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Self-Reference cover

Self-Reference

edited by Thomas Bolander, Vincent F. Hendricks and Stig Andur Pedersen

Here is an anthology of previously unpublished essays on self-reference from some of the most outstanding scholars in philosophy, mathematics, and computer science.

This volume is accessible to students and compelling for scholars as it reexamines the latest theories of self-reference, including those that attempt to explain and resolve the semantic and set-theoretic paradoxes.

A thorough introduction by the editors sets the stage for original contributions from Andrea Cantini, Melvin Fitting, Anil Gupta, Vann McGee, Don Perlis, Graham Priest, Raymond M. Smullyan, and Stephen Yablo.

For over 2000 years self-reference, in the form of the Liar's Paradox, was considered a philosophical oddity. In 1902, self-referential set-theoretic paradoxes triggered a foundational crisis in mathematics.

Since then, self-reference has continued to play a key role in philosophical and mathematical logic as well as, more recently, in theoretical computer science. This thought-provoking volume contains a collection of cutting-edge articles on this important topic.  –Moshe Y. Vardi

This is a book that every logician will want to read. The well-worn topics of self-reference and the paradoxes have been given new life in these papers by a distinguished group of logicians.  – Elliot Mendelson

Thomas Bolander is Assistant Professor of Logic and Computer Science at the Technical University of Denmark. Vincent F. Hendricks is Professor of Epistemology, Logic, and Methodology at Roskilde University in Denmark. Stig Andur Pedersen is Professor of Philosophy and Science Studies at Roskilde University in Denmark.

Contents

  • 1 Introduction 1
    T. Bolander, V.F. Hendricks, and S.A. Pedersen
  • 2 Fixed Point Constructions 27
    Andrea Cantini
  • 3 Bilattices are Nice Things 53
    Melvin Fitting
  • 4 Finite Circular Definitions 79
    Anil Gupta
  • 5 In Praise of Free Lunch 95
    Vann McGee
  • 6 Theory and Application of Self-Reference 121
    Don Perlis
  • 7 The Paradoxes of Denotation 137
    Graham Priest
  • 8 Self-Reference in All Its Glory! 151
    Raymond M. Smullyan
  • 9 Circularity and Paradox 165
    Stephen Yablo
  • Index 185

10/1/2006

ISBN (Paperback): 1575865165 (9781575865164)
ISBN (Electronic): 1575867761 (9781575867762)

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