B. Jack Copeland, Carl J. Posy, and Oron Shagrir, eds, Computability: Turing, Godel, Church, and Beyond. Cambridge, Mass.: MIT Press, 2013. ISBN 978-0-262-01899-9. Pp. x + 362

Abstract

Computability: Turing, Gödel, Church, and Beyond collects eleven essays focusing on the revolutionary work carried out in the 1930s and 1940s on computability by the thinkers named in the title, as well as by their students and colleagues such as Herbrand, Kleene, Post, Rosser, and von Neumann. The essays collected in the volume are not limited to the historical, however, as the final ‘Beyond’ suggests; the reader will also find extended discussions of more recent work on these topics and related issues. The essays range from the very technical (e.g., Martin Davis's ‘Computability and arithmetic’ or Solomon Feferman's ‘About and around computing over the reals’) to the historical (e.g., Robert Irving Soare's ‘Interactive computing and relativized computability’); from the philosophical (e.g., Stewart Shapiro's ‘The open texture of computability’ and Scott Aaronson's ‘Why philosophers should care about computational complexity’) to the slightly esoteric (e.g., Dorit Aharonov and Umesh V. Vazirani's ‘Is quantum mechanics falsifiable?’ and Carl J. Posy's ‘Computability and onstructibility’).1