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Artículos

Vol. 11 No. 1 (2008): Marzo

PHILOSOPHY OF MATHEMATICS IN HIGH SCHOOL

Submitted
May 21, 2024
Published
2008-02-25

Abstract

This work presents the experience of teaching the philosophy of mathematics to high school students (Mexican nivel medio superior). The problems they face are discussed and the content of the program followed is analyzed. The conclusion is drawn that the teaching of the philosophy of mathematics in high school is a way to simultaneously stimulate philosophical and scientific thought in students. In particular, the discussion on why mathematics is applicable to the world awakened enormous interest and it should be emphasized in similar courses. Due to the high level of student motivation observed during these courses it can be concluded that these topics should be included in traditional philosophy and/or mathematics programs.

References

  1. Aboites, V. (2004). Filosofia de la matemática. Colmena Universitaria 33, 67-92.
  2. Anglin, W. S. (1994). Mathematics: a concise history and philosophy. USA, New York: Springer.
  3. Austin, J.L. (1975), How to do Things with Words. USA, Cambridge: Harvard University Press
  4. Benacerraf, P. (1965). What numbers could not be. Philosophical Review 74, 47-58.
  5. Benacerraf, P. (1973). Mathematical truth. Journal of Philosophy 70, 661-679.
  6. Berkeley, G. (1999). Principles of Human Knowledge. Oxford World Classics.
  7. Bradley, F.H. (1922). The Principles of Logic. UK, Oxford: Oxford University Press.
  8. Brouwer, L. E. J. (1912). Intuitionisme et formalisme. Holland, Groningen: Noordhoff. Born, M. & Wolf, E. (1993). Principles of optics: electromagnetic theory of propagation, interference and diffraction of light. USA, New York: Pergamon Press.
  9. Burges, J. & Rosen G. (1997). A subject with no object: strategies for nominalistic interpretation of mathematics. USA, New York: Oxford University Press.
  10. Cartwright, N. (1999). The dappled world. A study of the boundaries of science. UK, Cambridge: Cambridge University Press.
  11. Chihara, C. (1990). Constructibility and mathematical existence. USA, New York: Oxford University Press.
  12. Descartes, R. (1993). Méditations Metaphysiques. Paris: Flammarion.
  13. Dummet, M. (1983). The philosophical basis of intuitionistic logic. In P. Benacerraf & H. Putnam (Eds.), Philosophy of Mathematics (pp. 97-129). USA, New York: Cambridge University Press.
  14. Durnin J. & Miceli, J:J. (1987). Diffraction-free beams. Phys. Rev. Lett. 58 (15), 1499-1501.
  15. Ellis, B. (1999). What science aims to do. In D. Papineau (Ed.), The Philosophy of Science (pp. 166-193). UK, Oxford: Oxford University Press.
  16. Eves, H. (1990). Fundamental concepts of mathematics. USA, New York: Dover Publications Inc. Feynman, R. (1992). The Character of a Physical Law. Penguin Books
  17. Field, H. (1980). Science without numbers. USA, New Jersey, Princeton: Princeton University Press.
  18. Frege, G. (1879). Begriffsschrift: eine der arithmetischen nachgebildete Formelsprache des reinen Denkens. Deutschland: Halle [traducción al inglés: Bauer-Mengelberg, S. (1967). In J. Van Heijenoort (Ed.), From Frege to Gödel: a source book in mathematical logic, 1879-1931. USA, Cambridge, Massachusetts: Harvard University Press).
  19. Frege, G. (1884). Die grundlagen der aritmetik. Breslau: Koebner. [traducción al inglés: Austin, J. (1960). The foundations of aritmetic. USA, New York: Harper].
  20. Frege, G. (1892, 1903). Die Grundgesetze der Arithmetik (Vol. 1, 1892; Vol. II, 1903). Deutschland, Jena: Verlag Hermann Pohle (traducción al inglés: Furth, M. (1964). The basic laws of arithmetic. USA, California: University of California Press).
  21. George, A. & Velleman, D. J. (2002). Philosophies of mathematics. USA, Malden, Massachusetts: Blackwell Publishers.
  22. Gödel , K. (1931).Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme 1. Montatshefte für Mathematik und Physicsk 37. 173-198. (trad. al inglés: Van Heijenoort, J. (Ed.), From Frege to Gödel: a source book in mathematical logic, 1879-1931. USA, Cambridge, Massachusetts: Harvard University Press).
  23. Gödel, K. (1965). On undecidable propositions of formal mathematical systems. In M. Davis (Ed.), The Undecidable: basic papers on undecidable propositions, unsolvable problems and computable functions. USA, New York: Raven Press.
