189. Before examining the value of the principle of contradiction as a basis for our cognitions, it will be well to fix its true and exact sense. This renders necessary some considerations upon an opinion of Kant, advanced in his Critic of Pure Reason, when treating of the form in which the principle of contradiction has hitherto been enunciated in all schools of philosophy. The German metaphysician grants, that whatever may be the matter of our cognitions, and in whatever manner they may relate to their object, it is a general, although a purely negative, condition of all our judgments, that they should not mutually contradict each other; otherwise, even without reference to their object, they are nothing in themselves. This doctrine established, he observes that what is called the principle of contradiction is the following: "A predicate that is opposed to a subject does not belong to it;" and then goes on to say, that this is a universal, although purely negative criterion of all truth; that it moreover belongs exclusively to logic, since it is of use to pure cognitions as to cognitions in general, without relation to their object, and he declares that the contradiction makes them completely disappear. "But of this celebrated principle, although stripped of all contents, and purely formal," he continues, "there is still a formula containing a synthesis, which has inadvertently, and quite unnecessarily, been mixed up therein. It is this: It is impossible for the same thing to be and not be at the same time. Not only has the apodictic certainty (by the word impossible) been unnecessarily added, which certainty would have been of itself understood from the proposition; but the proposition is affected by the condition of time, and says, as it were: a thing = A, which is something = B, cannot at the same time be not B, but it can very well be both (B as well as not B) in succession. For example: a man who is young, cannot at the same time be old; but the same person may very well be young at one time, at another not young, that is, old. Now, the principle of contradiction, as a mere logical principle, must not at all restrict its meaning to the relations of time, and consequently, such a formula is quite opposed to its intention. The misapprehension arises simply from this: that we first separate the predicate of a thing from its conception, and afterwards unite its opposite with this predicate, which never gives a contradiction with the subject, but only with its predicate, which is synthetically joined with that subject, and that only when the first and second predicates are asserted at the same time. If I say a man who is unlearned is not learned, the condition, at the same time, must be expressed; for he who is unlearned at one time may very well be learned at another. But if I say no unlearned man is learned, the proposition is analytic, since the sign (the unlearnedness) now constitutes the conception of the subject, and then the negative proposition is evident immediately from the principle of contradiction, without it being necessary for the condition, at the same time, to be added. This is also the cause why I have so changed the formula of this principle, that the nature of an analytic proposition might be clearly expressed."[16]
190. The reader will not easily comprehend the meaning of this passage, not very clear of itself, unless he knows what Kant understands by analytic and synthetic propositions. We will explain this. In all affirmative judgments, the relation of a predicate to a subject is possible in two manners: either the predicate belongs to the subject as contained in it, or is completely extraneous to it although joined with it. In the former case, the judgment is analytic; in the latter, it is synthetic. Analytic affirmative judgments are those in which the union of the predicate with the subject is conceived by identity: those are called synthetic in which this union is conceived without identity. Kant illustrates his idea by the following examples: "When I say all bodies are extended, I express an analytic judgment; for I need not go out of the conception of body in order to find that of extension, which I connect with it, but I have only to analyze the conception of body, that is, to become conscious of the diversity which I always think in this conception, in order to find the predicate. It is, therefore, an analytic judgment. But when I say, all bodies are heavy, the predicate heaviness is by no means included in my conception of the subject, that is, of body in general. It is a conception added to the conception of body. The addition in this way of the predicate to the subject gives a synthetic judgment."[17]
It is easy to see the reason of the new nomenclature employed by the German philosopher. He calls those judgments analytical, in which it suffices to decompose the subject to find therein the predicate, without the necessity of adding any thing not already thought, at least obscurely, in the very conception of the subject; and he calls synthetic those in which it is necessary to add something to the conception of subject, since the predicate is not found in this conception however much we decompose it.
191. This division of judgment, into analytic and synthetic, is much used in modern philosophy, above all among the Germans; certainly there are some who may imagine this to be a discovery made by the author of the Critic of Pure Reason; and the very novelty of the name may give occasion to equivocation. Yet, in all the scholastic writers who lie forgotten, and covered with dust, in the recesses of libraries, we find analytic and synthetic judgments, though not under these names. They said there were two kinds of judgments; some, in which the predicate was contained in the idea of subject, and others, in which it was not. They called the propositions which expressed judgments of the former class, per se notæ, or known by themselves, because, the meaning of the terms being understood, the predicate was seen to be contained in the idea, or the conception of the subject. They also called them first principles, and the perception of them, intelligence, intellectus, to distinguish them from reason, which is conversant about the cognitions of mediate evidence, or ratiocination.
See if 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