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. 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 the theory in Studtmann’s paper can interpret the axioms of Peano Arithmetic minus the induction schema. This fact allows for the development of arithmetic in a natural way. The development eventuates in a theory that can interpret second-order arithmetic. The conception of God that emerges by the end of the discussion is a conception of an infinite, ineffable, self-cause that contains objects that not only serve as numbers but also encode information about each other.

中文翻译：

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上帝与数字

根据奥古斯丁的说法，抽象物体是上帝心中的想法。因为数字是一种抽象对象，所以数字就是上帝心中的想法。将这种观点称为“奥古斯丁数字观”（AVN）。在本文中，我提出了 AVN 的正式理论。该理论源于 Studtmann (2021) 中出现的上帝的对称概念。我证明了 Studtmann 论文中的理论可以解释皮亚诺算术的公理，而不需要归纳模式。这一事实使得算术能够以自然的方式发展。这一发展最终产生了一种可以解释二阶算术的理论。讨论结束时出现的上帝概念是一种无限的、不可言喻的、自因的概念，其中包含的物体不仅充当数字，而且还编码彼此的信息。