Since then both number and unity are incompatible with the relation of identity, it must lie in something that is neither of them. But to tell the truth, at first sight this seems utterly impossible. Betwixt unity and number there can be no medium; no more than betwixt existence and non-existence. After one object is supposed to exist, we must either suppose another also to exist; in which case we have the idea of number: or we must suppose it not to exist; in which case the first object remains at unity. To remove this difficulty, let us have recourse to the idea of time or duration. I have already observed,[4] that time, in a strict sense, implies succession, and that, when we apply its idea to any unchangeable object, 'tis only by a fiction of the imagination by which the unchangeable object is supposed to participate of the changes of the co-existent objects, and in particular of that of our perceptions. This fiction of the imagination almost universally takes place; and 'tis by means of it that a single object, placed before us, and surveyed for any time without our discovering in it any interruption or variation, is able to give us a notion of identity. For when we consider any two points of this time, we may place them in different lights: we may either survey them at the very same instant; in which case they give us the idea of number, both by themselves and by the object; which must be multiplied in order to be conceived at once, as existent in these two different points of time: or, on the other hand, we may trace the succession of time by a like succession of ideas, and conceiving first one moment, along with the object then existent, imagine afterwards a change in the time without any _variation_ or _interruption_ in the object; in which case it gives us the idea of unity. Here then is an idea, which is a medium betwixt unity and number; or, more properly speaking, is either of them, according to the view in which we take it: and this idea we call that of identity. We cannot, in any propriety of speech, say that an object is the same with itself, unless we mean that the object existent at one time is the same with itself existent at another. By this means we make a difference betwixt the idea meant by the word _object_, and that meant by _itself_, without going the length of number, and at the same time without restraining ourselves to a strict and absolute unity. Thus the principle of individuation is nothing but the _invariableness_ and _uninterruptedness_ of any object, through a supposed variation of time, by which the mind can trace it in the different periods of its existence, without any break of the view, and without being obliged to form the idea of multiplicity or number.