr. I.B. Cohen, A. Whitman, J. Budenz, University of California Press, 1999. (Scholar)
  • de Pierris, G., 2012, “Hume on space, geometry, and diagrammatic reasoning”, Synthese, 186(1): 169–189. (Scholar)
  • Poincaré, H., 1882e. Théorie des groupes fuchsiens. Acta Mathematica 1, 1–62 in Oeuvres 2, 108–168. (Scholar)
  • Poincaré, H., 1898, “On the foundations of geometry” (translated by T. J. McCormack) Monist 9: 1–43. Reprinted in Ewald, 1996, From Kant to Hilbert: A Source Book in the Foundations of Mathematics, Oxford: Oxford University Press, 2: 982–1012. (Scholar)
  • –––, 1899, “Des fondements de la géométrie: à propos d’un livre de M. Russell,” Revue de métaphysique et de morale 7: 251–279. (Scholar)
  • –––, 1902, “Les fondements de la géométrie”, Journal des savants, 252–271. English translation by E. V. Huntington, 1903, “Poincaré’s review of Hilbert’s ‘foundations of geometry’”, Bulletin of the American Mathematical Society, 10(1): 1–23. [Poincaré 1902 (English) available online] (Scholar)
  • Poncelet, J.V., 1822, Traité des Propriétées Projectives des Figures, Paris: Gauthier-Villars. (Scholar)
  • Riemann, G.B.F., 1867 [1854], “Ueber die Hypothesen, welche der Geometrie zu Grunde liegen,” Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen, 13: 1–20. Republished in Gesammelte Mathematische Werke, Wissenschaftliche Nachlass und Nachträge. Collected Papers: Nach der Ausgabe von Heinrich Weber und Richard Dedekind, 1990, R. Narasimhan, (ed.) Berlin: Springer, pp. 304–319. Bernhard Riemann, Collected Papers, translated by Roger Baker, Charles Christenson and Henry Orde, Kendrick Press, 2005. (Scholar)
  • Russell, B., 1899, “Sur Les Axiomes de la Géométrie”, Revue de méetaphysique et de morale, 684–706, translated and reprinted as “On the Axioms of Geometry”, in N. Griffin and A. C. Lewis, (eds), 1990, The Collected Papers of Bertrand Russell, 2, London: Hyman Unwin, 394–415. (Scholar)
  • Scholz, E., 1982, “Herbart’s Influence on Bernhard Riemann,” Historia Mathematica, 9(4): 413–440. (Scholar)
  • –––, 2001, “Weyl’s Infinitesimalgeometrie”, in Hermann Weyl’s Raum–Zeit–Materie and a general introduction to his scientific work, E. Scholz (ed.) Basel, Birkhäuser. (Scholar)
  • Schweikart, F.K., 1818, “Notiz”, in Carl Friedrich Gauss Werke, 8: 180–181. (Scholar)
  • von Staudt, G.K.C., 1847, Geometrie der Lage, Nürnberg. (Scholar)
  • –––, 1856–1860, Beiträge zur Geometrie der Lage, 3 vols, Nürnberg. (Scholar)
  • Villaggio, P., 2006, “On Enriques’s foundations of mechanics”, in K. Williams (ed.) Two cultures: Essays in honour of David Speiser, Birkhäuser, 133–138. (Scholar)
  • Wallis, J., 1693, “De postulato quinto et definitione lib. 6 Euclidis deceptatio geometrica”, in Operum Mathematicorum, 2: 665–678. (Scholar)
  • Weyl, H., 1918, Raum–Zeit–Materie, Springer. English translation of the third edition (1920) Space-time-matter, London: Methuen. (Scholar)

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