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Mathematical Explanations and Mathematical Applications

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Handbook of the Mathematics of the Arts and Sciences

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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.

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Authors and Affiliations

  1. University of Helsinki, Helsinki, Finland

    Markus Pantsar

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  1. Markus Pantsar
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Correspondence to Markus Pantsar .

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Editors and Affiliations

  1. Dept of Mathematical Sciences, The University of Montana Dept of Mathematical Sciences, Missoula, MT, USA

    Bharath Sriraman

Section Editor information

  1. Department of Mathematical Sciences, The University of Montana, Missoula, MT, USA

    Bharath Sriraman

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Pantsar, M. (2019). Mathematical Explanations and Mathematical Applications. In: Sriraman, B. (eds) Handbook of the Mathematics of the Arts and Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-70658-0_30-1

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  • DOI: https://doi.org/10.1007/978-3-319-70658-0_30-1

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  • Print ISBN: 978-3-319-70658-0

  • Online ISBN: 978-3-319-70658-0

  • eBook Packages: Springer Reference MathematicsReference Module Computer Science and Engineering

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