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Mathematical Explanations and Mathematical Applications

In: Handbook of the Mathematics of the Arts and Sciences

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  • Markus Pantsar

    (University of Helsinki)

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 is. 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.

Suggested Citation

  • Markus Pantsar, 2021. "Mathematical Explanations and Mathematical Applications," Springer Books, in: Bharath Sriraman (ed.), Handbook of the Mathematics of the Arts and Sciences, chapter 98, pages 2587-2602, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-57072-3_30
    DOI: 10.1007/978-3-319-57072-3_30
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