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Academic Year 2005/2006

Introduction to Meta-Mathematics
PHIL 292 FA

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.

MAJOR READINGS

Selections from van Heijenoort (ed.), FROM FREGE TO GODEL.

EXAMINATIONS AND ASSIGNMENTS

Regular problem sets, a midterm and a final.

ADDITIONAL REQUIREMENTS and/or COMMENTS

This course requires some background in logic, but a fair amount of experience with mathematics. So, if you have not taken MATH 243, you should have taken PHIL 230 AND a mathematics course at the level of MATH 225 or COMP 301.

COURSE FORMAT: Lecture

REGISTRATION INFORMATION

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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