The ontological argument has run for a long time, regularly refuted, regularly re-appearing in a new form. Something can be learnt from its longevity. Its proponents must be on to something, or it would not have survived its many refutations. But equally, it must have been much misformulated, or it would not have seemed evidently fallacious to its many critics. Perhaps it does express a deep philosophical intimation. Certainly it has been taken to prove more than it really can establish. (...) Like many other philosophical arguments it has suffered by being made out to be more rigorous than in the nature of the case it can be. For some philosophers addressing some questions it may have been decisive in leading them to adopt one of the few options open to them: but it is quite inconclusive for others, with different presuppositions or different problems, and cannot be reduced into a valid proof cogent for all comers and compelling them to accept the conclusion it claims to demonstrate. (shrink)

The Modal Perfection Argument (MPA) for the existence of a Supreme Being is a new ontological argument that is rooted in the insights of Anselm, Leibniz and Gödel. Something is supreme if and only if nothing is possibly greater, and a perfection is a property that it is better to have than not. The premises of MPA are that supremity is a perfection, perfections entail only perfections, and the negation of a perfection is not a perfection. I do three things (...) in this paper. First, I prove that MPA is valid by constructing a formal deduction of it in second order modal logic. Second, I argue that its premises are true. Third, I defend the argument and the logic used against some likely objections. (shrink)

Anderson-like ontological proofs, studied in this paper, employ contingent identity, free principles of quantification of the 1st order variables and classical principles of quantification of the 2nd order variables. All these theories are strongly complete wrt. classes of modal structures containing families of world-varying objectual domains of the 1st order and constant conceptual domains of the 2nd order. In such structures, terms of the 1st order receive only rigid extensions, which are elements of the union of all 1st order domains. (...) Terms of the 2nd order receive extensions and intensions. Given a family of preselected world-varying objectual domains of the 2nd order, non-rigid extensions of the 2nd order terms belong always to a preselected domain connected with a given world. Rigid intensions of the 2nd order terms are chosen from among members of a conceptual domain of the 2nd order, which is the set of all functions from the set of worlds to the union of all 2nd order preselected domains such that values of these functions at a given world belong to a preselected domain connected with this world. (shrink)

We describe a KB Gödelian ontological system, and some other weak systems, in a fully formal way using theory of types and natural deduction, and present a completeness proof in its main and specific parts. We technically and philosophically analyze and comment on the systems (mainly with respect to the relativism of values) and include a sketch of some connected aspects of Gödel's relation to Kant.

The aim of this paper is to prove strong completeness theorems for several Anderson-like variants of Gödels theory wrt. classes of modal structures, in which: (i). 1st order terms order receive only rigid extensions in the constant objectual 1st order domain; (ii). 2nd order terms receive non-rigid extensions in preselected world-relative objectual domains of 2nd order and rigid intensions in the constant conceptual 2nd order domain.