Abstract
In the mid-eighteenth century, it was usually taken for granted that all curves described by a single mathematical function were continuous, which meant that they had a shape without bends and a well-defined derivative. In this paper I discuss arguments for this claim made by two authors, Emilie du Châtelet and Roger Boscovich. I show that according to them, the claim follows from the law of continuity, which also applies to natural processes, so that natural processes and mathematical functions have a shared characteristic of being continuous. However, there were certain problems with their argument, and they had to deal with a counterexample, namely a mathematical function that seemed to describe a discontinuous curve.
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Notes
- 1.
This fragment was later copied in the entry on the law of continuity in the Encyclopédie of Diderot and D’Alembert, without mention of the source (in Van Strien 2014, I have discussed this fragment without attributing it to Du Châtelet).
References
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Acknowledgements
Many thanks to Katherine Brading, Tal Glezer, Luca Guzzardi, Boris Kožnjak and others for helpful comments and discussion.
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van Strien, M. (2017). Continuity in Nature and in Mathematics: Du Châtelet and Boscovich. In: Massimi, M., Romeijn, JW., Schurz, G. (eds) EPSA15 Selected Papers. European Studies in Philosophy of Science, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-319-53730-6_7
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