Computability

In the 1930s a series of seminal works published by Alan Turing, Kurt Gödel, Alonzo
Church, and others established the theoretical basis for computability. This work, advancing precise
characterizations of effective, algorithmic computability, was the culmination of intensive
investigations into the foundations of mathematics. In the decades since, the theory of
computability has moved to the center of discussions in philosophy, computer science, and cognitive
science. In this volume, distinguished computer scientists, mathematicians, logicians, and
philosophers consider the conceptual foundations of computability in light of our modern
understanding. Some chapters focus on the pioneering work by Turing, Gödel, and Church, including
the Church-Turing thesis and Gödel's response to Church's and Turing's proposals. Other chapters
cover more recent technical developments, including computability over the reals, Gödel's influence
on mathematical logic and on recursion theory and the impact of work by Turing and Emil Post on our
theoretical understanding of online and interactive computing; and others relate computability and
complexity to issues in the philosophy of mind, the philosophy of science, and the philosophy of
mathematics.

Contributors:Scott Aaronson, Dorit Aharonov, B.
Jack Copeland, Martin Davis, Solomon Feferman, Saul Kripke, Carl J. Posy, Hilary Putnam, Oron
Shagrir, Stewart Shapiro, Wilfried Sieg, Robert I. Soare, Umesh V. Vazirani