Understanding Gödel's Incompleteness Proofs

Authors

Nanako ItoFollow

Abstract

This project investigates the proofs that Kurt Gödel published in 1931 for his incompleteness theorems. We first lay out the basic knowledge necessary to understand the incompleteness theorems and the foundations of mathematics. With Nagel and Newman's Gödel's Proof as the main reference, we then examine the motivation behind proving these theorems and walk through the main ideas of Gödel's original proofs. We conclude the project with the implications of the theorems and some thoughts regarding truth and provability in the context of mathematics.

Advisor

Zindulka, Ondrej

Second Advisor

Pierce, Pamela

Department

Mathematics

Recommended Citation

Ito, Nanako, "Understanding Gödel's Incompleteness Proofs" (2017). Senior Independent Study Theses. Paper 7428.
https://openworks.wooster.edu/independentstudy/7428

Disciplines

Logic and Foundations

Publication Date

2017

Degree Granted

Bachelor of Arts

Document Type

Senior Independent Study Thesis