RELATIONS OF THE IDEA OF TIME AND THE PRINCIPLE OF CONTRADICTION.
117. Let us explain the true meaning of the principle of contradiction. "It is impossible for any thing to be and not be at the same time." The connection of the ideas contained in this principle seems at first sight to be explained without any difficulty; so that, to raise questions as to its true sense is to place ourselves in contradiction with one of the fundamental truths on which rests the edifice of our knowledge. For, if there be any doubt as to the true meaning of the principle, it may be understood in several ways, and then there will be another doubt as to whether the generality of men understand it as they ought to, and whether, consequently, it is for them a solid foundation of knowledge.
This difficulty ceases to be one when we reflect that the most evident axioms may be considered in two manners: empirically, or scientifically; or in other words, inasmuch as they are the application, or the object of analytical examination. In the first manner, they are equally certain and equally clear to all men; in the second, they are subject to difficulties. The principle,—things equal to a third are equal to each other,—considered empirically, is absolutely certain and evident to all men: all men, from thewisest to the most ignorant, compare things with a third, when they wish to ascertain their equality or inequality; this is only an application of the principle. If you ask them the reason of this proceeding, although they may not enunciate the axiom in its precise terms, they refer to it in different ways: "These two tables are equal, because I have measured them, and they are each four feet square." Probably the generality of men, not accustomed to reflect on their knowledge, would not express the principle in universal and precise terms; as, "These two tables are equal, because they have a common measure, and things equal to a third are equal to each other." Yet they are just as clearly certain of the principle, and apply it, without any danger of error, in all real and possible cases. This is what I call the empirical knowledge of principles,—a knowledge which is perfect in the direct order, and is defective only in the reflex order.[32]
It is very easy to reconcile the difficulty in the analysis of the principle, with its clearness when applied to ordinary purposes, or to those of science. Thus, in the example given, the analysis of the termequalleads to the analysis of the termquantity: reflection can discover in this difficulties which, although they do not disturb mankind in the possession of truth, are difficulties notwithstanding. Geometry is undoubtedly a science perfectly evident and certain; but who can deny that the idea of extension presents serious difficulties, when examined before the tribunal of metaphysics? Universal arithmetic is, beyond all doubt, a science; yet the ideas of quantity and number, which are indispensable to it, give rise to the most abstruse questions of metaphysics and ideology. In general, it may be said that there is no branch of our knowledge which is exemptfrom difficulties, considered in its root; but these difficulties, arising from reflection, do not in any way lessen the certainty of direct knowledge.
Hence it is no objection that the analysis of the principle of contradiction presents difficulties; nor are we therefore to fear for the firmness of the edifice of our knowledge. It would be of no service to us not to attend to these difficulties, if they really existed; a difficulty does not vanish because we shut our eyes so as not to see it. Let us not, therefore, vainly fear to examine the true sense of the principle of contradiction.
118. It seems that this principle either does not exist, or has no meaning, unless we presuppose the idea of time; and, on the other hand, we cannot conceive time, unless we presuppose the principle of contradiction. Do we thus fall into a vicious circle, and this too in the fundamental principle of all our knowledge? This is a difficulty which I shall first develop and present more clearly.
The principle of contradiction presupposes the idea of time, because there would be no contradiction if being and not-being were not referred to the same time. This last condition is altogether indispensable; for, suppressing the simultaneousness, there is no contradiction in a thing both being and not-being. Not only is there no contradiction in this, but it is a thing which we constantly meet with, in every thing around us. We see being and not-being in things which pass from existence to non-existence, or from non-existence to existence.
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 isalways 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 forthe 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 ofvicious circleis 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 explainingthe 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 asimul, 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 indivisiblenow; 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 thetwo 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.
127. This is why the principle of contradiction requires the condition of time. The objects which we perceive are changeable; there is nothing either in their nature or in their modifications which involves existence. If they are, they may cease to be; and if this change does not constantly occur in their substance, it does in their accidents. Therefore we cannot affirm the absolute, but only the conditional contradiction of their being and not-being; it exists only on the supposition of simultaneousness.
128. If we conceived only necessary being, we could have no idea of time: its existence absolutely excludes its non-existence, and therefore the contradiction would be always absolute, never conditional.
129. A most important consequence results from this analysis. The perception of time with us implies the perception of the non-necessity of things. When we perceive a being which is not necessary, we perceive a being which may cease to be, in which case we have the idea of succession, of real or possible time. Here another reflection arises which is also important: the idea of time is the idea of contingency: the consciousness of time is the consciousness of our weakness.
130. The idea of time is so deep in our mind, that without it we could not form the idea of theme. The consciousness of the identity of themesupposes a link[34]which it is impossible to find without memory. Memory necessarily involves the relation ofpast, and, consequently, the idea of time.