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  1.  99
    Epistemic injustice in mathematics.Colin Jakob Rittberg, Fenner Stanley Tanswell & Jean Paul Van Bendegem - 2020 - Synthese 197 (9):3875-3904.
    We investigate how epistemic injustice can manifest itself in mathematical practices. We do this as both a social epistemological and virtue-theoretic investigation of mathematical practices. We delineate the concept both positively—we show that a certain type of folk theorem can be a source of epistemic injustice in mathematics—and negatively by exploring cases where the obstacles to participation in a mathematical practice do not amount to epistemic injustice. Having explored what epistemic injustice in mathematics can amount to, we use the concept (...)
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  2. Conceptual Engineering for Mathematical Concepts.Fenner Stanley Tanswell - 2018 - Inquiry: An Interdisciplinary Journal of Philosophy 61 (8):881-913.
    ABSTRACTIn this paper I investigate how conceptual engineering applies to mathematical concepts in particular. I begin with a discussion of Waismann’s notion of open texture, and compare it to Shapiro’s modern usage of the term. Next I set out the position taken by Lakatos which sees mathematical concepts as dynamic and open to improvement and development, arguing that Waismann’s open texture applies to mathematical concepts too. With the perspective of mathematics as open-textured, I make the case that this allows us (...)
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  3. Group Knowledge and Mathematical Collaboration: A Philosophical Examination of the Classification of Finite Simple Groups.Joshua Habgood-Coote & Fenner Stanley Tanswell - forthcoming - Episteme.
    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 (...)
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  4. Virtue Theory of Mathematical Practices: An Introduction.Andrew Aberdein, Colin Jakob Rittberg & Fenner Stanley Tanswell - 2021 - Synthese 199 (3-4):10167-10180.
    Until recently, discussion of virtues in the philosophy of mathematics has been fleeting and fragmentary at best. But in the last few years this has begun to change. As virtue theory has grown ever more influential, not just in ethics where virtues may seem most at home, but particularly in epistemology and the philosophy of science, some philosophers have sought to push virtues out into unexpected areas, including mathematics and its philosophy. But there are some mathematicians already there, ready to (...)
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  5.  47
    Proof, Rigour and Informality : A Virtue Account of Mathematical Knowledge.Fenner Stanley Tanswell - 2016 - St Andrews Research Repository Philosophy Dissertations.
    This thesis is about the nature of proofs in mathematics as it is practiced, contrasting the informal proofs found in practice with formal proofs in formal systems. In the first chapter I present a new argument against the Formalist-Reductionist view that informal proofs are justified as rigorous and correct by corresponding to formal counterparts. The second chapter builds on this to reject arguments from Gödel's paradox and incompleteness theorems to the claim that mathematics is inherently inconsistent, basing my objections on (...)
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  6.  32
    Mathematical Practice and Epistemic Virtue and Vice.Fenner Stanley Tanswell & Ian James Kidd - 2020 - Synthese 199 (1-2):407-426.
    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 (...)
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  7.  20
    Saving Proof From Paradox: Gödel’s Paradox and the Inconsistency of Informal Mathematics.Fenner Stanley Tanswell - 2016 - In Peter Verdee & Holger Andreas (eds.), Logical Studies of Paraconsistent Reasoning in Science and Mathematics. Springer. pp. 159-173.
    In this paper I shall consider two related avenues of argument that have been used to make the case for the inconsistency of mathematics: firstly, Gödel’s paradox which leads to a contradiction within mathematics and, secondly, the incompatibility of completeness and consistency established by Gödel’s incompleteness theorems. By bringing in considerations from the philosophy of mathematical practice on informal proofs, I suggest that we should add to the two axes of completeness and consistency a third axis of formality and informality. (...)
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  8.  10
    A Concise History of Mathematics, but Not for Philosophers: John Stillwell: A Concise History of Mathematics for Philosophers. Cambridge: Cambridge University Press, 2019. 69pp, £15.Fenner Stanley Tanswell - 2020 - Metascience 29 (3):519-521.
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  9.  8
    Using Crowdsourced Mathematics to Understand Mathematical Practice.Alison Pease, Ursula Martin, Fenner Stanley Tanswell & Andrew Aberdein - 2020 - ZDM 52 (6):1087-1098.
    Records of online collaborative mathematical activity provide us with a novel, rich, searchable, accessible and sizeable source of data for empirical investigations into mathematical practice. In this paper we discuss how the resources of crowdsourced mathematics can be used to help formulate and answer questions about mathematical practice, and what their limitations might be. We describe quantitative approaches to studying crowdsourced mathematics, reviewing work from cognitive history (comparing individual and collaborative proofs); social psychology (on the prospects for a measure of (...)
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