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
