New Waves in Philosophy of Mathematics [Paperback]

Thirteen promising young researchers write on what they take to be the right philosophical account of mathematics and discuss where the philosophy of mathematics ought to be going. New trends are revealed, such as an increasing attention to mathematical practice, a reassessment of the canon, and inspiration from philosophical logic.Series Preface Acknowledgements Notes on Contributors Introduction: O.Bueno & ?.Linnebo PART I: REASSESSING THE ORTHODOXY IN THE PHILOSOPHY OF MATHEMATICS New Waves on an Old Beach: Neo-Fregean Philosophy of Mathematics Today; R.Cook Reducing Arithmetic to Set Theory; A.Paseau PART II: THE QUESTION OF REALISM IN MATHEMATICS Mathematical Fictionalism; O.Bueno Truth in Mathematics: The Question of Pluralism; P.Koellner 'Algebraic' Approaches to Mathematics; M.Leng PART III: MATHEMATICAL PRACTICE AND THE METHODOLOGY OF MATHEMATICS Mathematical Accidents and the End of Explanation; A.Baker Applying Inconsistent Mathematics; M.Colyvan Towards a Philosophy of Applied Mathematics; C.Pincock PART IV: MATHEMATICAL LANGUAGE AND THE PSYCHOLOGY OF MATHEMATICS Formal Tools and the Philosophy of Mathematics; T.Hofweber The Individuation of the Natural Numbers; ?.Linnebo Towards a Trivialist Account of Mathematics; A.Rayo PART V: FROM PHILOSOPHICAL LOGIC TO THE PHILOSOPHY OF MATHEMATICS On Formal and Informal Provability; H.Leitgeb Quantification without a Domain; G.Uzquiano IndexALAN BAKER, Department of Philosophy, Swarthmore College, USAMARK COLYVAN, Department of Philosophy, University of Sydney, AustraliaROY COOK, Department of Philosophy, University of Minnesota, USATHOMAS HOFWEBER, University of North Carolina, Chapel Hill, USAPETER KOELLNER, Harvard University, USAHANNES LEITGEB, Department of Philosophy, University of Bristol, UKMARY LENG, Department of Philosophy, University of Liverpool, UKALEX PASEAU, Wadham College, Oxford, UKCHRIS PINCOCK, Purdue University, USAAGUST?N RAYO, MIT Department of Linguistics and Philosophy, USAGABRIEL UZQUl³C