Although the simultaneousness may not be expressed in the principle of contradiction, it is always understood, so that we should gain nothing by adopting Kant's formula.[33] In whatever terms the principle may be enunciated, it is always true that the same thing cannot both be and not be at the same time, but may very well be at one time and not be at another time.

The idea of time is therefore necessary in order that the contradiction may follow in some cases, and disappear in others. If the time implies simultaneousness, it generates the contradiction; if it implies succession, it destroys the contradiction; because being and not-being are impossible, unless we presuppose a successive duration, among the different parts of which, things that would otherwise be contradictory are distributed.

119. The idea of time also presupposes the principle of contradiction; for, if time, in things, is only being and not-being, and in the intellect, the perception of this being and not-being; we cannot perceive time without having perceived being and not-being; and as these ideas, without succession, involve a contradiction, we must perceive the principle of contradiction when we perceive time. I have said that succession implies the mutual exclusion of the things which succeed; now, the first exclusion is the principle of contradiction: in perceiving time, we perceive succession; therefore we have already perceived the contradiction.

120. These remarks might incline us to believe it necessary to choose between a vicious circle, which is inadmissible in the foundation of all our knowledge, and an explanation of time, independently of being and not-being. If we conceived time as existing by itself, as a sort of line prolonged to infinity; as a form of things, but distinct from them all; as a vague capacity in which successive beings might be placed, just as we situate co-existences in space,—then the idea of time would not be explained by the principle of contradiction, and we could only say that it was completed by it. "When we say that it is impossible for the same thing to be and not be at the same time, but that it is possible for the same thing to be and not be at different times, the contradiction is affirmed or taken away, accordingly as the being and not-being are referred to the same point or to different points in this vague extension, this infinite line, which we call successive duration, and in which we conceive changeable things to be distributed." This explanation is convenient; but it has a defect, that it cannot stand a philosophical examination, as we have seen in the preceding chapters. We must therefore have recourse to another class of considerations.

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.

125. A and not-A imply contradiction; but not so that they absolutely cannot be realized. The exclusion is conditional; that is, it exists as long as the contradictory extremes are simultaneous, or referred to an indivisible now; but we discover no intrinsic necessity of existence in the idea of A: consequently, although we know that while A is, not-A cannot be, we can very well conceive that A may cease to be, and not-A may begin to be. There is, in, that case, no contradiction, and we can easily reconcile in our mind the two ideas of A and not-A, by referring them to different instants.

126. Hence the perception of time implies the perception of beings that are not necessary,—of beings which, when they exist, may cease to exist, and when they do not exist, may begin to exist. The difference between necessary and contingent being is, that the existence of the former absolutely excludes its non-existence, while the existence of the latter excludes its non-existence only conditionally, or on the supposition of simultaneousness.