# Mathematics as Make-Believe: A Constructive Empiricist Account

Dissertation, University of Alberta (Canada) (1999)

**Abstract**

Any philosophy of science ought to have something to say about the nature of mathematics, especially an account like constructive empiricism in which mathematical concepts like model and isomorphism play a central role. This thesis is a contribution to the larger project of formulating a constructive empiricist account of mathematics. The philosophy of mathematics developed is fictionalist, with an anti-realist metaphysics. In the thesis, van Fraassen's constructive empiricism is defended and various accounts of mathematics are considered and rejected. Constructive empiricism cannot be realist about abstract objects; it must reject even the realism advocated by otherwise ontologically restrained and epistemologically empiricist indispensability theorists. Indispensability arguments rely on the kind of inference to the best explanation the rejection of which is definitive of constructive empiricism. On the other hand, formalist and logicist anti-realist positions are also shown to be untenable. It is argued that a constructive empiricist philosophy of mathematics must be fictionalist. Borrowing and developing elements from both Philip Kitcher's constructive naturalism and Kendall Walton's theory of fiction, the account of mathematics advanced treats mathematics as a collection of stories told about an ideal agent and mathematical objects as fictions. The account explains what true portions of mathematics are about and why mathematics is useful, even while it is a story about an ideal agent operating in an ideal world; it connects theory and practice in mathematics with human experience of the phenomenal world. At the same time, the make-believe and game-playing aspects of the theory show how we can make sense of mathematics as fiction, as stories, without either undermining that explanation or being forced to accept abstract mathematical objects into our ontology. All of this occurs within the framework that constructive empiricism itself provides the epistemological limitations it mandates, the semantic view of theories, and an emphasis on the pragmatic dimension of our theories, our explanations, and of our relation to the language we use

**Categories**

**PhilPapers/Archive ID**

HOFMAM

**Revision history**

Archival date: 2015-04-22

View upload history

View upload history

References found in this work BETA

No references found.

Citations of this work BETA

Mathematics and Fiction II: Analogy.Thomas, Robert

**Added to PP index**

2014-04-08

**Total views**

121 ( #22,789 of 41,616 )

**Recent downloads (6 months)**

20 ( #26,048 of 41,616 )

How can I increase my downloads?

**Downloads since first upload**

*This graph includes both downloads from PhilArchive and clicks to external links.*