If the word "nature" is taken merely in its formal
signification (inasmuch as the word "nature" signifies the primal, internal
principle of everything that belongs to the existence of a things), then
there can be as many natural sciences as there are specifically different
things, and each of these things must contain its specific internal principle
of the determinations belonging to its existence. On the other hand, "nature"
is also taken in a material signification to be not a quality but the sum
total of all things insofar as they can be objects of our senses and hence
also objects of experience, under which is therefore to be understood the
whole of all appearances, i.e., the sense-world with the exclusion of all
objects that are not sensible. Nature taken in this signification of the
word has two main parts according to the main distinction of our senses:
the one contains the objects of the external senses, the other the object
of the internal sense. Therefore, a twofold doctrine of nature is possible:
a doctrine of body and a doctrine of soul. The first considers extended
nature, and the second, thinking nature.
Every doctrine, if it is to be a system, i.e., a whole of cognition ordered according to principles, is called science. And since principles can be either of the empirical or of the rational connection of cognitions in a whole, so natural science, be it the doctrine of body or the doctrine of soul, would have to be divided into historical and rational natural science, were it not that the word "nature" (because this word designates the derivation of the manifold belonging to the existence of things from their internal principle) necessitates a rational cognition of the coherence of things, so far as this cognition is to deserve the name of natural science. Therefore, the doctrine of nature might better be divided into the historical doctrine of nature, which contains nothing but the systematically ordered facts regarding natural things (which again would consist of the description of nature as a system of classes of natural things ordered according to similarities, and the history of nature as a systematic presentation of natural things in different times and in different places), and natural science. Now, natural science would in turn be natural science either properly or improperly so called; the first would treat its object wholly according to a priori principles, and the second, according to laws of experience.
Only that whose certainty is apodeictic can be called science proper; cognition that can contain merely empirical certainty is only improperly called science. That whole of cognition which is systematic can therefore be called science, and, when the connection of cognition in this system is a coherence of grounds and consequents, rational science. But when these grounds or principles are ultimately merely empirical, as, for example, in chemistry, and when the laws from which reason explains the given facts are merely laws of experience, then they carry with themselves no consciousness of their necessity (are not apodeictically certain), and thus the whole does not in a strict sense deserve the name of science. Therefore, chemistry should be called systematic art rather than science.
A rational doctrine of nature, then, deserves the name of natural science only when the natural laws that underlie it are cognized a priori and are not mere laws of experience. Natural cognition of the first kind is called pure, but that of the second kind is called applied rational cognition. Since the word "nature" already carries with it the concept of laws and since this concept carries with it the concept of the necessity of all the determinations of a thing which belong to its existence, it is easily seen why natural science must derive the legitimacy of its designation only from a pure part of natural science, namely, from that part which contains the a priori principles of all remaining natural explications, and why natural science is only by virtue of this pure part science proper. And so every doctrine of nature must according to the demands of reason ultimately aim at natural science and terminate in it, inasmuch as the necessity of laws attaches inseparably to the concept of nature and must therefore be thoroughly understood. Hence the most complete explication of certain phenomena by chemical principles always leaves dissatisfaction in its wake, inasmuch as through these contingent laws learned by mere experience no a priori grounds can be adduced . . . . .
Natural science properly so called presupposes metaphysics of nature; for laws, i.e., principles of the necessity of what belongs to the existence of a thing, are occupied with a concept which does not admit of construction, because existence cannot be presented in any a priori intuition Therefore, natural science proper presupposes metaphysics of nature. Now, the latter must indeed always contain nothing but principles which are not empirical (for that reason it bears the name of a metaphysics). But either it can treat of the laws which make possible the concept of a nature in general even without reference to any determinate object of experience, and therefore undetermined regarding the nature of this or that thing of the sense-world, and in this case it is the transcendental part of the metaphysics of nature or it occupies itself with the special nature of this or that kind of things, of which an empirical concept is given in such a way that besides what lies in this concept, no other empirical principle is needed for cognizing the things. For example, it lays the empirical concept of a matter or of a thinking being at its foundation and searches the range of cognition of which reason is a priori capable regarding these objects. Such a science must still be called a metaphysics of nature, namely, of corporeal or of thinking nature; however, it is then not a general but a special metaphysical natural science (physics and psychology), in which the aforementioned transcendental principles are applied to the two species of sense-objects.
I maintain, however, that in every special doctrine of nature only so much science proper can be found as there is mathematics in it. For in accordance with the foregoing considerations, science proper, especially science of nature, requires a pure part, which lies at the foundation of the empirical part and is based upon an a priori cognition of natural things. Now, to cognize anything a priori is to cognize it from its mere possibility. But the possibility of determinate natural things cannot be cognized from their mere concepts; from these concepts the possibility of the thought (that it does not contradict itself) can indeed be cognized, but not the possibility of the object as a natural thing, which can be given (as existing) outside of the thought. Therefore, in order to cognize the possibility of determinate natural things, and hence to cognize them a priori, there is further required that the intuition corresponding to the concept be given a priori, i.e., that the concept be constructed. Now, rational cognition through the construction of concepts is mathematical. A pure philosophy of nature in general, i.e., one that only investigates what constitutes the concept of a nature in general, may indeed be possible without mathematics; but a pure doctrine of nature concerning determinate natural things (doctrine of body and doctrine of soul) is possible only by means of mathematics. And since in every doctrine of nature only so much science proper is to be found as there is a priori cognition in it, a doctrine of nature will contain only so much science proper as there is applied mathematics in it....
But in order to make possible the application of mathematics to the doctrine of body, which can become natural science only by means of such application, principles of the construction of concepts that belong to the possibility of matter in general must precede. Hence a complete analysis of the concept of a matter in general must be laid at the foundation of the doctrine of body. This is the business of pure philosophy, which for this purpose makes use of no particular experiences but uses only what it finds in the separated (although in itself empirical) concept [of matter] with regard to pure intuitions in space and time (according to laws which already depend essentially on the concept of nature in general); hence such a doctrine is an actual metaphysics of corporeal nature.
All natural philosophers who wanted to proceed mathematically in their work had therefore always (though unknown to themselves) made use of metaphysical principles, and had to make use of them, even though they otherwise solemnly repudiated any claim of metaphysics on their science. Doubtless they understood by metaphysics the illusion of inventing possibilities at will and playing with concepts which perhaps do not at all admit of presentation in intuition and have no other certification of their objective reality than the fact that they merely do not stand in contradiction with themselves. All true metaphysics is taken from the essential nature of the thinking faculty itself and therefore is by no means invented. This is because metaphysics is not borrowed from experience but contains the pure operations of thought, and hence contains concepts and principles a priori, which first of all bring the manifold of empirical representations into legitimate connection, whereby such a manifold can become empirical cognition, i.e., experience. Those mathematical physicists could not at all, then, dispense with metaphysical principles, and among these principles, not with such as make the concept of their own special object, namely, matter, available a priori for application to external experience (as in the cases of the concept of motion, of the filling of space, of inertia, etc.). However, they rightly held that letting merely empirical principles prevail in these questions would be not at all compatible with the apodeictic certainty which they wanted to give to their natural laws; therefore, they preferred to postulate such laws without investigating their a priori sources...