## Philosophy of Mathematics: Selected ReadingsThe 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. |

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Philosophy of Mathematics: Selected Readings Paul Benacerraf,Hilary Putnam No preview available - 1983 |

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accept analysis analytic analytic propositions applies argument arithmetic assertion axiom of choice axiom of infinity axiom of replacement axiomatic set theory belongs calculus Cantor's cardinal concept F concept of set consistency consistency proof construction contains continuum hypothesis convention deduction defined definition derived elementary elements empirical entities example existence expressions fact false finite number finitist formal system formula Frege function geometry given Godel Hilbert idea impredicative impredicative definitions induction infinite integers interpretation intuition intuitionism intuitionist intuitionistic logic iterative conception language logical truth mathe mathematical truth matical meaning method natural numbers notion number theory ordinal numbers paradoxes philosophical philosophy of mathematics possible postulates predicate primitive principle problem proof propositions proved purely quantifiers question real numbers reason recursive reference relation rules Russell semantics sense sentence sequence set theory stage subsets symbols theorem things tion transfinite true words Zermelo set theory