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. After 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 course we will periodically pause from the mathematics to discuss its philosophical implications.
COURSE FORMAT: Lecture
Level: UGRD Credit: 1 Gen Ed Area Dept: NSM PHIL Grading Mode: Student Option
Prerequisites: MATH243 OR (PHIL230 AND MATH225) OR (PHIL230 AND [COMP301 or COMP500]) Links to Web Resources For This Course.
Last Updated on MAR-30-2006
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