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But although phenomena are properly the appearances of things, but not ideas, or express the inner and absolute quality of objects, their cognition is nevertheless of the truest. For in the first place, being apprehended sensual concepts, they, being consequences, witness the presence of the object, contrary to Idealism; and as regards judgments concerning that which is sensuously known, since truth in judging consists in the agreement of the predicate with the given subject, and since the concept of the subject as a phenomenon is given only by relation to the sensuous cognitive faculty, the sensuously observable predicates being given according to the same, it is plain that the representations of subject and predicate are made according to common laws, and hence give occasion for perfectly true cognition.
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All sense-objects are phenomena, but that which, not touching our senses, contains the form only of sensuality, belongs to pure intuition, that is, an intuition devoid of sensations, but not on that account, intellectual. Phenomena of the external sense are examined and set forth in physics; those of the internal sense in empirical psychology. But pure human intuition is not a universal or logical concept under which, but a singular in which all sensible objects are thought, and hence contains concepts of space and time, which, since they determine nothing concerning sensible objects as to quality, are not the objects of science except as to quantity. Hence pure mathematics considers space in geometry and time in pure mechanics. To these is to be added a certain concept, intellectual to be sure in itself, but whose becoming actual in the concrete requires the auxiliary notions of time and space in the successive addition and simultaneous juxtaposition of separate units, which is the concept of number treated in arithmetic. Pure mathematics, then, expounding the form of our entire sensuous cognition, is the organon of all intuitive and distinct knowledge, and since its objects are not only the formal principles of all intuition, but themselves original intuitions, it confers cognition both perfectly true, and the model of the highest degree of clearness to others. There is given, therefore, a science of sensual things, though being phenomena there is not given a real intellection, but a logical one only; hence it is plain in what sense those borrowing from the Eleatic school are to be thought to have denied a science of phenomena.
SECTION III
ON THE PRINCIPLES OF THE FORM OF THE SENSIBLE WORLD
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The principle of the form of a universe is that which contains the cause of the universal tie by means of which all substances and their states pertain to one which is called a world. The principle of the form of the sensible world is that which contains the cause of the universal tie of all things regarded as phenomena. The form of the intelligible world acknowledges an objective principle, that is, some cause by which it is the colligation of what exists in it. But the world regarded as phenomenon, that is, in respect to the sensibility of the human mind, acknowledges no principle of form but a subjective one, that is, a certain mental law by which it is necessary that all things qualified for being objects of the senses would seem to pertain necessarily to the same whole. Whatever be, therefore, the principle of the form of the sensible world, it will comprise only actual things in as far as thought of as possibly falling under sense-perception; hence neither immaterial substances, which as such are excluded by definition from the external senses altogether, nor the cause of the world, which, since by it the mind exists and has the power of sense-perception, cannot be the object of the senses. These formal principles of the phenomenal universe which are absolutely primary, universal, and, so to speak, the outlines and conditions of anything else whatsoever in human sensuous cognition, I shall now show to be two: time and space.
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1. The idea of time does not originate in, but is presupposed by the senses. Whether things falling under sense-perception be simultaneous or in line of succession cannot be represented but by the idea of time; nor does succession beget the concept of time; it appeals to it. Hence the notion of time, though acquired by experience, is badly defined by a series of actual things existing one after another, for what the word after means I understand only by the previous concept of time. For those things are after one another which exist at different times, as those are simultaneous which exist at the same time.
2. The idea of time is singular, not general. For any time whatever is thought only as a part of one and the same unmeasured time. If you think two years you cannot represent them to yourself but in a mutually determinate position, and if they do not immediately follow one the other, you cannot think of them except as connected by some intermediate time. Which of different times is first and which later can be defined in no way by any marks conceivable by the intellect, unless you are willing to run into a circle, and the mind discerns it by no more than one intuition. Besides, we conceive of all actual things as posited in time, not as contained as common marks under a general notion of time.
3. The idea of time, therefore, is an intuition, and being conceived before all sensation as the condition of the relations occurring in sensible things, it is not a sensual but pure intuition.
4. Time is a continuous quantity and the principle of the laws of continuity in the changes of the universe. For a continuous quantity is one which does not consist of simple parts. But since by time are only thought relations without any mutually related data, there is in time—as a quantity—composition, which being conceived wholly removed leaves nothing over. But a composite of which, composition being removed, nothing is left, does not consist of simple parts. Therefore, etc. Any part of time, then, is time; and the simple things in time, namely, the moments, are not parts of it, but termini between which time intervenes. For two moments being given, time is not given, except as in them actualities succeed each other; hence, beside the given moment it is necessary that time be given in the latter part of which there is another moment.
The metaphysical law of continuity is this: All changes are continuous or flowing, that is, opposite states succeed each other only by an intermediate series of different states. For since two opposite states are in different moments of time, and some time is always intercepted between two moments, in which infinite series of moments the substance is neither in one assignable state nor the other, nor yet in none, it will be in different states, and so on infinitely.
The celebrated Kästner, calling in question this Leibnitzian law,[4] calls on its defenders to demonstrate that the continuous motion of a point around the sides of a triangle is impossible, it being necessary to prove this if the law of continuity be granted. Here is the demonstration required. Let the letters a b c denote the three angular points of a rectilineal triangle. If the point did move continuously over the lines ab, bc, ca, that is, over the perimeter of the figure, it would be necessary for it to move at the point b in the direction ab, and also at the same point b in the direction bc. These motions being diverse, they cannot be simultaneous. Therefore, the moment of presence of the movable point at vertex b, considered as moving in the direction ab, is different from the moment of presence of the movable point at the same vertex b, considered as moving in the same direction bc. But between two moments there is time; therefore, the movable point is present at point b for some time, that is, it rests. Therefore it does not move continuously, which is contrary to the assumption. The same demonstration is valid for motion over any right lines including an assignable angle. Hence a body does not change its direction in continuous motion except by following a line no part of which is straight, that is, a curve, as Leibnitz maintained.
5. Time is not something objective and real, neither a