On Some Approaches of Applications of the Modal System S5

Abstract

It is presented in this article: 1) Lewis' modal system S5, and its Kripke's semantics, 2) the interpretations of the modal operators for the system S5, and for the weaker systems, 3) an application of the system S5 to formalization of the ontological argument. The following theses are established: 1) Kripke's semantics is a purely formal construction, and gives only axioms for the predicate „to be a valid modal formula”, 2) the correct interpretation of the modal operator L for the system S5 is following: „it is analytically that...”, 3) logical modality is concerning concepts, not real things, and understanding of the logical modality depends on a concept of philosophy, 4) Hartshorne's ontological argument is the proof only in a pragmatic sense.