by immediate evidence; that the square of the hypothenuse is equal to the sum of the squares of the other two sides, is known by mediate evidence, that is, by demonstrative reasoning.
240. We have said that one of the distinctive characteristics of evidence is the necessity and universality of its object. This is a characteristic as well of mediate as of immediate evidence.
Besides this characteristic there is another, called with more reason essential, notwithstanding some doubt as to whether it extends to mediate evidence or not; it is that the idea of the predicate is found contained in that of the subject. This is the most complete essential notion of the criterion of immediate evidence, by which it is distinguished from the criteria of consciousness and common sense.
We have said there is some doubt as to this characteristic extending to mediate evidence; by this we mean that also in mediate evidence the idea of the predicate may be contained in that of the subject. In this it is not our intention to ignore the difference between theorems and axioms, but to call the reader's attention to a doctrine which we propose to develop, while treating of mediate evidence. In the present chapter we shall only treat of evidence in general, or of immediate evidence alone.
241. Evidence involves relation, for it implies comparison. When the understanding does not compare, it has no evidence, but only a perception, which is a pure fact of consciousness; and this evidence does not refer to perception alone, but always supposes or produces a judgment.
We find two things in every act where there is evidence: the pure intuition of the idea, and the decomposition of this idea into various conceptions accompanied with the perception of their mutual relations. This we will explain by an example from geometry. The triangle has three sides: this is an evident proposition, for in the very idea of triangle, we find the three sides; and in conceiving the triangle, we in some sense conceive the three sides. Had we limited ourselves to the contemplation of the simple idea of triangle, we should have had intuition of the idea, but not evidence, which begins only when we find, in decomposing the conception of triangle, and considering in it the idea of figure in general, of side, and of the number three, these all contained in the primitive conception. Evidence consists in the clear conception of this.
So true is this that the very nature of things makes common language philosophical. We do not say, an idea is evident, but a judgment is: no one calls a term evident, but a proposition only. And why? Because the term simply expresses the idea without any relation, or decomposition into its partial conceptions; whereas the proposition expresses the judgment, that is, affirms or denies that one conception is contained in another, which, in the present matter, supposes decomposition of the entire conception.
242. Immediate evidence is the perception of identity between various conceptions, separated by the analytical power of the intellect. Thus identity combined in a certain way with diversity is not a contradiction, as it might at first sight seem, but something very natural, if we observe one of the most constant facts of our intellect, the faculty of analyzing the most simple conceptions, and of seeing relations between identical things.
What are all axioms? What are all propositions per se notæ? Nothing but expressions, in which it is affirmed that a predicate belongs to the essence of the subject, or is contained in its idea. The mere conception of the subject includes the predicate: the term which denotes the first also denotes the second; yet the intellect, with a mysterious power of analysis, distinguishes between identical things, and then compares them in order to make them again identical. Whoever says triangle, expresses a figure composed of three sides and three angles; but the intellect may take this idea and consider in it the ideas of the number three, side, and angle, and compare them with the primitive conception. In this distinction there is no deception; there is only the exercise of the faculty, which regards the thing under different aspects, in order to arrive at the intuition and affirmation of the identity of the very things it had before distinguished.
243. Evidence is a sort of calculation of the intellect, whereby it finds in the conception analyzed whatever was placed in the principle or was contained in it. Hence the necessity and universality of the object of evidence, inasmuch as, and in the manner, in which it is expressed by the idea. To this there are no exceptions. Either a predicate is or is not placed in a primitive principle: if it is, it is there, according to the principle of contradiction. Either it was or was not excluded from the conception; if the conception itself excludes or denies it, this it does by virtue of the principle of contradiction.
Thus the more fundamental of the two characteristics of evidence given above is, that the idea of the predicate is contained in the idea of the subject. Hence the necessity and universality; since, in verifying this condition, it is impossible for the predicate not to belong necessarily to all the subjects.
244. Thus far we have encountered no difficulty, because we have treated only of evidence subjectively considered, that is, as relating to pure conceptions; but the intellect does not stop with the conception, but extends to the object, and says not only that it sees the thing, but that the thing is as it sees it. Thus the principle of contradiction, considered in the purely subjective order, means that the conception of being is opposed to that of not-being, which destroys it, just as the conception of being destroys that of not-being; it means, that in endeavoring to conceive jointly these two things, and to make them co-exist, a sort of struggle of thoughts, reciprocally annihilating each other, takes place in the depths of our soul—a struggle which the understanding is condemned to witness without hope of establishing peace between the combatants. If we confine ourselves to this phenomenon, no objection can be made. We experience it, and there is no further question about it; but in announcing the principle, we would announce something more than the incompatibility of the conceptions; we would transfer this incompatibility to the things themselves, and assert that not only our own conceptions, but also all real and possible beings are subjected to this law. Whatever be the object of which we treat, whatever the conditions under which we suppose it existent or possible, we say that while it is, it cannot not be; and while it is not it cannot be. We affirm, then, the law of contradiction, not only for our own conceptions, but also for things themselves; the intellect applies to every thing the law which it finds necessary to itself.
By what right? An incontestible right, for it is the law of necessity. With what reason? With none, for we are now at the foundation of reason; this is the ne plus ultra of the human understanding; philosophy can go no farther. Let us not, however, be thought to abandon the field to skeptics, or to entrench ourselves in necessity, contented with pointing out a fact of our nature. The question is susceptible of different solutions, which may not, indeed, go beyond the ne plus ultra of our mind, but which yet leaves the cause of skepticism in great straits.
245. To ask why the criterion of evidence is legitimate, is to ask why this proposition is true: "whatever is evident is true;" it is to raise the question of the objectiveness of ideas. The fundamental difference between dogmatists and skeptics, is not that the latter deny the facts of consciousness—the most refined skepticism has not come to this, and both agree in recognizing the purely subjective appearance of phenomena; but it is that dogmatists found science on consciousness, and skeptics maintain that this is an illegitimate transition, and that we must despair of science, and confine ourselves to mere consciousness.
According to this doctrine, ideas are empty forms of the understanding, mean nothing, and can lead to nothing; although they entertain the understanding, and offer to it an immense field for combinations, the world they present to it is purely illusory, and can serve for nothing in the real order. In contemplating these entirely empty forms, the intellect is the sport of fantastic visions, from the union of which results the spectacle which seems now to belong to reality, and now to possibility; either it is a mere nonentity, or something, and if so, it can never make us sure of the reality it possesses.
246. It is difficult to fight skepticism when it takes this ground: situated beyond the domains of reason, the decisions of reason cannot reach it. It will appeal from
