194. As a universal criterion, there is more exactness in the common formula than in that of Kant. The latter restricts the principle to the relation of predicate and subject, and consequently to the purely ideal order, making it of no value for the real, unless by a sort of enlargement. This enlargement, although legitimate and easy, is not needed in the common formula: by saying being excludes not-being, we embrace the ideal and the real, and present to the mind the impossibility, not only of contradictory judgments, but also of contradictory things.
Kant admits that the principle is the condition sine qua non of the truth of our cognitions, so that we must take care not to place ourselves in contradiction with it, under pain of annihilating all cognition. Let us put this to the proof. Give a man, unacquainted with these matters, although not ignorant of what is meant by predicate and subject, these two formulas; which will appear to him the best for all uses in the external as in the internal? Certainly not that of Kant. He sees in an instant, in all its generality, that a thing cannot both be and not be at the same time; and he applies the principle to all uses as well in the real as in the ideal order. Treating of an external object, he says, this cannot both be and not be at the same time; treating of contradictory judgments, of ideas which exclude one another, he says, without any difficulty, this cannot be, because it is impossible for the same thing to be and not be at the same time. But it is not so easily and so readily seen how transition is made from the ideal to the real order, or how the purely logical ideas of predicate and subject can be used in the order of facts. The common formula, then, besides being fully as exact as that of Kant, is more simple, more intelligible, and more easy of application. Are there any qualities more desirable than these in a universal criterion, in the condition sine qua non of the truth of our cognitions?
195. We have thus far supposed Kant's formula really to express the principle of contradiction; but this supposition is far from being exact. Undoubtedly there would be a contradiction, were a predicate opposed to a subject, and yet to belong to it; and in this sense it may be said that the principle of contradiction is in some manner expressed in Kant's formula. But this is not enough; for we should then be obliged to say that every axiom expresses the principle of contradiction, since no axiom can be denied without a contradiction. The formula of the principle must directly express reciprocal exclusion, opposition between being and not-being; this is what was intended, and nothing else was ever meant by the principle of contradiction. Kant, in his new formula, does not directly express this exclusion: what he expresses is, that when the predicate is excluded from the idea of the subject, it does not belong to it. So far from expressing the principle of contradiction, it is the famous principle of the Cartesians: "whatever is contained in the clear and distinct idea of any thing may be affirmed of it with all certainty." In substance the two formulas express the same thing, and are only distinguished by these purely accidental differences: first, that Kant's formula is the more concise; second, that it is negative, and that of the Cartesians affirmative.
196. Kant says: "whatever is excluded from the clear and distinct idea of any thing, may be denied of it." A predicate which is opposed to a subject "is the same thing as that which is excluded from the idea of any thing;" "does not belong to it" is the same as "may be denied of it." And as, on the other hand, the principle of the Cartesians must be understood in both senses, the affirmative and the negative, because when they say that whatever is contained in the clear and distinct idea of any thing may be affirmed of it, they mean also that when any thing is excluded, it may be denied; it follows that Kant says the same thing as the Cartesians; and thus, in attempting to correct all the schools, he has fallen into an equivocation not of a nature to acquire him any great credit for perspicacity.
It is clear that Kant's formula implies this: the predicate contained in the idea of a subject belongs to it. This condition is equally the condition sine qua non of all analytic affirmative judgments; for these disappear if that does not belong to the subject which is contained in its idea. In this case there is not even an apparent difference between Kant's formula and that of the Cartesians; the only difference is in terms; the propositions are exactly the same. Hence we see that instead of affirming that the schools expressed themselves inaccurately in the clearest and most fundamental point of human knowledge, we ought to proceed with great circumspection; witness the originality of Kant's formula.
197. The author of the Critic of Pure Reason was not more fortunate in censuring the condition, at the same time, which is generally added to the formula of the principle of contradiction. Since he took the liberty of believing that no philosopher before himself had expressed this formula in the proper manner, we beg to say that he did not himself well understand what the others intended to express, and we do not, in saying this, deem ourselves guilty of a philosophical profanation. If Kant is an oracle for certain persons, all philosophers together and all mankind are also oracles to be heard and respected.
According to Kant, the principle of contradiction is the condition sine qua non of all human cognitions. If, then, this condition is to serve as their object, it must be so expressed as to be applicable to all cases. Our cognitions are not composed solely of necessary elements, but admit, to a great extent, ideas connected with the contingent; since, as we have seen, purely ideal truths lead to nothing positive, unless brought down to the ground of reality. Contingent beings are subject to the condition of time, and all cognitions relating to them must always depend on this condition. Their existence is limited to a determinate space of time; and it is necessary to think and speak of it conformably to this determination. Even their essential properties are in some manner affected by the condition of time; because if abstracted from it, and considered in general, they are not as they are when realized; that is, when they cease to be a pure abstraction, and become something positive. Here, then, is the reason, and a very profound and cogent reason, why all the schools joined the idea of time to the formula of the principle of contradiction: the reason, we repeat, is very profound, and it is strange how it escaped the German philosopher's penetration.
198. The importance of this subject requires still further explanation. What is essential to the principle of contradiction, is the exclusion of being by not-being, and of not-being by being. The formula must express this fact, this truth, which is presented by immediate evidence, and is contemplated by the intellect in a most clear intuition, admitting neither doubt nor obscurity of any kind.
The word being may be taken in two senses: substantively, inasmuch as it signifies existence; and copulatively, as it expresses the relation of predicate to subject. Peter is: here the verb is signifies the existence of Peter, and is equivalent to this: Peter exists. The equilateral triangle is equiangular: here the verb is is taken copulatively, since it is not affirmed that any equilateral triangle exists; merely the relation of equality of angles to equality of sides is established absolutely, abstraction made from the existence of either.
The principle of contradiction must extend to the cases in which being is copulative, and to those in which it is substantive; for when we say it is impossible for the same thing to be and not be, we speak not only of the ideal order, or of the relations between predicates and subjects, but also of the real order. Were no reference made to this last, we should hold the entire world of existences to be deprived of this indispensable condition of all cognitions. Moreover this condition is not only necessary to every cognition, but also to every being in itself, abstracting its being known, or being intelligent. What would a being be that could both be and not be? What is the meaning of a contradiction realized? The principle must extend to the word being, not only as copulative, but also as substantive. All finite existences, our own included, are measured by a successive duration; therefore, if the formula of the principle of contradiction is to be applicable to whatever we know in the universe, it must be accompanied by the condition of time. All finite things, which now exist, at one time did not exist, and it may again be true that they do not exist. Of no one can it be truly said that its non-existence is impossible; this impossibility springs from existence in a given time, and can only be asserted with respect to that time. Therefore, the condition of time is absolutely necessary in the formula of the principle of contradiction, if this formula is to serve for the existent, that is, for that which is the real object of our cognitions.
199.