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Thinking about Mathematics

The Philosophy of Mathematics

Stewart Shapiro

July 2000

ISBN: 9780192893062

328 pages

In Stock

Price: £34.99



Thinking about Mathematics covers the range of philosophical issues and positions concerning mathematics. The text describes the questions about mathematics that motivated philosophers throughout history and covers historical figures such as Plato, Aristotle, Kant, and Mill. It also presents the major positions and arguments concerning mathematics throughout the twentieth century, bringing the reader up to the present positions and battle lines.

  • The only introductory guide to the philosophy of mathematics aimed at the general reader/undergraduate student
  • Uniquely guides reader through the 'history' of the subject providing an overview of major philosophical positions and debates, as well as the major philosophers of the 20th Century
  • Only basic prior knowledge of either philosophy or mathematics needed, making it ideal for the student or reader coming to the subject for the first time

About the Author(s)

Stewart Shapiro, Professor of Philosophy, Ohio State University at Newark, USA

Table of Contents

    Part I. Perspective
    Chapter 1. What is so interesting about mathematics (for philosopher)?
    Attraction - of opposites?
    Philosophy and mathematics: chicken or egg?
    Naturalism and mathematics
    Chapter 2. A Potpourri of questions and attempted answers
    Necessity and a priori knowledge
    Global matters: objects and objectivity
    The mathematical and the physical
    Local maters: theorems, theories, and concepts
    Part II. History
    Chapter 3. Plato's Rationalism, and Aristotle
    The world of Being
    Plato on mathematics
    Mathematics on Plato
    Aristotle, the worthy opponent
    Further reading
    Chapter 4. Near opposites: Kant and Mill
    Further reading
    Part III. The big three
    Chapter 5. Logicism: Is mathematics (just) logic?
    Carnap and logical positivism
    Contemporary views
    Further reading
    Chapter 6. Formalism: Do mathematical statements mean anything?
    Basic views: Freg's onslaught
    Deductivism: Hilbert's Grundlagen der Geometrie
    Finitism: the Hilbert program
    Further reading
    Chapter 7. Intuitionism: is something wrong with our logic?
    1. Revising classical logic
    2. The teacher, Brouwer
    3. The student, Heyting
    4. Dummett
    5. Further reading
    Part IV. The contemporary scene
    Chapter 8. Numbers exist
    The web of belief
    Set-theoretic realism
    Further reading
    Chapter 9. No they don't
    Modal construction
    What should we make of all this?
    Addendum: Young Turks
    Further reading
    Chapter 10. Structuralism
    The underlying idea
    Ante rem structures, and objects
    Structuralism without structures
    Knowledge of structures
    Further reading


""Stewart Shapiro admirably provides an accessible introduction to contemporary thinking in mathematics, while avoiding caricature of the technicalities. His ease with the subject and lucid style makes this book a succinct introduction to a fascinating intellectual discipline." Times Literary Supplement"