that such a proposition as 'All men are rational' is only analytical, for before we could form such an analytical proposition, we must have made the synthetical proposition that this man and that man, and, at last, that every man is rational. We cannot take out of a name anything beyond what we have put into it. Our making 'rational' a nominal attribute of man is in the first instance an act of synthesis, though not of arbitrary synthesis, for the very first reason why such a name as man (man-u-s) was framed at all was the wish to express our knowledge that 'here there is thought' (man-u-te). Truths. We have now, from the point of view which we have reached, to approach the question, Unconditional Can we form synthetical judgments without any limitation, or judgments professing to be necessarily and universally true, and depending for their truth, not on experience only, however often repeated, but on some authority higher than, or according to the usual, but rather objectionable terminology, prior to all experience? Kant has shown that we find such knowledge, first, in what he calls the forms of sensuous intuition, Space and Time; and, secondly, in the categories of the understanding. If he had expressed himself in simpler language, few people would have hesitated to accept his conclusions. We all know that mathematical knowledge claims the character of necessity and universality, Mathematics. both in geometry and in arithmetic. In geometry such statements as the straight line is the shortest, two straight lines cannot enclose a space, or even two things cannot be in the same place at the same time, though they may be perceived for the first time by the senses, possess a greater certainty than any number of repeated acts of experience could ever give us. They are more certain than that the sun will rise to-morrow. Space, therefore, and all that is connected with space, cannot be mere matter of experience. As all experience is possible in space only, space cannot be the result of experience; and though I can conceive all that fills space and is the result of experience, as gone, I can never conceive space as gone, because it is itself not the result of experience. And what applies to space applies to time. Time also is presupposed in every experience, because nothing could be the object of experience except as existing either at the same time or in succession, nor is it possible to imagine time as gone, though everything that has happened in time is gone. Arithmetical statements, being founded on counting successive units in time, are as certain as geometrical statements. Arithmetics may be called the Science of Time, as Geometry is the Science of Space. If, with Kant, we call the geometrical statement, that the straight line is the shortest, a synthetical judgment à priori, we produce the impression, which is utterly erroneous, that such a judgment could be made prior to all experience. This shows the mischief which is constantly done by ill-chosen words. It is quite possible that two persons fastening a rope between two poles would see that the straighter they pull it, the shorter length of rope is required. They might then simply state an observation made by them for the first time, that this straight rope, as we now hold it, is the shortest. But if that fact is once known, it would not require any repetitions than any to make it more certain in our eyes fact, It might be said, however, that 'shortest' is only a nominal attribute of straight line,' and in a certain sense, this is true. We should not call a line straight, unless it was also the shortest. But this is very different from saying that we should not call an island island, unless it was surrounded by water; or gold gold, unless it was a metal. Shortest cannot be called in logic the higher genus of straight, nor straight of shortest; and while, when we assert the fact that an island must be surrounded by water, we must in the end appeal to experience, we distinctly decline to appeal to experience in order to prove that the straight line is the shortest. = It is true, no doubt, that, like all truths, this class of apodictic truths also exists for us only after it has been named and clothed in language, and that some of these truths have the appearance of tautological truths. If straight line were expressed by linea directa, and short line by linea directa, the statement that linea directa linea directa or directissima would seem to be a tautological repetition. Still, though straightness and shortness may be but two aspects of the same thing-straightness being in space what shortness is in time-and though they might have been named by the same word, they are two aspects, and to know that they are so, requires some kind of synthesis, if only a synthesis of intuition. That synthesis of intuition, however, is not enough to give us knowledge, and whereas Kant tries to explain all that we know about space and time as the immediate result of sensuous intuition, I cannot admit any kind of knowledge that has not passed through the phases of concept and name. There might be ever so many lines, straight, crooked, short, long, they would be nothing to us, if simply seen, and not conceived and named. Again, a hundred would never be a hundred by mere sight; we must count it and name it. Attempts have sometimes been made to prove these geometrical and arithmetical truths, which are nothing if they are not self-evident, but all such proofs are simply tautological. There are no higher truths to which these truths could be referred, and by which they could be confirmed or disproved. We might attempt to prove that the straight line is the shortest by saying that if it ever went out of its way it would lose time, and therefore lose space. But this is no more than repeating that a straight line does not lose time or space, and is therefore what it is, namely the shortest. And by what higher truth could we prove that it is impossible for two straight lines to enclose a space? We see that it is so, even without using our eyes, but we cannot prove it by any independent standard. It has been said that every rectilinear figure must have as many angles as sides, and as a triangle is the simplest figure or mode of enclosing space by straight lines, no figure could have less than three sides. It has also been argued that space is a general abstract term, derived from triangles, quadrangles, and other figures, and that as none of these consists of less than three sides, space in general too cannot be enclosed by less than three sides. But all this is only repeating one and the same fact, a fact which is above proof, because it is the result of what we are ourselves, a necessity to which all experience must submit. If we call these local and temporal intuitions à priori, we mean nothing innate or cognate, nothing mysterious, but simply the sine quà non, the very essence, of all sensuous perception. Categories derstanding. And what applies to these necessities of intuition, applies likewise to the necessities of our understanding. Here, too, we mean by of the unà priori truth simply truth which cannot be explained à posteriori. Experience, like a quarrel, requires two, a receiver and something that is received. Now we receive what is given on our own conditions, and what these conditions are we can only discover by separating in our knowledge what can be and what cannot be the result of experience. If the qualities of space and time, as we saw, cannot be the result of experience, because without these two forms, no experience would be possible, neither can the categories of our understanding, for without them we should understand nothing. Causality. The most general and the most important of these categories is that of Causality, or of suf ficient reason, which was expressed in scholastic Latin by the well-known maxim, Nihil est sine ratione cur potius sit quam non sit. That this cannot be a conviction acquired and strengthened by experience is best proved by the fact that our creation of the very first object, or our intuition of an objective world, would be impossible without it. All that is given us consists in affections of the senses. It is we who at once, and without any wish or will of our own, change these affections into objects by which they are supposed to be caused. We do this in the very act of naming. The sensation is there, say of bitterness. As soon as we become |