Truth, Objects, Infinity

1. Front Matter

   Pages i-xxxviii

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2. Benacerraf’s Dilemma

   1. Front Matter

      Pages 1-1

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   2. McEvoy on Benacerraf’s Problem and the Epistemic Role Puzzle

      • Jody Azzouni

      Pages 3-15

   3. What Is the Benacerraf Problem?

      • Justin Clarke-Doane

      Pages 17-43

   4. Benacerraf’s Mathematical Antinomy

      • Brice Halimi

      Pages 45-62

   5. On Benacerraf’s Dilemma, Again

      • Marco Panza

      Pages 63-92

   6. A Dilemma for Benacerraf’s Dilemma?

      • Andrea Sereni

      Pages 93-125

3. Logicism, Fictionalism and Structuralism

   1. Front Matter

      Pages 127-127

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   2. Benacerraf on Logicism

      • Sébastien Gandon

      Pages 129-145

   3. Truth, Fiction, and Stipulation

      • Mary Leng

      Pages 147-158

   4. Identification and Transportability: Another Moral for Benacerraf’s Parable of Ernie and Johnny

      • Philippe de Rouilhan

      Pages 159-176

   5. What Numbers Could Be; What Objects Could Be

      • Stewart Shapiro

      Pages 177-191

4. Supertasks

   1. Front Matter

      Pages 193-193

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   2. Tasks, Subtasks and the Modern Eleatics

      • Jon Pérez Laraudogoitia

      Pages 195-221

   3. Supertasks, Physics and the Axiom of Infinity

      • Antonio León-Sánchez, Ana C. León-Mejía

      Pages 223-259

5. Retrospection: Mathematical Truth, Mathematical Objects

   1. Front Matter

      Pages 261-261

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   2. Mathematical Truth (1968 Version)

      • Paul Benacerraf

      Pages 263-287

   3. Comments on Reduction (Lecture in a Graduate Seminar ~1975)

      • Paul Benacerraf

      Pages 289-296

6. Back Matter

   Pages 297-309

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This volume features essays about and by Paul Benacerraf, whose ideas have circulated in the philosophical community since the early nineteen sixties, shaping key areas in the philosophy of mathematics, the philosophy of language, the philosophy of logic, and epistemology. The book started as a workshop held in Paris at the Collège de France in May 2012 with the participation of Paul Benacerraf. The introduction addresses the methodological point of the legitimate use of so-called “Princess Margaret Premises” in drawing philosophical conclusions from Gödel’s first incompleteness theorem. The book is then divided into three sections. The first is devoted to an assessment of the improved version of the original dilemma of “Mathematical Truth” due to Hartry Field: the challenge to the platonist is now to explain the reliability of our mathematical beliefs given the very subject matter of mathematics, either pure or applied. The second addresses the issue of the ontological status ofnumbers: Frege’s logicism, fictionalism, structuralism, and Bourbaki’s theory of structures are called up for an appraisal of Benacerraf’s negative conclusions of “What Numbers Could Not Be.” The third is devoted to supertasks and bears witness to the unique standing of Benacerraf’s first publication: “Tasks, Super-Tasks, and Modern Eleatics” in debates on Zeno’s paradox and associated paradoxes, infinitary mathematics, and constructivism and finitism in the philosophy of mathematics.

Two yet unpublished essays by Benacerraf have been included in the volume: an early version of “Mathematical Truth” from 1968 and an essay on “What Numbers Could Not Be” from the mid 1970’s. A complete chronological bibliography of Benacerraf’s work to 2016 is provided.
Essays by Jody Azzouni, Paul Benacerraf, Justin Clarke-Doane, Sébastien Gandon, Brice Halimi, Jon Pérez Laraudogoitia, Mary Leng, Antonio León-Sánchez and Ana C. León-Mejía, Marco Panza, Fabrice Pataut, Philippe de Rouilhan, Andrea Sereni, and Stewart Shapiro.

• Benacerraf's dilemma
• Logicism
• Mathematical knowledge
• Mathematical objects
• Mathematical truth
• Platonism

• FRE Sciences, Normes, Décision, CNRS, Paris, France

  Fabrice Pataut

Policies and ethics