Conceptual engineering for mathematical concepts


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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 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.
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DOI 10.1080/0020174x.2017.1385526
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References found in this work BETA

The Set-Theoretic Multiverse.Joel David Hamkins - 2012 - Review of Symbolic Logic 5 (3):416-449.
What Good Are Our Intuitions: Philosophical Analysis and Social Kinds.Sally Haslanger - 2000 - Aristotelian Society Supplementary Volume 80 (1):89-118.
Proofs and Refutations.Imre Lakatos - 1980 - Noûs 14 (3):474-478.

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Citations of this work BETA

How To Conceptually Engineer Conceptual Engineering?Manuel Gustavo Isaac - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy:1–24.

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