Logical arguments for the existence of God go back a long way.

Fitting’s book [1] provides a higher-order modal logic formulation of such an argument, given by Kurt Gödel to Dana Scott. He also surveys emendations of the argument made by Anderson, Hajek, Sobel, and others.

This article works in such a logic with the additional property that the semantics is free; that is, any existence or identity requirements in the model have to be explicitly made. One of Anderson’s axioms says that if there is a godlike person, then any individual identical to (or different from) this person is necessarily so. The semantics of this is tricky, but the author shows that an adequate semantics exists. The paper is technical and will be of interest to specialists in modal logic.