Salverda, Josephine;
(2019)
Towards a philosophical account of explanation in mathematics.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
All proofs show that their conclusions are true; some also explain why they are true. But what makes a proof (or argument) explanatory, if it is? That is the central question of my thesis. I begin by identifying four accounts of scientific explanation which look like they might be useful for the intra-mathematical case, assessing the prospects for extending each account to the mathematical case. I examine whether we could get to a general result about mathematical explanation while drawing only on general assumptions about explanation. I argue that this methodology is flawed and that we need to pay serious attention to specific examples from mathematical practice, not just to general assumptions. I examine two existing accounts of intra-mathematical explanation: first, Steiner’s 1978 account. I propose a new and sympathetic reading that provides a better understanding of his account than can be found in the existing literature. Although Steiner’s account seems to focus on ontic aspects of explanation, I show how (my extension of) Steiner’s proposal can also account for what I take to be the primary epistemic function of an explanation, namely, to help us see why the fact to be explained is true. Second, I examine Lange’s 2017 account, which focuses on salient features. Of the features proposed by Lange, I suggest that symmetry is the best candidate for a feature of mathematical explanation, and I argue that we should see symmetry as an objective mathematical property that may have the propensity to appear salient to creatures like us in certain contexts. I argue that it is philosophically fruitful to play close attention to candidate examples of mathematical explanation, and in Chapter 5 I present an in-depth case study of a proof in Galois theory and propose a positive account of its explanatory value.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Towards a philosophical account of explanation in mathematics |
| Event: | UCL (University College London) |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2019. Original content in this thesis is licensed under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) Licence (https://creativecommons.org/licenses/by/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL SLASH UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities UCL > Provost and Vice Provost Offices > UCL SLASH > Faculty of Arts and Humanities > European and Intl Social and Political Studs |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10072645 |
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