Plotinos: Complete Works, v. 3 / In Chronological Order, Grouped in Four Periods

by Plotinus

THE NUMBER WITHIN IS THE NUMBER CONSTITUTIVE OF OUR BEING.

In what sense does the number which is within us (before we enumerate) have a mode (of existence) other (than the one we produce in enumeration)? Because it is the number constitutive of our being, which, as Plato says,[40] participates in number and harmony, and is a number and harmony; for the soul is said to be neither a body nor an extension; she therefore is a number, since she is a being. The number of the body is a being of the same nature as the body; the number of the soul consists in the beings which are incorporeal like souls. Then, for the intelligible entities, if the animal itself be plurality, if it be a triad, the triad that exists in the animal is essential. As to the triad which subsists, not in the animal, but in essence, it is the principle of being. If you enumerate the animal and the beautiful, each of these two in itself is a unity; but (in enumerating them), you beget number in yourself, and you conceive a certain quantity, the pair. If (like the Pythagoreans) you say that virtue is a group of four, or tetrad, it is one so far as its parts (justice, prudence, courage, and temperance) contribute to the formation of a unity; you may add that this group of four, or tetrad, is a unity, so far as it is a kind of substrate; as to you, you connect this tetrad with the one that is inside of you.[41]

HOW A NUMBER MAY BE CALLED INFINITE.[42]

17. As the reasons here advanced would seem to imply that every number is limited, we may ask in which sense may a number be said to be infinite? This conclusion is right, for it is against the nature of number to be infinite. Why do people then often speak of a number as infinite? Is it in the same sense that one calls a line infinite? A line is said to be infinite, not that there really exists an infinite line of this kind, but to imply the conception of a line as great as possible, greater than any given line. Similarly with number. When we know which is the number (of certain objects), we can double it by thought, without, on that account, adding any other number to the first. How indeed would it be possible to add to exterior objects the conception of our imagination, a conception that exists in ourselves exclusively? We shall therefore say that, among intelligible entities, a line is infinite; otherwise, the intelligible line would be a simple quantative expression. If however the intelligible line be not this, it must be infinite in number; but we then understand the word "infinite" in a sense other than that of having no limits that could not be transcended. In what sense then is the word "infinite" here used? In the sense that the conception of a limit is not implied in the being of a line in itself.

INTELLIGIBLE LINE POSTERIOR TO NUMBER, AND EXISTS IN THE INTELLIGIBLE.

What then is the intelligible line, and where does it exist? It is posterior to number[43]; for unity appears in the line, since this starts from the unity (of the point), and because it has but one dimension (length); now the measure of dimension is not a quantative (entity). Where then does the intelligible Line exist? It exists only in the intelligence that defines it; or, if it be a thing, it is but something intellectual. In the intelligible world, in fact, everything is intellectual, and such as the thing itself is. It is in this same world, likewise, where is made the decision where and how the plane, the solid, and all other figures are to be disposed. For it is not we who create the figures by conceiving them. This is so because the figure of the world is anterior to us, and because the natural figures which are suitable to the productions of nature, are necessarily anterior to the bodies, and in the intelligible world exist in the state of primary figures, without determining limits, for these forms exist in no other subjects; they subsist by themselves, and have no need of extension, because the extension is the attribute of a subject.

THE INTELLIGIBLE SPHERICAL FIGURE THE PRIMITIVE ONE.

Everywhere, therefore, in essence, is a single (spherical) figure,[44] and each of these figures (which this single figure implicitly contained) has become distinct, either in, or before the animal. When I say that each figure has become distinct, I do not mean that it has become an extension, but that it has been assigned to some particular animal; thus, in the intelligible world, each body has been assigned its own characteristic figure, as, for instance, the pyramid to the fire.[45] Our world seeks to imitate this figure, although it cannot accomplish this, because of matter. There are other figures here below that are analogous to the intelligible figures.

FIGURES PRE-EXIST IN THE INTELLIGIBLE.

But are the figures in the living Organism as such, or, if it cannot be doubted that they are in the living Organism, do they anteriorly exist in the Intelligence? If the Organism contained Intelligence, the figures would be in the first degree in the Organism. But as it is the Intelligence that contains the Organism, they are in the first degree in Intelligence. Besides, as the souls are contained in the perfect living Organism, it is one reason more for the priority of the Intelligence. But Plato says,[46] "Intelligence sees the Ideas comprised within the perfect living Organism." Now, if it see the Ideas contained in the perfect living Organism, Intelligence must be posterior to the latter. By the words "it sees" it should be understood that the existence of the living Organism itself is realized in this vision. Indeed, the Intelligence which sees is not something different from the Organism which is seen; but (in Intelligence) all things form but one. Only, thought has a pure and simple sphere, while the Organism has an animated sphere.[47]