Abstract
Among the universal attributes of homo sapiens, several have become established as special fields of study—language, art and music, religion, political economy. But mathematics, another universal attribute of our species, is still modeled separately by logicians, historians, neuroscientists, and others. Could it be integrated into “mathematics studies,” a coherent, many-faceted branch of empirical science? Could philosophers facilitate such a unification? Some philosophers of mathematics identify themselves with “positions” on the nature of mathematics. Those “positions” could more productively serve as models of mathematics.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Balaguer, M.: Platonism and Anti-Platonism in Mathematics. Oxford University Press, Oxford (2001)
Balaguer, M.: A guide for the perplexed: what mathematicians need to know to understand philosophers of mathematics. http://sigmaa.maa.org/pom/PomSigmaa/Balaguer1-13.pdf (2013)
Burgess, J.P., Rosen, G.: A Subject With No Object. Oxford University Press, Oxford (1997)
Byers, W.: How Mathematicians Think. Princeton University Press, Princeton (2010)
Cellucci, C.: Introduction to Filosofia e matematica. In: Hersh, R. (ed.) 18 Unconventional Essays on the Nature of Mathematics, pp. 17–36. Springer, New York (2006)
Connes, A., Changeux, J.-P.: Conversations on mind, matter and mathematics, Princeton University Press, Princeton (1995)
Dehaene, S.: The Number Sense. Oxford University Press, Oxford (1997)
Ernest, P.: Social Constructivism in the Philosophy of Mathematics. SUNY Press, New York (1997)
Feferman, S.: In the Light of Logic. Oxford University Press, Oxford (1998)
Grosholz, E.: Representation and Productive Ambiguity in Mathematics and the Sciences. Oxford University Press, Oxford (2007)
Hersh, R.: On mathematical method and mathematical proof, with an example from elementary algebra. Eureka, December 2013
Hersh, R.: Why the Faulhaber polynomials are sums of even or odd powers of (n + 1/2). College Math. J. 43(4), 322–324 (2012)
Hersh, R.: Experiencing Mathematics. American Mathematical Society, Rhode Island (2014)
Kitcher, P.: The Nature of Mathematical Knowledge. Oxford University Press, Oxford (1983)
Lakatos, I.: Proofs and Refutations. Cambridge University Press, Cambridge (1976)
Lakoff, G., Nunez, R.: Where mathematics comes from: How the embodied mind brings mathematics into being. Basic Books, New York (2000)
Ruelle, D.: The Mathematician’s Brain. Princeton University Press, Princeton (2007)
Shapiro, S.: The Oxford Handbook of Philosophy of Mathematics and Logic. Oxford University Press, Oxford (2005)
Thomas, R.: The comparison of mathematics with narrative. In: van Kerkhove, B., van Bendegem, J.P. (eds.) Perspectives on Mathematical Practices, pp. 43–60. Springer, Dordrecht (2007)
Thomas, R.: 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 (2014)
Thurston, W.: On proof and progress in mathematics. In: Hersh, R. (ed.) 18 Unconventional Essays on the Nature of Mathematics, pp. 37–55. Springer, New York (2006)
Tiles, M.: Mathematics and the Image of Reason. Routledge, London (1991)
Weil, A.: History of mathematics: why and how. In: Proceedings of the International Congress of Mathematicians, Helsinki (1978)
Zalamea, F.: Synthetic Philosophy of Contemporary Mathematics. Urbanomic/Sequence Press, New York (2012)
Acknowledgments
I value the contributions to the understanding of mathematics made by Carlo Cellucci (2006), Emily Grosholz (2007), George Lakoff and Rafael Nunez (2000), David Ruelle (2007), Paul Livingston, Philip Kitcher (1983), Paul Ernest (1997), Mark Steiner, William Byers (2010), Mary Tiles (1991), Fernando Zalamea (2012) and Penelope Maddy. I thank Vera John-Steiner, Stephen Pollard, Carlo Cellucci and Robert Thomas (2007, 2014) for their suggestions for improving this article.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Hersh, R. (2016). Mathematics as an Empirical Phenomenon, Subject to Modeling. In: Ippoliti, E., Sterpetti, F., Nickles, T. (eds) Models and Inferences in Science. Studies in Applied Philosophy, Epistemology and Rational Ethics, vol 25. Springer, Cham. https://doi.org/10.1007/978-3-319-28163-6_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-28163-6_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-28162-9
Online ISBN: 978-3-319-28163-6
eBook Packages: Religion and PhilosophyPhilosophy and Religion (R0)