This occurs in all cases of sensation, and so the understanding can anticipate even sensations, which constitute the peculiar quality of empirical representations (appearances), by means of the principle: "that they all have (consequently that what is real in all phenomena has) a degree." Here is the second application of mathematics (mathesis intensortim) to the science of nature. Sect. 25. Anent the relation of appearances merely with a view to their existence, the determination is not mathematical but dynamical, and can never be objectively valid, consequently never fit for experience, if it does not come under a priori principles by which the cognition of experience relative to appearances becomes even possible. Hence appearances must be subsumed under the concept of Substance, which is the foundation of all determination of existence, as a concept of the thing itself; or secondly so far as a succession is found among phenomena, that is, an event-under the concept of an Effect with reference to Cause; or lastly-so far as coexistence is to be known objectively, that is, by a judgment of experience-under the concept of Community (action and reaction). 15 Thus a priori principles form the basis of objectively valid, though empirical judgments, that is, of the possibility of experience so far as it must connect objects as existing in nature. These principles are the proper laws of nature, which may be termed dynamical. Finally the cognition of the agreement and connection not only of appearances among themselves in experience, but of their relation to experience in general, belongs to the judgments of experience. This relation contains either their agreement with the formal conditions, which the understanding knows, or their coherence with the materials of the senses and of perception, or combines both into one concept. Consequently it contains Possibility, Actuality, and Necessity according to universal laws of nature; and this constitutes the physical doctrine of method, or the distinction of truth and of hypotheses, and the bounds of the certainty of the latter. Sect. 26. The third table of Principles drawn from the nature of the understanding itself after the critical method, shows an inherent perfection, which raises it far above every other table which has hitherto though in vain been tried or may yet be tried by analyzing the objects themselves dogmatically. It exhibits all synthetical a priori principles completely and according to one principle, viz., the faculty of judging in general, constituting the essence of experience as regards the understanding, so that we can be certain that there are no more such principles, which affords a satisfaction such as can never be attained by the dogmatical method. Yet is this not all: there is a still greater merit in it. We must carefully bear in mind the proof which shows the possibility of this cognition a priori, and at the same time limits all such principles to a condition which must never be lost sight of, if we desire it not to be misunderstood, and extended in use beyond the original sense which the understanding attaches to it. This limit is that they contain nothing but the conditions of possible experience in general so far as it is Subjected to laws a priori . Consequently I do not say, that things in themselves possess a quantity, that their actuality possesses a degree, their existence a connection of accidents in a substance, etc. This nobody can prove, because such a synthetical connection from mere concepts, without any reference to sensuous intuition on the one side, or connection of it in a possible experience on the other, is absolutely impossible. The essential limitation of the concepts in these principles then is: That all things stand necessarily a priori under the aforementioned conditions, as objects of experience only. Hence there follows secondly a specifically peculiar mode of proof of these principles: they are not directly referred to appearances and to their relations, but to the possibility of experience, of which appearances constitute the matter only, not the form. Thus they are referred to objectively and universally valid synthetical propositions, in which we distinguish judgments of experience from those of perception. This takes place because appearances, as mere intuitions, occupying a part of space and time, come under the concept of Quantity, which unites their multiplicity a priori according to rules synthetically. Again, so far as the perception contains, besides intuition, sensibility, and between the latter and nothing (i.e., the total disappearance of sensibility), there is an ever-decreasing transition, it is apparent that that which is in appearances must have a degree, so far as it (viz., the perception) does not itself occupy any part of space or of time. 16 Still the transition to actuality from empty time or empty space is only possible in time; consequently though sensibility, as the quality of empirical intuition, can never be known a priori, by its specific difference from other sensibilities, yet it can, in a possible experience in general, as a quantity of perception be intensely distinguished from every other similar perception. Hence the application of mathematics to nature, as regards the sensuous intuition by which nature is given to us, becomes possible and is thus determined. Above all, the reader must pay attention to the mode of proof of the principles which occur under the title of Analogies of experience. For these do not refer to the genesis of intuitions, as do the principles of applied mathematics, but to the connection of their existence in experience; and this can be nothing but the determination of their existence in time according to necessary laws, under which alone the connection is objectively valid, and thus becomes experience. The proof therefore does not turn on the synthetical unity in the connection of things in themselves, but merely of perceptions, and of these not in regard to their matter, but to the determination of time and of the relation of their existence in it, according to universal laws.
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