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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).
In the early 1970s, Gödel circulated among his friends an elaboration of Leibniz's version of Anselm of Canterbury's ontological proof of God's existence. This is now known as Gödel's ontological proof .
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 ...
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). St.
Kurt Gödel created a formalization of Leibniz' version, known as Gödel's ontological proof. [1] A more recent argument was made by Stephen D. Unwin in 2003, who suggested the use of Bayesian probability to estimate the probability of God's existence. [2]
Gödel shows that many properties of these proofs can be defined within any theory of arithmetic that is strong enough to define the primitive recursive functions. (The contemporary terminology for recursive functions and primitive recursive functions had not yet been established when the paper was published; Gödel used the word rekursiv ...
Thus one can define the Gödel number of a proof. 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
It was first proved by Kurt Gödel in 1929. It was then simplified when Leon Henkin observed in his Ph.D. thesis that the hard part of the proof can be presented as the Model Existence Theorem (published in 1949). [2] Henkin's proof was simplified by Gisbert Hasenjaeger in 1953. [3]