Time Schedule:
David Keyt
PHIL 471
Seattle Campus
Study of the first-order predicate calculus with identity and function symbols. Consistency, soundness, completeness, compactness. Skolem-Lowenheim theorem. Formalized theories. Prerequisite: PHIL 470.
Class description
This course is on UNCOMPUTABILITY AND INCOMPLETENESS. We will study the proofs of several of the most profound results of modern logic—that there is no consistent, complete, axiomatization of arithmetic (Gödel’s first incompleteness theorem); that if arithmetic is consistent, its consistency is not provable in arithmetic (Gödel’s second incompleteness theorem); and that there is no mechanical test for validity in first-order logic (Church’s theorem). On our way to these theorems we will need to study computability and uncomputability in some depth, which we will do with the aid of some marvelous software (Turing’s World).
Student learning goals
General method of instruction
Recommended preparation
Class assignments and grading
