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 substance, nor an accident, nor a relation. It is the subjective condition necessary by the nature of the human mind for coordinating any sensible objects among themselves by a certain law; time is a pure intuition. Substances as well as accidents we co-ordinate whether according to simultaneity or succession by the concept only of time; hence the notion of time as the principle of form outranks the concepts of the former. Any relations so far as occurring in sense-perception, whether simultaneous or successive, involve nothing but the determination of positions in time, to wit, either in the same point or in different points of the latter.
Those who assert the objective reality of time either conceive of it as a continuous flow in what exists, without, however, any existing thing, as is done especially by the English philosophers, an absurd fiction, or as something real abstracted from the succession of inner states, as it has been put by Leibnitz and his followers. The falsity of the latter opinion, besides obviously exposing it to the vicious circle in the definition of time, and, moreover, plainly neglecting simultaneity, the most important consequence of time, disturbs all sound reason, because it demands instead of the determining of the laws of motion by the measure of time, that time itself, as to its nature, be determined by what is observed in motion or some series of inner changes, whereby plainly all certitude of rules is abolished. That we can estimate the quantity of time only in the concrete, namely, either by motion or by a series of thoughts, arises from the concept of time resting only on an inherent mental law, it not being a connate intuition; whence the act of the mind co-ordinating the impressions is elicited only by the aid of the senses. So far from its being possible to deduce and explain the concept of time from some other source by force of reason, it is presupposed by the very principle of contradiction, it underlies it by way of condition. For a and not-a are not repugnant unless thought of the same thing simultaneously, that is, at the same time; they may belong to the same thing after each other, at different times. Hence the possibility of changes is not thinkable except in time. Time is not thinkable by changes, but reversely.[5]
6. But although time posited in itself and absolutely be an imaginary thing, yet as appertaining to the immutable law of sensible things as such, it is a perfectly true concept, and the patent condition of intuitive representation throughout all the infinite range of possible sense-objects. For since simultaneous things as such cannot be placed before the senses but by the aid of time, and since changes are unthinkable except by time, it is obvious that this concept contains the universal form of phenomena, and that, indeed, all events observable in the world, all motions, all internal changes, agree necessarily with the temporal axioms of cognition which we have partly expounded, since only under these conditions can they become sense-objects and be co-ordinated. It is, therefore, absurd to excite reason against the primary postulates of pure time, as, for example, continuity, etc., since they follow from laws prior and superior to which nothing is found, and since reason herself in the use of the principle of contradiction cannot dispense with the support of this concept, so primitive and original is it.
7. Time, then, is the absolutely first formal principle of the sensible world. For all sensible things of whatsoever description are unthinkable except as posited either simultaneously or one after another, and, indeed, as if involved and mutually related by determinate position in the tract of unique time, so that by this primary concept of everything sensuous originates necessarily that formal whole which is not a part of another, that is, the phenomenal World.
Paragraph 15 OF SPACE
A. The concept of space is not abstracted from external sensations. For I am unable to conceive of anything posited without me unless by representing it as in a place different from that in which I am, and of things as mutually outside of each other unless by locating them in different places in space. Therefore the possibility of external perceptions, as such, presupposes and does not create the concept of space, so that, although what is in space affects the senses, space cannot itself be derived from the senses.
B. The concept of space is a singular representation comprehending all things in itself, not an abstract and common notion containing them under itself. What are called several spaces are only parts of the same immense space mutually related by certain positions, nor can you conceive of a cubic foot except as being bounded in all directions by surrounding space.
C. The concept of space, therefore,
