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.

Autorentext
ALAN BAKER, Department of Philosophy, Swarthmore College, USA MARK COLYVAN, Department of Philosophy, University of Sydney, Australia ROY COOK, Department of Philosophy, University of Minnesota, USA THOMAS HOFWEBER, University of North Carolina, Chapel Hill, USA PETER KOELLNER, Harvard University, USA HANNES LEITGEB, Department of Philosophy, University of Bristol, UK MARY LENG, Department of Philosophy, University of Liverpool, UK ALEX PASEAU, Wadham College, Oxford, UK CHRIS PINCOCK, Purdue University, USA AGUSTÍN RAYO, MIT Department of Linguistics and Philosophy, USA GABRIEL UZQUIANO, Pembroke College, Oxford, UK

Inhalt
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