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Gödel's ontological proof is a formal argument by the mathematician Kurt Gödel (1906–1978) for the existence of God. The argument is in a line of development that goes back to Anselm of Canterbury (1033–1109).
Gödel believed that God was personal, [47] and called his philosophy "rationalistic, idealistic, optimistic, and theological". [48] He formulated a formal proof for the existence of God known as Gödel's ontological proof.
In Spinoza's Short Treatise on God, Man, and His Well-Being, he wrote a section titled "Treating of God and What Pertains to Him", in which he discusses God's existence and what God is. He starts off by saying: "whether there is a God, this, we say, can be proved". [27] His proof for God follows a similar structure as Descartes' ontological ...
Therefore, the question of God's existence may lie outside the purview of modern science by definition. [27] The Catholic Church maintains that knowledge of the existence of God is the "natural light of human reason". [28] Fideists maintain that belief in God's existence may not be amenable to demonstration or refutation, but rests on faith alone.
Gödel's original proofs of the incompleteness theorems, like most mathematical proofs, were written in natural language intended for human readers. Computer-verified proofs of versions of the first incompleteness theorem were announced by Natarajan Shankar in 1986 using Nqthm ( Shankar 1994 ), by Russell O'Connor in 2003 using Coq ( O'Connor ...
Moreover, one may define a statement form Proof(x,y), which for every two numbers x and y is provable if and only if x is the Gödel number of a proof of the statement S and y = G(S). Proof(x,y) is in fact an arithmetical relation, just as "x + y = 6" is, though a much more complicated one.
During his lifetime three English translations of Gödel's paper were printed, but the process was not without difficulty. The first English translation was by Bernard Meltzer; it was published in 1963 as a standalone work by Basic Books and has since been reprinted by Dover and reprinted by Hawking (God Created the Integers, Running Press, 2005:1097ff).
Gödel's proof may refer to: Gödel's incompleteness theorems; Gödel's ontological proof; See also: Gödel's theorem (disambiguation) This page was last edited on 19 ...