Philosophy of Mathematics

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 (Hil [...]
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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.