College of Arts and Sciences
Theorems of Kurt Godel
Logic and Foundations
Swarey, Derick, "Gödel's Incompleteness Theorems" (2022). Senior Honors Theses. 1177.
The Incompleteness Theorems of Kurt Godel are very famous both within and outside of mathematics. They focus on independence and consistency within mathematics and hence a more thorough understanding of these is beneficial to their study. The proofs of the theorems involve many ideas which may be unfamiliar to many, including those of formal systems, Godel numbering, and recursive functions and relations. The arguments themselves mirror the Liar’s Paradox in that Godel constructs a statement asserting its own unprovability and then shows that such a statement and its negation must both be independent of the system, otherwise the system is inconsistent. We then proceed to survey various interpretations of the Incompleteness Theorems, focusing on potential misapplications of the theorems.