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2017 | 9 | 85-98
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On Conceptual Metaphors In Mathematics

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This paper contains a few critical remarks concerning some fundamental assumptions and claims propagated by Lakoff and Núñez in their monograph Lakoff, Núñez (2000). Our attitude is skeptical (cf. also Pogonowski,2011). We agree with the idea that conceptual metaphors may play some role in the formation of elementary mathematical notions. However, we disagree with the authors’ claim that such metaphors provide the main mechanism in the emergence of new notions in advanced mathematics.
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Bibliografia
  • Auslander, J.: 2001, Embodied mathematics, American Scientist 89, 366–367.
  • Brożek, B., Hohol, M.: 2014, Umysł matematyczny, Copernicus Center Press, Kraków.
  • Bryll, G., Sochacki, R.: 2009, Wybrane zagadnienia dydaktyki matematyki, GARMOND Oficyna Wydawnicza, Poznań.
  • Devlin, K.: 2008, How do learn math? Mathematical Association of America, http://www.maa.org/devlin_12_08.html.
  • Elglaly, Y. N., Quek, F.: 2009, Review of ”Where Mathematics comes from: How the Embodied Mind Brings Mathematics Into Being” by George Lakoff and Rafael E. Núñez, CHI 2009, Boston.
  • Gelbaum, B. R., Olmsted, J. M. H.: 2003, Counterexamples in Analysis, Dover Publications, Inc., Mineola, New York.
  • Gold, B.: 2001, Review of Lakoff, Núñez 2000. www.maa.org/reviews/wheremath.html.
  • Goldin, G. A.: 2001, Counting on the metaphorical, Nature 413, 18–19.
  • Hartogs, F.: 1915, Über das Problem der Wohlordnung, Mathematische Annalen 76, 438–443.
  • Henderson, D. W.: 2002, Review of: Where Mathematics comes from: How the Embodied Mind Brings Mathematics Into Being, The Mathematical Intelligencer 24(1), 75–76.
  • Hilbert, D.: 1926, Über das Unendliche, Mathematische Annalen 95, 161–190.
  • Lakoff, G., Johnson, M.: 1980, Metaphors we live by, University of Chicago Press, Chicago.
  • Lakoff, G., Johnson, M.: 1999, Philosophy in the Flesh, Basic Books, New York.
  • Lakoff, G., Núñez, R.: 2000, Where Mathematics Comes From. How the Embodied Mind Brings Mathematics into Being, Basic Books, New York.
  • Madden, J. J.: 2001, Review of: Where Mathematics comes from: How the Embodied Mind Brings Mathematics Into Being, Notices of the AMS 48, 1182–1188.
  • Núñez, R. E.: 2005, Creating mathematical infinities: Metaphor, blending, and the beauty of transfinite cardinals, Journal of Pragmatics 37, 1717–1741.
  • Pogonowski, J.: 2011, Geneza matematyki wedle kognitywistów, Investigationes Linguisticae 23, 106–147.Accessible at: http://inveling.amu.edu.pl/, http://www.logic.amu.edu.pl/images/3/3c/Littlejill01.pdf.
  • Schiralli, M., Sinclair, N.: 2003, A constructive response to ’Where Mathematics Comes From’, Educational Studies in Mathematics 52, 79–91.
  • Siegfried, T.: 2001, Math may be not in the stars, but in ourselves, The Dallas Morning News, May 3, 2011 .
  • Steen, L. A., Seebach, J. A. Jr.: 1995, Counterexamples in Topology, Dover Publications, Inc., New York.
  • Thurston, W. P.: 1994, On proof and progress in mathematics, Bulletin of the American Mathematical Society 30(2), 161–177.
  • Voorhees, B.: 2004, Embodied Mathematics. Comments on Lakoff & Núñez, Journal of Consciousness Studies 11(9), 83–88.
  • Wise, G. L., Hall, E. B.: 1993, Counterexamples in Probability and Real Analysis, Oxford University Press, New York.
Typ dokumentu
Bibliografia
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bwmeta1.element.ojs-issn-2450-341X-year-2017-volume-9-article-4322
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