Can the existence of God be proven through a mathematical theorem?
Austrian mathematician Kurt Gödel, who died in 1978, came up with a theorem that used modal logic to prove the existence of a higher being, but some are more enthusiastic about the implications the proof has on technological possibilities, Spiegel Online reported.
Researchers claim they have "proven" Gödel's formula. The mathematician argued "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," Spiegel reported.
Gödel went on to use a mathematical proof to necessity of the existence of a Supreme Being. The proof converts "theorems and axioms" which cannot be proven, to mathematical formulas which can be.
Christoph Benzmüller of Berlin's Free University and Bruno Woltzenlogel Paleo of Vienna's Technical University used an ordinary MacBook to show Gödel's proof works.
"Attempts to prove the existence (or non-existence) of God by means of abstract ontological arguments are an old tradition in philosophy and theology. Gödel's proof is a modern culmination of this tradition, following particularly the footsteps of Leibniz," the researchers wrote in their arXiv.org submission.
"Gödel defines God as a being who possesses all positive properties. He does not extensively discuss what positive properties are, but instead he states a few reasonable (but debatable) axioms that they should satisfy. Various slightly different versions of axioms and definitions have been considered by Gödel's and by several philosophers who commented on his proof," they wrote.
The researchers believe their work could help advance artificial intelligence and take some of the burden off mathematicians. They hope using such an attention-grabbing example will also shine the light on the useful computation method.
"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 method could also be used to verify hardware and software.
