Mathematical thought and its objects

著者

書誌事項

Mathematical thought and its objects

Charles Parsons

Cambridge University Press, 2008

  • : hardback
  • : paperback

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注記

Includes bibliographical references (p. 343-363) and index

内容説明・目次

内容説明

Charles Parsons examines the notion of object, with the aim to navigate between nominalism, denying that distinctively mathematical objects exist, and forms of Platonism that postulate a transcendent realm of such objects. He introduces the central mathematical notion of structure and defends a version of the structuralist view of mathematical objects, according to which their existence is relative to a structure and they have no more of a 'nature' than that confers on them. Parsons also analyzes the concept of intuition and presents a conception of it distantly inspired by that of Kant, which describes a basic kind of access to abstract objects and an element of a first conception of the infinite.

目次

  • Preface
  • 1. Objects and logic
  • 2. Structuralism and nominalism
  • 3. Modality and structuralism
  • 4. A problem about sets
  • 5. Intuition
  • 6. Numbers as objects
  • 7. Intuitive arithmetic and its limits
  • 8. Mathematical induction
  • 9. Reason.

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