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. Let us now see what happens in the purely ideal order, where the word being is taken copulatively. Propositions of the purely ideal order are of two classes; in the first, the subject is a generic idea, which, by the union of the specific difference, becomes a determinate species; in the second, the subject is this determinate species, or the generic idea joined with the difference. The word angle expresses the generic idea comprehending all angles, which, united with the corresponding difference, constitutes the species of acute, obtuse, or right angle. At every step we modify the generic idea in various ways, and as a succession, in which are represented to us distinct conceptions, all having for their basis the generic idea, necessarily enters into it, it follows that we consider this idea as a being which is successively transformed. To express this succession, which is purely intellectual, we employ the idea of time; and here is one of the reasons which justify the use of this condition even in the purely ideal order. Thus we say, an angle cannot at the same time be both a right angle and a not-right angle; for the idea of angle may be successively determined by the difference which constitutes it a right angle, and a not-right angle; but these determinations cannot co-exist even in our conception, for which reason we do not assert the union of the difference with the genus to be absolutely impossible, but limit the impossibility to the condition of simultaneousness.
In this proposition, a right angle cannot be obtuse; the subject is not the generic idea alone, but is united with the difference expressed by the word right. In the conception formed of these two ideas, right and angle, we see the impossibility of uniting the idea obtuse with them. This is without any condition of time, and here there is none expressed. We frequently say, an angle cannot be at the same time right and obtuse; but we never say, a right angle can never at the same time be obtuse, but, absolutely, a right angle cannot be obtuse.
200. Kant observes that the equivocation proceeds from commencing by separating the predicate of a thing from the conception of this thing, and afterwards joining to this same predicate its opposite, which never makes a contradiction to the subject, but to the predicate, which is synthetically united with it; a contradiction which happens only when the first and second predicates are supposed at the same time. This observation of Kant is at bottom very true, but it has its defects: first, it pretends to be original, when it only says things already well known; and secondly, it is used to combat an equivocation existing only in the mind of the philosopher who wants to free others from it. The two propositions analyzed in the last paragraph confirm what we have just said. An angle cannot be both right and not right. Here the condition of time is necessary, because the opposition is not between the predicate and the subject, but between the two predicates. The angle may be right or not right, only at different times. A right angle cannot be obtuse; here the condition of time must not be expressed, because the idea right entering into the conception of the subject, entirely excludes the idea obtuse.
201. If the principle of contradiction were to serve only for analytic judgments, that is, for those in which the predicate is contained in the idea of the subject, the condition of time should never be expressed; but as this principle is to guide us in all other judgments, it follows that, in the general formula, we cannot abstract a condition absolutely indispensable in most cases. In the present state of our understanding, while we are in this life, non-abstraction of time is the rule, abstraction the exception; and would you have a general formula conform to the exception and neglect the rule?