As we enter into the mystery of the One-and-the-Many, things begin to get more complicated. Even from Wikipedia, it is obvious (apart from the caveat that Iamblichus did not “introduce” any “notions” at all) that Iamblichus is essentially creating a parallel system that in many ways is similar to Christianity. This is why Julian the Apostate admired him so much, and why Porphyry disagreed with him so vehemently (Porphyry thought that purely notional contemplation ought to suffice for attaining divinization). From his doctrine of the One-and-the-Many, to his insistence that the lower types of men need physical theurgy, to his peopling the cosmos with various divinities and powers that are subject to Number, Iamblichus’ world highly resembles that of the Church Fathers.
He introduces his doctrine of Dyad:
“So each thing and the universe as a whole is one as regards the natural and constitutive monad, but again each is divisible, in so far as it necessarily partakes of the material dyad as well. Hence the first conjunction of monad and dyad results in the first finite plurality, the element of things, which would be a triangle of quantities and numbers, both corporeal and incorporeal. For just as the sap of a fig tree congeals liquid milk because of its active and productive property, so when the unificatory power of the monad approaches the dyad, which is the fount of flowing and liquidity it instills limit and gives form (ie., number) to the triad. For the triad is the source in actuality of number, which is by definition a system of monads. But in a sense, a dyad is like a monad on account of being like a source.”
The Dyad (therefore) is the Feminine Principle; in relation to the Monad, She is passive, as matter is to God. However, in relation to what comes after, by her productive powers, she is the Fount or Center of things, like a Monad, because in her Life originates (and multiplicity is created). This gives a good idea of the sophistication of Iamblichus’ thought: “opposition” to the Monad (for him) doesn’t mean resistance or lack of submission, but (precisely) submission through being opposite, or complementary – in other contexts (the material realms) it is the Dyad that takes on the characteristics of the Monad: the Queen stands in the place of the King (one can’t help but think of this doctrine, at this point).
I am not arguing that he is a pseudo-Christian, but rather that both Iamblichus and the Church Fathers were partaking of the same divine pattern, even (and up to) the particular manifestations of it at that time and place in history: see this article (for instance) as to how theosis and henosis differ, and how they do not. It might not be going too far to say that Iamblichus’ teachings represent a possible locus for reconciling paganism with Christianity (by purifying paganism and refining Christianity), thus creating the possibility of “white” theurgy.
These possibilities arise from the subtlety of Iamblichus’ method & manner of dealing with the One-And-The-Many, as he unfolds a doctrine of the Dyad (II – 2). Rather than posit a merely crude opposition, he shows how the Dyad is both Isis & Ison, Equal and Unequal, Generator and Destroyer.
2, mathematically, is composed of 1s, and is therefore (from arithmetic linear) a Greater or Non-Equal. When viewed as a plane (2 squared), it becomes a Lesser, since 2 itself is less than 4. The undoubted metaphysical conclusion is that the Dyad contains elements of being both Greater and Lesser within it. This is an example of the kind of paradox that Iamblichus is seeking. The number 3 (as we will see) is the first truly diverse equal (1 is equal to itself, but is not diverse): 1+2 = 3, so that the preceding sequence of numbers added together is equal to the number itself. This is not true when we come to 4: 1+2+3 does not equal 4 (Iamblichus will draw conclusions from this, as well).
The Dyad has special properties (also) because 2+2 = 4, which is the same as 2 taken to the plane (2 squared). This is the only number like this. The Dyad is another Monad (being a 1 added to a 1), but the Monad does not generate this truth of equality between arithmetic and plane extension.
Yet in another sense the Dyad cannot create a plane figure, because two angles don’t construct a plane figure: so the Triad is anticipated – it alone can create planar figures. The Dyad, on the other hand, can construct infinity, in a sense, because it can create a line running from a point, indefinitely, in two dimensions. This line may, or may not, return to its Origin.
The Dyad, therefore, is not to be mistaken for the original Monad, despite its functioning in relation to other numbers as a Monad itself. This is because the Monad stands alone – if, therefore, the Monad stands alone as Unity, something else has to take its place as the new principle of Unity to give unity to the other numbers. The Dyad, therefore, becomes “Monadic” towards the other numbers.
Numbers, therefore, inculcate the appreciation of metaphysical truths, such as the interplay between Microcosm and Macrocosm: the Moon or the Queen can become or stand in place of the Original Unity, precisely because of the primal unity of the One. Opposition can not exist, except to reinforce the One.