Gödel’s Paradigm: Finiteness vs Universality

A Discussion Inspired by Wittgenstein’s Critique of Gödel’s Incompleteness Theory

The signature of Kurt Gödel, from , edited by the author

Introduction

Rebecca Goldstein, a prominent American philosopher, wrote a book in 2006 about Gödel’s life and work titled Incompleteness: The Proof and Paradox of Kurt Gödel.

In the book, she examines Gödel’s revolutionary incompleteness theorems and their philosophical implications, while also exploring his biography, including his close friendship with Albert Einstein during their days at Princeton, and the broader intellectual landscape of his era.

The book is excellent, as is its subject matter. After reading it, I only noticed how complementary discussions around his theorems were slightly left aside. So I will offer here some insights into these discussions, which may help readers to grasp more fully, and I hope fairly, the consequences of Gödel’s theorems.

Einstein and Gödel

As Rebecca points out quite well in her book, Gödel was deeply unsatisfied with how his work was often misunderstood, much like Einstein’s frustration with the popular misinterpretations of his theory of relativity.