Logic's Lost Genius and Gentzen's Centenary

摘要

Among the mathematical disciplines, logic may have the dubious distinction of being the one that always seems to belong somewhere else. As a study of the fundamental principles of reasoning, the subject has a philosophical side and touches on psychology, cognitive science, and linguistics. Because understanding the principles of reasoning is a prerequisite to mechanizing them, logic is also fundamental to a number of branches of computer science, including artificial intelligence, automated reasoning, database theory, and formal verification. It has, in addition, given rise to subjects that are fields of mathematics in their own right, such as model theory, set theory, and computability theory. But even these are black sheep among the mathematical disciplines, with distinct subject matter and methods. The situation calls to mind the words of Georges Simenon, the prolific Belgian author and creator of the fictional detective Jules Maigret, who told Life magazine in 1958, "I am at home everywhere, and nowhere. I am never a stranger and I never quite belong." If we use his self-assessment to characterize mathematical logic instead, the description is apt.