121. To solve this difficulty, it is necessary to determine precisely the meaning of our ideas. The expression of _vicious circle_ is improperly applied to this case. If we understand this, the whole difficulty is solved at once. In explaining things, which are not identical, a circle is a defect, and is called vicious; but when two things are identical at bottom, although they appear distinct, because presented under various aspects, it is impossible to explain one without stumbling, so to speak, on the other, or to approach one without meeting the other. Because they are presented under different aspects we are led to believe them distinct; but examining them analytically, we abstract the difference of aspect, and penetrate to the reality, and discover the point where they are united, or, rather, where they are absolutely identified. 122. We may draw from these observations a criterion which we may use in a great many cases. When, in explaining two objects, we find ourselves led alternately from the one to the other, without any possibility of avoiding a circle, we may suspect that objects, which appear distinct, are not so in reality, and that the objects presented to the eyes of our understanding are not two objects, but only one object perceived in different ways. 123. This is true in the present instance. In explaining the principle of contradiction we encounter the idea of time, and in defining time we encounter the principle of contradiction, or the ideas of being and not-being. This is a circle, but an inevitable one; and therefore it ceases to be vicious. 124. What is the meaning of the principle of contradiction? Its true meaning is, that being excludes not-being, and not-being excludes being; that the nature of these conceptions is such that the affirmation of one implies the negation of the other, not only in the order of our ideas, but in reality. Let us call A any being whatever: the principle of contradiction means that A excludes not-A, and not-A excludes A. If we think A, the conception of not-A disappears; and if we think not-A, the conception of A disappears. If we affirm A in reality, we deny not-A, and if we affirm not-A in reality, we deny A. This is the true meaning of the principle of contradiction. If we reflect, we shall find that, as far as possible, we have abstracted the idea of time; for we have only considered the mutual exclusion of A and not-A, in reference to a _simul_, an indivisible point of duration, which, involving no succession, does not give us the idea of time. I said, _as far as possible_; because as soon as we think A and not-A, the idea of succession, and consequently of time, arises in our mind.