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Theological Underpinnings of the Modern Philosophy of Mathematics. Cover

Theological Underpinnings of the Modern Philosophy of Mathematics.

Open Access
|Mar 2016

References

  1. Bell, E.T. (1945). The development of mathematics (2nd ed.). New York, NY: McGraw-Hill.
  2. Benacerraf, P., & Putnam, H. (Eds.). (1983). Philosophy of mathematics: Selected readings (2nd ed.). New York, NY: Cambridge University Press.
  3. Bergmans, L. (2005). Gerrit Mannoury and his fellow significians on mathematics and mysticism. In T. Koetsier & L. Bergmans (Eds.), Mathematics and the divine: A historical study (pp. 549–568). Amsterdam: Elsevier B.V.
  4. Bishop, E. (1967). Foundations of constructive analysis. New York, NY: McGraw-Hill.
  5. Brouwer, L.E.J. (1975). Collected works, vol. 1: Philosophy and foundations of mathematics (A. Heyting, Ed.). Amsterdam: North-Holland Publishing Company.
  6. Brouwer, L.E.J. (1996). Life, art, and mysticism (W.P. van Stigt, Intr. and trans.). Notre Dame Journal of Formal Logic, 37, 381–429. (Original work published 1905)
  7. Cellucci, C. (2005). Mathematical discourse vs. mathematical intuition. In C. Cellucci & D. Gillies (Eds.), Mathematical reasoning and heuristics (pp. 137–165). London: King’s College Publications.
  8. Cohen, D.J. (2007). Equations from God: Pure mathematics and Victorian faith. Baltimore, MD: The Johns Hopkins University Press.10.1353/book.3301
  9. Davis, P.J. (2004). A brief look at mathematics and theology. The Humanistic Mathematics Network Journal Online, 27. Retrieved from http://www2.hmc.edu/www_common/HMNJ-OLD/davis2brieflook1and2.pdf10.5642/hmnj.200401.27.14
  10. Ewald, W.B. (1996). From Kant to Hilbert: A source book in the foundations of mathematics. New York, NY: Oxford University Press.
  11. Ferreirós, J. (2004). The motives behind Cantor’s set theory – physical, biological, and philosophical questions. Science in Context, 17, 49–83.10.1017/S0269889704000055
  12. Frege, G. (1980). Philosophical and mathematical correspondence (G. Gabriel et al., Eds., B. McGuinness, Abr., H. Kaal, Trans.). Oxford, UK: Basil Blackwell.
  13. Gray, J.J. (2004). Anxiety and abstraction in nineteenth-century mathematics. Science in Context, 17, 23–47.10.1017/S0269889704000043
  14. Gray, J.J. (2008). Plato’s ghost: The modernist transformation of mathematics. Princeton, NJ: Princeton University Press.10.1515/9781400829040
  15. Heijerman, E. (1990). Relativism and significs: Gerrit Mannoury on the foundations of mathematics. In H.W. Schmitz (Ed.), Essays on significs: Papers presented on the occasion of the 150th anniversary of the birth of Victoria Lady Welby, 1837–1912 (pp. 247–272). John Benjamins B.V.
  16. Hesseling, D.E. (2003). Gnomes in the fog: The reception of Brouwer’s intuitionism in the 1920s. Basel, Switzerland: Birkhäuser Verlag.10.1007/978-3-0348-7989-7
  17. Heyerman, E. (1981). Intuition and the intellect: On the relation between mathematics, philosophy and mysticism in the work of L.E.J. Brouwer, including a comparison with Nicolas of Cusa. Preprint No. 208. Utrecht: Utrecht University, Department of Mathematics.
  18. Hilbert, D. (1900). Mathematische Probleme. In Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-Physikalische Klasse aus dem Jahre 1900 (pp. 253–297). Göttingen: Dieterichsche Universitätsbuchhandlung.
  19. Hilbert, D. (1926). Über das Unendliche. Mathematische Annalen, 95, 161–190. English translation (van Heijenoort, 1967, pp. 367–392).10.1007/BF01206605
  20. Hilbert, D. (1928). Die Grundlagen der Mathematik. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 6, 65–85. English translation (van Heijenoort, 1967, pp. 464–479).
  21. Hilbert, D. (1930). Naturerkennen und Logik. Naturwissenschaften, 18, 959–963. English translation (Ewald, 1996, pp. 1157–1165).10.1007/BF01492194
  22. Hilbert, D. (2013). David Hilbert’s lectures on the foundations of arithmetic and logic 1917–1933 (W. Ewald & W. Sieg, Eds.). Heidelberg: Springer-Verlag.
