Mathematical practice and epistemic virtue and vice

Fenner Stanley Tanswell, Ian James Kidd

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

What sorts of epistemic virtues are required for effective mathematical practice? Should these be virtues of individual or collective agents? What sorts of corresponding epistemic vices might interfere with mathematical practice? How do these virtues and vices of mathematics relate to the virtue-theoretic terminology used by philosophers? We engage in these foundational questions, and explore how the richness of mathematical practices is enhanced by thinking in terms of virtues and vices, and how the philosophical picture is challenged by the complexity of the case of mathematics. For example, within different social and interpersonal conditions, a trait often classified as a vice might be epistemically productive and vice versa. We illustrate that this occurs in mathematics by discussing Gerovitch’s historical study of the aggressive adversarialism of the Gelfand seminar in post-war Moscow. From this we conclude that virtue epistemologies of mathematics should avoid pre-emptive judgments about the sorts of epistemic character traits that ought to be promoted and criticised.

Original languageEnglish
Pages (from-to)407-426
Number of pages20
JournalSynthese
Volume199
Issue number1-2
DOIs
Publication statusPublished - Dec 2021

Keywords

  • Virtue epistemology
  • Mathematical practice
  • Vice epistemology
  • Character epistemology
  • Productive vice
  • Gelfand seminar
  • Mathematical virtue

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