an:06748779
Zbl 1417.03153
Kanckos, Annika; Woltzenlogel Paleo, B.
Variants of G??del's ontological proof in a natural deduction calculus
EN
Stud. Log. 105, No. 3, 553-586 (2017).
00366739
2017
j
03B45 03F03 03A05
ontological argument; higher-order logics; modal logics; natural deduction
Summary: 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 G??del'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 \textbf{KB} instead of \textbf{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 Bj??rdal's variants of the ontological argument, which are known to be immune to modal collapse.