All Properties are Divine or God exists

Logic and Logical Philosophy 3 (27):329-350 (2018)
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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.

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Frode Bjørdal
University of Oslo

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References found in this work

Semantical Considerations on Modal Logic.Saul Kripke - 1963 - Acta Philosophica Fennica 16:83-94.
The proper treatment of quantification in ordinary English.Richard Montague - 1973 - In Patrick Suppes, Julius Moravcsik & Jaakko Hintikka (eds.), Approaches to Natural Language. Dordrecht. pp. 221--242.
English as a Formal Language.Richard Montague - 1970 - In Bruno Visentini (ed.), Linguaggi nella societa e nella tecnica. Edizioni di Communita. pp. 188-221.
Completeness in the theory of types.Leon Henkin - 1950 - Journal of Symbolic Logic 15 (2):81-91.

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