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Mathematics as an Empirical Phenomenon, Subject to Modeling

  • Reuben HershEmail author
Chapter
Part of the Studies in Applied Philosophy, Epistemology and Rational Ethics book series (SAPERE, volume 25)

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.

Keywords

Nonstandard Analysis Mathematical Entity Empirical Phenomenon Model Heat Conduction Mathematical Behavior 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

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.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Santa FeUSA

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