Abstract
Platonism is the view according to which there are abstract entities (such as sets, functions, and numbers), and mathematical theories truly describe such objects and the relations among them.2 Given the nature of mathematical entities—especially the fact that they are not located in space and time, and are causally inert—the postulation of such objects doesn’t come lightly. Platonists are, of course, well aware of this fact It’s important, then, to highlight the benefits that immediately emerge from positing mathematical objects.
In this chapter, I highlight five desiderata that an account of mathematics should meet to make sense of mathematical practice. After briefly indicating that current versions of platonism and nominalism fail to satisfy all of the desiderata, I sketch two versions of mathematical fictionalism that meet them. One version is based on an empiricist view of science, and has the additional benefit of providing a unified account of both mathematics and science. The other version of fictionalism is based on the metaphysics of fiction and articulates what can be considered a truly fictionalist account of mathematics. I indicate that both versions of fictionalism satisfy all of the desiderata, and I take it that they are best developed if adopted together. As a result, mathematical fictionalism is alive and well.
I’d like to thank my colleagues in the Philosophy Department at the University of Miami, the participants of the New Waves in Philosophy of Mathematics Conference, and Jody Azzouni for their extremely helpful responses to earlier versions of this work.
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© 2009 Otávio Bueno
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Bueno, O. (2009). Mathematical Fictionalism. In: Bueno, O., Linnebo, Ø. (eds) New Waves in Philosophy of Mathematics. New Waves in Philosophy. Palgrave Macmillan, London. https://doi.org/10.1057/9780230245198_4
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DOI: https://doi.org/10.1057/9780230245198_4
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