A Formal Reading of Leibniz’s Cosmological Argument

Abstract

In this paper the cosmological argument of Gottfried-Wilhelm Leibniz is revisited. We propose an interpretation of the argument as being an argument based on the structure of the logical space of all abstract facts. For this we view Leibnizian philosophy as providing a picture theory of language. This structure is given by the metaphysical foundations of Leibnizian philosophy: Leibniz’s theory of truth in the form of praedicatum inesse subiecto, the Principle of Sufficient Reason and the distinction between necessary and contingent facts. The theory of truth is interpreted as being provided by a formal calculus of abstract concepts in the sense of Edward Zalta. The other metaphysical requirements are also briefly discussed. Using these the structure on logical space is realised by an antisymmetric, transitive relation which admits arbitrary joins. Such a relation must admit a minimum, which is interpreted as the existence of God. This interpretation entails the difficulties of explicating existence in Leibniz’s metaphysics, which are also discussed.