Mathematical Epistemology and Psychology

  • Authors
  • Evert W. Beth
  • Jean Piaget

Part of the Synthese Library book series (SYLI, volume 12)

Table of contents

  1. Front Matter
    Pages I-XXI
  2. Evert W. Beth

    1. Front Matter
      Pages 1-5
    2. Evert W. Beth, Jean Piaget
      Pages 24-35
    3. Evert W. Beth, Jean Piaget
      Pages 36-85
    4. Evert W. Beth, Jean Piaget
      Pages 86-100
    5. Evert W. Beth, Jean Piaget
      Pages 101-113
    6. Evert W. Beth, Jean Piaget
      Pages 114-126
  3. Jean Piaget

    1. Front Matter
      Pages 129-135
    2. Evert W. Beth, Jean Piaget
      Pages 163-190
    3. Evert W. Beth, Jean Piaget
      Pages 191-225
    4. Evert W. Beth, Jean Piaget
      Pages 226-258
    5. Evert W. Beth, Jean Piaget
      Pages 259-280
    6. Evert W. Beth, Jean Piaget
      Pages 305-312
  4. Back Matter
    Pages 313-326

About this book

Introduction

One of the controversial philosophical issues of recent years has been the question of the nature of logical and mathematical entities. Platonist or linguistic modes of explanation have become fashionable, whilst abstrac­ tionist and constructionist theories have ceased to be so. Beth and Piaget approach this problem in their book from two somewhat different points of view. Beth's approach is largely historico-critical, although he discusses the nature of heuristic thinking in mathematics, whilst that of Piaget is psycho-genetic. The major purpose of this introduction is to summarise some of the main points of their respective arguments. In the first part of this book Beth makes a detailed study of the history of philosophical thinking about mathematics, and draws our attention to the important role played by the Aristotelian methodology of the demon­ strative sciences. This, he tells us, is characterised by three postulates: (a) deductivity, (b) self-evidence, and (c) reality. The last postulate asserts that the primitive notions of a demonstrative science must have reference to a domain of real entities in order to have significance. On the Aristote­ lian view discursive reasoning plays a major role in mathematics, whilst pure intuition plays a somewhat subordinate one.

Keywords

Plato epistemological problem epistemology reason

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-017-2193-6
  • Copyright Information Springer Science+Business Media B.V. 1974
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-8328-9
  • Online ISBN 978-94-017-2193-6
  • About this book