PHIL232

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PHIL232

Introduction to Metamathematics PHIL232 FA

Crosslistings: MATH232

Not Currently Offered

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 theorums, 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 up to epsilon zero, we will prove the consistency of first order arithmetic via Goodstein's Theorum, 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. 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: Discussion Lecture

REGISTRATION INFORMATION

Level: UG Credit: 1.00 Gen Ed Area & Dept: SBS PHIL

Prerequisites: MATH243 or PHIL230 and MATH225 or PHIL230 and COMP301

Last Updated on MAR-22-1999

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