New Waves in Philosophy of Mathematics

1. Front Matter

   Pages i-ix

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2. Introduction Philosophy of Mathematics: Old and New

   1. Introduction Philosophy of Mathematics: Old and New

      • Otávio Bueno, Øystein Linnebo

      Pages 1-9

3. Reassessing the Orthodoxy in the Philosophy of Mathematics

   1. Front Matter

      Pages 11-11

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   2. New Waves on an Old Beach: Fregean Philosophy of Mathematics Today

      • Roy Cook

      Pages 13-34

   3. Reducing Arithmetic to Set Theory

      • Alexander Paseau

      Pages 35-55

4. The Question of Realism in Mathematics

   1. Front Matter

      Pages 57-57

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   2. Mathematical Fictionalism

      • Otávio Bueno

      Pages 59-79

   3. Truth in Mathematics: The Question of Pluralism

      • Peter Koellner

      Pages 80-116

   4. “Algebraic” Approaches to Mathematics

      • Mary Leng

      Pages 117-134

5. Mathematical Practice and the Methodology of Mathematics

   1. Front Matter

      Pages 135-135

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   2. Mathematical Accidents and the End of Explanation

      • Alan Baker

      Pages 137-159

   3. Applying Inconsistent Mathematics

      • Mark Colyvan

      Pages 160-172

   4. Towards a Philosophy of Applied Mathematics

      • Christopher Pincock

      Pages 173-194

6. Mathematical Language and the Psychology of Mathematics

   1. Front Matter

      Pages 195-195

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   2. Formal Tools and the Philosophy of Mathematics

      • Thomas Hofweber

      Pages 197-219

   3. The Individuation of the Natural Numbers

      • Øystein Linnebo

      Pages 220-238

   4. Toward a Trivialist Account of Mathematics

      • Agustín Rayo

      Pages 239-260

7. From Philosophical Logic to the Philosophy of Mathematics

   1. Front Matter

      Pages 261-261

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   2. On Formal and Informal Provability

      • Hannes Leitgeb

      Pages 263-299

   3. Quantification Without a Domain

      • Gabriel Uzquiano

      Pages 300-323

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.

• knowledge
• logic
• mathematics
• philosophical logic
• philosophy of mathematics

• University of Miami, USA

  Otávio Bueno

• University of Bristol, UK

  Øystein Linnebo

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

Policies and ethics