an:00937367
Zbl 0859.03010
H??jek, Petr
Magari and others on G??del's ontological proof
EN
Ursini, Aldo (ed.) et al., Logic and algebra. Proceedings of the international conference dedicated to the memory of Roberto Magari, April 26--30, 1994, Pontignano, Italy. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 180, 125-135 (1996).
1996
a
03B45 03A05
comprehension axiom; completeness; G??del's proof of the existence of God
The paper is a continuation of the author's German ``Der Mathematiker und die Frage der Existenz Gottes'' [in: Buld et al. (eds.), Wahrheit und Beweisbarkeit -- Leben und Werk K. G??dels (to appear)]. Concerning G??del's Proof of the Existence of God it is shown:
1) Magari is not right in claiming that the first three axioms of G??del's are enough to prove the existence of a godlike being.
2) There are systems with full comprehension schema (Anderson's) for which Magari's claim holds.
3) Magari models can be strengthened to be adequate, completeness is shown.
4) It is sufficient to use a weaker logic than S5 (in fact: KD45).
For the entire collection see [Zbl 0846.00022].
U.Scheffler (Berlin)