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Poincaré: intuitionism, intuition, and convention

  • Gerhard Heinzmann
  • Philippe Nebonnand
Part of the Publications des Archives Henri Poincaré / Publications of the Henri Poincaré Archives book series (PAHP)

Abstract

Arend Heyting in the introduction of his famous volume Mathematische Grundlagenforschung, Intuitionismus, Beweistheorie, speaks of Poincaré’s influence on ‘contemporary intuitionists’, i.e., mathematicians who agree with the opinion that
  1. (1)

    Mathematics has not only a formal but also a contentual signification.

     
  2. (2)

    Mathematical objects are directly grasped by the thinking mind; hence mathematical knowledge is independent of experience. (Heyting 1934, p.3)1

     

Keywords

Euclidean Geometry Mathematical Entity Geometrical Space Induction Principle Euclidean Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag AG 2008

Authors and Affiliations

  • Gerhard Heinzmann
    • 1
  • Philippe Nebonnand
    • 1
  1. 1.Archives Henri PoincaréFrance

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