Hankel's principle as an anti-Kantian program
1Institute Vienna Circle, University of Vienna, Vienna, Austria.
Archive for History of Exact Sciences
|July 26, 2026
Summary
Hankel
Area of Science:
- History of Mathematics
- Philosophy of Mathematics
Background:
- Hermann Hankel's principle of the permanence of formal laws (PFL) guided number system extensions.
- Hankel recognized limitations of PFL, particularly with hypercomplex and irrational numbers.
Purpose of the Study:
- To analyze Hankel's persistent commitment to PFL despite its limitations.
- To explore the philosophical underpinnings of mathematical conservatism.
Main Methods:
- Historical analysis of Hankel's work and its influences (Peacock, Hamilton).
- Examination of critiques by Schubert and Pringsheim.
- Philosophical interpretation of mathematical conservatism.
Main Results:
- Hankel's commitment to PFL stemmed from a conservative strategy allowing law revision under specific conditions.
- Schubert and Pringsheim adopted an anti-revisionary stance, limiting mathematical scope.
- Distinct philosophical differences exist between revisionary and anti-revisionary mathematical conservatism.
Conclusions:
- Hankel's PFL represents a flexible conservatism in mathematics.
- Contrasting conservative approaches highlight fundamental philosophical divergences in mathematical development.
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