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ANSELM’S ONTOLOGICAL ARGUMENT AND GRADES OF BEING

Part of: Philosophical aspects of logic and foundations

Published online by Cambridge University Press:  13 September 2024

CHARLES McCARTY
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Abstract

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.

Keywords

ontological argumentAnselmDescartesBoolean valued models

MSC classification

Primary: 03A05: Philosophical and critical
Type
Research Article
Information
The Review of Symbolic Logic , Volume 17 , Issue 3 , September 2024 , pp. 635 - 653
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of The Association for Symbolic Logic

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Footnotes

†

Deceased

References

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