Enneads VI.6: Of Numbers
Unity, Though by Participation Existing in Sense-objects, Is Intelligible
Just as we predicate being of every sense-thing, as well as of every intelligible thing, we predicate it in a higher degree of intelligible things, attributing a higher degree (of substantiality) to the (beings that are veritable than to sense-objects), and to sense-objects than to other genera (of physical objects); likewise, clearly seeing unity in sense-objects in a degree higher than in the intelligible (essences), we recognize the existence of unity in all its modes, and we refer them all to Unity in itself. Besides, just as “being and essence” are nothing sensual, though sense-objects participate therein, so unity, though by participation it inhere in sense-objects, is not any the less an intelligible Unity. Judgment grasps it by an intellectual conception; by seeing one thing (which is sensual) it also conceives another which it does not see (because it is intelligible); it therefore knew this thing in advance; and if judgment knew it in advance, judgment was this thing, and was identical with that whose existence it asserted. When it says, “a certain” object, it asserts the unity, as, when it speaks of “certain” objects, it says that they are two or more. If then one cannot conceive of any object whatever without “one,” “two,” or some other number, it becomes possible to insist that the thing without which nothing can be asserted or conceived, does not at all exist. We cannot indeed deny existence to the thing without whose existence we could not assert or conceive anything. Now that which is everywhere necessary to speak and to conceive must be anterior to speech and conception, so as to contribute to their production. If, besides, this thing be necessary to the hypostatic existence of every essence—for there is no essence that lacks unity—it must be anterior to being, and being must be begotten by it. That is why we say “an essence” instead of first positing “essence,” and “a” only thereafter, for there must be “one” in essence, to make “several” possible; but (the converse is not true; for) unity does not contain essence, unless unity itself produce it by applying itself to the begetting of it. Likewise, the word “that” (when employed to designate an object) is not meaningless; for instead of naming the object, it proclaims its existence, its presence, its “being,” or some other of its kinds of “essence.” The word “that” does not therefore express something without reality, it does not proclaim an empty conception, but it designates an object as definitely as some proper name.
UNITY ONLY AN ACCIDENT IN SENSE-THINGS, BUT SOMETHING IN ITSELF IN THE INTELLIGIBLE.
14. As to those who consider unity as relative, they might be told that unity could not lose its proper nature merely as a result of the affection experienced by some other being without itself being affected. It cannot cease being one without experiencing the privation of unity by division into two or three. If, on being divided, a mass become double without being destroyed in respect to its being a mass, evidently, besides the subject, there existed unity; and the mass lost it because the unity was destroyed by the division. So this same thing which now is present, and now disappears, should be classified among essences wherever it be found; and we must recognize that, though it may be an accident of other objects, it nevertheless exists by itself, whether it manifest in sense-objects, or whether it be present in intelligent entities; it is only an accident in posterior (beings, namely, the sense-objects); but it exists in itself in the intelligible entities, especially in the first Essence, which is One primarily, and only secondarily essence.
TWO IS NOT AN ADDITION TO ONE, BUT A CHANGE (REFUTATION OF ARISTOTLE).
The objection that unity, without itself experiencing anything, by the mere addition of something else, is no longer one, but becomes double, is a mistake. The one has not become two, and is not that which has been added to it, nor that to which something has been added. Each of them remains one, such as it was; but two can be asserted of their totality, and one of each of them separately. Two therefore, not any more than “pair,” is by nature a relation. If the pair consisted in the union (of two objects), and if “being united” were identical with “to duplicate,” in this case the union, as well as the pair, would constitute two. Now a “pair” appears likewise in a state contrary (to that of the reunion of two objects); for two may be produced by the division of a single object. Two, therefore, is neither reunion nor division, as it would have to be in order to constitute a relation.
OBJECTS PARTICIPATE IN NUMBERS JUST AS THEY PARTICIPATE IN ALL INTELLIGIBLE ENTITIES.
What then is the principal cause (by virtue of which objects participate in numbers)? A being is one by the presence of one; double, because of the presence of the pair; just as it is white because of the presence of whiteness; beautiful, because of the presence of beauty; and just by that of justice. If that be not admitted, we shall be reduced to asserting that whiteness, beauty and justice are nothing real, and that their only causes are simple relations; that justice consists in some particular relation with some particular being; that beauty has no foundation other than the affection that we feel; that the object which seems beautiful possesses nothing capable of exciting this affection either by nature, or by acquirement. When you see an object that is one, and that you call single, it is simultaneously great, beautiful, and susceptible of receiving a number of other qualifications. Now why should unity not inhere in the object as well as greatness and magnitude, sweetness and bitterness, and other qualities? We have no right to admit that quality, whatever it be, forms part of the number of beings, whilst quantity is excluded; nor to limit quantity to continuous quantity, while discrete quantity is excluded from the conception of quantity; and that so much the less as continuous quantity is measured by discrete quantity. Thus, just as an object is great because of the presence of magnitude, as it is one by the presence of unity; so is it double because of the presence of being a pair, and so forth.
Should we be asked to describe the operation of the participation of objects in unity and in numbers, we shall answer that this question connects with the more general problem of the participation of objects in intelligible forms. Besides, we shall have to admit that the decad presents itself under different aspects, according as it is considered to exist either in discrete quantities, or in continuous quantities, or in the reduction of many great forces to unity, or, last, into the intelligible entities to which we are later raised. It is among them, indeed, that are found the veritable Numbers (spoken of by Plato,) which, instead of being considered as discovered in other (beings), exist within themselves; such is the Decad-in-itself, which exists by itself, instead of simply being a decad composed of some intelligible entities.