Truth, Objects, Infinity

This volume features essays about and by Paul Benacerraf, whose ideas have circulated in the philosophical community since the late nineteen sixties, shaping key areas in the philosophy of mathematics. The first part of the book focuses on "Benacerraf's dilemma", looking at mathematical language and mathematical knowledge, touching on Platonism and examining mathematical objects and their modes of presentation. The second part is concerned with logicism, fictionalism and structuralism, and the third part focuses on supertasks. The January 1968 version of Benacerraf's work "Mathematical Truth" is published here for the first time with updated footnotes, and the reader will find Paul Benacerraf's own replies to the essays presented in this volume. According to Benacerraf's dilemma, either we benefit from a Tarskian account of truth for mathematical language or we have a reliable explanation of mathematical knowledge, but we may not have both. Essays in this book explore this dilemma from new approaches, as well as offering new perspectives on logicism, structuralism and supertasks. This book first began to take shape at a workshop held in Paris at the Collčge de France, in May 2012, with the participation of Paul Benacerraf. The book is enhanced by the editor's introduction, a chronological bibliography of Paul Benacerraf, a subject index, a names index and a general bibliography.