Overview

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 Two yet unpublished essays by Benacerraf have been included in the volume: an early version of “Mathematical Truth” from 1968 and an essay on “What Numbers Could Not Be” from the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.

Full Product Details

Author:   Fabrice Pataut
Publisher:   Springer International Publishing AG
Imprint:   Springer International Publishing AG
Edition:   Softcover reprint of the original 1st ed. 2016
Volume:   28
Weight:   0.534kg
ISBN:  

9783319834122

ISBN 10:   3319834126
Pages:   309
Publication Date:   13 July 2018
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Acknowledgements.- Notes on contributors.-  Introduction; Pataut, Fabrice.-  Part 1: Benacerraf’s Dilemma.- Chapter 1. McEvoy on Benacerraf's Problem and the Epistemic Role Puzzle; Azzouni, Jody.- Chapter 2.  What is the Benacerraf Problem?; Clarke-Doane, Justin.- Chapter 3. Benacerraf's Mathematical Antinomy; Halimi, Brice.- Chapter 4.  A Dilemma for Benacerraf's Dilemma?; Sereni, Andrea.- Part 2.  Logicism, fictionalism and structuralism.- Chapter 5.  Benacerraf on Logicism; Gandon, Sébastien.- Chapter 6.  Truth, Fiction and Stipulation; Leng, Mary.- Chapter 7. A Methodological Moral for the Story of Ernie and Johnny; de Rouilhan, Philippe.- Chapter 8.  What Numbers Could Be; What Objects Could Be; Shapiro, Stuart.- Part 3. Supertasks.- Chapter 9.  Motionless Gödel's Long Strides - A Note on the Contemporary Versions of Zeno's Arguments; Dubucs, Jacques.- Part 4. Paul Benacerraf's replies to essays.- Replies to Essays 1 to 9; Benacerraf, Paul.- Part 5. Mathematical truth '68.- Mathematical Truth (January 1968 version), with updated footnotes; Benacerraf, Paul.- Chronological Bibliography of Paul Benacerraf to 2014.- General Bibliography.

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