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.
Highlights
To understand an intellectual virtue is to understand how it may manifest in an epistemic situation
Virtue theorists of mathematics stand to benefit from appropriating accounts of the intellectual virtues provided by the virtue epistemologists
Virtue epistemology is enriched through analyses of the virtues in the context of real life practices
Summary
To understand an intellectual virtue is to understand how it may manifest in an epistemic situation. I investigate how well accounts of intellectual humility as a generic epistemic virtue trace specific instances of (failed) manifestations of the virtue in mathematical practices. In this paper I explore how apt the accounts of the virtue epistemologists of intellectual humility as a generic virtue (in the sense of Tanswell and Kidd) are at tracking (failed) manifestations of the virtue in mathematical practices by employing them in three case studies. I move to a discussion of intellectual humility in which I present three accounts of the virtue (Whitcomb et al 2017; Kidd 2016; Roberts and Wood 2007), which I will employ in my case studies . Virtue epistemology is enriched through analyses of the virtues in the context of real life practices
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