ANSELM'S ONTOLOGICAL ARGUMENT AND GRADES OF BEING

Anselm described god as "something than which nothing greater can be thought" [1, p. 93], and Descartes viewed him as "a supreme being" [7, p. 122]. I first capture those characterizations formally in a simple language for monadic predicate logic. Next, I construct a model class inspired by Stoic and medieval doctrines of grades of being [8, 20]. Third, I prove the models sufficient for recovering, as internal mathematics, the famous ontological argument of Anselm, and show that argument to be, on this formalization, valid. Fourth, I extend the models to incorporate a modality fit for proving that any item than which necessarily no greater can be thought is also necessarily real. Lastly, with the present approach, I blunt the sharp edges of notable objections to ontological arguments by Gaunilo and by Grant. A trigger warning: every page of this writing flouts the old saw "Existence is not a predicate" and flagrantly.