Philosophy of Mathematics 2ed: Selected Readings - Brossura

Benacerraf, Paul

Brossura

ISBN 10: 052129648X ISBN 13: 9780521296489

Casa editrice: Cambridge University Press, 1984

Riassunto

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.

Su questo libro

Descrizione del libro:

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.

Contenuti:

Preface to the second edition; Introduction; Part I. 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; 4. Disputation Arend Heyting; 5. Intuitionism and formalism L. E. J. Brouwer; 6. Consciousness, philosophy, and mathematics L. E. J. Brouwer; 7. The philosophical basis of intuitionistic logic Michael Dummett; 8. The concept of number Gottlob Frege; 9. Selections from Introduction to Mathematical Philosophy Bertrand Russell; 10. On the infinite David Hilbert; 11. Remarks on the definition and nature of mathematics Haskell B. Curry; 12. Hilbert's programme Georg Kreisel; Part II. The Existence of Mathematical Objects: 13. Empiricism, semantics, and ontology Rudolf Carnap; 14. On Platonism in mathematics Paul Bernays; 15. What numbers could not be Paul Benacerraf; 16. Mathematics without foundations Hilary Putnam; Part III. Mathematical Truth: 17. The a priori Alfred Jules Ayer; 18. Truth by convention W. V. Quine; 19. On the nature of mathematical truth Carl G. Hempel; 20. On the nature of mathematical reasoning Henri Poincaré; 21. Mathematical truth Paul Benacerraf; 22. Models and reality Hilary Putnam; Part IV. The Concept of Set: 23. Russell's mathematical logic Kurt Gödel; 24. What in Cantor's continuum problem? Kurt Gödel; 25. The iterative concept of set George Boolos; 26. The concept of set Hao Wang; Bibliography.

Su questa edizione

• Editore: Cambridge University Press
• Data di pubblicazione: 1984
• ISBN 10: 052129648X
• ISBN 13: 9780521296489
• Rilegatura: Copertina flessibile
• Numero edizione: 2
• Numero di pagine: 612