In 1931 Kurt Godel proved the famous Incompleteness Theorem, showing that any formal logical formulation of ordinary arithmetic must contain a statement which can neither be proved nor refuted. This discovery led to questions of solvability, computability, and decidability. Beginning with the rise of Intuitionism as a reaction to non-Euclidean geometry and to transfinite arithmetic, the course concentrates on Hilbert's Formalism: rigorous construction of the propositional and predicate calculus and of the natural numbers, treating questions of completeness and consistency. Primitive recursive functions are used to prove the Incompleteness Theorem. The course concludes with consideration of computability, decidability, and Turing machines. Evaluation will be based primarily on performance on problem assignments and a final exam. Prerequisite: Mathematics 211 or 251.