Advertisement

  • Reinhard KahleEmail author
Chapter
  • 197 Downloads
Part of the Logic, Epistemology, and the Unity of Science book series (LEUS, volume 43)

Abstract

This paper provides a discussion to which extent the Mathematician David Hilbert could or should be considered as a Philosopher, too. In the first part, we discuss some aspects of the relation of Mathematicians and Philosophers. In the second part we give an analysis of David Hilbert as Philosopher.

References

  1. Ackermann, W. (1933). Letter to David Hilbert, August 23rd, 1933, Niedersächsische Staats- und Universitätsbibliothek Göttingen, Cod. Ms. D. Hilbert 1.Google Scholar
  2. Bernays, P. (1935). Hilberts Untersuchungen über die Grundlagen der Arithmetik. In David Hilbert: Gesammelte Abhandlungen (Hilbert 1935) (Vol. III, pp. 196–216). Berlin: Springer.Google Scholar
  3. Bernays, P. (1954). Zur Beurteilung der Situation in der beweistheoretischen Forschung. Revue Internationale de Philosophie, 27–28(1–2), 1–5.Google Scholar
  4. Bernays, P. (1935). Über den Platonismus in der Mathematik. In Abhandlungen zur Philosophie der Mathematik (pp. 62–78). Darmstadt: Wissenschaftliche Buchgesellschaft, 1976 (German translation of a talk given in 1934 and published in French in 1935).Google Scholar
  5. Bourbaki, N. (1994). Elements of the History of Mathematics. Berlin: Springer.Google Scholar
  6. Brouwer, L. E. J. (1927). Intuitionistische Betrachtungen über den Formalismus. Koninklijke Akademie van wetenschappen te Amsterdam, Proceedings of the section of sciences, 31, 374–379. Translation in Part in Intuitionistic reflections on formalism (van Heijenoort 1967) pp. 490–492.Google Scholar
  7. Crozet, P. (2018). Avicenna and number theory. In H. Tahiri (Ed.), The Philosophers and Mathematics (pp. 67–80). Berlin: Springer.Google Scholar
  8. Diogenes Laertius (1959). Lives of Eminent Philosophers. Volume I. Cambridge Mass.: Harvard University Press.Google Scholar
  9. Eliae (1900). In Aristotelis Categorias. Commentarium. In A. Busse (Ed.), Commentaria in Aristotelem graeca (Vol. XVIII, Part I, pp. 1-255). Berlin: Georg Reimer.Google Scholar
  10. Ewald, W. (Ed.). (1996). From Kant to Hilbert (Vol. 1). Oxford: Clarendon Press.Google Scholar
  11. Gentzen, G. (1938). Die gegenwärtige Lage in der mathematischen Grundlagenforschung. Forschungen zur Logik und zur Grundlegung der exakten Wissenschaften, Neue Folge, 4, 5–18. also in Deutsche Mathematik, 3, 255–268, 1939. English translation in (Gentzen 1969 #7).Google Scholar
  12. Gentzen, G. (1969). Collected Works. Amsterdam: North-Holland.Google Scholar
  13. Hilbert, D., & Bernays, P. (1934). Grundlagen der Mathematik I, volume 40 of Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen. Berlin: Springer. (2nd ed. 1968). Partly translated into English in the bilingual edition (Hilbert and Bernays 2011).Google Scholar
  14. Hilbert, D., & Bernays, P. (1939). Grundlagen der Mathematik II, volume 50 of Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen. Berlin: Springer (2nd ed. 1970).Google Scholar
  15. Hilbert, D., & Bernays, P. (2011). Grundlagen der Mathematik I/Foundations of Mathematics I. Washington, DC: College Publications (Bilingual edition of Prefaces and §§1–2 of Hilbert and Paul Bernays 1934).Google Scholar
  16. Hilbert, D. (1899). Grundlagen der Geometrie. Festschrift zur Feier der Enthüllung des Gauss-Weber-Denkmals in Göttingen, herausgegeben vom Fest-Comitee (pp. 1–92). Leipzig: Teubner.Google Scholar
  17. Hilbert, D. (1935). Gesammelte Abhandlungen, vol. III: Analysis, Grundlagen der Mathematik, Physik, Verschiedenes, Lebensgeschichte. Berlin: Springer (2nd ed. 1970).Google Scholar
  18. Hilbert, D. (1967). The foundations of mathematics. In J. Heijenoort (Ed.), From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931 (pp. 464–479) (van Heijenoort 1967). Cambridge, MA: Harvard University Press.Google Scholar
  19. Jourdain, P. E. B. (1915). Mathematicians and philosophers. The Monist, 25(4), 633–638.CrossRefGoogle Scholar
