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Mathematical Epistemology and Psychology

  • Book
  • © 1974

Overview

Authors:
  1. Evert W. Beth
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  2. Jean Piaget
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Part of the book series: Synthese Library (SYLI, volume 12)

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Table of contents (13 chapters)

  1. Front Matter

    Pages I-XXI
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  2. Evert W. Beth

    1. Front Matter

      Pages 1-5
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    2. Mathematical Reasoning Cannot be Analysed by Traditional Syllogistics

      • Evert W. Beth, Jean Piaget
      Pages 6-23

    3. The Psychological Interpretation of Mathematical Reasoning

      • Evert W. Beth, Jean Piaget
      Pages 24-35

    4. The Logicist Tradition

      • Evert W. Beth, Jean Piaget
      Pages 36-85

    5. Strict Demonstration and Heuristic Procedures

      • Evert W. Beth, Jean Piaget
      Pages 86-100

    6. Intuitive Structures and Formalised Mathematics

      • Evert W. Beth, Jean Piaget
      Pages 101-113

    7. “Thinking Machines” and Mathematical Thought

      • Evert W. Beth, Jean Piaget
      Pages 114-126

  3. Jean Piaget

    1. Front Matter

      Pages 129-135
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    2. Lessons of the History of the Relations between Logic and Psychology

      • Evert W. Beth, Jean Piaget
      Pages 137-162

    3. General Psychological Problems of Logico-Mathematical Thought

      • Evert W. Beth, Jean Piaget
      Pages 163-190

    4. General Psychological Problems of Logico-Mathematical Thought

      • Evert W. Beth, Jean Piaget
      Pages 191-225

    5. The Psychological Problems of “Pure” Thought

      • Evert W. Beth, Jean Piaget
      Pages 226-258

    6. Some Convergences between Formal and Genetic Analyses

      • Evert W. Beth, Jean Piaget
      Pages 259-280

    7. Epistemological Problems with Logical and Psychological Relevance

      • Evert W. Beth, Jean Piaget
      Pages 281-303

    8. General Conclusions

      • Evert W. Beth, Jean Piaget
      Pages 305-312

  4. Back Matter

    Pages 313-326
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Mathematical Epistemology and Psychology

  • Authors: Evert W. Beth, Jean Piaget

  • Series Title: Synthese Library

  • DOI: https://doi.org/10.1007/978-94-017-2193-6

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 1974

  • Hardcover ISBN: 978-90-277-0071-1Published: 30 June 1974

  • Softcover ISBN: 978-90-481-8328-9Published: 25 December 2010

  • eBook ISBN: 978-94-017-2193-6Published: 09 March 2013

  • Series ISSN: 0166-6991

  • Series E-ISSN: 2542-8292

  • Edition Number: 1

  • Number of Pages: XXI, 326

  • Additional Information: Originally published in French

  • Topics: Psycholinguistics, History, general

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