139. Let us apply this doctrine to the most certain and most evident ideal principles, to those which contain the most general ideas, and which ought, therefore, to possess the fecundity in question, if, indeed, it be anywhere to be encountered. "It is impossible for the same thing to be and not be at the same time." This is the famous principle of contradiction, which may undoubtedly claim to be regarded as one source of truth to the human understanding. The ideas contained in it are the clearest and most simple conceivable; in it is affirmed the repugnance of being to not-being, and of not-being to being, at the same time, which is most evident. But what advance can we make with this principle alone? Present it to the most penetrating mind, to the most powerful genius; leave them alone with it, and there will result only a sterile, although pure and most clear intuition. Since it does not affirm that any thing is or is not, nothing can be inferred either for or against any existence: it only offers to the mind this conditional relation: that if any thing does exist, it is repugnant for it not to exist at the same time that it exists, or to exist at the same time that it does not exist. But if the condition of existence or non-existence be not given, _yes_ and _no_ in the real order are indifferent; nothing is known concerning them, however great the evidence in the ideal order. To pass from the logical world to that of reality, all that is required is a fact to serve as a bridge. If this fact be offered to the understanding, the two banks are joined, and science commences. I feel, I think, I exist: these are facts of consciousness; combine any one of them with the principle of contradiction, and what before were sterile intuitions become prolific ratiocinations, embracing at once the world of ideas, and that of reality. 140. Even in the purely ideal order, the principle of contradiction is sterile unless joined with particular truths of the same order. In geometry, for example, it is often argued thus: such a quantity is either greater or less than another, or equal to it; for otherwise it would be both greater and less, equal and unequal, at the same time, which is absurd. Here the principle of contradiction is effectively applied, not alone, but together with a particular truth which makes such an application available. Thus, in the above argument, no use could be made of the principle of contradiction, to prove equality or inequality were not the existence or non-existence of one of the two previously proved or supposed: since this neither does nor can result from the principle of contradiction which includes, not a particular idea, but the most general ideas presented to the human mind.