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CAVAILLÈS, MATHEMATICAL PROBLEMS AND QUESTIONS

CAVAILLÈS, MATHEMATICAL PROBLEMS AND QUESTIONS AbstractThis paper concerns the role of mathematical problems in the epistemology of Jean Cavaillès. Most occurrences of the term “problem” in his texts refer to mathematical problems, in the sense in which mathematicians themselves use the term: for an unsolved question which they hope to solve. Mathematical problems appear as breaking points in the succession of mathematical theories, both giving a continuity to the history of mathematics and illuminating the way in which the history of mathematics breaks up into successive theories with different kinds of operations and, in a sense, different kinds of a prioris. We briefly compare mathematical becoming to the succession of episteme in Foucault’s Les Mots et les choses. We then come back to the necessity that Cavaillès attributes to mathematical becoming, and which the position of mathematical problems illustrates, in order to discuss its various consequences in Cavaillès’ later works but also in Canguilhem’s discussion of Cavaillès’ role in the Resistance. Finally, we study other types of problems, in Cavaillès’ writings: philosophical problems and what we will call “questions” rather than “problems,” and which contrary to mathematical problems, as Cavaillès uses the term, cannot be solved but pervade the whole of the history of mathematics. We will put these “questions” in relation to Lautman’s Ideas. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Angelaki: Journal of Theoretical Humanities Taylor & Francis

CAVAILLÈS, MATHEMATICAL PROBLEMS AND QUESTIONS

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CAVAILLÈS, MATHEMATICAL PROBLEMS AND QUESTIONS

Abstract

AbstractThis paper concerns the role of mathematical problems in the epistemology of Jean Cavaillès. Most occurrences of the term “problem” in his texts refer to mathematical problems, in the sense in which mathematicians themselves use the term: for an unsolved question which they hope to solve. Mathematical problems appear as breaking points in the succession of mathematical theories, both giving a continuity to the history of mathematics and illuminating the way in which...
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Publisher
Taylor & Francis
Copyright
© 2018 Informa UK Limited, trading as Taylor & Francis Group
ISSN
1469-2899
eISSN
0969-725X
DOI
10.1080/0969725X.2018.1451463
Publisher site
See Article on Publisher Site

Abstract

AbstractThis paper concerns the role of mathematical problems in the epistemology of Jean Cavaillès. Most occurrences of the term “problem” in his texts refer to mathematical problems, in the sense in which mathematicians themselves use the term: for an unsolved question which they hope to solve. Mathematical problems appear as breaking points in the succession of mathematical theories, both giving a continuity to the history of mathematics and illuminating the way in which the history of mathematics breaks up into successive theories with different kinds of operations and, in a sense, different kinds of a prioris. We briefly compare mathematical becoming to the succession of episteme in Foucault’s Les Mots et les choses. We then come back to the necessity that Cavaillès attributes to mathematical becoming, and which the position of mathematical problems illustrates, in order to discuss its various consequences in Cavaillès’ later works but also in Canguilhem’s discussion of Cavaillès’ role in the Resistance. Finally, we study other types of problems, in Cavaillès’ writings: philosophical problems and what we will call “questions” rather than “problems,” and which contrary to mathematical problems, as Cavaillès uses the term, cannot be solved but pervade the whole of the history of mathematics. We will put these “questions” in relation to Lautman’s Ideas.

Journal

Angelaki: Journal of Theoretical Humanities – Taylor & Francis

Published: Mar 4, 2018

Keywords: Cavaillès; Foucault; mathematics; problems; a priori; history; becoming

References

  • Inauguration de l’amphithéâtre Jean Cavaillès
  • Introduction
  • What is Cantor’s Continuum Problem?
  • Cavaillès and the Historical a priori in Foucault