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.