A new report at ABC News, “Computer scientists ‘prove’ God exists”, says that two German scientists using a MacBook have proven the existence of God. That’s the bad news. The good news is that it appears to be old news: that is, they have somehow mathematically formalized the ontological proof of God, which has always been known to be wrong, as channeled through Kurt Gödel, who had his own modal-logic proof of God resting on similar arguments.
In case you’ve forgotten this old chestnut, the ontological argument, first formulated by St. Anselm, runs like this (I give Wikipedia‘s characterization of Anselm’s argument, which resembles all the succeeding ones):
- Our understanding of God is a being than which no greater can be conceived.
- The idea of God exists in the mind.
- A being which exists both in the mind and in reality is greater than a being that exists only in the mind.
- If God only exists in the mind, then we can conceive of a greater being—that which exists in reality.
- We cannot be imagining something that is greater than God.
- Therefore, God exists.
The problem with this is that “existence” is not a quality of an object like beauty or size. There may be a most beautiful existing horse, if you define your notion of horse beauty in advance, but you can’t do the same thing for God, for, as the philosophers say, “existence is not a predicate.” Finding the most beautiful horse (“the God horse”) takes as a given that horses exist. Having an idea of something says absolutely nothing about whether it exists or not.
Using such arguments, one could “prove” the existence of many nonexistent things, like unicorns, fairies, or Santa (“a unicorn that exists in reality is greater than one that exists only in the mind.”
I was only dimly aware that Kurt Gödel had constructed a logical proof for the existence of God (read about it here), but that’s been criticized as well, though I don’t understand modal logic. All I know is that you simply can’t prove that something exists by logic alone.
But the two Germans seem to claim otherwise. As the ABC report notes:
When Gödel died in 1978, he left behind a tantalizing theory based on principles of modal logic — that a higher being must exist. The details of the mathematics involved in Gödel’s ontological proof are complicated, but in essence the Austrian was arguing that, by definition, God is that for which no greater can be conceived. And while God exists in the understanding of the concept, we could conceive of him as greater if he existed in reality. Therefore, he must exist.
Even at the time, the argument was not exactly a new one. For centuries, many have tried to use this kind of abstract reasoning to prove the possibility or necessity of the existence of God. But the mathematical model composed by Gödel proposed a proof of the idea. Its theorems and axioms — assumptions which cannot be proven — can be expressed as mathematical equations. And that means they can be proven.
That is where Christoph Benzmüller of Berlin’s Free University and his colleague, Bruno Woltzenlogel Paleo of the Technical University in Vienna, come in. Using an ordinary MacBook computer, they have shown that Gödel’s proof was correct — at least on a mathematical level — by way of higher modal logic. Their initial submission on the arXiv.org research article server is called “Formalization, Mechanization and Automation of Gödel’s Proof of God’s Existence.”
The fact that formalizing such complicated theorems can be left to computers opens up all kinds of possibilities, Benzmüller told SPIEGEL ONLINE. “It’s totally amazing that from this argument led by Gödel, all this stuff can be proven automatically in a few seconds or even less on a standard notebook,” he said.
Yes, it is amazing, and it surely must be wrong. (As always, I suspend judgment on God until the data are in, but that data cannot be purely logical). I kindly request some math-minded reader to find the arXiv paper and provide us with a brief analysis. The ABC article ends as follows:
Ultimately, the formalization of Gödel’s ontological proof is unlikely to win over many atheists, nor is it likely to comfort true believers, who might argue the idea of a higher power is one that defies logic by definition. For mathematicians looking for ways to break new ground, however, the news could represent an answer to their prayers.
I don’t get the last sentence at all. Why is this kind of mathematical trickery “breaking new ground”?