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?
202. We cannot conceive what reason Kant had to illustrate this subject with the examples above cited. Nothing can be more common and inopportune than what he adds in illustration of this matter by examples. "If I say a man who is unlearned is not learned, the condition at the same time must be understood; for he who is unlearned at one time, may very well be learned at another." This is not only very common and inopportune, but it is exceedingly inexact. If the proposition were: a man cannot be ignorant and instructed; then the condition at the same time should be added, because not giving preference to either predicate over the other indicates the manner of the opposition, which is of predicate to predicate, and not of predicate to subject. But in the example adduced by Kant, "the man that is ignorant is not instructed." The subject is not man alone, but an ignorant man; the predicate instructed devolves on man modified by the predicate ignorant, and, consequently, the expression of time is not necessary, nor is it used in ordinary language.
There is a great difference between these two propositions: a man that is ignorant is not instructed; and a man that is ignorant cannot be instructed. The condition of time must not be expressed in the former, for the reason already given; it must be in the latter, because speaking of the impossibility in an absolute manner, we should deny the ignorant man even the power to be instructed.
203. Kant's other example is the following: "But if I say no unlearned man is learned, the proposition is analytical, since the sign of unlearnedness now constitutes the conception of the subject, and then the negative proposition is immediately evident from the principle of contradiction, without it being necessary for the condition at the same time to be added." We cannot see why Kant makes so great difference between these two propositions: a man who is unlearned is not learned, and no unlearned man is learned; in both, the predicate relates not only to man, but to an unlearned man; and it is the same to say, a man that is unlearned, as, an unlearned man. If, then, the expression of time is not necessary in the one, neither is it in the other.
If the idea of unlearned affects the subject, the predicate is necessarily excluded, because the ideas, learned and unlearned, are contradictory; and we encounter the rule of logic, that in necessary matters, an indefinite is equivalent to a universal proposition.
The principle of contradiction must, therefore, be preserved as it is; the condition of time must not be suppressed, for this would render the formula, in many cases, inapplicable.(20)
CHAPTER XXI.
DOES THE PRINCIPLE OF CONTRADICTION MERIT THE TITLE OF FUNDAMENTAL; AND IF SO, IN WHAT SENSE?
204. Having cleared up the true sense of the principle of contradiction, let us now see whether it merits to be called fundamental, whether it possesses all the characteristics requisite to such a dignity. These characteristics are three in number: first, that it depend on no other principle; secondly, that its fall involve the ruin of all others; thirdly, that it may, while it remains firm, be conclusively urged against all who deny the others, and be of avail to bring them back to the truth by a demonstration at least indirect.
205. In order completely to solve all questions depending on the principle of contradiction, we shall state a few propositions, and accompany them with their proper demonstrations:
FIRST PROPOSITION.
If the principle of contradiction be denied, all certainty, all truth, and all knowledge are at an end.
Demonstration.– If a thing may be and not be at the same time, we may be certain and not certain, know and not know, exist and not exist; affirmation may be joined with negation, contradictory things united, distinct things identified, and identical things distinguished: the intellect is a chaos to the full extent of the word; reason is overturned; language is absurd; subject and object clash in the midst of frightful darkness, and all intellectual light is for ever extinguished. All principles are involved in the universal wreck, and consciousness itself would totter, were it not, when this absurd supposition is made, upheld by the invincible hand of nature. Consciousness, indeed, in this absurd hypothesis, does not perish, for this is impossible, but it sees itself carried away by this violent whirlwind, which precipitates it and every thing else into chaotic darkness. In vain does it strive to save its ideas; they all vanish before the force of contradiction: in vain does it generate new ideas to be substituted for those it loses; these also disappear: in vain does it seek new objects, for they, too, disappear in like manner, and it endures only to feel the radical impossibility of all thought, and see contradiction lording it over the intellect, and destroying, with irresistible might, whatever would germinate there.
SECOND PROPOSITION.
206. It is not enough not to suppose the principle of contradiction false; we must suppose it to be true, if we would not have all certainty, all knowledge, all truth to perish.
Demonstration.– The reasons given for the first proposition avail also to prove this. In the one case the principle of contradiction is supposed to be denied; in the other, it is neither supposed true nor false; but this evidently is not enough, for, until the principle of contradiction is placed beyond all doubt, we remain in darkness, and must doubt of every thing. We do not mean to say that it is impossible for us to have certainty of any thing, if we do not think explicitly of this principle; but that it must be so firmly established, that we cannot raise the least doubt concerning it, and that, when we see any thing connected with it, we must, of necessity, consider that thing as founded upon an immovable basis: the least vacillation, the least doubt of this principle utterly destroys it; the possibility of an absurdity is itself an absurdity.
THIRD PROPOSITION.
207. The certainty of the principle of contradiction rests upon no other principle.
Demonstration.– It is, as we have seen, necessary in every cognition to suppose the truth of the principle of contradiction; therefore, no one can avail to demonstrate it. Every argument, made to demonstrate this, necessarily involves a vicious circle; the principle of contradiction is proved by another principle, which, in its turn, supposes that of contradiction; and so we shall have a superstructure resting upon a foundation, which foundation rests upon the superstructure itself.
