Philosophy of Mathematics Selected Readings [Paperback]

Seminal articles in the philosophy of mathematics by Russell, Quine, G?del and other major thinkers.Includes several classic essays from the first edition, a representative selection of the most influential work of the past twenty years, a substantial introduction, and an extended bibliography. Originally published by Prentice-Hall in 1964.Includes several classic essays from the first edition, a representative selection of the most influential work of the past twenty years, a substantial introduction, and an extended bibliography. Originally published by Prentice-Hall in 1964.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 G?del. 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 G?del 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.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 lóÑ