Godel’s Proof and Its Philosophical Ramifications
|Logic and Foundations; Logic and Foundations of Mathematics; Mathematics; Philosophy
|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.
|Godel’s Proof and Its Philosophical Ramifications