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Wronski's Foundations of Mathematics
1ETH ZürichE-mail:roi.wagner@mail.huji.ac.il.
Science in Context
|August 31, 2016
Summary
This paper explores Wronski's philosophy of mathematics, highlighting his critique of algebraic analysis and his universal law. His work offers an alternative perspective, bridging early modern and twentieth-century mathematical foundations.
Area of Science:
- Philosophy of Mathematics
- History of Mathematics
Background:
- Wronski's critique of Lagrange's algebraic analysis introduced significant mathematical problems.
- These problems and Wronski's contributions have been historically undervalued by contemporaries and commentators.
Purpose of the Study:
- To reconstruct Wronski's philosophical foundations of mathematics.
- To contextualize Wronski's objections to Lagrange through his mathematical law of creation and notions of theory and techne.
- To analyze Wronski's proof of his universal law within this reconstructed philosophical framework.
Main Methods:
- Philosophical reconstruction of Wronski's ideas.
- Analysis of Wronski's critique of Lagrange's algebraic analysis.
- Review of Wronski's proof of his universal law.
Main Results:
- Wronski's philosophical approach offers an alternative to mainstream mathematical views of his time.
- His work highlights the contingency of mathematical choices made by his contemporaries.
- Wronski's ideas bridge foundational concerns from early modernity to the twentieth-century crisis.
Conclusions:
- Wronski's philosophy of mathematics provides a unique perspective on mathematical foundations.
- His work can inform contemporary philosophy of mathematical practice, particularly when metaphysical aspects are considered.
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