Gödel’s Proof, the Pope, and the problem of fundamentalism
The peripatetic 20th century logician Kurt Gödel formulated a theorem that closed, internally consistent, systems are incomplete regarding their own truth:
For any consistent formal theory that proves basic arithmetical truths, it is possible to construct an arithmetical statement that is true but not provable in the theory. That is, any theory capable of expressing elementary arithmetic cannot be both consistent and complete.
“Any theory….cannot be both consistent and complete.” This is, in a way, the issue that the Pope dealt with in his famous talk that caused such controversy in the Islamic world. The Pope, in the address that we have discussed, said that we can judge whether something is Godly or not by whether it is reasonable. In other words, Reason gives us a means to stand outside the allegedly “consistent and complete” system of religion and judge God. The Pope said:
[A]s far as understanding of God and thus the concrete practice of religion is concerned, we are faced with an unavoidable dilemma. Is the conviction that acting unreasonably contradicts God’s nature merely a Greek idea, or is it always and intrinsically true? I believe that here we can see the profound harmony between what is Greek in the best sense of the word and the biblical understanding of faith in God…
[T]he emperor also knew the instructions…recorded in the Qur’an, concerning holy war…[H]e addresses his interlocutor…on the central question about the relationship between religion and violence in general, saying: “Show me just what Mohammed brought that was new…such as his command to spread by the sword the faith he preached.” The emperor…goes on to explain in detail the reasons why spreading the faith through violence is something unreasonable. Violence is incompatible with the nature of God and the nature of the soul. “God”, he says, “is not pleased by blood – and not acting reasonably is contrary to God’s nature.”
The Pope framed the problem this way: In Christianity, God’s commandments have to pass the smell test of human Reason. “But for Muslim teaching, God is absolutely transcendent. His will is not bound up with any of our categories, even that of rationality.” This is the central issue of our time.
Fundamentalist movements and beliefs share a common flaw. While they may possess the appearance of being “consistent and complete” systems, they give up something terribly important about being human in order to do so — because, as Gödel said, they can’t really be both consistent and complete at the same time. This goes for fundamentalist Islam, pacifist Catholicism, as well as Marxism, feminism and the Church of Liberalism. At the present moment, as we have written, there are two social pathologies on a collision course — the Worst of the East versus the Worst of the West. The greatest achievement of modern man — the emergence of Reason as the arbiter of human affairs — hangs in the balance. If Reason is not victorious, we face a thousand years of darkness.
Special fun bonus
Since this piece has been such a downer, we offer a bright spot that we discovered this morning — Gödel’s mathematical formulation of Anselm of Canterbury’s Ontological Argument. Enjoy!