ALAN BAKER, Department of Philosophy, Swarthmore College, USAMARK COLYVAN, Department of Philosophy, University of Sydney, Australia ROY COOK, Department of Philosophy, University of Minnesota, USATHOMAS HOFWEBER, University of North Carolina, Chapel Hill, USAPETER KOELLNER, Harvard University, USA HANNES LEITGEB, Department of Philosophy, University of Bristol, UKMARY LENG, Department of Philosophy, University of Liverpool, UKALEX PASEAU, Wadham College, Oxford, UK CHRIS PINCOCK, Purdue University, USA AGUSTÍN RAYO, MIT Department of Linguistics and Philosophy, USAGABRIEL UZQUIANO, Pembroke College, Oxford, UK

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• Series Preface Acknowledgements Notes on Contributors Introduction: O.Bueno & Ø.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; Ø.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 Index