Frode Alfson Bjørdal: "All Properties are Divine or God exists"
Abstract. A metaphysical system engendered by a third order quantiﬁed modal logic S5 plus impredicative comprehension principles is used to isolate a third order predicate D, and by being able to impredicatively take a second order predicate G to hold of an individual just if the individual necessarily has all second order properties which are D we in Section 2 derive the thesis (40) that all properties are D or some individual is G. In Section 3 theorems 1 to 3 suggest a suﬃcient kinship to Gödelian ontological arguments so as to think of thesis (40) in terms of divine property and Godly being; divine replaces positive with Gödel and others. Thesis (40), the sacred thesis, supports the ontological argument that God exists because some property is not divine. In Section 4 a ﬁxed point analysis is used as diagnosis so that atheists may settle for the minimal ﬁxed point. Theorem 3 shows it consistent to postulate theistic ﬁxed points, and a monotheistic result follows if one assumes theism and that it is divine to be identical with a deity. Theorem 4 (the Monotheorem) states that if Gg and it is divine to be identical with g, then necessarily all objects which are G are identical with g. The impredicative origin of D suggests weakened Gaunilo-like objections that oﬀer related theses for other second order properties and their associated diverse presumptive individual bearers. Nevertheless, in the last section we ﬁnesse these Gaunilo-like objections by adopting what we call an apathiatheistic opinion which suggest that the best concepts ‘God’ allow thorough indiﬀerence as to whether God exists or not.
On October 16th Frode Alfson Bjørdal (professor emeritus at The University of Oslo) presented a talk "All Properties are Divine or God exists" at the joint meeting of Logico-philosophical club and Formal philosophy group (HSE)
All Properties are Divine or God Exists - The Sacred Thesis and its Ontological Argument, first online in Logic and Logical Philosophy 2017.