(Christian) theology as mathesis universalis

The Spinozist heresy is to have violated the hierarchy of the Aristotelian categories: God is not one being among many but Being itself. But there is more than one way to blur the ontological difference, i.e., as many ways as there are to count. There is, for example, the dialectic of the one and the nothing in Neoplatonic mathematics by which infinite progression telescopes to the one. It was the Christians, however, who taught us how to count directly from one to three: “we do not say that union is begotten from oneness or from equality of oneness, since union is not from oneness either through repetition or through multiplication. And although equality of oneness is begotten from oneness and although union proceeds from both [of these], nevertheless oneness, equality of oneness, and the union proceeding from both are one and the same thing …” (Cusanus).

The trinity is not only an ontological but a mathematical mystery: the simplicity and unicity of God is also the unicity of order. God is not only the infinite geometer, according to Plutarch, but infinitely arithmetizes; creation proceeds not from the word but from the number. “Number was the principal exemplar in the mind of the creator”, Boethius says (long before Leibniz’ “divine mathematician”), which is in itself a substance to which no other substance is joined (which is thus how number is then the measure of all things but not of itself). The echoes of Neoplatonic mathematics are clear: the unity of a being is at once its limit.

Cusanus gives us a clue to the passage from the ontological to the mathematical: “God is the being of things; for He is the Form of things and, hence, is also being”. For Plotinus, being consists of emanation from the one. Cusanus, however, following Thierry of Chartes (who was himself inspired by Boethius), introduces the concept of the fold into philosophy and mathematics:

a point is the enfolding of a line as oneness is the enfolding of a number. For anywhere in a line is found nothing but a point, even as in number there is nowhere found anything but oneness … Movement is the unfolding of rest, because in movement there is found nothing but rest. Similarly, the now is unfolded by way of time, because in time there is found nothing but the now.

All of these are images of the enfoldings of the Infinite Simplicity; in other words, Cusanus explains divine simplicity as nothing other than the enfolding of all things. Since, moreover, divine simplicity is the infinite mind, such that the thought of the divine mind is the creation of all things, our thought is an image of the eternal unfolding, hence guaranteeing the unity of thought and being.

The fold places multiplicity at the heart of being such that “God is so one that He is, actually, everything which is”. Cusanus is explicit in denying that oneness is number, “for number, which can be comparatively greater, cannot at all be either an unqualifiedly minimum or an unqualifiedly maximum. Rather, oneness is the beginning of all number, because it is the minimum; and it is the end of all number, because it is the maximum”. This proposition supports the paradoxes of De Docta Ignorantia: the coincidence of the absolute maximum and minimum and the assertion that “if there were an infinite line, it would be a straight line, a triangle, a circle, and a sphere” (so too Cusanus invokes an image of the divine trinity as a triangle whose angles are all right angles). More importantly, like Conway’s notion of the “intimate presence” of God to all creatures (“without any increase” in their being), the union of oneness and multiplicity folds all things in the divine without reducing being to the being of the divine (God is not-other). Against the Aristotelian convertibility of being and unity, then, Platonism in mathematics asserts not the being of number but the subordination of being to number. “The whole of nature is akin” (Meno 81d) only if the being of beings proceeds from the equality of one to one.