# Philosophy of Mathematics

Summary |
The philosophy of mathematics studies the nature of mathematical truth, mathematical proof, mathematical evidence, mathematical practice, and mathematical explanation. Three philosophical
views of mathematics are widely regarded as the ‘classic’ ones. In recent
decades, some new views have entered the fray. An important newer arrival is |

Key works |
On the more traditional views, it is hard to beat the selection of readings in Benacerraf & Putnam 1964. Non-eliminative structuralism is defended in Resnik 1997, Shapiro 1997, and Parsons 2007. A modal version of eliminative structuralism derives from Putnam 1967 and is developed in Hellman 1989. Two classic defenses of logicism are Frege 1884/1950 and Russell 1919. A neo-Fregean programme was initiated in Wright 1983; see the essays collected in Hale & Wright 2001 and, for critical discussion, Dummett 1991. Nominalism is often driven by the epistemic challenge due to Benacerraf 1973 and Field 1989, ch. 1 and 7. Field’s classic attempt to vindicate nominalism is Field 1980. For a comprehensive overview of the subject, see Burgess & Rosen 1997. On fictionalism, see Yablo 2010. The indispensability argument derives from Quine but crystallized in Putnam 1971; for a recent defense, see Colyvan 2001. On mathematical naturalism, see Maddy 1997 and Maddy 2007. |

Introductions |
Introductory book: Shapiro 2000. Anthologies: Benacerraf & Putnam 1964, Hart 1996, Bueno & Linnebo 2009, and Marcus & McEvoy 2016 (with lots of historical material). Handbook: Shapiro 2005. |