### Abstract

Following Quine, many philosophers have also contended that if there are indispensable mathematical applications in the natural sciences, then the mathematical objects posited in those applications have an independent existence like the scientific objects. Thus the question of mathematical explanations and applications has an important relevance for the ontology of mathematics.

Original language | English |
---|---|

Title of host publication | Handbook of The Mathematics of The Arts and Sciences |

Editors | Bharath Sriraman |

Number of pages | 16 |

Publisher | Springer |

Publication date | 23 Dec 2018 |

Pages | 1-16 |

ISBN (Print) | 978-3-319-57071-6 |

ISBN (Electronic) | 978-3-319-57072-3 |

Publication status | Published - 23 Dec 2018 |

MoE publication type | A3 Book chapter |

### Fields of Science

- 111 Mathematics

### Cite this

*Handbook of The Mathematics of The Arts and Sciences*(pp. 1-16). Springer.

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*Handbook of The Mathematics of The Arts and Sciences.*Springer, pp. 1-16.

**Mathematical Explanations and Mathematical Applications.** / Pantsar, Markus.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Scientific › peer-review

TY - CHAP

T1 - Mathematical Explanations and Mathematical Applications

AU - Pantsar, Markus

PY - 2018/12/23

Y1 - 2018/12/23

N2 - One of the key questions in the philosophy of mathematics is the role and status of mathematical applications in the natural sciences. The importance of mathematics for science is indisputable, but philosophers have disagreed on what the relation between mathematical theories and scientific theories are. This chapter presents these topics through a distinction between mathematical applications and mathematical explanations. Particularly important is the question whether mathematical applications are ever indispensable. If so, it has often been argued, such applications should count as proper mathematical explanations. Following Quine, many philosophers have also contended that if there are indispensable mathematical applications in the natural sciences, then the mathematical objects posited in those applications have an independent existence like the scientific objects. Thus the question of mathematical explanations and applications has an important relevance for the ontology of mathematics.

AB - One of the key questions in the philosophy of mathematics is the role and status of mathematical applications in the natural sciences. The importance of mathematics for science is indisputable, but philosophers have disagreed on what the relation between mathematical theories and scientific theories are. This chapter presents these topics through a distinction between mathematical applications and mathematical explanations. Particularly important is the question whether mathematical applications are ever indispensable. If so, it has often been argued, such applications should count as proper mathematical explanations. Following Quine, many philosophers have also contended that if there are indispensable mathematical applications in the natural sciences, then the mathematical objects posited in those applications have an independent existence like the scientific objects. Thus the question of mathematical explanations and applications has an important relevance for the ontology of mathematics.

KW - 111 Mathematics

M3 - Chapter

SN - 978-3-319-57071-6

SP - 1

EP - 16

BT - Handbook of The Mathematics of The Arts and Sciences

A2 - Sriraman, Bharath

PB - Springer

ER -