## Abstract

In this paper, I argue that there are cases of explanatory induction in mathematics. To do so, I first introduce the notion of *explanatory definition* in the context of mathematical explanation. A large part of the paper is dedicated to introducing and analyzing this notion of explanatory definition and the role it plays in mathematics. After doing so, I discuss a particular inductive definition in advanced mathematics—\({ CW}\)-complexes—and argue that it is explanatory. With this, we see that there are cases of explanatory induction.

## Keywords

Philosophy of mathematics Explanation Mathematical induction Mathematical definition Mathematical practice## Notes

### Acknowledgements

I would like to thank both Curtis Franks and Tim Bays for their feedback on various drafts of this paper, and also the anonymous reviewers who provided numerous helpful comments on an earlier draft of this paper.

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