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Mathematical Domains: Social Constructs?

In Bonnie Gold & Roger Simons (eds.), Proof and Other Dilemmas: Mathematics and Philosophy. Mathematics Association of America. pp. 109--128 (2008)

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  1. Creativity, Freedom, and Authority: A New Perspective On the Metaphysics of Mathematics.Julian C. Cole - 2009 - Australasian Journal of Philosophy 87 (4):589-608.
    I discuss a puzzle that shows there is a need to develop a new metaphysical interpretation of mathematical theories, because all well-known interpretations conflict with important aspects of mathematical activities. The new interpretation, I argue, must authenticate the ontological commitments of mathematical theories without curtailing mathematicians' freedom and authority to creatively introduce mathematical ontology during mathematical problem-solving. Further, I argue that these two constraints are best met by a metaphysical interpretation of mathematics that takes mathematical entities to be constitutively constructed (...)
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  • Social constructivism in mathematics? The promise and shortcomings of Julian Cole’s institutional account.Jenni Rytilä - 2021 - Synthese 199 (3-4):11517-11540.
    The core idea of social constructivism in mathematics is that mathematical entities are social constructs that exist in virtue of social practices, similar to more familiar social entities like institutions and money. Julian C. Cole has presented an institutional version of social constructivism about mathematics based on John Searle’s theory of the construction of the social reality. In this paper, I consider what merits social constructivism has and examine how well Cole’s institutional account meets the challenge of accounting for the (...)
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  • On What There is—Infinitesimals and the Nature of Numbers.Jens Erik Fenstad - 2015 - Inquiry: An Interdisciplinary Journal of Philosophy 58 (1):57-79.
    This essay will be divided into three parts. In the first part, we discuss the case of infintesimals seen as a bridge between the discrete and the continuous. This leads in the second part to a discussion of the nature of numbers. In the last part, we follow up with some observations on the obvious applicability of mathematics.
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  • Towards an Institutional Account of the Objectivity, Necessity, and Atemporality of Mathematics.Julian C. Cole - 2013 - Philosophia Mathematica 21 (1):9-36.
    I contend that mathematical domains are freestanding institutional entities that, at least typically, are introduced to serve representational functions. In this paper, I outline an account of institutional reality and a supporting metaontological perspective that clarify the content of this thesis. I also argue that a philosophy of mathematics that has this thesis as its central tenet can account for the objectivity, necessity, and atemporality of mathematics.
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