Here is an anthology of previously unpublished essays on self-reference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.

- 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