## Abstract

In this work we argue that there is no strong demarcation between pure and applied mathematics. We show this first by stressing non-deductive components within pure mathematics, like axiomatization and theory-building in general. We also stress the “purer” components of applied mathematics, like the theory of the models that are concerned with practical purposes. We further show that some mathematical theories can be viewed through either a pure or applied lens. These different lenses are tied to different communities, which endorse different evaluative standards for theories. We evaluate the distinction between pure and applied mathematics from a late Wittgensteinian perspective. We note that the classical exegesis of the later Wittgenstein’s philosophy of mathematics, due to Maddy, leads to a clear-cut but misguided demarcation. We then turn our attention to a more niche interpretation of Wittgenstein by Dawson, which captures aspects of the aforementioned distinction more accurately. Building on this newer, maverick interpretation of the later Wittgenstein’s philosophy of mathematics, and endorsing an extended notion of meaning as use which includes social, mundane uses, we elaborate a fuzzy, but more realistic, demarcation. This demarcation, relying on family resemblance, is based on how direct and intended technical applications are, the kind of evaluative standards featured, and the range of rhetorical purposes at stake.

Original language | English |
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Article number | 1 |

Pages (from-to) | 1-22 |

Number of pages | 22 |

Journal | European Journal for Philosophy of Science |

Volume | 12 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 2022 |

### Bibliographical note

Funding Information:The second author is thankful for the financial and ideal support of the Studienstiftung des deutschen Volkes and the Claussen-Simon-Stiftung. All authors are very thankful for the advice and helpful comments by A. Okupnik and C. Wetcholowsky. The views stated here are not necessarily the views of the supporting organizations and people mentioned in this acknowledgement.

Publisher Copyright:

© 2021, The Author(s).

Copyright:

Copyright 2021 Elsevier B.V., All rights reserved.

## Keywords

- Embodied mathematics
- Later Wittgenstein
- Meaning as use
- Meaning of mathematics
- Philosophy of applied mathematics
- Philosophy of mathematics
- Theory choice