Conceptual Engineering for Mathematical Concepts 7 FINAL.pdf (335.14 kB)
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Conceptual engineering for mathematical concepts

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journal contribution
posted on 18.09.2018, 15:37 by Fenner Tanswell
In 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 to deploy the tools of conceptual engineering in mathematics. I will examine Cappelen’s recent argument that there are no conceptual safe spaces and consider whether mathematics constitutes a counterexample. I argue that it does not, drawing on Haslanger’s distinction between manifest and operative concepts, and applying this in a novel way to set-theoretic foundations. I then set out some of the questions that need to be engaged with to establish mathematics as involving a kind of conceptual engineering. I finish with a case study of how the tools of conceptual engineering will give us a way to progress in the debate between advocates of the Universe view and the Multiverse view in set theory.

History

School

  • Science

Department

  • Mathematics Education Centre

Published in

Inquiry (United Kingdom)

Volume

61

Issue

8

Pages

881-913

Citation

TANSWELL, F.S., 2017. Conceptual engineering for mathematical concepts. Inquiry, 61 (8), pp.881-913.

Publisher

© Taylor & Francis

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Acceptance date

22/08/2017

Publication date

2017-10-10

Notes

This is an Accepted Manuscript of an article published by Taylor & Francis in Inquiry on 10 Oct 2017, available online: https://doi.org/10.1080/0020174X.2017.1385526

ISSN

0020-174X

eISSN

1502-3923

Language

en