Continuing with my theme of extracting mathematics from theological study, I now turn my attention to a subject of particularly mathematical interest: divine infinity. Happily, there have been a few intrepid souls who have examined the ideas of various Saints on the subject, and I will be reporting on some of their ideas. It will turn out, as I hope to show, that the concept of divine infinity is inextricably bound in the Western tradition with divine incomprehensibility and divine simplicity, so if God wills, this examination may actually prove helpful for putting into context just what the West means by these concepts.
To begin, we turn to Arkadi Choufrine's analysis of Clement in Gnosis, Theophany, Theosis, Chapter III. Choufrine notes that the attribution of infinity in the sense of apeiron (lit. without limit) to the highest metaphysical principle is often thought to begin with Plotinus, as Plato considered the term pejorative, reflecting the thought that things were good to the extent they were limited by form. Having no limit, no form, was therefore not a characteristic that would have been considered desirable in Greek metaphysics.
In endorsing a kind of infinity, later authors drew on pre-Socratic insight for their ideas, and in particular, on the problem of infinity as examined in Plato's Parminides. In distinction from Plotinus, however, Clement introduces an original idea by bringing in a separate concept from Aristotle, that of the unending end, in place of Plato's infinity of multiplicity ("And so the one, if it is, must be infinite in multiplicity? Clearly."). Plato's concept really captures the basic Greek prejudice that formless things are inferior. The basic line of the Clementine response is this. An infinity of the sort when steps are reached and surpassed is impossible for Aristotle (and rightly so, I should imagine), but an infinity in which the end is never achieved (the unending end, an asymptotic progression) is not. This corresponds to what Aristotle calls an infinite magnitude, and Aristotle uses this term interchangeably with Plato's term for infinity of parts. In this case, the infinite is still technically without parts, as the end is not included within the asymptotic series, but it is not without limit (apeiron) in the sense of having no limit whatsoever (as opposed to having no self-limiting principle). This allows Clement to conceive of the "magnitude of Christ" as a bridge to the infinite, that which is spanned in divinization.
With respect to the Father's own infinity, Clement adheres relatively closely also to Plato's presentation of apeiron, but with one major difference: he rejects the idea that a multiplicity of parts is necessary for wholeness (which is logical, since Aristotle has shown the ability to use the same term without requiring the parts/limits to actually be included in the thing itself, overriding the default Greek prejudice), and on this account, concludes that infinity can then be inferred directly from indivisibility into parts (adiastaton). This equation of infinity and simplicity at least foreshadows (if not anticipates) the usage of infinity in several later Christian authors, as I hope to show soon. With the addition of infinite magnitude of the monad allowing a bridge between the infinity of the One (the Father) and the monad (Christ), Clement has managed to circumvent the rather notorious problem of how the One can be truly infinite, in the sense of apeiron, without being entirely inaccessible to multiplicity or motion, in that Aristotle's concepts of the unending end and infinite magnitude show how both can be truly infinite (apeiron) while still being distinct and in intimate relation with one another. Plotinus, apparently lacking the insight from Aristotle, ends up having to resort to one or another subordinationist solution (as indeed, Middle Platonists were wont to do even among Christians, leading to struggles with subordination as evident in Justin Martyr, Origen, et al.).
I suspect that the Stoic influence on Clement had some bearing on his receptivity to this solution. Clement was a fan of the concept of logos spermatikos, particularly in the context of the wisdom of God delivered to man, and it may be that this concept of Christ as the end of a process implanted in creation helped his receptivity to the Aristotelian concept of infinity.
It is difficult to say how much direct influence Clement had on his successors in this regard. With Augustine, it was probably little, but the common threads of influence (particularly Aristotelian and Stoic) appear to emerge in Augustine's own original synthesis. Origen seems to be more rigorously Platonic, although there are certainly shades of these ideas in Origen's notion of apokatastasis, particularly its relationship with paidagagos (thinking of the divine process as received teaching, much like Clement's idea of wisdom as logos spermatikos dropped down onto humanity). Gregory of Nyssa is a more likely candidate for direct adoption of Clement's ideas, something a parallel discussion of his doctrine of infinity should illustrate. In any event, Clement's own views illustrate a parallel concept of divine infinity and simplicity distinct from that of Plotinus and Origen within the Christian tradition. Confusion of the two can lead to misguided charges of "Origenism," but I believe that a rigorous survey of historical development supports the thesis that the Clementine and Plotinian ideas are independent of one another. I will argue, therefore, that the essential concept of Clement (i.e., that of an unending progress toward an end of infinite magnitude) will appear over and over again in Christian history and, furthermore, that this represents an orthodox solution to the problem of the One and the Many, parallel to the Neoplatonic solution adopted by Pseudo-Dionysius and more thoroughly Christianized by St. Maximus Confessor.
