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.
Highlights
This paper offers a preliminary investigation of the sorts of epistemic virtues and epistemic vices that are especially pertinent to the case of mathematics and its practices
The upshot for character epistemology are new ways of thinking about the central normative question: what is the basis for assessing the normative status of epistemic character traits? Before we explore the contributions that reflection on mathematics can make to this question, we first need to sketch out some of the main features of contemporary virtue and vice epistemology, which we will do in Sect
This paper offered a preliminary effort to draw connections between philosophy of mathematics and character epistemology
Summary
This paper offers a preliminary investigation of the sorts of epistemic virtues and epistemic vices that are especially pertinent to the case of mathematics and its practices. Synthese that epistemic virtues and vices will typically be domain-sensitive in ways that encourage the idea that there are domain-specific virtue and vice epistemologies—including character epistemologies of mathematics. Subsequent work has moved towards virtuepluralism, admitting attitudes, sensibilities, and ways of thinking as other things that can be virtues Such ontological debates have, recently, been focused within vice epistemology. Mathematics is a very epistemically conservative discipline with respect to its established body of knowledge—you trust your inheritance and do not admit new things (for instance, when new, peculiar methods are proposed, or, crossing between subdisciplines in maths) Such conservatism is typically principled rather than reactionary, usually justified by confidence in rigorous processes of proof.
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