sdi: Photograph of the title page of Plotinus' "The Six Enneads." (enneads)
[personal profile] sdi

This was a very valuable tractate to me, I think, clarifying a lot of the moving pieces in Plotinus' cosmology and helping to see how they all fit together. It's another one I recommend in full, though I imagine it's not very accessible without first having read a lot of the others: Porphyry says he placed the more difficult essays later in the text, and that seems the case to me as well.

VI 6: On Numbers

We have elsewhere expressed a definite ordering of principles: the One, the Intellect, the Soul, etc., and there we stated that the Intellect was dual. This must imply that Number transcends the Intellect, for how can something be "dual" before there is "two?" Consequently we must assume that Number is latent within the One, and the Intellect is the expression or unfolding of Number. That is to say, the Intellect is the reflection of Number, and each Idea is the reflection of a particular number.

This is why number is such a slippery thing: if you have ten objects, those are merely objects; they each exist due to their participation in Being, and they each have their own unity due to their participation in the One. But when we count them, it is we who are making the statement: the objects each have their individual existences, but the ten exists within our minds, which is itself a reflection of the true Ten in the Intellect. You have given Life to that ten by counting them, but if you had merely been content with your own Being, resting within your own unity, you wouldn't have been counting anything! So while Number has true existence (in the One), knowledge of Number is a lesser thing (in the Intellect), and the process of working with Number is a lesser thing still (in the Soul).

What of "infinity?" We take it that the Intellect is limitless in scope, and that all numbers must exist there; but it is not possible to count them up, since individual souls must be limited by whatever number is involved in their composition. Thus infinity exists, but you cannot, say, count to it.

Plotinus uses the term "henad" a lot in this tractate, and by it he just means a reflection of the One at a given level of existence: the One is the original henad (and, of course, the henad at its own level of existence), the Intellect is the henad of the Intellectual level of existence, the Soul is the henad of the Psychic level of existence, etc. But of course, the whole universe is reproduced at each level from this henad—at least, in the best way that henad is able. Indeed, even individual souls are the henad of the microcosmic universe within, which is the basis of Plotinian mysticism: it is why you can look within yourself to find the All. Nowadays we might simply say that the cosmos is fractal at all scales.

This principle is usually stated in Neoplatonism as "All is in all, but each in a manner appropriate to each." This formulation is commonly cited from Proclus (Elements of Theology CIII) but is due to Porphyry (Sentences X, but be advised that many manuscripts badly mangle it: hence, for example, Thomas Taylor's translation is nonsensical). §7 contains the principle in Plotinus' own words.

I had been wondering about Turing Machines and Oracle Machines before. It's nice to see Plotinus directly answer my questions in §18.

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