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Wronski's Foundations of Mathematics

Published online by Cambridge University Press:  30 August 2016

Roi Wagner
Roi Wagner*
Affiliation:
ETH Zürich E-mail: roi.wagner@mail.huji.ac.il
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Argument

This paper reconstructs Wronski's philosophical foundations of mathematics. It uses his critique of Lagrange's algebraic analysis as a vignette to introduce the problems that he raised, and argues that these problems have not been properly appreciated by his contemporaries and subsequent commentators. The paper goes on to reconstruct Wronski's mathematical law of creation and his notions of theory and techne, in order to put his objections to Lagrange in their philosophical context. Finally, Wronski's proof of his universal law (the expansion of a given function by any series of functions) is reviewed in terms of the above reconstruction. I argue that Wronski's philosophical approach poses an alternative to the views of his contemporary mainstream mathematicians, which brings up the contingency of their choices, and bridges the foundational concerns of early modernity with those of the twentieth-century foundations crisis. I also argue that Wronski's views may be useful to contemporary philosophy of mathematical practice, if they are read against their metaphysical grain.

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Type
Research Article
Information
Science in Context , Volume 29 , Issue 3 , September 2016 , pp. 241 - 271
Copyright
Copyright © Cambridge University Press 2016 

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