Mathematical Explanations and Mathematical Applications

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Sammanfattning

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.
Originalspråkengelska
Titel på gästpublikationHandbook of The Mathematics of The Arts and Sciences
RedaktörerBharath Sriraman
Antal sidor16
FörlagSpringer
Utgivningsdatum23 dec 2018
Sidor1-16
ISBN (tryckt)978-3-319-57071-6
ISBN (elektroniskt)978-3-319-57072-3
StatusPublicerad - 23 dec 2018
MoE-publikationstypA3 Del av bok eller annan forskningsbok

Vetenskapsgrenar

  • 111 Matematik

Citera det här

Pantsar, M. (2018). Mathematical Explanations and Mathematical Applications. I B. Sriraman (Red.), Handbook of The Mathematics of The Arts and Sciences (s. 1-16). Springer.
Pantsar, Markus. / Mathematical Explanations and Mathematical Applications. Handbook of The Mathematics of The Arts and Sciences. redaktör / Bharath Sriraman. Springer, 2018. s. 1-16
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Pantsar, M 2018, Mathematical Explanations and Mathematical Applications. i B Sriraman (red.), Handbook of The Mathematics of The Arts and Sciences. Springer, s. 1-16.

Mathematical Explanations and Mathematical Applications. / Pantsar, Markus.

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

Forskningsoutput: Kapitel i bok/rapport/konferenshandlingKapitelVetenskapligPeer review

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Pantsar M. Mathematical Explanations and Mathematical Applications. I Sriraman B, redaktör, Handbook of The Mathematics of The Arts and Sciences. Springer. 2018. s. 1-16