Philosophy of mathematics : selected readings

Other titles
  • Cambridge Core
Edition
  • 2nd ed.
Published
  • Cambridge : Cambridge University Press 1983
Physical description
1 online resource (viii, 600 p. )
ISBN
  • 1-139-17151-8
ISRC
  • 8788496
ISSN
  • 8202-5257
Notes
  • Bibliographic Level Mode of Issuance: Monograph
  • Bibliography: p. 571-600.
  • Service provider: Cambridge University Press (EBA)
  • Previous ed. : Prentice-Hall, 1964.
  • Source of acquisition: Bequeathed by John Fauvel and held by the Open University Library on behalf of the British Society for the History of Mathematics
  • English
  • Print version record.
Contents
  • Symposium on the foundations of mathematics -- 1. The logicist foundations of mathematics / Rudolf Carnap -- 2. The intuitionist foundations of mathematics / Arend Heyting -- 3. The formalist foundations of mathematics / Johann Von Neumann -- Disputation / Arend Heyting -- Intuitionism and formalism / L.E.J. Brouwer -- Consciousness, philosophy, and mathematics / L.E.J. Brouwer -- The philosophical basis of intuitionistic logic / Michael Dummett -- The concept of number / Gottlob Frege -- Selections from Introduction to mathematical philosophy / Bertrand Russell -- On the infinite / David Hilbert -- Remarks on the definition and nature of mathematics / Haskell B. Curry -- Hilbert's programme / Georg Kreisel -- Empiricism, semantics, and ontology / Rudolf Carnap -- On platonism in mathematics / Paul Bernays -- What numbers could not be / Paul Benacerraf -- Mathematics without foundations / Hilary Putnam -- The a priori / Alfred Jules Ayer -- Truth by convention / W.V. Quine -- Carnap and logical truth / W.V. Quine -- On the nature of mathematical reasoning / Henri Poincare -- Mathematical truth / Paul Benacerraf -- Models and reality / Hilary Putnam -- Russell's mathematical logic / Kurt Gödel -- What is Cantor's continuum problem? / Kurt Gödel -- The iterative concept of set / George Boolos -- What is the iterative conception of set? / Charles Parsons -- The concept of set / Hao Wang.
Related item
  • Other format: ; ISBN: 0-521-29648-X
  • Other format: ; ISBN: 0-521-22796-8
  • http://catdir.loc.gov/catdir/description/cam022/82025257.html
  • http://www.loc.gov/catdir/description/cam022/82025257.html
Genre
  • Aufsatzsammlung.
  • Electronic books
  • text
Language
  • English

Summary

  • The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a world-famous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a world-famous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gödel. In the same period, the cross-fertilization of mathematics and philosophy resulted in a new sort of 'mathematical philosophy', associated most notably (but in different ways) with Bertrand Russell, W. V. Quine, and Gödel himself, and which remains at the focus of Anglo-Saxon philosophical discussion. The present collection brings together in a convenient form the seminal articles in the philosophy of mathematics by these and other major thinkers. It is a substantially revised version of the edition first published in 1964 and includes a revised bibliography. The volume will be welcomed as a major work of reference at this level in the field.

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