Kurt Gödel
Faith and Science
Reflections on Kurt Gödel’s Mathematical and Scientific.
Perspective of the Divine: A Rational Theology
Hector Rosario, Ph.D. Department of Mathematical Sciences, University of Puerto Rico, Mayaguez Campus December 9, 2006
Abstract: Kurt Gödel had a profound rational theology. Gödel was not only a theist, but a personalist and a believer in the afterlife. I will explore his philosophical stance through exchanges with Albert Einstein and others to understand how such a foremost mathematician and physicist held such views. I will also address Gödel’s ontological argument.
Kurt Gödel, the preeminent mathematical logician of the twentieth century, is best known for his celebrated Incompleteness Theorems; yet he also had a profound rational theology worthy of serious consideration. “The world is rational,” (Wang, 1996: 316) asserted Gödel, evoking philosophical theism, “according to which the order of the world reflects the order of the supreme mind governing it” (Yourgrau, 2005: 104-105).
Gödel’s “Incompleteness Theorems” are an “extraordinary comment on the relationship between the mission of mathematics and the manner in which it formulates its deductions” (Mazur, 2006: 3-4). They have been interpreted as a limitation on rationality, since a possible semantics for the results is that, in any axiomatic and consistent system capable of doing arithmetic, there are truths that cannot be proved within the system. This has very profound philosophical implications that shattered the hopes of many a previous mathematician and philosopher, including thinkers of the stature of David Hilbert, Bertrand Russell, and Ludwig Wittgenstein. Frustration notwithstanding, “[Gödel’s] works on the limits of logic have inspired awe, respect, endless development and speculation among mathematicians, and indeed among all theoretical scientists” (Davis, 2002: 22).
Among the theoretical scientists influenced by Gödel was his friend Albert Einstein. Between the years 1940 and 1955 they developed an intimate relationship as colleagues at the Institute for Advanced Study in Princeton. According to colleague Oskar Morgenstern, the co-founder of Game Theory, when Einstein had lost enthusiasm for his own work, he went to his office “just to have the privilege of walking home with Kurt Gödel” (Wang, 1996: 57). Indeed, according to Institute colleague and physicist Freeman
Dyson (the discoverer of combinatorial proofs of Ramanujan’s famous partition identities), Gödel was “the only one who walked and talked on equal terms with Einstein” (Dyson, 1993: 161). However, I would argue that Gödel’s intellect was in many ways subtler than Einstein’s, in philosophy and perhaps even in physics.
God and Gödel
As his correspondence with Burke D. Grandjean attests, Gödel was a self-confessed theist, going as far as developing an ontological argument in an attempt to prove the existence of God. He chose the framework of modal logic, a useful formal language for proof theory, which also has important applications in computer science (Blackburn, de Rijke & Venema, 2001). This logic is the study of the deductive behavior of the expressions ‘it is necessary that’ and ‘it is possible that,’ which arise frequently in ordinary (philosophical) language. However, according to his biog rapher John Dawson, he never published his ontological argument for fear of ridicule by his peers.
An important aspect of Gödel’s theology – one that has been greatly overlooked by those studying his works – is that not only was he a theist but a personalist; not a pantheist as some apologetic thinkers may portray him. To be precise, he rejected the notion that God was impersonal, as God was for Einstein. Einstein believed in “Spinoza’s God who reveals Himself in the harmony of all that exists, not in a God who concerns Himself with the fate and actions of men” (Einstein, 1929). Gödel in turn thought “Einstein’s religion [was] more abstract, like Spinoza and impersonalist philosophy. Spinoza’s god is less than a person; mine is more than a person; because God can play the role of a person” (Wang, 1996: 152). This is significant since a God who lacks the ability to “play the role of a person” would obviously lack the property of omnipotence and thus violate a defining property universally accepted as pertaining to God. Therefore if God existed, reasoned Gödel, then He must at least be able to play the role of a person. The question for Gödel was how to determine the truth value of the antecedent in the previous statement.
A relevant issue in Gödel’s discussions on the Divine with Einstein is his mention of “Indian philosophy.” Gödel considers Spinoza’s concept of God and the Advaitavada impersonalist concept to be in the same category, which is not a correct understanding of these notions. Spinoza’s stance on God is impersonal, akin to Sankaracarya’s monism (c. 788-820 CE). Unfortunately, although familiar with such Sankara’s view, Gödel was apparently unaware of the philosophical conclusions of Ramanujacarya (10171137 CE) and Madhavacarya (1238-1317 CE), who would also reject Spinoza’s God. The rejection comes not because they deny God’s presence in all that exists, but because such view is considered subservient to one in which a personal relationship with the Supreme can be established and nurtured. Taking omnipotence seriously, “playing the role of a person” is one of God’s unlimited potencies which these sages do not compromise in their theology.
Certainly, Gödel was also unaware of the philosophy of Caitanya Mahaprabhu (1486-1534 CE), who follows Ramanujacarya and Madhavacarya in the essential points. However, the detailed description and practice of divine love in service of purusottama –devotional service to the Supreme Person – given by Caitanya Mahaprabhu and his followers arguably make this a subtler and more revealing theology than those presented by his predecessors. In it Gödel would have found his theological conclusions realized in completion five centuries earlier.
Gödel’s Philosophy of Physics
In physics, Gödel’s contributions are well-known. However, physics was not a detour Gödel took to amuse himself, but rather an essential part of his philosophical fabric. In 1949 Gödel expressed his ideas in an essay that in Einstein’s own words, “constitutes […] an important contribution to the general theory of relativity, especially to the analysis of the concept of time” (Schilpp, 1949: 687). Unfortunately, even with Einstein’s high estimation of Gödel’s work, modern physicists have been wont to discard Gödel’s ideas, trying (without success) to find an error in his physics (Yourgrau, 2005: 7-8).
Gödel’s unsuspected solutions to the field equations of general relativity, solutions in which time undergoes a peculiar transformation, made the discussion of time-travel respectable in scientific circles. In fact, Gödel concluded that time travel is indeed theoretically possible, rendering time, as we know it, meaningless. Time, “that mysterious and seemingly self-contradictory being,” as Gödel put it, “which, on the other hand, seems to form the basis of the world’s and our own existence,” turned out in the end to be the world’s greatest illusion (Yourgrau, 2005: 111). For Gödel, time was a crucial philosophical question, but I am unaware of any direct connection Gödel might have made between time and God. However, his belief in the afterlife might give some insight into how he understood the relationship between them. Gödel expressed his belief in the hereafter in the following terms, “I am convinced of the afterlife, independent of theology. If the world is rationally constructed, there must be an afterlife” (Davis, 2002: 22). “His arguments were, as always, rationally based on the principle that the world and everything in it has meaning, or reasons. This is closely related to the causality principle that underlies all of science: Everything has a cause, and events don’t just ‘happen’” (Casti & DePauli, 2000: 87).
Mathematics, Science, and Faith
An ultra-rationalist like Gödel was a theist, a personalist and a believer in the afterlife, and he appealed to reason as his witness. Atheists and agnostics usually portray their philosophy as rational, discarding the theist conclusion as a mere psychological refuge of the ignorant or self-deceiving. Nevertheless, ultra-rational thinkers like Gödel, Leibniz,and Descartes have reached the theist conclusion. Is there an apparent disconnect between rational thinkers and rational thought, or is it that the theists’ view is the rational conclusion, even if often embraced by fanatics in unimaginably irrational ways? An objector may argue that