Godel’s Proof and Its Philosophical Ramifications

Abstract

The most significant theorem of 20th century logic was Godel’s incompleteness theorem. In the thesis Godel’s theorem, both how it works and what it means philosophically, is given a penetrating analysis. I explain both the mathematics of Godel’s proof, as it is presented in his paper On Formally Undecidable Propositions of Principia Mathematica and Related Systems, and the presentation only assumes a basic knowledge of symbolic logic and the patience to follow mathematical arguments on the part of the reader. Preceding the exposition of Godel’s proof is a philosophical discussion of logic, and at the end of the exposition I discuss the proof’s philosophical ramifications.