This is the first of two volumes of essays in commemoration of Alan Turing, whose pioneering work in the theory of artificial intelligence and computer science continues to provoke wide discussion. The essays focus on three questions: What, if any, are the limits on machine "thinking"? Can a machine be genuinely intelligent? And, Might we ourselves be biological machines? Contributors include Chris Fields, Joseph Ford, Robert M. French, Anthony Galton, Robin Gandy, Clark Glymour, J. R. Lucas, Donald Michie, Peter Mott, Ajit Narayanan, Herbert A. Simon, Aaron Sloman, Ian Stewart, and Blay Whitby.