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Intellectual humility in mathematics
TLDR
In this paper, the authors explore how intellectual humility manifests in mathematical practices, and employ accounts of this virtue as developed by virtue epistemologists in three case studies of mathematical activity.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.read more
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Realism in mathematics
TL;DR: Realism: Pre-theoretic realism Realism in philosophy Realism and truth realism in mathematics Perception and intuition: What is the question? Perception Intuition Godelian Platonism Numbers: What numbers could not be Numbers as properties Frege numbers Axioms: Reals and sets of reals Axiomization Open problems Competing theories The challenge Monism and beyond: Monism Field's nominalism Structuralism as mentioned in this paper
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The Man Who Loved Only Numbers
TL;DR: Ebrahimi and Erdős as discussed by the authors pointed out that the younger the child was, the deeper his connection with the child, and that the older the child the deeper the connection.
References
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Beyond Good and Evil: Prelude to a Philosophy of the Future
TL;DR: On the prejudices of philosophers the free spirit the religious nature maxims and interludes on the natural history of morals we scholars our virtues people and fatherlands what is noble? from high mountains - epode as discussed by the authors.
Book
Realism in Mathematics
TL;DR: Realism: Pre-theoretic realism Realism in philosophy Realism and truth realism in mathematics Perception and intuition: What is the question? Perception Intuition Godelian Platonism Numbers: What numbers could not be Numbers as properties Frege numbers Axioms: Reals and sets of reals Axiomization Open problems Competing theories The challenge Monism and beyond: Monism Field's nominalism Structuralism Summary References Index as mentioned in this paper
Book
Intellectual Virtues: An Essay in Regulative Epistemology
TL;DR: In this paper, the authors discuss the relationship between epistemology, faithfulness, and practical wisdom in the context of practical wisdom and love of knowledge, and propose a set of practices for practical wisdom.
BookDOI
The Routledge Handbook of Epistemic Injustice
TL;DR: In this article, the authors present a book that discusses the principal themes of epistemic injustice, highlights numerous connections to other academic literatures and contemporary debates, and opens the door to potential areas of further study that will make projects such as identifying and resisting immigration injustices in US policy much easier.
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Intellectual Humility: Owning Our Limitations
TL;DR: The usual manner of presenting philosophical work puzzles me as discussed by the authors... it is written as though their authors believe them to be the absolutely final word on their subject, but it is not, surely, that each philosopher thinks that he finally, thank God, has found the truth and built an impregnable fortress around it.