Fundamental Philosophy (Vol. 1&2). Jaime Luciano Balmes
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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)
CHAPTER XXII.
THE PRINCIPLE OF EVIDENCE.
216.