116. This theory does not make time a purely subjective condition, nor grant it a nature independent of things; it reconciles the pure intellectual order with the order of experience; and places man in communication with the real world, without creating a contradiction in his ideas.
[CHAPTER XVII.]
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 the wisest 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 term equal leads to the analysis of the term quantity: 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 exempt from 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.