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LAUTMAN ON PROBLEMS AS THE CONDITIONS OF EXISTENCE OF SOLUTIONS

LAUTMAN ON PROBLEMS AS THE CONDITIONS OF EXISTENCE OF SOLUTIONS AbstractAlbert Lautman (1908–44) was a philosopher of mathematics whose views on mathematical reality and on the philosophy of mathematics parted with the dominant tendencies of mathematical epistemology of the time. Lautman considered the role of philosophy, and of the philosopher, in relation to mathematics to be quite specific. He writes that “in the development of mathematics, a reality is asserted that mathematical philosophy has as a function to recognize and describe” (Mathematics, Ideas and the Physical Real (London: Bloomsbury, 2011) 87). He goes on to characterise this reality as an “ideal reality” that “governs” the development of mathematics. The relation between mathematical problems as they arise in the historical development of mathematics and the solutions that are provided to these problems by mathematicians, in the form of new mathematical theories, definitions or axioms, are governed by what Lautman characterises as a dialectics of mathematics. The aim of this paper is to give an account of this Lautmanian dialectic and of how it can be understood to govern the development of solutions to mathematical problems. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Angelaki: Journal of Theoretical Humanities Taylor & Francis

LAUTMAN ON PROBLEMS AS THE CONDITIONS OF EXISTENCE OF SOLUTIONS

Duffy, Simon B.
Angelaki: Journal of Theoretical Humanities , Volume 23 (2): 15 – Mar 4, 2018
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LAUTMAN ON PROBLEMS AS THE CONDITIONS OF EXISTENCE OF SOLUTIONS

Abstract

AbstractAlbert Lautman (1908–44) was a philosopher of mathematics whose views on mathematical reality and on the philosophy of mathematics parted with the dominant tendencies of mathematical epistemology of the time. Lautman considered the role of philosophy, and of the philosopher, in relation to mathematics to be quite specific. He writes that “in the development of mathematics, a reality is asserted that mathematical philosophy has as a function to recognize and describe”...
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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.2018.1451469
Publisher site
See Article on Publisher Site

Abstract

AbstractAlbert Lautman (1908–44) was a philosopher of mathematics whose views on mathematical reality and on the philosophy of mathematics parted with the dominant tendencies of mathematical epistemology of the time. Lautman considered the role of philosophy, and of the philosopher, in relation to mathematics to be quite specific. He writes that “in the development of mathematics, a reality is asserted that mathematical philosophy has as a function to recognize and describe” (Mathematics, Ideas and the Physical Real (London: Bloomsbury, 2011) 87). He goes on to characterise this reality as an “ideal reality” that “governs” the development of mathematics. The relation between mathematical problems as they arise in the historical development of mathematics and the solutions that are provided to these problems by mathematicians, in the form of new mathematical theories, definitions or axioms, are governed by what Lautman characterises as a dialectics of mathematics. The aim of this paper is to give an account of this Lautmanian dialectic and of how it can be understood to govern the development of solutions to mathematical problems.

Journal

Angelaki: Journal of Theoretical Humanities – Taylor & Francis

Published: Mar 4, 2018

Keywords: mathematical real; dialectic; structure; problem; genesis

References

  • Continental Genealogies: Mathematical Confrontations in Albert Lautman and Gaston Bachelard
  • L’Objectivité mathématique selon Albert Lautman: entre Idées dialectiques et réalité physique
  • Review of: Essai sur L’Unite des Sciences Mathematiques dans Leur Developpement Actuel. Albert Lautman
  • La Pensée mathématique
  • Albert Lautman et le souci logique
  • Preface
  • The Crisis in the Foundations of Mathematics
  • Cavaillès et Lautman: deux pionniers
  • The Question Concerning Technology
  • Structuralism
  • Uber das Unendliche
  • Preface
  • Refaire le Timée. Introduction à la philosophie mathématique d’Albert Lautman
  • Recovering Mathematics after Heidegger’s Critique