Book 4 — ON THE ONE.

PROPOSITION I.

All multitude participates in a certain respect of the one.

For if it in no respect participates of the one, neither will the whole be one whole, nor each of the many from which the multitude is composed: but each of these will also be multitude, and this will be the case in infinitum; and each of these infinites will again be infinite multitude. For if it in no respect participates of the one, neither according to its whole self, nor according to each of its parts, every where, and throughout there will be infinite multitude. For each of these manys, which ever you assume, will either be one or not one, will either be multitude or nothing. But if each of these manys be nothing, that which is composed from them shall also be nothing. But if each be many, then each shall consist from infinite infinites. But these consequencies are impossible. Since no being is composed from infinite infinities[101]. For there is nothing greater than infinite. But that which is constituted from all is greater than each particular. Nor can any thing be composed from nothing. All multitude therefore participates in a certain respect of the one.

PROPOSITION II.

Every thing which participates of the one, is both one and not one.

For if it be not the one itself (αὐτοὲν) (since it participates of the one) because it is something different from the one, it suffers the one, by participation, and sustains itself to become one. If then it be nothing else besides the one, it is one alone, and does not participate of the one, but is the one itself. But if it be something different from the one, which is not the one, but its participant, it is both not one and one, not indeed the self-subsisting one, but one being, as participating of the one itself. This then is neither one, nor does it subsist as the one, but it is one being, at the same time participating of the one, and on this account, since it is not the self-subsisting one, it is both one and not one, because it is something different from the one. For so far as it abounds it is not one; but so far as it is passive from participation, it becomes one. Every thing therefore which participates of one, is both one, and not one.

PROPOSITION III.

Every thing which becomes one, becomes so through the participation of one; and is one, so far as it suffers the participation of one.

For if things which are not one, become one, it must be by a conjunction, and communication with each other: and they will sustain the presence of one, without being one itself. Hence they will participate one, so far as they suffer themselves to become one. For if they are already one, they will not become one: since that which is, does not become that which it already is. But if they are formed from non-one, and privation, they will in the first place possess one, from some one, being ingenerated in their nature.

PROPOSITION IV.

Every thing united, is different from the one itself.

For if it is united it will participate of one, so far as it is called united. And that which participates of one is both one, and non-one. But one itself, is by no means one and non-one. For if this also was both one and non-one, the one which it contains will also possess both, and this in infinitum; since there is no one itself in which the progression can stop; but every thing will be both one and non-one. That which is united therefore is something different from one. For if that which is united was the same with one, one would be infinite multitude; and in like manner each of the parts from which the united nature is composed.

PROPOSITION V.

All multitude is posterior to the one itself.

For if multitude is prior to the one, the one indeed will participate of multitude, but the multitude which is prior to the one, will not participate of the one: since it is multitude prior to the subsistence of the one. For it cannot participate that which is not: because that which participates of the one, is both one and non-one. But the one does not yet subsist, since multitude is the first. It is however impossible, that there should be any multitude, which in no respect participates of the one. Multitude therefore is not prior to the one. But if multitude subsists together with the one, it will be of the same order with the one: for time cannot hinder such a conjunction. Hence neither the one can be essentially many, nor multitude one, because they are at the same time contra-distinguished; since neither is prior, or posterior to the other. Multitude therefore will not be essentially one, and every thing it contains will be a non-one, and this in infinitum, which is impossible. Hence it naturally participates of the one, nor can any part of it be assumed which is not one: for if any part is not one, it will be an infinite composed from infinites, as we have demonstrated. And hence it entirely participates of the one. But if the one which is one itself, in no respect participates of multitude, multitude will be perfectly posterior to the one; participating indeed of the one, but not participated by the one. But if the one should participate of multitude in such a manner as to exist as one according to subsistence, but as not one according to participation; the one itself will be multiplied, in the same manner as multitude is united by the one. Hence the one will communicate with multitude, and multitude with the one. But things which coalesce, and communicate after a manner with each other, if they are congregated by something else, that something must have a prior existence. But if they connect themselves, they are not opposed to each other: for opposites do not hasten to a mutual conjunction. But if the one, and multitude have a contrary division, and multitude, so far as multitude, is not one, and the one so far as one, is not multitude; hence the one cannot subsist in the other: for they would be at the same time both one and two. But if there be any thing prior to the one, and multitude which collects them into one, this will either be one, or non-one. And if non-one, it will either be many, or nothing. But it is not many; lest multitude should be prior to the one. Nor is it nothing: for how can that congregate which is nothing? Hence it is the one alone. For this one is not also many, lest we should advance in an infinite progression. It is therefore the one itself; and all multitude proceeds from the one.