Synthese

, Volume 192, Issue 6, pp 1799–1820 | Cite as

Platitudes in mathematics

Article

Abstract

The term ‘continuous’ in real analysis wasn’t given an adequate formal definition until 1817. However, important theorems about continuity were proven long before that. How was this possible? In this paper, I introduce and refine a proposed answer to this question, derived from the work of Frank Jackson, David Lewis and other proponents of the ‘Canberra plan’. In brief, the proposal is that before 1817 the meaning of the term ‘continuous’ was determined by a number of ‘platitudes’ which had some special epistemic status.

Keywords

Analyticity Platitude Canberra plan Mathematics Quine Rayo Trivialism 

Notes

Acknowledgments

For helpful comments on this work, I would like to thank Agustín Rayo, Brian Weatherson, Jennifer Wang, Clay Cordova, Kate Manne, Andy Egan, Ernie Lepore, and two anonymous referees at Synthese. Most of all I would like to thank Zeynep Soysal and Antony Eagle, both of whom were amazingly generous with their time and provided tremendously helpful comments.

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Department of PhilosophyStanford UniversityStanfordUSA

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