Formalization, Mechanization and Automation of Gödel's Proof of God's Existence
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 [12,13] is a modern culmination of this tradition, following particularly the footsteps of Leibniz. 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 and by several philosophers who commented on his proof (cf. [19,2,11,1,10]). Dana Scott’s version of Gödel’s proof [18] employs the following axioms (A), definitions (D), corollaries (C) and theorems (T), and it proceeds in the following order: