Mathematical Explanations and Mathematical Applications

Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-review

Abstract

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.
Original languageEnglish
Title of host publicationHandbook of The Mathematics of The Arts and Sciences
EditorsBharath Sriraman
Number of pages16
PublisherSpringer
Publication date23 Dec 2018
Pages1-16
ISBN (Print)978-3-319-57071-6
ISBN (Electronic)978-3-319-57072-3
Publication statusPublished - 23 Dec 2018
MoE publication typeA3 Book chapter

Fields of Science

  • 111 Mathematics

Cite this

Pantsar, M. (2018). Mathematical Explanations and Mathematical Applications. In B. Sriraman (Ed.), Handbook of The Mathematics of The Arts and Sciences (pp. 1-16). Springer.
Pantsar, Markus. / Mathematical Explanations and Mathematical Applications. Handbook of The Mathematics of The Arts and Sciences. editor / Bharath Sriraman. Springer, 2018. pp. 1-16
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Pantsar, M 2018, Mathematical Explanations and Mathematical Applications. in B Sriraman (ed.), Handbook of The Mathematics of The Arts and Sciences. Springer, pp. 1-16.

Mathematical Explanations and Mathematical Applications. / Pantsar, Markus.

Handbook of The Mathematics of The Arts and Sciences. ed. / Bharath Sriraman. Springer, 2018. p. 1-16.

Research output: Chapter in Book/Report/Conference proceedingChapterScientificpeer-review

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Pantsar M. Mathematical Explanations and Mathematical Applications. In Sriraman B, editor, Handbook of The Mathematics of The Arts and Sciences. Springer. 2018. p. 1-16