God and the Numbers

Abstract

According to Augustine, abstract objects are ideas in the Mind of God. Because numbers are a type of abstract object, it would follow that numbers are ideas in the Mind of God. Let us call such a view the Augustinian View of Numbers (AVN). In this paper, I present a formal theory for AVN. The theory stems from the symmetry conception of God as it appears in Studtmann (2021). I show that Robinson’s Arithmetic, Q, can be interpreted by the theory in Studtmann’s paper. The interpretation is made possible by identifying the set of natural numbers with God, 0 with Being, and the successor function with the essence function. The resulting theory can then be augmented to include Peano Arithmetic by adding a set-theoretic version of induction and a comprehension schema restricted to arithmetically definable properties. In addition to these formal matters, the paper provides a characterization of the mind of God. According to the characterization, the Being essences that constitute God’s mind act as both numbers and representations – each has all the properties of some number and encodes all the properties of that number’s predecessor. The conception of God that emerges by the end of the discussion is a conception of an infinite, ineffable, axiologically and metaphysically ultimate entity that contains objects that not only serve as numbers but also encode information about each other.

Author's Profile

Paul Studtmann
Davidson College

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2021-12-16

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