Turing's legacy: developments from Turing's ideas in logic

§1. Introduction . The year 2012 was the centenary of the birth of one of the most brilliant mathematicians of the 20th century. There were many celebrations of this fact, and many conferences based around Turing's work and life during 2012. In particular, there was a half year program (Syntax and Semantics) at the Newton Institute in Cambridge, and many “Turing 100/Centenary” conferences throughout the year. These events included truly major meetings featuring many of the world's best mathematicians and computer scientists (and even Gary Kasparov) around his actual birth day of June 23, including The Incomputable, ACM A. M. Turing Centenary Celebration, How the World Computes (CiE 2012), and The Turing Centenary Conference . There are also a number of publications devoted to Turing's life, work and legacy. To the general public, Turing is probably best known for his part in Bletchley Park and the war-winning efforts of the code-breakers at Hut 8. To biologists, Turing is best known for his work on morphogenesis, the paper “A Chemical Basis for Morphogenesis” being his most highly cited work. To logicians, and computer scientists, Alan Turing is best known for his work in computation, arguably leading to the development of the digital computer. This development has caused almost certainly the most profound change in human history in the last century. Turing's work in computation grew from philosophical questions in logic. Thus it seems fitting that the Association for Symbolic Logic sponsored this volume.