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The twentieth century has witnessed an unprecedented 'crisis in the foundations of mathematics', featuring a worldfamous paradox (Russell's Paradox), a challenge to 'classical' mathematics from a worldfamous mathematician (the 'mathematical intuitionism' of Brouwer), a new foundational school (Hilbert's Formalism), and the profound incompleteness results of Kurt Gdel. In the same period, the crossfertilization 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 Gdel himself, and which remains at the focus of AngloSaxon 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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