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. (shrink)

In this paper we apply social epistemology to mathematical proofs and their role in mathematical knowledge. The most famous modern collaborative mathematical proof effort is the Classification of Finite Simple Groups. The history and sociology of this proof have been well-documented by Alma Steingart (2012), who highlights a number of surprising and unusual features of this collaborative endeavour that set it apart from smaller-scale pieces of mathematics. These features raise a number of interesting philosophical issues, but have received very little (...) attention. In this paper, we will consider the philosophical tensions that Steingart uncovers, and use them to argue that the best account of the epistemic status of the Classification Theorem will be essentially and ineliminably social. This forms part of the broader argument that in order to understand mathematical proofs, we must appreciate their social aspects. (shrink)

The domain of modal epistemology tackles questions regarding the sources of our knowledge of modalities (i.e., possibility and necessity), and what justifies our beliefs about modalities. Virtue epistemology, on the other hand, aims at explaining epistemological concepts like knowledge and justification in terms of properties of the epistemic subject, i.e., cognitive capacities and character traits. While there is extensive literature on both domains, almost all attempts to analyze modal knowledge elude the importance of the agent’s intellectual character traits in justifying (...) beliefs about what is possible or necessary. My aim in this paper is to argue that intellectual traits of character, like thoroughness, autonomy, epistemic courage and open-mindedness, are relevant to modal epistemology. (shrink)