Abstract
We consider three levels of pluralism: (1) within mathematics, (2) with regard to philosophy of mathematics, and (3) personal pluralism.
Reprinted with permission from Springer Science. The original version of this article appeared in a special issue of the Journal of the Indian Council of Philosophical Research, guest edited byMichele Friend and Mihir Chakraborty.
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Balaguer, M., 2001, Platonism and anti-Platonism in mathematics, Oxford University Press
Balaguer, M., 2013, “A Guide for the Perplexed: What Mathematicians Need to Know to Understand Philosophers of Mathematics”, http://sigmaa.maa.org/pom/PomSigmaa/Balaguer 1–13.pdf
Burgesss, J. P. and G. Rosen, 1997, A subject with no object, Oxford University Press.
Burgess, J. P., 2015, Rigor and Structure, Princeton University Press
Byers, W., 2010, How Mathematicians Think, Princeton University Press
Cellucci, C., 2006, “Introduction to Filosofia e matematica”, in R. Hersh ed., 18 unconventional essays on the nature of mathematics, 17–36, Springer
Cohen, P. J., 1971, “Comments on the foundations of set theory,” in D. Scott ed., Axiomatic Set Theory, 9–15, American Mathematical Society
Connes, A. and J.-P. Changeux, 1995, Conversations on mind, matter and mathematics, Princeton University Press
Davies, E. B., 2005, “A Defence of Mathematical Pluralism,” in Philosophia Mathematica (III) 13, 252–276
Dehaene, S., 1997, The number sense, Oxford University Press
Dieudonne, J., 1970, “The work of Nicolas Bourbaki,” American Mathematical Monthly, 77, 134–145
Doxiadis, A. and B. Mazur, 2012, Circles Disturbed, Princeton University Press
Ernest, P., 1997, Social constructivism in the philosophy of mathematics, SUNY Press
Feferman, S., 1998, In the light of logic, Oxford University Press
Friend, M., 2014, Pluralism in Mathematics: A New Position in the Philosophy of Mathematics, Springer
Grosholz, E., 2007, Representation and productive ambiguity in mathematics and the sciences, Oxford University Press
Hersh, R., 1979, “Some proposals for reviving the philosophy of mathematics”, Advances in Mathematics 31, 31–50, reprinted in New directions in the philosophy of mathematics, ed.T.Tymoczko, Birkhauser, 1985
Hersh, R., 2014, Experiencing Mathematics, American Mathematical Society
Hersh, R., 2015, “Mathematics as an empirical phenomenon, subject to modeling,” in Models and Inferences in Science, Springer
Kitcher, P., 1983, The nature of mathematical knowledge, Oxford University Press
Lakatos, I., 1976, Proofs and refutations, Cambridge University Press
Lakoff, G. and R. Nunez, 2000, Where mathematics comes from, Basic Books
Priest, G., 2014, “Mathematical Pluralism,” in P. Allo and B. Van Kerkhove ed., Modestly radical or radically modest, 111–125, College Publications
Ruelle, D., 2007, The Mathematician’s Brain, Princeton University Press
Shapiro, S., 2005, The Oxford Handbook of Philosophy of Mathematics and Logic, Oxford University Press
Thomas, R., 2007, “The comparison of mathematics with narrative”, in B. v. Kerkhove and J.P.v. Bendegem ed., Perspectives on mathematical practices, 43–60, Springer
Thomas, R., 2014, `The judicial analogy for mathematical publication”, paper delivered at the meeting of Canadian Society for History and Philosophy of Mathematics, May 25, Brock University, St Catherines, Ontario.
Thurston, W., 2006, “On proof and progress in mathematics”, in R. Hersh ed., 18 unconventional essays on the nature of mathematics, 37–55, Springer
Tiles, M., 1991, Mathematics and the image of reason, Routledge
Weil, A., 1978, “History of mathematics: why and how”, Proceedings of the International congress of mathematicians, Helsinki
Zalamea, F., 2012, Synthetic philosophy of contemporary mathematics, Urbanomic/Sequence Press
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Thanks to Vera John-Steiner and to Brendan Larvor, for suggestions for improving this article.
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Hersh, R. (2017). Pluralism as Modeling and as Confusion. In: Sriraman, B. (eds) Humanizing Mathematics and its Philosophy. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-61231-7_3
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