6 found
Fenner Stanley Tanswell [5]Fenner Tanswell [1]
  1.  50
    A Problem with the Dependence of Informal Proofs on Formal Proofs.Fenner Tanswell - 2015 - Philosophia Mathematica 23 (3):295-310.
    Derivationists, those wishing to explain the correctness and rigour of informal proofs in terms of associated formal proofs, are generally held to be supported by the success of the project of translating informal proofs into computer-checkable formal counterparts. I argue, however, that this project is a false friend for the derivationists because there are too many different associated formal proofs for each informal proof, leading to a serious worry of overgeneration. I press this worry primarily against Azzouni's derivation-indicator account, but (...)
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  2.  84
    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.  35
    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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  4.  12
    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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  5.  41
    Epistemic Injustice in Mathematics.Colin Jakob Rittberg, Fenner Stanley Tanswell & Jean Paul Van Bendegem - forthcoming - Synthese:1-30.
    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, (...)
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  6. Mathematical Practice and Epistemic Virtues and Vices.Fenner Stanley Tanswell & Ian James Kidd - forthcoming - Synthese.
    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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