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Gödel's ontological proof
From Wikipedia, the free encyclopedia
Gödel's ontological proof is a formal argument for God's existence by the mathematician Kurt Gödel. It is in a line of development that goes back to Anselm of Canterbury. St. Anselm's ontological argument, in its most succinct form, is as follows: "God, by definition, is that forwhich 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." A more elaborate version was given by Gottfried Leibniz; this is the version that Gödel studied and attempted to clarify with his ontological argument.
The first version of the ontological proof in Gödel'spapers is dated "around 1941". Gödel is not known to have told anyone about his work on the proof until 1970, when he thought he was dying. In February, he allowed Dana Scott to copy out a version of the proof, which circulated privately. In August 1970, Gödel told Oskar Morgenstern that he was "satisfied" with the proof, but Morgenstern recorded in his diary entry for 29 August 1970, that Gödelwould not publish because he was afraid that others might think "that he actually believes in God, whereas he is only engaged in a logical investigation (that is, in showing that such a proof with classical assumptions (completeness, etc.) correspondingly axiomatized, is possible)."[1] Gödel died January, 14 1978. Another version, slightly different from Scott's, was found in his papers. It wasfinally published, together with Scott's version, in 1987.[2]
Morgenstern's diary is an important and usually reliable source for Gödel's later years, but the implication of the August 1970 diary entry—that Gödel did not believe in God—is not consistent with the other evidence. In letters to his mother, who was not a churchgoer and had raised Kurt and his brother as freethinkers,[3] Gödel argued atlength for a belief in an afterlife.[4] He did the same in an interview with a skeptical Hao Wang, who said: "I expressed my doubts as G spoke [...] Gödel smiled as he replied to my questions, obviously aware that his answers were not convincing me."[5] Wang reports that Gödel's wife, Adele, two days after Gödel's death, told Wang that "Gödel, although he did not go to church, was religious and readthe Bible in bed every Sunday morning."[6] In an unmailed answer to a questionnaire, Gödel described his religion as "baptized Lutheran (but not member of any religious congregation). My belief is theistic, not pantheistic, following Leibniz rather than Spinoza."[7]
Gödel left a fourteen-point outline of his philosophical beliefs in his papers. Points relevant to the ontological proof include
4.There are other worlds and rational beings of a different and higher kind.
5. The world in which we live is not the only one in which we shall live or have lived.
13. There is a scientific (exact) philosophy and theology, which deals with concepts of the highest abstractness; and this is also most highly fruitful for science.
14. Religions are, for the most part, bad—but religion is not.[8]Contents [hide] * 1 The proof * 2 Modal logic * 3 Axioms * 4 Criticisms * 5 Derivation * 6 See also * 7 Notes * 8 References * 9 External links |
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[edit]The proof
Symbolically:

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[edit]Modal logic
The proof uses modal logic, which distinguishes between necessary truthsand contingent truths.
A truth is necessary if its negation entails a contradiction, such as 2 + 2 = 4; by contrast, a truth is contingent if it just happens to be the case, for instance, "more than half of the earth is covered by water". In the most common interpretation of modal logic, one considers "all possible worlds". If a statement is true in all possible worlds, then it is a necessary truth....
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