  23. Kleene, S.C. (1952). Introduction to metamathematics. Amsterdam: North-Holland.
  24. Klein, F. (1909). Elementarmathematik vom höheren Standpunkte aus, Teil II: Geometrie, Vorlesung gehalten in Sommersemester 1908. Leipzig: B.G. Teubner.
  25. Koetsier, T. (2005). Arthur Schopenhauer and L.E.J. Brouwer: A comparison. In T. Koetsier & L. Bergmans (Eds.), Mathematics and the divine: A historical study (pp. 569–593). Amsterdam: Elsevier B.V.
  26. Kragh, H. (2014). The true (?) story of Hilbert’s infinite hotel. Retrieved from http://arxiv.org/abs/1403.0059
  27. Kunen, K. (2009). The foundations of mathematics. London, UK: College Publications.
  28. Lakatos, I. (1976). Proofs and refutations: The logic of mathematical discovery (J. Worrall & E. Zahar, Eds.). Cambridge, UK: Cambridge University Press.10.1017/CBO9781139171472
  29. McLarty, C. (2012). Hilbert on theology and its discontents. In A. Doxiadis & B. Mazur (Eds.), Circles disturbed: the interplay of mathematics and narrative (pp. 105–129). Princeton, NJ: Princeton University Press.
  30. Minkowski, H. (1905). Peter Gustav Lejeune Dirichlet und seine Bedeutung für die heutige Mathematik. Jahresberichte der Deutschen Mathematiker-Vereinigung, 14, 149–163.
  31. Mendelson, E. (1979). Introduction to mathematical logic (2nd ed.). New York, NY: D. Van Nostrand Company. (First edition 1964)
  32. Plato (1997). Complete works (J.M. Cooper, Ed.). Indianapolis, IN: Hackett Publishing Company.
  33. Rasiowa, H. & Sikorski, R. (1963). Mathematics of metamathematics. Warszawa: Państwowe Wydawnictwo Naukowe.
  34. Reid, C. (1970). Hilbert. Berlin – Heidelberg: Springer.10.1007/978-3-662-28615-9
  35. Russell, B. (1917). Mysticism and logic and other essays. London: Allen & Unwin.
  36. Russell, B. (1919). Introduction to mathematical philosophy. London, UK: Allen & Unwin, New York, NY: The MacMillan Co.
  37. Russell, B. (1956). Portraits from memory and other essays. New York, NY: Simon & Schuster.
  38. Russell, B. (1959). My philosophical development. New York, NY: Simon & Schuster.
  39. van Atten, M. & Tragesser, R. (2003). Mysticism and mathematics: Brouwer, Gödel, and the common core thesis. In W. Deppert & M. Rahnfeld (Eds.), Klarheit in Religionsdingen (pp. 145–160). Leipzig: Leipziger Universitätsverlag. Reprinted in (van Atten, 2015, pp. 173–187).
  40. van Atten, M. (2015). Essays on Gödel’s reception of Leibniz, Husserl, and Brouwer. Cham: Springer.10.1007/978-3-319-10031-9
  41. van Dalen, D. (2008). Another look at Brouwer’s dissertation. In M. van Atten et al. (Eds.), One hundred years of intuitionism (1907–2007): The Cerisy conference (pp. 3–20) Berlin: Birkhäuser.
  42. van Dalen, D. (2011). The selected correspondence of L.E.J. Brouwer. London, UK: Springer-Verlag.10.1007/978-0-85729-537-8
  43. van Dalen, D. (2013). L.E.J. Brouwer – topologist, intuitionist, philosopher: How mathematics is rooted in life. London, UK: Springer-Verlag.
  44. van Heijenoort, J. (1967). From Frege to Gödel: A source book in mathematical logic, 1879–1931. Cambridge, MA: Harvard University Press.
  45. van Stigt, W.P. (1979). The rejected parts of Brouwer’s dissertation on the foundations of mathematics. Historia Mathematica, 6, 385–404. The rejected parts reprinted in (van Stigt, 1990, pp. 405–415).10.1016/0315-0860(79)90025-9
  46. van Stigt, W.P. (1990). Brouwer’s intuitionism. Amsterdam: North-Holland Publishing Company.
  47. Weyl, H. (1921). Über die neue Grundlagenkrise der Mathematik. Mathematische Zeitschrift, 10, 39–79.10.1007/BF02102305
  48. Weyl, H. (1946). Mathematics and logic. American Mathematical Monthly, 53, 2–13.
DOI: https://doi.org/10.1515/slgr-2016-0009 | Journal eISSN: 2199-6059 | Journal ISSN: 0860-150X
Language: English
Page range: 147 - 168
Published on: Mar 17, 2016
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
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© 2016 Vladislav Shaposhnikov, published by University of Białystok
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