FOURTH PROPOSITION.
208. Whoever denies the principle of contradiction can neither directly nor indirectly be refuted by any other.
Demonstration.– It would be amusing to hear the arguments directed against a man who admits both affirmation and negation to be at the same time possible; although forced to admit the affirmative, he will still hold the negative, and vice versa. It is impossible not only to argue, but even to speak, or to think on such a supposition.
FIFTH PROPOSITION.
209. It is not exact to say, as is generally said, that by the principle of contradiction, we may argue conclusively against whoever denies the others.
Here take notice that we only say it is not exact, for we believe it at bottom to be true, although not free from inexactness. To show this, let us examine the weight of the demonstration ordinarily given. The reasons, arguments, and replies may be presented most clearly and strongly in the form of a dialogue. Let us suppose some one to deny this axiom: the whole is greater than its part.
If you deny this, you admit that the same thing may both be and not be at the same time. This is what you have to prove. With you the whole is the whole and not the whole, and the part the part and not the part. Why so? First, it is the whole by supposition. Admitted. And at the same time it is not. Denied. It is not the whole because it is not greater than its part. An excellent way of arguing! This is a petitio principii. I commence by asserting that the whole is not greater than its part, and you argue on the contrary supposition; for you tell me the whole would not be the whole were it not greater than its part. If I had conceded that the whole is greater than its part, and then denied this property, I should indeed fall into a contradiction, making that a whole, which, according to my principles, is not a whole; but as I now deny that the whole must be greater than its part, I must also deny that it ceases to be a whole by not being greater than its part.
210. What will you reply to one reasoning thus. Certainly nothing in the form of an argument: all that you can do is to call his attention to the absurdity of his position; but this is to be done not by argument, but by exactly determining the meaning of the words and analyzing the conceptions which they express. This is all that can or should be done. The contradiction exists; this is certain; but what is wanted is, that he see that he has fallen into it; and if the explanation of the terms, and the analysis of the conceptions do not suffice, nothing else will.
Let us see how this may be done in the same example. The whole is greater than its part. What is the whole? The collection of the parts, the parts themselves united. The idea of the parts then enters into the idea of the whole. What is the meaning of greater? One thing is said to be greater than another, when, besides containing an equal quantity, it also contains something else. Seven is greater than five, because, besides the same five, it contains also two. The whole contains one part and also the other parts; therefore, the idea of greater than its part enters into the idea of whole. Thus it is that we must refute whoever denies this principle; and this method, better than that of argumentation, may be said to explain the terms and analyze the conceptions, for it clearly does nothing but define the former and decompose the latter.
SIXTH PROPOSITION.
211. The principle of contradiction is known only by immediate evidence.
Demonstration.– Two things are here to be proved: that the knowledge is by evidence, and that the evidence is immediate. As regards the former we will remark that the principle of contradiction is not a simple fact of consciousness, but a purely ideal truth. Every fact of consciousness involves reality, and cannot be expressed without the assertion of some existence: the principle of contradiction neither affirms nor denies any thing positive; that is, it does not say that any thing exists or does not exist; it only expresses the opposition of being to not-being, and of not-being to being, abstraction made from our taking the word being copulatively or substantively.
212. Every fact of consciousness is not only something existent, but something determinate; it is not a thought in the abstract, but is this or that thought. The principle of contradiction contains nothing determinate; it abstracts not only the existence, but also the essence of things, since it relates not only to existing things, but also to things possible: it distinguishes no species among them, but embraces them all in their greatest generality. When we say, "it is impossible for the same thing to be and not be," the word thing does not at all restrict the meaning; it expresses being in general, in its greatest indeterminateness. In the to be or not be, the word be expresses not only existence, but also every class of essences in their most complete indeterminateness. Thus the principle is equally applicable in these two propositions: it is impossible for the moon to be and not be; it is impossible for a circle to be and not be a circle; although the first is in the real order, and there the word be expresses existence, and the second is in the ideal order, and the word be expresses only the relation of predicate to subject.
213. Every fact of consciousness is individual; the principle of contradiction is the most universal imaginable: every fact of consciousness is contingent; the principle of contradiction is absolutely necessary, a necessity which is a mark of truths known by evidence.
214. The principle of contradiction is a law of all intelligence; it is of absolute necessity for the finite as for the infinite; not even the infinite intelligence is beyond this necessity, for infinite perfection cannot be an absurdity. Every fact of consciousness as purely individual, relates only to the being that experiences it; neither the order of intelligences, nor that of truth suffers any mutation from my existence or non-existence.
215. The principle of contradiction, besides the marks of necessity and universality, which distinguish truths of evidence, possesses also that of being seen with that immediate, intellectual clearness, of which we have already treated. In the idea of being we see most clearly the exclusion of not-being.
Hence the proof of the second part of the proposition: because there is immediate evidence of the relation of the predicate to the subject, when the sole idea of the subject, without the necessity of combination with other ideas, enables us to perceive this relation: this is so in the present case, for not only no combination is needed, but all combinations are impossible if the truth of this principle be not supposed.(21)