6.6 (34) is largely about number, although the nominal subject is not number as such, but a question from Plato’s Parmenides 144A6–7, namely whether number can appear unlimited, without participating in being. The treatment of number concentrates on what numbers are, and how they play a role in cosmology.
§1 prepares the question about unlimited number, §2 then poses it. The problem is that, while all being is limited, someone counting can always produce another number; thus we are faced with unlimited beings, apparently. For numbers are not produced when counted, they are already in the unlimited. §3 raises the question of unlimitedness in itself.
§§4–16 form the core of the treatise, a discussion of the status of number. §§4–10 go back to the origin of number. §§11–14 deal with objections. §§15–16 provide Plotinus’ own position.
§4. The problem of the relation between numbers and Forms.
§5. One possible way of understanding number, namely, as an accident of things. But everything in the intelligible must be on its own account, hence numbers must be Forms too, which participate in other Forms. Then the question is how number plays a role in the structure of the intelligible. The clue to Plotinus’ answer to this question lies in the triad Being–Life–Thinking.
§6. The intelligible is Being, but also Intellect; and finally, it is a living being.
§§7–8. Number is attributed to Being, which moves in a unified and harmonious manner. Number thus permits the differentiation of beings, as it were as the rule governing the Forms when they come to govern individuals through the activity of Soul.
§9. The question of whether or not Being gives rise to number, or whether number divides Being. Plotinus distinguishes between Substantial Number and the number we count with; the latter is an image of the former.
§10. Analysis of counting: we have the number, and apply it to the thing counted, such that it is such and such a number.
§11. Against a Peripatetic objection, namely, that he is positing a unity which cannot be added up, and cannot compose numbers, Plotinus replies that number is in fact the unity of a multiplicity, and he goes on to explain how a multiplicity can become a unity through number.
§12. Plotinus responds to a Stoic view which makes number the affection of a soul, namely relative to the objects affecting it. But if number is an affection of the soul, it must be in the sensible, whereas in the end it relates back to a Form, as does an expressed principle in the sensible.
§13. He continues his criticism of the Stoics by arguing that unity can be neither an affection of the soul, nor a ‘sayable’, and hence only of a lesser status.
§14. In fact, neither the One nor Number is a relative.
§15. Plotinus’ account of Substantial Number: Beings are numbered, that is to say their essence is determined by Number, which constitutes them.
§16. Analysis of the distinction between the numbering number – Substantial Number – and the numbered number, the number we count with.
§§17–18. The final two chapters return to the original problem of unlimited being: number is not compatible with being unlimited, just as with lines and figures. But as with the intelligible, the limit here is internal to the thing itself, not imposed from outside, so there is no opposition to there being unlimited number.