Philosophy of Mathematics: Selected ReadingsPaul Benacerraf, Hilary Putnam 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. |
Contents
Symposium on thefoundations of mathematics 1 The logicist foundations of mathematics | |
Disputation | |
Intuitionism and formalism | |
E J BROUWER | |
The philosophical basis of intuitionistic logic | |
MICHAELDUMMETT The conceptof number | |
Selections from Introduction to Mathematical Philosophy | |
Remarks on the definition and nature of mathematics | |
Hilberts programme | |
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Common terms and phrases
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