The Interplay Between Logic and Mathematics: Intuitionism

  • A. S. Troelstra
Part of the Synthese Library book series (SYLI, volume 149)


There are several ways in which the title of this lecture can be interpreted, depending on our interpretation of logic’, ‘mathematics’, and ‘intuitionism’. For a start, let us remark that we take intuitionism here to refer to a certain body of concepts and principles which can be used in the development of mathematics, and which are in the line of L. E. J. Brouwer’s reconstruction of mathematics; however, we do not claim exlcusiveness for these concepts and principles, that is to say we do not claim that they are the only legitimate and intelligible ones. In other words, intuitionism in regarded here as an interesting (and meaningful) object of study, not as an exclusive philosophy of mathematics.


Classical Logic Intuitionistic Logic Kripke Model Atomic Sentence Choice Sequence 
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  22. Postscript added in proof (July 1980). Since this lecture was held, three years have elapsed and new material has become available. To help the reader, we indicate some directly relevant supplementary references below.Google Scholar
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Copyright information

© D. Reidel Publishing Company 1981

Authors and Affiliations

  • A. S. Troelstra
    • 1
  1. 1.Mathematisch InstituutUniversiteit van AmsterdamThe Netherlands

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