Two scientists believe that they have proven that God exists.
Analyzing a theorem from the late Austrian mathematician Kurt Gödel with a Macbook has proven that God exists, say the two scientists–Christoph Benzmüller of Berlin’s Free University and his colleague, Bruno Woltzenlogel Paleo of the Technical University in Vienna.
Gödel’s theorem is based on modal logic, a type of formal logic that, narrowly defined, involves the use of the expressions “necessarily” and “possibly,” according to Stanford University.
The theorem says that God, or a supreme being, is that for which no greater can be conceived. God exists in the understanding. If God exists in the understanding, we could imagine Him to be greater by existing in reality. Therefore, God must exist.
Paleo and Benzmüller say that they have proven that the theorem is correct, at least on a mathematical level.
In their initial submission on a research server, “Formalization, Mechanization and Automation of Gödel’s Proof of God’s Existence,” the pair say that “Goedel’s ontological proof has been analysed for the first-time with an unprecedent degree of detail and formality with the help of higher-order theorem provers.”
They add: “The following has been done (and in this order): A detailed natural deduction proof. A formalization of the axioms, definitions and theorems in the TPTP THF syntax. Automatic verification of the consistency of the axioms and definitions with Nitpick. Automatic demonstration of the theorems with the provers LEO-II and Satallax. A step-by-step formalization using the Coq proof assistant. A formalization using the Isabelle proof assistant, where the theorems (and some additional lemmata) have been automated with Sledgehammer and Metis.”
Benzmüller told Der Spiegel that it’s fascinating how the theorem could be analyzed through mathematics.
“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.
The mathematicians say that their proof of Gödel’s axioms has more to do with demonstrating how superior technology can help bring about new achievements in science.
“I didn’t know it would create such a huge public interest but (Gödel’s ontological proof) was definitely a better example than something inaccessible in mathematics or artificial intelligence,” Benzmüller said. “It’s a very small, crisp thing, because we are just dealing with six axioms in a little theorem. … There might be other things that use similar logic. Can we develop computer systems to check each single step and make sure they are now right?”
The scientists believe that their work can benefit areas such as artificial intelligence and the verification of software and hardware.