  24. Haack, S. (1978), Philosophy of logics. USA, New York: Cambridge University Press.
  25. Hale, B. (1987). Abstract objetcts. UK, London: Basil Blackwell.
  26. Hellman, G. (1989), Mathematics without numbers. USA, New York: Oxford University Press.
  27. Heyting, A. (1953). Intuitionism: An introduction. Holland, Amsterdam: North-Holland.
  28. Hilbert, D. (1899). Grundlagen der Geometrie. Deutschland: Leipzig. [trad. al inglés: Townsend E. J. (1959). Foundations s of Geometry, USA, Illinois: Open Court Publishing Company).
  29. Hilbert, D. (1935). Gesammelte Abhandlungen. Deutschland, Berlin: Springer.
  30. Hume, D. (1993), An Enquiry Concerning Human Understanding in Beauchamp, T. (Ed). Hackett James, W. (2003), The Will to Believe and other Essays. USA, New York: Dover Publications
  31. Kant, 1. (2005). Critica de la razón pura. Madrid, España: Taurus.
  32. Kitcher, P. (1993). The advancement of science, USA, New York: Oxford University Press.
  33. Körner, A. S. (1960). The philosophy of mathematics. UK, London: Hutchinson University Library.
  34. Landau, L. D. & Lifshitz, E. M. (1981). Electrodynamics of continuous media. USA, New York: Pergamon Press.
  35. Laudan, L. (1996). Beyond positivism and relativism. USA, Boulder, Colorado: Westview Press.
  36. Locke, J. (1997). An Essay Concerning Human Understanding. Penguin Classics
  37. Maddy, P. (1990). Realism in mathematics. USA, New York: Oxford University Press.
  38. Maiman, T. H., Hoskins, R.H., D'Haenens, I.J., Asawa, C.K. & Evtuhov, V. (1961). Stimulated optical emission in fluorescent solids. II. Spectroscopy and stiumulated emission in ruby. Phys. Rev. 123 (4), 1151-1157.
  39. Matrix (1999). Dir. Andy y Larry Wachowsky, Warner Bros
  40. Mill, J. S. (1973). A system of logic, racionative and inductive. UK, London: Routledge and Keagan Paul.
  41. Peirce, C.S. (1998). How to make our ideas clear. In The Essential Writings. Prometheus Books UK
  42. Platón (2002). Thethetus. En Diálogos (Vol. V). Madrid, España: Gredos.
  43. Psillos, S. (2000). The present state of the scientific realism debate. The British Journal for the Philosophy of Science 51, 705-728, ,
  44. Putnam H. (1990). Realism with a human face. USA, Cambridge, Massachusetts: Harvard University Press.
  45. Putnam, H. (1983). Mathematics without foundations. In P. Benacerraf & H. Putnam (Eds.), Philosophy of Mathematics. USA, New York: Cambridge University Press.
  46. Putnam, H. (1971). Philosophy of logic. USA, New York: Harper and Row.
  47. Quine, W. V. O. (1941). The philosophy of Alfred North Whitehead. USA, New York: Tudor Publishing.
  48. Quine, W. V. O. (1951). Two dogmas of empiricism. The Philosophical Review 60, 20-43 [compilado en From a logical point of view. USA, Cambridge, Massachusetts: Harvard University Press).
  49. Quine, W. V. O. (1981). Theories and things. USA, Cambridge, Massachusetts: Harvard University Press.
  50. Ramsey, F.P. (1990). Philosophical Papers. Cambridge University Press
  51. Rescher, N. (2003). Epistemogoly: An Introduction to the Theory of Knowledge. State University of New York Press
  52. Resnik, M. (1997). Mathematics as a science of patterns. USA, New York: Oxford University Press.
  53. Russell, B. (1912). The Problems of Philosophy. London: Ed. Williams and Norgate
  54. Rota, G. C. (1997). Ten lessons i wish i had been taught. Notices of the AMS 44 (1), 22-25.
  55. Shapiro, S. (1997), Philosophy of mathematics: structure and ontology. USA, New York: Oxford University Press.
  56. Shapiro, S. (2000). Thinking about mathematics. USA, New York: Oxford University Press.
  57. Suppe, F. (1989). The semantic conception of theories and scientific realism. USA, Chicago, Illinois: University of Illinois Press. Suppe,
  58. F. (1989). The Semantic conception of Theories and Scientific Realism. USA, Chicago: Chicago University of Illinois Press
  59. Tarski, A. (1994). Introduction to Logic and to the Methodology of Deductive Sciences. UK, Oxford: Oxford University Press
  60. Van Fraassen, B. (1980). The scientific image. USA, New York, Oxford: Clarendon Press. Wittgenstein, L. (2001). Tractatus. Routledge. Classics

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