This book introduces the technical tools and concepts that are indispensable for advanced work in philosophy. Beginning with the fundamentals of set theory, the author guides the reader through relations, functions and the theory of arithmetic before using these tools to clarify the metatheory of the predicate calculus. There are discussions of recursive definitions, Godel's Theorem, and completeness for the predicate calculus. The text emphasizes the structure of these systems and the metatheory behind them.
Table of Contents
Part 1 Set theory: the logical framework; the basic concepts of set theory; relations; functions; recursive definitions; arithmetic. Part 2 Logic: the predicate calculus; first-order theories; higher order logic.
John L. Pollock is professor of philosophy at the University of Arizona. Joseph Cruz is assistant professor of philosophy and cognitive science at Hampshire College in Amherst, Massachusetts.