Studia Logica 105 (3):553-586 (2017)

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Abstract
This paper presents detailed formalizations of ontological arguments in a simple modal natural deduction calculus. The first formal proof closely follows the hints in Scott’s manuscript about Gödel’s argument and fills in the gaps, thus verifying its correctness. The second formal proof improves the first one, by relying on the weaker modal logic KB instead of S5 and by avoiding the equality relation. The second proof is also technically shorter than the first one, because it eliminates unnecessary detours and uses Axiom 1 for the positivity of properties only once. The third and fourth proofs formalize, respectively, Anderson’s and Bjørdal’s variants of the ontological argument, which are known to be immune to modal collapse.
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DOI 10.1007/s11225-016-9700-1
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References found in this work BETA

Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.
A Formulation of the Simple Theory of Types.Alonzo Church - 1940 - Journal of Symbolic Logic 5 (2):56-68.
A Formulation of the Simple Theory of Types.Alonzo Church - 1940 - Journal of Symbolic Logic 5 (3):114-115.
A Logical Journey. From Gödel to Philosophy.Hao Wang - 1998 - Philosophy 73 (285):495-504.

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