Each category has its own schema. The schema of quantity is number, as comprehending the successive addition of homogeneous parts. Filled time (being in time) is the schema of reality, empty time (not-being in time) the schema of negation, and more or less filled time (the intensity of sensation, indicating the degree of reality) the schema of limitation. Permanence in time is the sign for the application of the category of substance;[1] regular succession, for the application of the concept of cause; the coexistence of the determinations of one substance with those of another, the signal for their subsumption under the concept of reciprocity. The schemata of possibility, actuality, and necessity, finally, are existence at any time whatever (whensoever), existence at a definite time, and existence at all times. By such schematic syntheses the pure concept is brought near to the empirical intuition, and the way is prepared for an application of the former to the latter, or, what is the same thing, for the subsumption of the latter under the former.
[Footnote 1: This determination is important for psychology. Since the inner sense shows nothing constant, but everything in a continual flux,—for the permanent subject of our thoughts is an identical activity of the understanding, not an intuitable object,—the concept of substance is not applicable to psychical phenomena. Representations of a permanent (material substances) exist, indeed, but not permanent representations. The abiding self (ego, soul) which we posit back of internal phenomena is, as the Dialectic will show, a mere Idea, which, or, rather, the object of which, maybe "thought" as substance, it is true, but cannot be "given" in intuition, hence cannot be "known.">[
As a result of the fact that the schematism permits a presentation of the categories in time intuition antecedent to all experience, the possibility is given of synthetic judgments a priori concerning objects of possible experience. Such judgments, in so far as they are not based on higher and more general cognitions, are termed "principles," and the system of them—to be given, with the table of the categories as a guide, in the Analytic of Principles or the Doctrine of the Faculty of Judgment—furnishes the outlines of "pure natural science." When thus the rules of the subsumption to be effected have been found in the pure concepts, and the conditions and criteria of the subsumption in the schemata, it remains to indicate the principles which the understanding, through the aid of the schemata, actually produces a priori from its concepts.
The principle of quantity is the Axiom of Intuition, the principle of quality the Anticipation of Perception; the principles of relation are termed Analogies of Experience, those of modality Postulates of Empirical Thought in General. The first runs, "All intuitions are extensive quantities"; the second, "In all phenomena sensation, and the real which corresponds to it in the object, has an intensive quantity, i.e., a degree." The principle of the "Analogies" is, "All phenomena, as far as their existence is concerned, are subject a priori to rules, determining their mutual relation in time" (in the second edition this is stated as follows: "Experience is possible only through the representation of a necessary connection of perceptions"). As there are three modes of time, there result three "Analogies," the principles of permanence, of succession (production), and of coexistence. These are: (1) "In all changes of phenomena the substance is permanent, and its quantum is neither increased nor diminished in nature." (2) "All changes take place according to the law of connection between cause and effect"; or, "Everything that happens (begins to be) presupposes something on which it follows according to a rule." (3) "All substances, in so far as they are coexistent, stand in complete community, that is, reciprocity, one to another." And, finally, the three "Postulates": "That which agrees with the formal conditions of experience (in intuition and in concepts) is possible," "That which is connected with the material conditions of experience (sensation) is actual" (perception is the only criterion of actuality). "That which, in its connection with the actual, is determined by universal conditions of experience, is (exists as) necessary."
As the categories of substance and causality are specially preferred to the others by Kant and the Kantians, and are even proclaimed by some as the only fundamental concepts, so also the principles of relation have an established reputation for special importance. The leading ideas in the proofs of the "Analogies of Experience"—for in spite of their underivative character the principles require, and are capable of, proof—may next be noted.
