Kurt Friedrich Gödel is one of the most outstanding mathematical logicians of the twentieth century, best known for his Incompleteness Theorem. Kurt Gödel’s seminal works include the completeness of first-order logic, the consistency of the axiom of choice and of the generalized continuum-hypothesis, as well as other axioms: set theory, decision problem, intuitionism and notions of computability.
As a child, Gödel was exceptionally inquisitive. At about the age of four, Gödel acquired the nickname “Der Herr Warum” (Mr. Why) because he persistently asked “unanswerable” questions. Gödel advanced rapidly through school, excelling in mathematics, languages, and religion at a German high school in Brno. By the age of seventeen, he had mastered the university level mathematics. In 1930, he received his doctorate in mathematics with his dissertation providing the completeness theorem for first-order logic. In the very next year, Gödel published his work of incompleteness theorem that brought him worldwide recognition. The implications of his incompleteness theorem are vast, applying not only to mathematics but also touching on areas such as computer science, economics, physics, philosophy, and epistemology. John von Neumann, Princeton’s “human calculator,” in a speech given in 1951 when Gödel received the Einstein Award, remarked: “Kurt Gödel’s achievement in modern logic is singular and monumental – indeed it is more than a monument, it is a landmark which will remain visible far in space and time.”
From 1943, after his great success in logic, Gödel was chiefly occupied with philosophy and metaphysics. When he was at Princeton University, Albert Einstein was one of his closest friends. Like Einstein, he too expressed that the interaction between science and philosophy was fruitful for both fields. His project in philosophy was to find an exact theory of metaphysics. Gödel characterized his philosophical outlook in the following way: (i) “My theory is a monadology with a central monad [namely, God]. It is like the monadology by Leibniz in its general structure. (ii) My theory is rationalistic, idealistic, optimistic, and theological.”
An important aspect of Gödel’s theological work shows that was he was not only a theist but a personalist. He rejected the notion that God was impersonal, as thought by Einstein. He remarked, “Einstein’s religion [was] more abstract, like Spinoza and Indian philosophy. Spinoza’s God is less than a person; mine is more than a person; because God can play the role of a person”. Gödel argued in private discussions that a system of postulates could be phrased for notions such as “God” and the “soul”. Based on this far-reaching rational belief he attempted to formalize Anselm’s ontological proof of the existence of God. The proof was less than a page long, which caused quite a stir when circulated among his colleagues in the early 1970s. While reading his correspondence and conversations, we come across Gödel’s discussions on deeper aspects of reality such as afterlife, theological world-view, time, mathematical intuition, mind and matter. These explanations link a familiar and fundamental human concern with more or less abstract philosophical deliberations. In one of his letters, Gödel writes, “we not only don’t know where we came from and why we are here, we also don’t know what we are …. But if we could once look deeply enough within ourselves with scientific methods of self-examination in order to answer this question, it would probably turn out … with quite definite characteristics.”
Indeed there is growing attention to Gödel’s work due its relevance for the increasingly widespread computer applications. However, it could point towards other aspects of reality, just like Einstein’s work, as expressed by Gödel himself, “…Einstein’s discoveries in the first place made the atom bomb possible, is an erroneous comprehension. … but the essence of his work lies in an entirely other direction.” Hao Wang, who was in close contact with Gödel in his last years, made a similar statement about the connection between Gödel’s work and computers. In his book “Reflections on Kurt Gödel”, Hao Wang remarked, “The ‘entirely other direction’ is fundamental theory, which constituted the (central) purpose of life for both Gödel and Einstein”.