Abstract
In this paper I explore how intellectual humility manifests in mathematical practices. To do this I employ accounts of this virtue as developed by virtue epistemologists in three case studies of mathematical activity. As a contribution to a Topical Collection on virtue theory of mathematical practices this paper explores in how far existing virtue-theoretic frameworks can be applied to a philosophical analysis of mathematical practices. I argue that the individual accounts of intellectual humility are successful at tracking some manifestations of this virtue in mathematical practices and fail to track others. There are two upshots to this. First, the accounts of the intellectual virtues provided by virtue epistemologists are insightful for the development of a virtue theory of mathematical practices but require adjustments in some cases. Second, the case studies reveal dimensions of intellectual humility virtue epistemologists have thus far overlooked in their theoretical reflections.
| Original language | English |
|---|---|
| Pages (from-to) | 5571-5601 |
| Number of pages | 31 |
| Journal | Synthese |
| Volume | 199 |
| Issue number | 3-4 |
| Early online date | 11 Feb 2021 |
| DOIs | |
| Publication status | Published - Dec 2021 |
Bibliographical note
Funding Information:I wish to thank Juliette Kennedy for inspiring my work on intellectual humility in mathematics, Jouko V??n?nen for lengthy personal discussions about his views on set theory, and Andrew Aberdein, Joachim Frans, Brendan Larvor, Andrew Morris, Pieter Present, Aleksandra Samonek, Alessandra Tanessini, Fenner Stanley Tanswell, Jean Paul Van Bendegem, Jip Van Besouw, and two anonymous reviewers for helpful comments and criticisms. Early drafts were presented at the SPSP2018, the Novembertagnug 2018, and at a research seminar of the Center for Logic and Philosophy of Science at the Vrije Universiteit Brussel , and I am grateful for the engaging discussions with the audiences. Research for this paper has been funded by the Research Foundation?Flanders (FWO), project G056716N, the Centre for Mathematical Cognition at Loughborough University, and the European Commission via the Marie Sk?odowska-Curie Individual Fellowship scheme (Grant Agreement ID: 883724).
Funding Information:
I wish to thank Juliette Kennedy for inspiring my work on intellectual humility in mathematics, Jouko Väänänen for lengthy personal discussions about his views on set theory, and Andrew Aberdein, Joachim Frans, Brendan Larvor, Andrew Morris, Pieter Present, Aleksandra Samonek, Alessandra Tanessini, Fenner Stanley Tanswell, Jean Paul Van Bendegem, Jip Van Besouw, and two anonymous reviewers for helpful comments and criticisms. Early drafts were presented at the SPSP2018, the Novembertagnug 2018, and at a research seminar of the Center for Logic and Philosophy of Science at the Vrije Universiteit Brussel, and I am grateful for the engaging discussions with the audiences. Research for this paper has been funded by the Research Foundation—Flanders (FWO), project G056716N, the Centre for Mathematical Cognition at Loughborough University, and the European Commission via the Marie Skłodowska-Curie Individual Fellowship scheme (Grant Agreement ID: 883724).
Publisher Copyright:
© 2021, The Author(s).
Funding
I wish to thank Juliette Kennedy for inspiring my work on intellectual humility in mathematics, Jouko V??n?nen for lengthy personal discussions about his views on set theory, and Andrew Aberdein, Joachim Frans, Brendan Larvor, Andrew Morris, Pieter Present, Aleksandra Samonek, Alessandra Tanessini, Fenner Stanley Tanswell, Jean Paul Van Bendegem, Jip Van Besouw, and two anonymous reviewers for helpful comments and criticisms. Early drafts were presented at the SPSP2018, the Novembertagnug 2018, and at a research seminar of the Center for Logic and Philosophy of Science at the Vrije Universiteit Brussel , and I am grateful for the engaging discussions with the audiences. Research for this paper has been funded by the Research Foundation?Flanders (FWO), project G056716N, the Centre for Mathematical Cognition at Loughborough University, and the European Commission via the Marie Sk?odowska-Curie Individual Fellowship scheme (Grant Agreement ID: 883724). I wish to thank Juliette Kennedy for inspiring my work on intellectual humility in mathematics, Jouko Väänänen for lengthy personal discussions about his views on set theory, and Andrew Aberdein, Joachim Frans, Brendan Larvor, Andrew Morris, Pieter Present, Aleksandra Samonek, Alessandra Tanessini, Fenner Stanley Tanswell, Jean Paul Van Bendegem, Jip Van Besouw, and two anonymous reviewers for helpful comments and criticisms. Early drafts were presented at the SPSP2018, the Novembertagnug 2018, and at a research seminar of the Center for Logic and Philosophy of Science at the Vrije Universiteit Brussel, and I am grateful for the engaging discussions with the audiences. Research for this paper has been funded by the Research Foundation—Flanders (FWO), project G056716N, the Centre for Mathematical Cognition at Loughborough University, and the European Commission via the Marie Skłodowska-Curie Individual Fellowship scheme (Grant Agreement ID: 883724).
| Funders | Funder number |
|---|---|
| H2020 Marie Skłodowska-Curie Actions | 883724 |
| European Commission | |
| Fonds Wetenschappelijk Onderzoek | G056716N |
| Centre for Mathematical Cognition, Loughborough University |
Keywords
- Abc-conjecture
- Erdős–Selberg dispute
- Humility
- Multiverse logic
- Philosophy of mathematical practices
- Virtue
- Virtue epistemology