Coexistence and succession can be represented only in a permanent substratum; they are merely the modes in which the permanent exists. Since time (in which all change takes place, but which itself abides and does not change) in itself cannot be perceived, the substratum of simultaneity and succession must exist in phenomena themselves: the permanent in relation to which alone all the time relations of phenomena can be determined, is substance; that which alters is its determinations, accidents, or special modes of existing. Alteration, i.e., origin and extinction, is true of states only, which can begin and cease to be, and not of substances, which change (sich verändern), i.e., pass from one mode of existence into another, but do not alter (wechseln), i.e., pass from non-existence into existence, or the reverse. It is the permanent alone that changes, and its states alone that begin and cease to be. The origin and extinction of substances, or the increase and diminution of their quantum, would remove the sole condition of the empirical unity of time; for the time relations of the coexistent and the successive can be perceived only in an identical substratum, in a permanent, which exists always. The law "From nothing nothing comes, and nothing can return to nothing," is everywhere assumed and has been frequently advanced, but never yet proved, for, indeed, it is impossible to prove it dogmatically. Here the only possible proof for it, the critical proof, is given: the principle of permanence is a necessary condition of experience. The same argument establishes the principle of sufficient reason, and the principle of the community of substances, together with the unity of the world to be inferred from this. The three Analogies together assert: "All phenomena exist in one nature and must so exist, because without such a unity a priori no unity of experience, and therefore no determination of objects in experience, would be possible."—In connection with the Postulates the same transcendental proof is given for a series of other laws of nature a priori, viz., that in the course of the changes in the world—for the causal principle holds only for effects in nature, not for the existence of things as substances—there can be neither blind chance nor a blind necessity (but only a conditional, hence an intelligible, necessity); and, further, that in the series of phenomena, there can be neither leap, nor gap, nor break, and hence no void—in mundo non datur casus, non datur fatum, non datur saltus, non datur hiatus.
While the dynamical principles have to do with the relation of phenomena, whether it be to one another (Analogies), or to our faculty of cognition (Postulates), the mathematical relate to the quantity of intuitions and sensations, and furnish the basis for the application of mathematics to natural science.[1] An extensive quantity is one in which the representation of the parts makes the representation of the whole possible, and so precedes it. I cannot represent a line without drawing it in thought, i.e., without producing all parts of it one after the other, starting from a point. All phenomena are intuited as aggregates or as collections of previously given parts. That which geometry asserts of pure intuition (i.e., the infinite divisibility of lines) holds also of empirical intuition. An intensive quantity is one which is apprehended only as unity, and in which plurality can be represented only by approximation to negation = 0. Every sensation, consequently every reality in phenomena, has a degree, which, however small it may be, is never the smallest, but can always be still more diminished; and between reality and negation there exists a continuous connection of possible smaller intermediate sensations, or an infinite series of ever decreasing degrees. The property of quantities, according to which no part in them is the smallest possible part, and no part is simple, is termed their continuity. All phenomena are continuous quantities, i.e., all their parts are in turn (further divisible) quantities. Hence it follows, first, that a proof for an empty space or empty time can never be drawn from experience, and secondly, that all change is also continuous. "It is remarkable," so Kant ends his proof of the Anticipation, "that of quantities in general we can know one quality only a priori, namely, their continuity, while with regard to quality (the real of phenomena) nothing is known to us a priori but their intensive quantity, that is, that they must have a degree. Everything else is left to experience."
[Footnote 1: In each particular science of nature, science proper (i.e., apodictically certain science) is found only to the extent in which mathematics can be applied therein. For this reason chemistry can never be anything more than a systematic art or experimental doctrine; and psychology not even this, but only a natural history of the inner sense or natural description of the soul. That which Kant's Metaphysical Elements of Natural Science, 1786—in four chapters, Phoronomy, Dynamics, Mechanics, and Phenomenology—advances as pure physics or the metaphysics of corporeal nature, is a doctrine of motion. The fundamental determination of matter (of a somewhat which is to be the object of the external senses) is motion, for it is only through motion that these senses can be affected, and the understanding itself reduces all other predicates of matter to this. The second and most valuable part of the work defines matter as the movable, that which fills space by its moving force, and recognizes two original forces, repulsive, expansive superficial force or force of contact, by which a body resists the entrance of other bodies into its own space, and attractive, penetrative force or the force which works at a distance, in virtue of which all particles of matter attract one another. In order to a determinate filling of space the co-operation of both fundamental forces is required. In opposition to the mechanical theory of the atomists, which explains forces from matter and makes them inhere in it, Kant holds fast to the dynamical view which he had early adopted (cf. p. 324), according to which forces are the primary factor and matter is constituted by them.]
The outcome of the Analytic of Principles sounds bold enough. The understanding is the lawgiver of nature: "It does not draw its laws a priori from nature, but prescribes them to it"; the principles of the pure understanding are the most universal laws of nature, the empirical laws of nature only particular determinations of these. All order and regularity take their origin in the spirit, and are put into objects by this. Universal and necessary knowledge remained inexplicable so long as it was assumed that the understanding must conform itself to objects; it is at once explained if, conversely, we make objects conform themselves to the understanding. This is a reversal of philosophical opinion which may justly be compared to the Copernican revolution in astronomy; it is just as paradoxical as the latter, but just as incontestably true, and just as rich in results. The sequel will show that this strangely sounding principle, that things conform themselves to our representations and the laws of nature are dependent on the understanding, is calculated to make us humble rather than proud. Our understanding is lawgiver within the limits of its knowledge, no doubt, but it knows only within the limits of its legislative authority; nature, to which it dictates laws, is nothing but a totality of phenomena; beyond the limits of the phenomenal, where its commands become of no effect, its wishes also find no hearing.
