the following texts of St. Thomas leave any thing to be desired in clearness or precision: "A proposition is known by itself, per se notæ, when the predicate is contained in the subject, as; man is an animal; for animal is of the essence of man. If, then, it is known to all, what the subject and the predicate are, that proposition will be known by itself to all, as is seen in the first principles of demonstration, which are certain, common things, not unknown to any one, as being and not-being, the whole, the part, and others similar."[18]
"Any proposition the predicate of which is of the essence of the subject, is known by itself, although such a proposition is not known by itself for any one who is ignorant of the definition of the subject. Thus this proposition, man is rational, is by its nature known by itself, because whoever says man, says rational."[19]
192. By these, and many other examples, which it would be easy to adduce, it is seen that the distinction between analytic and synthetic judgments was common in the schools centuries before Kant flourished. Analytic judgments were all those formed by immediate evidence; and synthetic, those resulting from mediate evidence, whether of the purely ideal order, or in some sense depending on experience. It was well known that there were conceptions of the subject, in which the predicate was thought, at least confusedly; and thus union, or identity, was explained by saying that the propositions, in which it was found, were per se notæ ex terminis. In analytic judgments, the predicate is in the subject; nothing is added, according to Kant, it is only unfolded. Whoever says man says rational, are the words of St. Thomas: the idea is the same as that of the German philosopher.
193. But let us see if it is necessary to change the formula by which the principle of contradiction has hitherto been expressed.
The first observation of Kant refers to the word impossible, which he considers unnecessarily added, since the apodictic certainty, which we wish to express, should be contained in the proposition itself. Kant's formula of the principle is this: "a predicate which is opposed to a subject, does not belong to it." What is the meaning of the word impossible? "Possible and impossible absolutely, are said in relation to the terms. Possible, because the predicate is not opposed to the subject; impossible, because the predicate is opposed to the subject;" says St. Thomas,[20] and with him agree all the schools. Therefore, impossibility is the opposition of the predicate to the subject, and to be repugnant is the same thing as to be impossible, and Kant uses the very language which he blames in others. The common formula might be expressed in this manner: "there is opposition in the same thing being and not-being at the same time," or, "being is opposed to not-being," or, "being excludes not-being," or, "every thing is equal to itself;" and Kant expresses nothing more when he says: "a predicate which is opposed to a subject does not belong to it."
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
