LOGIC IN THE SECOND HALF OF THE TWENTIETH CENTURY

Modern logic emerged in the period from 1879 to the Second World War. In the post-war period what we know as classical first-order logic largely replaced traditional syllogistic logic in introductory textbooks, but the main development has been simply enormous growth: The publications of the Association for Symbolic Logic, the main professional organization for logicians, became ever thicker. While 1950 saw volume 15 of the Journal of Symbolic Logic, about 300 pages of articles and reviews and a six-page member list, 2000 saw volume 65 of that journal, over 1, 900 pages of articles, plus volume 6 of the Bulletin of Symbolic Logic, 570 pages of reviews and a sixty-page member list. Of so large a field, the present survey will have to be ruthlessly selective, with no coverage of the history of informal or inductive logic, or of philosophy or historiography of logic, and slight coverage of applications. Remaining are five branches of pure, formal, deductive logic, four being the branches of mathematical logic recognized in Barwise 1977, first of many handbooks put out by academic publishers: set theory, model theory, recursion theory, proof theory. The fifth is philosophical logic, in one sense of that label, otherwise called non-classical logic, including extensions of and alternatives to textbook logic. For each branch, a brief review of pre-war background will be followed by a few highlights of subsequent history. The references will be a mix of primary and secondary sources, landmark papers and survey articles.