Philosophy 220 - INCOMPLETENESS & INCONSISTENCY

Among the most important and philosophically intriguing results in 20th-century logic are the limitative theorems such as Gödel’s incompleteness theorem and Tarski’s demonstration of the indefinability of truth in certain languages. A wide variety of approaches to resolving fundamental mathematical and semantical paradoxes have emerged in the wake of these results, as well as a variety of alternative logics including paraconsistent logics in which contradictions are tolerated. This course examines logical and semantic paradoxes and their philosophical significance, as well as the choice between accepting incompleteness and inconsistency in logic and knowledge. Prerequisite: one course in logic.