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Journal for General Philosophy of Science

, Volume 49, Issue 3, pp 393–412 | Cite as

Importance and Explanatory Relevance: The Case of Mathematical Explanations

  • Gabriel Târziu
Article
  • 67 Downloads

Abstract

A way to argue that something (e.g. mathematics, idealizations, moral properties, etc.) plays an explanatory role in science is by linking explanatory relevance with importance in the context of an explanation. The idea is deceptively simple: a part of an explanation is an explanatorily relevant part of that explanation if removing it affects the explanation either by destroying it or by diminishing its explanatory power, i.e. an important part (one that if removed affects the explanation) is an explanatorily relevant part. This can be very useful in many ontological debates. My aim in this paper is twofold. First of all, I will try to assess how this view on explanatory relevance can affect the recent ontological debate in the philosophy of mathematics—as I will argue, contrary to how it may appear at first glance, it does not help very much the mathematical realists. Second of all, I will show that there are big problems with it.

Keywords

Mathematical explanations Explanatory relevance Explanatory power Baker’s enhanced indispensability argument 

Notes

Acknowledgements

This paper was written while I held a Visiting Fellowship offered by The European Philosophy of Science Association (EPSA) at the Centre for Logic and Philosophy of Science at Ghent University. I wish to express my gratitude to EPSA and to the Centre for the opportunity to develop my research, as well as for hospitality and support during my visit. I owe very special thanks to Professor Erik Weber for many helpful discussions and for providing invaluable comments on earlier drafts of this paper.

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Centre for Logic and Philosophy of ScienceGhent University (UGent)GhentBelgium
  2. 2.Institute for Research in the HumanitiesUniversity of BucharestBucharestRomania

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