The time determinations of phenomena, the knowledge of their duration, their succession, and their coexistence, form an indispensable part of our experience, not only of scientific experience, but of everyday experience as well. How is the objective time-determination of things and events possible? If the matter in hand is the determination of the particulars of a fight with a bloody ending, the witnesses are questioned and testify: We heard and saw how A began the quarrel by insulting B, and the latter answered the insult with a blow, whereupon A drew his knife and wounded his opponent. Here the succession of perceptions on the part of the persons present is accepted as a true reproduction of the succession of the actual events. But the succession of perceptions is not always the sure indication of an actual succession: the trees along an avenue are perceived one after the other, while they are in reality coexistent. We might now propose the following statement: The representation of the manifold of phenomena is always successive, I apprehend one part after another. I can decide whether these parts succeed one another in the object also, or whether they are coexistent, by the fact that, in the second case, the series of my perceptions is reversible, while in the first it is not. I can, if I choose, direct my glance along the avenue in such a way that I shall begin the second time with the tree at which I left off the first time; if I wish to assure myself that the parts of a house are coexistent, I cause my eye to wander from the upper to the lower portions, from the right side to the left, and then to perform the same motions in the opposite direction. On the other hand, it is not left to my choice to hear the thunder either before or after I see the lightning, or to see a passing wagon now here, now there, but in these cases I am bound in the succession of my sensuous representations. The possibility of interchange in the series of perceptions proves an objective coexistence, the impossibility of this, an objective succession. But this criterion is limited to the immediate present, and fails us when a time relation between unobserved phenomena is to be established. If I go at evening into the dining room and see a vessel of bubbling water, which is to be used in making tea, over a burning spirit lamp, whence do I derive the knowledge that the water began, and could begin, to boil only after the alcohol had been lighted, and not before? Because I have often seen the flame precede the boiling of the water, and in this the irreversibility of the two perceptions has guaranteed to me the succession of the events perceived? Then I may only assume that it is very probable, not that it is certain, that in this case also the order of the two events has been the same as I have observed several times before. As a matter of fact, however, we all assert that the water could not have come into a boiling condition unless the generation of heat had preceded; that in every case the fire must be there before the boiling of the water can commence. Whence do we derive this must? Simply and alone from the thought of a causal connection between the two events. Every phenomenon must follow in time that phenomenon of which it is the effect, and must precede that of which it is the cause. It is through the relation of causality, and through this alone, that the objective time relation of phenomena is determined. If nothing preceded an event on which it must follow according to a rule,[1] then all succession in perception would be subjective merely, and nothing whatever would be objectively determined by it as to what was the antecedent and what the consequent in the phenomenon itself. We should then have a mere play of representations without significance for the real succession of events. Only the thought of a rule, according to which the antecedent state contains the necessary condition of the consequent state, justifies us in transferring the time order of our representations to phenomena.[2] Nay, even the distinction between the phenomenon itself, as the object of our representations, and our representations of it, is effected only by subjecting the phenomenon to this rule, which assigns to it its definite position in time after another phenomenon by which it is caused, and thus forbids the inversion of the perceptions. We can derive the rule of the understanding which produces the objective time order of the manifold from experience, only because we have put it into experience, and have first brought experience into being by means of the rule. We recapitulate in Kant's own words: The objective (time) relation of phenomena remains undetermined by mere perception (the mere succession in my apprehension, if it is not determined by means of a rule in relation to an antecedent, does not guarantee any succession in the object). In order that this may be known as determined, the relation between the two states must be so conceived (through the understanding's concept of causality) that it is thereby determined with necessity which of them must be taken as coming first, and which second, and not conversely. Thus it is only by subjecting the succession of phenomena to the law of causality that empirical knowledge of them is possible. Without the concept of cause no objective time determination, and hence, without it, no experience.
[Footnote 1: "A reality following on an empty time, that is, a beginning of existence preceded by no state of things, can as little be apprehended as empty time itself.">[
[Footnote 2: "If phenomena were things in themselves no one would be able, from the succession of the representations of their manifold, to tell how this is connected in the object.">[
That which the relation of cause and effect does for the succession[1] of phenomena, the relation of reciprocity does for their coexistence, and that of substance and accident for their duration. Since absolute time is not an object of perception, the position of phenomena in time cannot be directly determined, but only through a concept of the understanding. When I conclude that two objects (the earth and the moon) must be coexistent, because perceptions of them can follow upon one another in both ways, I do this on the presupposition that the objects themselves reciprocally determine their position in time, hence are not isolated, but stand in causal community or a relation of reciprocal influence. It is only on the condition of reciprocity between phenomena, through which they form a whole, that I can represent them as coexistent.
[Footnote 1: Against the objection that cause and effect are frequently, indeed in most cases, simultaneous (e.g. the heated stove and the warmth of the room), Kant remarks that the question concerns the order of time merely, and not the lapse of time. The ball lying on a soft cushion is simultaneous, it is true, with its effect, the depression in the cushion. "But I, nevertheless, distinguish the two by the time relation of dynamical connection. For if I place the ball on the cushion, its previously smooth surface is followed by a depression, but if there is a depression in the cushion (I know not whence) a leaden ball does not follow from it.">[