In the second edition the Analytic of Principles contains as a supplement a "Refutation of Idealism," which, in opposition to Descartes's position that the only immediate experience is inner experience, from which we reach outer experience by inference alone, argues that, conversely, it is only through outer experience, which is immediate experience proper, that inner experience—as the consciousness of my own existence in time—is possible. For all time determination presupposes something permanent in perception, and this permanent something cannot be in me (the mere representation of an external thing), but only actually existing things which I perceive without me. There is, further, a chapter on the "Ground of the Distinction of all Objects in general into Phenomena and Noumena," with an appendix on the Amphiboly (ambiguity) of the Concepts of Reflection. The latter shows that the concepts of comparison: identity and difference, agreement and opposition, the internal and the external, matter and form, acquire entirely different meanings when they relate to phenomena and to things in themselves (in other words, to things in their relation to the sensibility, and in relation to the understanding merely); and further, in a criticism of the philosophy of Leibnitz, reproaches him with having intellectualized phenomena, while Locke is said to have sensationalized the concepts of the understanding.
The chapter on the distinction between phenomena and noumena very much lessens the hopes, aroused, perchance, by the establishment of the non-empirical origin of the categories, for an application of these not confined to any experience. Although the categories, that is, are in their origin entirely independent of all experience (so much so that they first make experience possible), they are yet confined in their application within the bounds of possible experience. They "serve only to spell phenomena, that we may be able to read them as experience," and when applied to things in themselves lose all significance.[1] Similarly the principles which spring from them are "nothing more than principles of possible experience," and can be referred to phenomena alone, beyond which they are arbitrary combinations without objective reality. Things in themselves may be thought, but they can never be known; for knowledge, besides the empty thought of an object, implies intuitions which must be subsumed under it or by which the object must be determined. In themselves the pure concepts relate to all that is thinkable, not merely to that which can be experienced, but the schemata, which assures their applicability in the field of experience, at the same time limit them to this sphere. The schematism makes the immanent use of the categories, and thus a metaphysics of phenomena, possible, but the transcendent use of them, and consequently the metaphysics of the suprasensible, impossible. The case would be different if our intuition were intellectual instead of sensuous, or, which is the same thing, if our understanding were intuitive instead of discursive; then the objects which we think would not need to be given us from another source (through sensuous intuition), but would be themselves produced in the act by which we thought them. The divine spirit may be such an archetypal, creative understanding (intellectus archetypus), which generates objects by its thought; the human spirit is not such, and therefore is confined, with its knowledge, within the circle of possible perception.—The conception of "intellectual intuition" leads to a distinction in regard to things in themselves: in its negative meaning noumenon denotes a thing in so far as it is not the object of our sensuous intuition, in its positive meaning a thing which is the object of a non-sensuous intuition. The positive thing in itself is a problematical concept; its possibility depends on the existence of an intuitive understanding, something about which we are ignorant. The negative thing in itself cannot be known, indeed, but it can be thought; and the representation of it is a possible concept, one which is not self-contradictory[2] (a principle which is of great importance for practical philosophy). Still further, it is an indispensable concept, which shows that the boundary where our intuition ends is not the boundary of the thinkable as well; and even if it affords no positive extension of knowledge[3] it is, nevertheless, very useful, since it sets bounds to the use of the understanding, and thus, as it were, negatively extends our knowledge. That which lies beyond the boundary, the "how are they possible" (Wiemöglichkeit) of things in themselves is shrouded in darkness, but the boundary itself, i.e., the "that they are possible" (Dassmöglichkeit), of things in themselves, and the unknowableness of their nature, belongs to that which is within the boundary and lies in the light. In this way Kant believed that the categories of causality and substance might be applied to the relation of things in themselves to phenomena without offending against the prohibition of their transcendent use, since here the boundary appeared only to be touched, and not overstepped.
[Footnote 1: "A pure use of the categories is no doubt possible, that is, not self-contradictory, but it has no kind of objective validity, because it refers to no intuition to which it is meant to impart the unity of an object. The categories remain forever mere functions of thought by which no object can be given to me, but by which I can only think whatever may be given to me in intuition" (Critique of Pure Reason, Max Müller's translation, vol. ii. p. 220). Without the condition of sensuous intuition, for which they supply the synthesis, the categories have no relation to any definite object; for without this condition they contain nothing but the logical function, or the form of the concept, by means of which alone nothing can be known and distinguished as to any object belonging to it (Ibid., pp. 213, 214).]
[Footnote 2: The thing in itself denotes the object in so far as it can be thought by us, but not intuited, and consequently not determined by intuitions, i.e., cannot be known. It is only through the schematism that the categories are limited to phenomena. O. Liebmann (Kant und die Epigonen, p. 27, and passim) overlooks or ignores this when he says: Kant here allows himself to "recognize an object emancipated from the forms of knowledge, therefore an irrational object, i.e., to represent something which is not representable—wooden iron." The thing in itself is insensible, but not irrational, and the forms of intuition and forms of thought joined by Liebmann under the title forms of knowledge have in Kant a by no means equal rank.]
[Footnote 3: A category by itself, freed from all conditions of intuition (e.g., the representation of a substance which is thought without permanence in time, or of a cause which should not act in time), can yield no definite concept of an object.]
Though the concepts of the understanding possess a cognitive value in the sphere of phenomena alone, the hope still remains of gaining an entrance into the suprasensible sphere through the concepts of reason. It is indubitable that our spirit is conscious of a far higher need than that for the mere connection of phenomena into experience; it is that which cannot be experienced, the Ideas God, freedom, and immortality, which form the real end of its inquiry. Can this need be satisfied, and how? Can this end be attained, and reality be given to the Ideas? This is the third question of the Critique of Reason.