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Gödel's Ontological Proof and its Variants

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    0361226 - UIVT-O 2012 RIV US eng M - Část monografie knihy
    Hájek, Petr
    Gödel's Ontological Proof and its Variants.
    Kurt Gödel and the Foundations of Mathematics: Horizons of Truth. Cambridge: Cambridge University Press, 2011 - (Baaz, M.; Papadimitriou, C.; V, H.; Scott, D.; Harper, C.), s. 307-321. ISBN 978-0-521-76144-4
    Grant CEP: GA AV ČR IAA100300503
    Výzkumný záměr: CEZ:AV0Z10300504
    Klíčová slova: ontological proof * Gödel
    Kód oboru RIV: BA - Obecná matematika

    In the early 1970s, we learned that Gödel had produced a proof of the existence of God after he showed it to Dana Scott, who discussed it in a seminar at Princeton. Notes began to circulate, and the first public analysis of the proof was performed by Sobel (1987). Only after Gödel's death, in the third volume of his collected works (Gödel, 1995), was the proof finally published. It is just one page, preceded by an extensive and very informative introduction by Adams (Gödel, 1995). The volume also contains notes from Gödel's Nachlass, dated 1940, containing his first drafts of the proof. Presently, there exist several papers on the topic, including two extremely interesting monographs (Sobel, 2004; Fitting, 2002). A very important variant of Gödel's system, resulting from the first criticisms made of it, was generated by Anderson (1990). Anderson's variant will play an important role in this chapter. Gödel is famous for his completeness and incompleteness theorems as well as for his work with set theory, so his ontological proof has never received the same attention. The proof belongs to the family of ontological arguments, that is to say, arguments that try to establish the existence of God by relying only on pure logic. Such arguments were presented by Anselm (1033–1109), Descartes (1598–1650), Leibniz (1646–1716), and others, and Gödel is known to have studied particularly Leibniz's works (the two books mentioned earlier are recommended for information on the old ontological proofs and their relation to Gödel's proof).
    Trvalý link: http://hdl.handle.net/11104/0198591
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