Truth, Objects, Infinity : New Perspectives on the Philosophy of Paul Benacerraf / edited by Fabrice Pataut.

Format:

Book

Contributor:

Pataut, Fabrice., Editor.

Series:

Logic, Epistemology, and the Unity of Science, 2214-9783 ; 28

Language:

English

Subjects (All):

Language and languages--Philosophy.

Language and languages.

Knowledge, Theory of.

Science--Philosophy.

Science.

Ontology.

Philosophy of Language.

Epistemology.

Philosophy of Science.

Local Subjects:

Philosophy of Language.

Epistemology.

Philosophy of Science.

Ontology.

Physical Description:

1 online resource (332 pages) : illustrations.

Edition:

1st ed. 2016.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2016.

Summary:

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 Two yet unpublished essays by Benacerraf have been included in the volume: an early version of “Mathematical Truth” from 1968 and an essay on “What Numbers Could Not Be” from the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

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.

Notes:

Includes bibliographical references at the end of each chapters and indexes.

ISBN:

3-319-45980-5