  20. Kahle, R. (2013). David Hilbert and the Principia Mathematica. In N. Griffin & B. Linsky (Eds.), The Palgrave Centenary Companion to Principia Mathematica (pp. 21–34). London: Palgrave Macmillan.CrossRefGoogle Scholar
  21. Kahle, R. (2014). Poincaré in Göttingen. In M. de Paz & R. DiSalle (Eds.), Poincaré, Philosopher of Science, volume 79 of The Western Ontario Series in Philosophy of Science (pp. 83–99). Berlin: Springer.Google Scholar
  22. Kahle, R. (2015). Gentzen’s consistency proof in context. In R. Kahle & M. Rathjen (Eds.), Gentzen’s Centenary (pp. 3–24). Berlin: Springer.CrossRefGoogle Scholar
  23. Korselt, A. (1903). Über die Grundlagen der Geometrie. Jahresbericht der Deutschen Mathematiker-Vereinigung, 12, 402–407.Google Scholar
  24. Kreisel, G. (2011). Logical hygiene, foundations, and abstractions: Diversity among aspects and options. In M. Baaz, et al. (Eds.), Kurt Gödel and the Foundations of Mathematics (pp. 27–53). Cambridge, MA: Cambridge University Press.CrossRefGoogle Scholar
  25. Mazliak, L. (Ed.) (2013). La voyage de Maurice Janet á Göttingen. Les Éditions Materiologiques.Google Scholar
  26. McLarty, C. (2012). Hilbert on theology and its discontents. In A. Doxiadis & B. Mazur (Eds.), Circles Disturbed (pp. 105–129). Princeton: Princeton University Press.Google Scholar
  27. Peckhaus, V. (1990). Hilbertprogramm und Kritische Philosophie, volume 7 of Studien zur Wissenschafts-, Sozial- und Bildungsgeschichte der Mathematik. Vandenhoeck & Ruprecht, Göttingen.Google Scholar
  28. Peters, C. A. F. (Ed) (1862). Briefwechsel zwischen C. F. Gauss und H. C. Schumacher, vol. 4. Gustav Esch, Altona.Google Scholar
  29. Philoponus, J. (1897). Ioannis Philoponi in Aristotelis De anima libros commentaria. In M. Heyduck (Ed.), Commentaria in Aristotelem graeca (Vol. XV). Berlin: Georg Reimer.Google Scholar
  30. von Plato, J. (2016). In search of the roots of formal computation. In F. Gadducci, M. Tavosanis (Eds.), History and Philosophy of Computing. HaPoC 2015, volume 487 of IFIP Advances in Information and Communication Technology (pp. 300–320). Berlin: Springer.Google Scholar
  31. Rashed, R. (2008). The philosophy of mathematics. In S. Rahman, T. Street, & H. Tahiri (Eds.), The Unity of Science in the Arabic Tradition, volume 11 of Logic, Epistemology, and the Unity of Scienced (pp. 153–182). Berlin: Springer.Google Scholar
  32. Rashed, R. (2018). Avicenna: Mathematics and philosophy. In H. Tahiri (Ed.), The Philosophers and Mathematics (pp. 67–80). Berlin: Springer.Google Scholar
  33. Reid, C. (1970). Hilbert. Berlin: Springer.CrossRefGoogle Scholar
  34. Sinaceur, H. B. (2018). Scientific Philosophy and Philosophical Science. In H. Tahiri (Ed.), The Philosophers and Mathematics (pp. 25–66). Berlin: Springer.Google Scholar
  35. Smoryński, C. (1994). Review of Brouwer’s Intutionism by W. P. van Stigt. The American Mathematical Monthly, 101(8), 799–802.Google Scholar
  36. Tapp, C. (2005). Kardinalität und Kardinäle, volume 53 of Boethius. Stuttgart: Franz Steiner.Google Scholar
  37. Tapp, C. (2013). An den Grenzen des Endlichen. Mathematik im Kontext. Berlin: Springer.CrossRefGoogle Scholar
  38. Toepell, M. (1999). Zur Entstehung und Weiterentwicklung von David Hilberts “Grundlagen der Geometrie”. In David Hilbert: Grundlagen der Geometrie (14th ed., pp. 283–324). Stuttgart: Teubner.Google Scholar
  39. van Dalen, D. (2013). L.E.J. Brouwer. Berlin: Springer.Google Scholar
  40. van Heijenoort, J. (Ed.). (1967). From Frege to Gödel: A Source Book in Mathematical Logic, 1879–1931. Cambridge, MA: Harvard University Press.Google Scholar
  41. Volk, O. (1925). Kant und die Mathematik. In Mathematik und Erkenntnis (pp. 74–77). Königshausen & Neumann (German translation of a paper originally written in Lithuanian and published in Kosmos, vol. 6, pp. 320–323Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.CMA and DM, FCTUniversidade Nova de LisboaCaparicaPortugal

Personalised recommendations