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Crosslistings: MATH 232 |
This course traces developments in mathematical logic that grew out of attempts to carry out David Hilbert's program for providing logical and philosophical foundations for mathematical practice. After a brief discussion of the philosophical and mathematical aims of Hilbert's program, we will study Godel's incompleteness theorems as he proved them in his 1931 papers. Then we will study the elementary recursion theory and provability logic that arise directly from the incompleteness results. Afte r a detour in transfinite recursion on ordinals, we will prove the consistency of first order arithmetic via Goodstein's Theorem and use this result to study the reasons for the failure of early attempts to implement Hilbert's program. Throughout the cou rse we will periodically pause from the mathematics to discuss its philosophical implications.
Unless preregistered students attend the first class meeting or communicate directly with the instructor prior to the first class, they will be dropped from the class list. NOTE: Students must still submit a completed Drop/Add form to the Registrar's Office.
COURSE FORMAT: Lecture
Level: UGRD Credit: 1 Gen Ed Area Dept: SBS PHIL Grading Mode: Student Option
Prerequisites: MATH243 OR (PHIL230 AND MATH225) OR (PHIL230 AND COMP301)
Last Updated on MAR-26-2001
Copyright Wesleyan University, Middletown, Connecticut, 06459